Finite Group Databasebeta

← C2×#72236737 #72315019

Subgroups — C2×#72236737 #72315019

Order 2048.

At least 15318 conjugacy classes of subgroups; only the 5000 normal subgroups are shown.

The subgroup lattice has 1633 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10993C211yesmaximal, characteristic, complemented
2C2×#123600C211yesmaximal, characteristic, complemented
3C22×#11030C211yesmaximal, characteristic, complemented
4C22×#10987C211yesmaximal, characteristic, complemented
5C2×#123605C211yesmaximal, characteristic, complemented
6C22×#11012C211yesmaximal, characteristic, complemented
7C22×#10984C211yesmaximal, characteristic, complemented
8C22×#23400C211yesmaximal, characteristic, complemented
9C2×#6431707C211yesmaximal, characteristic, complemented
10C22×#23443C211yesmaximal, characteristic, complemented
11C2×#123531C211yesmaximal, characteristic, complemented
12C22×#10994C211yesmaximal, characteristic, complemented
13C22×#20598C211yesmaximal, characteristic, complemented
14C22×#35222C211yesmaximal, characteristic, complemented
15#72236737C2116yesmaximal, direct product factor
16C23×#3003C211yesmaximal, characteristic, complemented
17C26×D4C2211yescharacteristic
18C24×AGL(1,ℤ/8)C2211yescharacteristic
19C24×AGL(1,ℤ/8)C2211yescharacteristic
20C22×#3449C2211yescharacteristic, complemented
21C23×#535C2211yescharacteristic
22C23×#535C2211yescharacteristic
23C23×#525C2211yescharacteristic
24C23×#525C2211yescharacteristic
25C22×#3003C2218yescomplemented
26C22×#2879C2211yescharacteristic, complemented
27C23×#407C2211yescharacteristic
28C23×#407C2211yescharacteristic
29C23×#410C2211yescharacteristic, complemented
30C23×#410C2211yescharacteristic, complemented
31C22×#2896C2211yescharacteristic, complemented
32C23×#413C2211yescharacteristic, complemented
33C23×#421C2211yescharacteristic, complemented
34C23×#418C2211yescharacteristic
35C23×#418C2211yescharacteristic
36C23×#418C2211yescharacteristic
37C23×#418C2211yescharacteristic
38C23×#418C2211yescharacteristic
39C23×#418C2211yescharacteristic
40C2×#35222C2218yescomplemented
41C22×#2309C2211yescharacteristic
42C22×#2309C2211yescharacteristic
43C22×#2280C2211yescharacteristic
44C22×#2280C2211yescharacteristic
45C2×#23443C2218yescomplemented
46C2×#23400C2218yescomplemented
47#6431707C2218yescomplemented
48C2×#20598C2218yescomplemented
49C23×#344C2211yescharacteristic, complemented
50C23×#344C2211yescharacteristic, complemented
51C22×#1740C2211yescharacteristic, complemented
52C2×#20347C2211yescharacteristic, complemented
53C22×#1733C2211yescharacteristic, complemented
54C22×#1733C2211yescharacteristic, complemented
55C22×#1733C2211yescharacteristic, complemented
56C23×H(3,ℤ/4)C2211yescharacteristic, complemented
57C23×H(3,ℤ/4)C2211yescharacteristic, complemented
58C2×#11030C2218yescomplemented
59C2×#11012C2218yescomplemented
60C2×#10994C2218yescomplemented
61C2×#10993C2218yescomplemented
62C2×#10987C2218yescomplemented
63C2×#10984C2218yescomplemented
64#123605C2218yescomplemented
65#123600C2218yescomplemented
66#123531C2218yescomplemented
67C24×#41C2311yescharacteristic
68C24×#41C2311yescharacteristic
69C25×D4D418yescomplemented
70C25×D4C2314yes—
71C25×D4C2311yescharacteristic
72C25×D4C2311yescharacteristic
73C26×C4C2311yescharacteristic
74C23×AGL(1,ℤ/8)D418yescomplemented
75C23×AGL(1,ℤ/8)D414yescomplemented
76C23×AGL(1,ℤ/8)C2314yes—
77C23×AGL(1,ℤ/8)C2314yes—
78C24×SD16D412yescomplemented
79C24×D8D412yescomplemented
80C24×M16C2311yescharacteristic
81C24×M16C2311yescharacteristic
82C24×M16C2311yescharacteristic
83C24×M16C2311yescharacteristic
84C2×#3449C2314yescomplemented
85C22×#535D414yescomplemented
86C22×#535D414yescomplemented
87C22×#535C2314yes—
88C22×#535C2314yes—
89C23×#127D412yescomplemented
90C23×#124D412yescomplemented
91C22×#525D414yes—
92C22×#525D418yescomplemented
93C22×#525C2314yes—
94C22×#525C2314yes—
95C23×#123D412yes—
96C23×#121D414yescomplemented
97C23×#120D412yes—
98C23×#117C2311yescharacteristic
99C23×#117C2311yescharacteristic
100C23×#117C2311yescharacteristic
101C23×#117C2311yescharacteristic
102C23×#117C2311yescharacteristic
103C23×#117C2311yescharacteristic
104C22×#421C2314yescomplemented
105C2×#2896C2314yescomplemented
106C22×#418D418yescomplemented
107C22×#418D418yescomplemented
108C22×#418D418yescomplemented
109C22×#418D414yescomplemented
110C22×#418C2314yes—
111C22×#418C2314yes—
112C22×#418C2314yes—
113C22×#418C2314yes—
114C22×#418C2314yes—
115C22×#418C2314yes—
116C23×#102D414yescomplemented
117C22×#413C2314yescomplemented
118C22×#410C2314yescomplemented
119C22×#410C2314yescomplemented
120C2×#2879C2314yescomplemented
121C22×#407D418yescomplemented
122C22×#407C2314yes—
123C22×#407C2314yes—
124C2×#2309D418yescomplemented
125C2×#2309D418yescomplemented
126C2×#2309C2314yes—
127C2×#2309C2314yes—
128C2×#2280D418yescomplemented
129C2×#2280D418yescomplemented
130C2×#2280C2314yes—
131C2×#2280C2314yes—
132C22×#344C2314yescomplemented
133C22×#344C2314yescomplemented
134C2×#1740C2314yescomplemented
135#20347C2314yescomplemented
136C2×#1733C2314yescomplemented
137C2×#1733C2314yescomplemented
138C2×#1733C2314yescomplemented
139C22×H(3,ℤ/4)C2314yescomplemented
140C22×H(3,ℤ/4)C2314yescomplemented
141C27C2×D411yescharacteristic
142C23×#41C2×D414yes—
143C23×#41C2×D414yes—
144C23×#41C2×D412yes—
145C23×#41C2×D412yes—
146C23×#41C2×D412yes—
147C23×#41C2×D412yes—
148C23×#41C2412yes—
149C23×#41C2412yes—
150C24×Q8C2×D411yescharacteristic
151C24×Q8C2×D411yescharacteristic
152C24×D4C2×D412yes—
153C24×D4C2×D411yescharacteristic
154C24×D4C2×D411yescharacteristic
155C24×D4C2×D412yes—
156C24×D4C2×D412yes—
157C24×D4C2×D412yes—
158C24×D4C2×D412yes—
159C24×D4C2×D412yes—
160C24×D4C2×D414yes—
161C24×D4C2×D414yes—
162C24×D4C2×D414yes—
163C24×D4C2×D412yes—
164C24×D4C2×D412yes—
165C24×D4C2×D414yes—
166C24×D4C2×D414yes—
167C24×D4C2×D414yes—
168C24×D4C2×D412yes—
169C24×D4C2×D414yes—
170C24×D4C2×D414yes—
171C24×D4C2×D4116yescomplemented
172C24×D4#4114yes—
173C24×D4#4114yes—
174C24×D4C2412yes—
175C24×D4C2412yes—
176C25×C4C2×D412yes—
177C25×C4C2×D411yescharacteristic
178C25×C4C2×D412yes—
179C25×C4C2×D414yes—
180C25×C4C2×D414yes—
181C25×C4C2×D414yes—
182C25×C4C2×D414yes—
183C25×C4C2×D414yes—
184C25×C4#4114yes—
185C25×C4C2412yes—
186C25×C4C2411yescharacteristic
187C22×AGL(1,ℤ/8)C2×D4116yescomplemented
188C23×SD16C2×D418yescomplemented
189C23×D8C2×D418yescomplemented
190C23×M16C2×D414yes—
191C23×M16C2×D414yes—
192C23×M16C2×D414yes—
193C23×M16C2×D414yes—
194C23×M16C2×D414yes—
195C23×M16C2×D414yes—
196C23×M16C2×D412yes—
197C23×M16C2×D412yes—
198C23×M16C2412yes—
199C23×M16C2412yes—
200C23×M16C2412yes—
201C23×M16C2412yes—
202C24×C8C2×D412yes—
203C24×C8C2×D412yes—
204C22×#127C2×D418yescomplemented
205C22×#124C2×D418yescomplemented
206C2×#525C2×D4116yescomplemented
207C22×#123C2×D418yes—
208C22×#121C2×D4116yescomplemented
209C22×#120C2×D418yes—
210C22×#117C2×D414yes—
211C22×#117C2×D412yes—
212C22×#117C2×D414yes—
213C22×#117C2×D414yes—
214C22×#117C2×D414yes—
215C22×#117C2×D414yes—
216C22×#117C2×D414yes—
217C22×#117C2×D414yes—
218C22×#117C2×D414yes—
219C22×#117C2×D414yes—
220C22×#117C2×D414yes—
221C22×#117C2×D412yes—
222C22×#117C2×D412yes—
223C22×#117C2×D414yes—
224C22×#117C2×D414yes—
225C22×#117C2×D412yes—
226C22×#117C2412yes—
227C22×#117C2412yes—
228C22×#117C2412yes—
229C22×#117C2412yes—
230C22×#117C2412yes—
231C22×#117C2412yes—
232C23×C4⋊C4C2×D412yes—
233C23×C4⋊C4C2×D412yes—
234C23×C22⋊C4C2×D412yes—
235C23×C42C2×D412yes—
236C2×#418C2×D4116yescomplemented
237C2×#418C2×D4116yescomplemented
238C2×#418C2×D4116yescomplemented
239C22×#102C2×D4116yescomplemented
240C2×#407C2×D4116yescomplemented
241#2309C2×D4116yescomplemented
242#2309C2×D4116yescomplemented
243#2280C2×D4116yescomplemented
244#2280C2×D4116yescomplemented
245C26#12012yes—
246C26#12014yes—
247C26#12014yes—
248C26#12114yes—
249C26C22×D412yes—
250C26C22×D411yescharacteristic
251C22×#41#12018yescomplemented
252C22×#41C22×D414yes—
253C22×#41C22×D414yes—
254C23×Q8#12012yes—
255C23×Q8#12014yescomplemented
256C23×Q8C22×D412yes—
257C23×Q8C22×D412yes—
258C23×D4#12014yes—
259C23×D4#12012yes—
260C23×D4#12018yes—
261C23×D4#12018yes—
262C23×D4#12018yes—
263C23×D4#120116yes—
264C23×D4#12018yes—
265C23×D4#12018yes—
266C23×D4#12018yes—
267C23×D4#12014yes—
268C23×D4#12014yes—
269C23×D4#12014yes—
270C23×D4#12018yes—
271C23×D4#12014yes—
272C23×D4#12018yes—
273C23×D4#12014yescomplemented
274C23×D4#121116yes—
275C23×D4#12118yes—
276C23×D4#12118yes—
277C23×D4#12118yes—
278C23×D4#12118yes—
279C23×D4#12118yes—
280C23×D4#12118yes—
281C23×D4#12118yes—
282C23×D4#121116yes—
283C23×D4#12118yes—
284C23×D4#12718yes—
285C23×D4#127116yes—
286C23×D4#12718yes—
287C23×D4C22×D414yes—
288C23×D4C22×D412yes—
289C23×D4C22×D412yes—
290C23×D4C22×D414yes—
291C23×D4C22×D414yes—
292C23×D4C22×D414yes—
293C23×D4C22×D414yes—
294C23×D4C22×D414yes—
295C23×D4C22×D414yes—
296C23×D4C22×D414yes—
297C23×D4C22×D414yes—
298C23×D4C22×D414yes—
299C23×D4C22×D414yes—
300C23×D4C22×D414yes—
301C23×D4C22×D414yes—
302C23×D4C2×#4114yes—
303C23×D4C2×#4114yes—
304C24×C4#12012yes—
305C24×C4#12014yes—
306C24×C4#120116yes—
307C24×C4#12014yes—
308C24×C4#12018yes—
309C24×C4#12014yes—
310C24×C4#12018yes—
311C24×C4#121116yes—
312C24×C4#121116yes—
313C24×C4#12114yes—
314C24×C4#12118yes—
315C24×C4#127116yes—
316C24×C4C22×D414yes—
317C24×C4C22×D412yes—
318C24×C4C22×D414yes—
319C24×C4C22×D414yes—
320C24×C4C22×D414yes—
321C24×C4C22×D414yes—
322C24×C4C22×D414yes—
323C24×C4C22×D412yes—
324C24×C4C22×D411yescharacteristic
325C24×C4C22×D411yescharacteristic
326C24×C4C22×D412yes—
327C24×C4C22×D411yescharacteristic
328C24×C4C22×D411yescharacteristic
329C24×C4C22×D411yescharacteristic
330C24×C4C22×D411yescharacteristic
331C24×C4C22×D411yescharacteristic
332C24×C4C22×D412yes—
333C24×C4C22×D412yes—
334C24×C4C22×D412yes—
335C24×C4C22×D412yes—
336C24×C4C22×D412yes—
337C24×C4C22×D412yes—
338C24×C4C22×D412yes—
339C24×C4C22×D411yescharacteristic
340C24×C4C22×D412yes—
341C24×C4C22×D411yescharacteristic
342C24×C4C22×D412yes—
343C24×C4C2×#4114yes—
344C24×C4C2×#4112yes—
345C24×C4C2×#4112yes—
346C24×C4C2×#4112yes—
347C24×C4H(5,𝔽2)11yescharacteristic
348C24×C4H(5,𝔽2)11yescharacteristic
349C24×C4H(5,𝔽2)12yes—
350C24×C4H(5,𝔽2)11yescharacteristic
351C24×C4H(5,𝔽2)11yescharacteristic
352C24×C4H(5,𝔽2)12yes—
353C24×C4H(5,𝔽2)12yes—
354C24×C4H(5,𝔽2)12yes—
355C24×C4H(5,𝔽2)12yes—
356C24×C4H(5,𝔽2)12yes—
357C24×C4H(5,𝔽2)12yes—
358C24×C4H(5,𝔽2)12yes—
359C24×C4H(5,𝔽2)12yes—
360C24×C4H(5,𝔽2)12yes—
361C24×C4C2511yescharacteristic
362C22×M16#120116yescomplemented
363C22×M16#12018yescomplemented
364C22×M16C22×D414yes—
365C22×M16C22×D414yes—
366C22×M16C22×D414yes—
367C22×M16C22×D414yes—
368C22×M16C22×D414yes—
369C22×M16C22×D414yes—
370C23×C8#12018yescomplemented
371C23×C8C22×D414yes—
372C23×C8C22×D414yes—
373C2×#117#12018yes—
374C2×#117#12018yes—
375C2×#117#12018yes—
376C2×#117#120116yescomplemented
377C2×#117#12018yescomplemented
378C2×#117C22×D414yes—
379C2×#117C22×D414yes—
380C2×#117C22×D414yes—
381C2×#117C22×D414yes—
382C2×#117C22×D414yes—
383C2×#117C22×D414yes—
384C2×#117C22×D414yes—
385C2×#117C22×D414yes—
386C2×#117C22×D414yes—
387C2×#117C22×D414yes—
388C2×#117C22×D414yes—
389C2×#117C22×D414yes—
390C22×C4⋊C4#12018yes—
391C22×C4⋊C4#12018yescomplemented
392C22×C4⋊C4C22×D414yes—
393C22×C4⋊C4C22×D414yes—
394C22×C22⋊C4#12018yes—
395C22×C22⋊C4C22×D414yes—
396C22×C42#12018yes—
397C22×C42C22×D414yes—
398C25#392116yes—
399C25C2×#12011yescharacteristic
400C25C2×#12014yes—
401C25C2×#12014yes—
402C25C2×#12014yes—
403C25C2×#12012yes—
404C25C2×#12011yescharacteristic
405C25C2×#12012yes—
406C25C2×#12012yes—
407C25C2×#12114yes—
408C25C2×#12112yes—
409C25#53412yes—
410C25#53412yes—
411C25D4211yescharacteristic
412C25D4211yescharacteristic
413C25D4212yes—
414C25D4211yescharacteristic
415C25D4212yes—
416C25D4212yes—
417C25D4211yescharacteristic
418C25D4212yes—
419C25#54612yes—
420C25#54612yes—
421C25C23×D411yescharacteristic
422C22×Q8C2×#12014yescomplemented
423C22×D4#392116yes—
424C22×D4#392116yes—
425C22×D4#392132yes—
426C22×D4#392116yes—
427C22×D4#392132yes—
428C22×D4#392116yes—
429C22×D4C2×#12018yes—
430C22×D4C2×#12018yes—
431C22×D4C2×#12018yes—
432C22×D4C2×#12018yes—
433C22×D4C2×#12018yes—
434C22×D4C2×#12018yes—
435C22×D4C2×#12014yescomplemented
436C22×D4C2×#12118yes—
437C22×D4C2×#12118yes—
438C22×D4C2×#12118yes—
439C22×D4C2×#12118yes—
440C22×D4C2×#12118yes—
441C22×D4C2×#12118yes—
442C22×D4C2×#12718yes—
443C22×D4C2×#12718yes—
444C23×C4#392116yes—
445C23×C4#392132yes—
446C23×C4C2×#12014yes—
447C23×C4C2×#12014yes—
448C23×C4C2×#12014yes—
449C23×C4C2×#12018yes—
450C23×C4C2×#12012yes—
451C23×C4C2×#12012yes—
452C23×C4C2×#12014yes—
453C23×C4C2×#12012yes—
454C23×C4C2×#12014yes—
455C23×C4C2×#12011yescharacteristic
456C23×C4C2×#12011yescharacteristic
457C23×C4C2×#12012yes—
458C23×C4C2×#12012yes—
459C23×C4C2×#12012yes—
460C23×C4C2×#12014yes—
461C23×C4C2×#12012yes—
462C23×C4C2×#12012yes—
463C23×C4C2×#12014yes—
464C23×C4C2×#12012yes—
465C23×C4C2×#12012yes—
466C23×C4C2×#12012yes—
467C23×C4C2×#12012yes—
468C23×C4C2×#12012yes—
469C23×C4C2×#12012yes—
470C23×C4C2×#12012yes—
471C23×C4C2×#12012yes—
472C23×C4C2×#12012yes—
473C23×C4C2×#12012yes—
474C23×C4C2×#12012yes—
475C23×C4C2×#12011yescharacteristic
476C23×C4C2×#12011yescharacteristic
477C23×C4C2×#12011yescharacteristic
478C23×C4C2×#12012yes—
479C23×C4C2×#12012yes—
480C23×C4C2×#12011yescharacteristic
481C23×C4C2×#12114yes—
482C23×C4C2×#12118yes—
483C23×C4C2×#12118yes—
484C23×C4C2×#12114yes—
485C23×C4C2×#12112yes—
486C23×C4C2×#12112yes—
487C23×C4C2×#12114yes—
488C23×C4C2×#12112yes—
489C23×C4C2×#12112yes—
490C23×C4C2×#12112yes—
491C23×C4C2×#12112yes—
492C23×C4C2×#12112yes—
493C23×C4C2×#12112yes—
494C23×C4C2×#12114yes—
495C23×C4C2×#12112yes—
496C23×C4C2×#12114yes—
497C23×C4#52512yes—
498C23×C4#52512yes—
499C23×C4#52514yes—
500C23×C4#52514yes—
501C23×C4C2×#12718yes—
502C23×C4C2×#12712yes—
503C23×C4C2×#12714yes—
504C23×C4C2×#12712yes—
505C23×C4C2×#12714yes—
506C23×C4#53414yes—
507C23×C4#53412yes—
508C23×C4#53412yes—
509C23×C4#53414yes—
510C23×C4#53412yes—
511C23×C4#53412yes—
512C23×C4#53414yes—
513C23×C4#53414yes—
514C23×C4#53412yes—
515C23×C4#53412yes—
516C23×C4#53412yes—
517C23×C4#53414yes—
518C23×C4#53412yes—
519C23×C4#53412yes—
520C23×C4#53412yes—
521C23×C4#53412yes—
522C23×C4#53412yes—
523C23×C4#53412yes—
524C23×C4#53412yes—
525C23×C4#53412yes—
526C23×C4#53412yes—
527C23×C4#53414yes—
528C23×C4#53411yescharacteristic
529C23×C4#53412yes—
530C23×C4#53411yescharacteristic
531C23×C4#53412yes—
532C23×C4#53411yescharacteristic
533C23×C4#53412yes—
534C23×C4#53412yes—
535C23×C4#53411yescharacteristic
536C23×C4#53412yes—
537C23×C4#53412yes—
538C23×C4#53412yes—
539C23×C4#53412yes—
540C23×C4#53412yes—
541C23×C4#53412yes—
542C23×C4#53514yes—
543C23×C4#53512yes—
544C23×C4#53512yes—
545C23×C4#53514yes—
546C23×C4#53514yes—
547C23×C4#53514yes—
548C23×C4#53512yes—
549C23×C4#53512yes—
550C23×C4#53514yes—
551C23×C4#53512yes—
552C23×C4#53512yes—
553C23×C4#53514yes—
554C23×C4#53512yes—
555C23×C4#53512yes—
556C23×C4#53514yes—
557C23×C4#53514yes—
558C23×C4#53512yes—
559C23×C4#53514yes—
560C23×C4#53512yes—
561C23×C4#53514yes—
562C23×C4#53814yes—
563C23×C4#53812yes—
564C23×C4#53812yes—
565C23×C4#53814yes—
566C23×C4#53814yes—
567C23×C4#53812yes—
568C23×C4#53812yes—
569C23×C4#53814yes—
570C23×C4D4211yescharacteristic
571C23×C4D4212yes—
572C23×C4D4211yescharacteristic
573C23×C4D4212yes—
574C23×C4D4212yes—
575C23×C4D4211yescharacteristic
576C23×C4D4212yes—
577C23×C4D4212yes—
578C23×C4D4212yes—
579C23×C4D4212yes—
580C23×C4D4211yescharacteristic
581C23×C4D4211yescharacteristic
582C23×C4D4211yescharacteristic
583C23×C4D4212yes—
584C23×C4D4212yes—
585C23×C4D4212yes—
586C23×C4D4212yes—
587C23×C4D4212yes—
588C23×C4D4212yes—
589C23×C4D4212yes—
590C23×C4D4212yes—
591C23×C4D4212yes—
592C23×C4D4212yes—
593C23×C4D4212yes—
594C23×C4D4212yes—
595C23×C4D4214yes—
596C23×C4D4211yescharacteristic
597C23×C4D4212yes—
598C23×C4D4211yescharacteristic
599C23×C4D4212yes—
600C23×C4D4212yes—
601C23×C4D4212yes—
602C23×C4D4212yes—
603C23×C4D4212yes—
604C23×C4D4214yes—
605C23×C4D4214yes—
606C23×C4D4214yes—
607C23×C4D4212yes—
608C23×C4D4212yes—
609C23×C4D4211yescharacteristic
610C23×C4D4212yes—
611C23×C4D4212yes—
612C23×C4D4212yes—
613C23×C4D4212yes—
614C23×C4D4212yes—
615C23×C4D4212yes—
616C23×C4D4212yes—
617C23×C4D4212yes—
618C23×C4D4212yes—
619C23×C4D4211yescharacteristic
620C23×C4D4212yes—
621C23×C4D4212yes—
622C23×C4D4212yes—
623C23×C4D4211yescharacteristic
624C23×C4D4212yes—
625C23×C4D4211yescharacteristic
626C23×C4D4212yes—
627C23×C4D4214yes—
628C23×C4D4212yes—
629C23×C4D4214yes—
630C23×C4D4214yes—
631C23×C4D4212yes—
632C23×C4D4214yes—
633C23×C4D4212yes—
634C23×C4D4212yes—
635C23×C4D4212yes—
636C23×C4D4214yes—
637C23×C4D4212yes—
638C23×C4D4212yes—
639C23×C4D4214yes—
640C23×C4D4212yes—
641C23×C4D4214yes—
642C23×C4D4212yes—
643C23×C4D4212yes—
644C23×C4D4214yes—
645C23×C4D4212yes—
646C23×C4D4214yes—
647C23×C4D4214yes—
648C23×C4D4214yes—
649C23×C4D4214yes—
650C23×C4#54612yes—
651C23×C4#54612yes—
652C23×C4#54612yes—
653C23×C4#54612yes—
654C23×C4#54614yes—
655C23×C4#54612yes—
656C23×C4#54612yes—
657C23×C4#54612yes—
658C23×C4#54612yes—
659C23×C4#54612yes—
660C23×C4#54612yes—
661C23×C4#54612yes—
662C23×C4#54612yes—
663C23×C4#54612yes—
664C23×C4#54612yes—
665C23×C4#54614yes—
666C23×C4#54614yes—
667C23×C4#54614yes—
668C23×C4#54612yes—
669C23×C4#54612yes—
670C23×C4#54614yes—
671C23×C4#54614yes—
672C23×C4#54614yes—
673C23×C4#54614yes—
674C23×C4#54612yes—
675C23×C4#54612yes—
676C23×C4#54614yes—
677C23×C4#54614yes—
678C23×C4#54612yes—
679C23×C4#54614yes—
680C23×C4#54612yes—
681C23×C4#54612yes—
682C23×C4#54614yes—
683C23×C4#54612yes—
684C23×C4#56014yes—
685C23×C4#56014yes—
686C23×C4#56014yes—
687C23×C4#56012yes—
688C23×C4#56012yes—
689C23×C4#56012yes—
690C23×C4#56012yes—
691C23×C4#56014yes—
692C23×C4H(3,𝔽4)12yes—
693C23×C4H(3,𝔽4)12yes—
694C23×C4H(3,𝔽4)12yes—
695C23×C4H(3,𝔽4)12yes—
696C23×C4C23×D411yescharacteristic
697C23×C4C23×D411yescharacteristic
698C23×C4C23×D411yescharacteristic
699C23×C4C23×D411yescharacteristic
700C23×C4C23×D411yescharacteristic
701C23×C4C23×D411yescharacteristic
702C23×C4C23×D411yescharacteristic
703C23×C4C23×D411yescharacteristic
704C23×C4C23×D411yescharacteristic
705C23×C4C23×D411yescharacteristic
706C23×C4C23×D411yescharacteristic
707C23×C4C23×D411yescharacteristic
708C23×C4C23×D411yescharacteristic
709C23×C4C23×D411yescharacteristic
710C23×C4C23×D411yescharacteristic
711C23×C4C22×#4111yescharacteristic
712C23×C4C22×#4111yescharacteristic
713C23×C4C22×#4111yescharacteristic
714C23×C4C2×H(5,𝔽2)11yescharacteristic
715C23×C4C2×H(5,𝔽2)11yescharacteristic
716C23×C4C2×H(5,𝔽2)11yescharacteristic
717C23×C4C2×H(5,𝔽2)11yescharacteristic
718C23×C4C2×H(5,𝔽2)11yescharacteristic
719C23×C4C2×H(5,𝔽2)11yescharacteristic
720C23×C4C2×H(5,𝔽2)11yescharacteristic
721C23×C4C2×H(5,𝔽2)11yescharacteristic
722C23×C4C2×H(5,𝔽2)11yescharacteristic
723C23×C4C2×H(5,𝔽2)11yescharacteristic
724C23×C4C2×H(5,𝔽2)11yescharacteristic
725C23×C4C2×H(5,𝔽2)11yescharacteristic
726C2×M16C2×#12018yescomplemented
727C22×C8C2×#12018yescomplemented
728#117C2×#12018yescomplemented
729C2×C4⋊C4C2×#12018yes—
730C2×C4⋊C4C2×#12018yescomplemented
731C2×C22⋊C4C2×#12018yes—
732C2×C42C2×#12018yes—
733C24C2×#39218yes—
734C24C2×#39214yes—
735C24#240311yescharacteristic
736C24#240312yes—
737C24#240312yes—
738C24#240311yescharacteristic
739C24#240312yes—
740C24#240311yescharacteristic
741C24#240312yes—
742C24#240312yes—
743C24#240312yes—
744C24#240312yes—
745C24#240312yes—
746C24#240312yes—
747C24#240312yes—
748C24#240314yes—
749C24#240314yes—
750C24#240314yes—
751C24#240311yescharacteristic
752C24#240414yes—
753C24#240812yes—
754C24#240812yes—
755C24#240812yes—
756C24#240814yes—
757C24#240812yes—
758C24#240814yes—
759C24#241012yes—
760C24#241012yes—
761C24#241012yes—
762C24#241012yes—
763C24#241012yes—
764C24#241014yes—
765C24#241012yes—
766C24#241012yes—
767C24#241012yes—
768C24#241014yes—
769C24#242412yes—
770C24#242412yes—
771C24#242414yes—
772C24#243312yes—
773C24#243312yes—
774C24#243314yes—
775C24#261314yes—
776C24#266812yes—
777C24#266812yes—
778C24#266814yes—
779C24#266912yes—
780C24#266912yes—
781C24#266914yes—
782C24#267814yes—
783C24#267814yes—
784C24#267912yes—
785C24#267912yes—
786C24#267912yes—
787C24#267912yes—
788C24#284612yes—
789C24#284612yes—
790C24C22×#12011yescharacteristic
791C24C22×#12011yescharacteristic
792C24C22×#12011yescharacteristic
793C24C22×#12011yescharacteristic
794C24C22×#12111yescharacteristic
795C24C2×#53411yescharacteristic
796C24C2×#53411yescharacteristic
797C24C2×D4211yescharacteristic
798C24C2×D4211yescharacteristic
799C24C2×D4211yescharacteristic
800C24C2×D4211yescharacteristic
801C24C2×D4211yescharacteristic
802C24C2×D4211yescharacteristic
803C24C2×#54611yescharacteristic
804C24C2×#54611yescharacteristic
805C2×D4C2×#392116yes—
806C2×D4C2×#392116yes—
807C22×C4C2×#39218yes—
808C22×C4C2×#39214yes—
809C22×C4C2×#39214yes—
810C22×C4C2×#39212yes—
811C22×C4C2×#39212yes—
812C22×C4C2×#39212yes—
813C22×C4C2×#39212yes—
814C22×C4C2×#39214yes—
815C22×C4#240311yescharacteristic
816C22×C4#240311yescharacteristic
817C22×C4#240311yescharacteristic
818C22×C4#240312yes—
819C22×C4#240312yes—
820C22×C4#240312yes—
821C22×C4#240311yescharacteristic
822C22×C4#240312yes—
823C22×C4#240312yes—
824C22×C4#240312yes—
825C22×C4#240312yes—
826C22×C4#240312yes—
827C22×C4#240312yes—
828C22×C4#240312yes—
829C22×C4#240312yes—
830C22×C4#240312yes—
831C22×C4#240312yes—
832C22×C4#240312yes—
833C22×C4#240312yes—
834C22×C4#240312yes—
835C22×C4#240312yes—
836C22×C4#240312yes—
837C22×C4#240312yes—
838C22×C4#240312yes—
839C22×C4#240312yes—
840C22×C4#240312yes—
841C22×C4#240312yes—
842C22×C4#240312yes—
843C22×C4#240312yes—
844C22×C4#240314yes—
845C22×C4#240312yes—
846C22×C4#240314yes—
847C22×C4#240314yes—
848C22×C4#240312yes—
849C22×C4#240314yes—
850C22×C4#240314yes—
851C22×C4#240312yes—
852C22×C4#240314yes—
853C22×C4#240312yes—
854C22×C4#240312yes—
855C22×C4#240312yes—
856C22×C4#240312yes—
857C22×C4#240314yes—
858C22×C4#240314yes—
859C22×C4#240314yes—
860C22×C4#240312yes—
861C22×C4#240312yes—
862C22×C4#240312yes—
863C22×C4#240312yes—
864C22×C4#240314yes—
865C22×C4#240312yes—
866C22×C4#240312yes—
867C22×C4#240314yes—
868C22×C4#240314yes—
869C22×C4#240314yes—
870C22×C4#240414yes—
871C22×C4#240412yes—
872C22×C4#240412yes—
873C22×C4#240414yes—
874C22×C4#240412yes—
875C22×C4#240414yes—
876C22×C4#240412yes—
877C22×C4#240812yes—
878C22×C4#240812yes—
879C22×C4#240814yes—
880C22×C4#240814yes—
881C22×C4#240812yes—
882C22×C4#240814yes—
883C22×C4#240812yes—
884C22×C4#240814yes—
885C22×C4#240814yes—
886C22×C4#240814yes—
887C22×C4#240814yes—
888C22×C4#240812yes—
889C22×C4#240812yes—
890C22×C4#240814yes—
891C22×C4#240814yes—
892C22×C4#240814yes—
893C22×C4#240814yes—
894C22×C4#240812yes—
895C22×C4#240812yes—
896C22×C4#240814yes—
897C22×C4#240812yes—
898C22×C4#240812yes—
899C22×C4#240814yes—
900C22×C4#240812yes—
901C22×C4#240812yes—
902C22×C4#240814yes—
903C22×C4#241014yes—
904C22×C4#241014yes—
905C22×C4#241014yes—
906C22×C4#241014yes—
907C22×C4#241014yes—
908C22×C4#241014yes—
909C22×C4#241012yes—
910C22×C4#241012yes—
911C22×C4#241014yes—
912C22×C4#241014yes—
913C22×C4#241014yes—
914C22×C4#241014yes—
915C22×C4#241014yes—
916C22×C4#241014yes—
917C22×C4#241014yes—
918C22×C4#241012yes—
919C22×C4#241012yes—
920C22×C4#241014yes—
921C22×C4#241014yes—
922C22×C4#241014yes—
923C22×C4#241014yes—
924C22×C4#241014yes—
925C22×C4#241014yes—
926C22×C4#241014yes—
927C22×C4#241014yes—
928C22×C4#241014yes—
929C22×C4#241014yes—
930C22×C4#241014yes—
931C22×C4#241014yes—
932C22×C4#241014yes—
933C22×C4#241014yes—
934C22×C4#241014yes—
935C22×C4#241014yes—
936C22×C4#241014yes—
937C22×C4#241012yes—
938C22×C4#241012yes—
939C22×C4#241014yes—
940C22×C4#241012yes—
941C22×C4#241014yes—
942C22×C4#241012yes—
943C22×C4#241014yes—
944C22×C4#241012yes—
945C22×C4#241012yes—
946C22×C4#241012yes—
947C22×C4#241012yes—
948C22×C4#241012yes—
949C22×C4#241012yes—
950C22×C4#241012yes—
951C22×C4#241012yes—
952C22×C4#241014yes—
953C22×C4#242414yes—
954C22×C4#242414yes—
955C22×C4#242414yes—
956C22×C4#242414yes—
957C22×C4#242414yes—
958C22×C4#242414yes—
959C22×C4#242414yes—
960C22×C4#242412yes—
961C22×C4#242412yes—
962C22×C4#242412yes—
963C22×C4#242414yes—
964C22×C4#242414yes—
965C22×C4#242414yes—
966C22×C4#242414yes—
967C22×C4#242414yes—
968C22×C4#242412yes—
969C22×C4#242414yes—
970C22×C4#242414yes—
971C22×C4#242414yes—
972C22×C4#242414yes—
973C22×C4#242414yes—
974C22×C4#242414yes—
975C22×C4#242412yes—
976C22×C4#242412yes—
977C22×C4#242414yes—
978C22×C4#243314yes—
979C22×C4#243314yes—
980C22×C4#243314yes—
981C22×C4#243314yes—
982C22×C4#243314yes—
983C22×C4#243314yes—
984C22×C4#243314yes—
985C22×C4#243314yes—
986C22×C4#243312yes—
987C22×C4#243314yes—
988C22×C4#243314yes—
989C22×C4#243312yes—
990C22×C4#243314yes—
991C22×C4#243314yes—
992C22×C4#243314yes—
993C22×C4#243312yes—
994C22×C4#243314yes—
995C22×C4#243314yes—
996C22×C4#243314yes—
997C22×C4#243314yes—
998C22×C4#243312yes—
999C22×C4#243314yes—
1000C22×C4#243314yes—
1001C22×C4#243314yes—
1002C22×C4#243314yes—
1003C22×C4#243314yes—
1004C22×C4#243314yes—
1005C22×C4#243314yes—
1006C22×C4#243312yes—
1007C22×C4#243312yes—
1008C22×C4#243314yes—
1009C22×C4#253914yes—
1010C22×C4#253914yes—
1011C22×C4#253914yes—
1012C22×C4#253914yes—
1013C22×C4#253914yes—
1014C22×C4#253914yes—
1015C22×C4#261314yes—
1016C22×C4#261314yes—
1017C22×C4#261314yes—
1018C22×C4#261312yes—
1019C22×C4#261312yes—
1020C22×C4#261314yes—
1021C22×C4#261312yes—
1022C22×C4#261314yes—
1023C22×C4#261312yes—
1024C22×C4#261314yes—
1025C22×C4#261314yes—
1026C22×C4#261314yes—
1027C22×C4#261314yes—
1028C22×C4#261714yes—
1029C22×C4#261714yes—
1030C22×C4#261714yes—
1031C22×C4#261714yes—
1032C22×C4#261714yes—
1033C22×C4#261714yes—
1034C22×C4#266814yes—
1035C22×C4#266814yes—
1036C22×C4#266812yes—
1037C22×C4#266812yes—
1038C22×C4#266812yes—
1039C22×C4#266814yes—
1040C22×C4#266814yes—
1041C22×C4#266814yes—
1042C22×C4#266812yes—
1043C22×C4#266814yes—
1044C22×C4#266812yes—
1045C22×C4#266812yes—
1046C22×C4#266814yes—
1047C22×C4#266914yes—
1048C22×C4#266914yes—
1049C22×C4#266914yes—
1050C22×C4#266914yes—
1051C22×C4#266912yes—
1052C22×C4#266912yes—
1053C22×C4#266914yes—
1054C22×C4#266914yes—
1055C22×C4#266914yes—
1056C22×C4#266912yes—
1057C22×C4#266912yes—
1058C22×C4#266914yes—
1059C22×C4#266914yes—
1060C22×C4#266914yes—
1061C22×C4#266914yes—
1062C22×C4#266914yes—
1063C22×C4#266914yes—
1064C22×C4#266914yes—
1065C22×C4#266914yes—
1066C22×C4#266914yes—
1067C22×C4#266914yes—
1068C22×C4#266914yes—
1069C22×C4#266914yes—
1070C22×C4#266914yes—
1071C22×C4#266914yes—
1072C22×C4#266914yes—
1073C22×C4#266914yes—
1074C22×C4#266914yes—
1075C22×C4#266914yes—
1076C22×C4#266914yes—
1077C22×C4#266914yes—
1078C22×C4#266914yes—
1079C22×C4#266914yes—
1080C22×C4#266914yes—
1081C22×C4#266912yes—
1082C22×C4#266912yes—
1083C22×C4#266914yes—
1084C22×C4#267014yes—
1085C22×C4#267014yes—
1086C22×C4#267014yes—
1087C22×C4#267014yes—
1088C22×C4#267014yes—
1089C22×C4#267014yes—
1090C22×C4#267014yes—
1091C22×C4#267014yes—
1092C22×C4#267014yes—
1093C22×C4#267014yes—
1094C22×C4#267014yes—
1095C22×C4#267014yes—
1096C22×C4#267814yes—
1097C22×C4#267814yes—
1098C22×C4#267814yes—
1099C22×C4#267814yes—
1100C22×C4#267812yes—
1101C22×C4#267812yes—
1102C22×C4#267814yes—
1103C22×C4#267814yes—
1104C22×C4#267812yes—
1105C22×C4#267812yes—
1106C22×C4#267812yes—
1107C22×C4#267812yes—
1108C22×C4#267814yes—
1109C22×C4#267814yes—
1110C22×C4#267814yes—
1111C22×C4#267814yes—
1112C22×C4#267814yes—
1113C22×C4#267814yes—
1114C22×C4#267812yes—
1115C22×C4#267812yes—
1116C22×C4#267814yes—
1117C22×C4#267814yes—
1118C22×C4#267814yes—
1119C22×C4#267814yes—
1120C22×C4#267814yes—
1121C22×C4#267814yes—
1122C22×C4#267912yes—
1123C22×C4#267912yes—
1124C22×C4#267912yes—
1125C22×C4#267912yes—
1126C22×C4#267912yes—
1127C22×C4#267912yes—
1128C22×C4#267912yes—
1129C22×C4#267912yes—
1130C22×C4#267912yes—
1131C22×C4#267912yes—
1132C22×C4#267912yes—
1133C22×C4#267912yes—
1134C22×C4#267912yes—
1135C22×C4#267912yes—
1136C22×C4#267912yes—
1137C22×C4#267912yes—
1138C22×C4#267912yes—
1139C22×C4#267912yes—
1140C22×C4#267912yes—
1141C22×C4#267912yes—
1142C22×C4#281214yes—
1143C22×C4#281214yes—
1144C22×C4#281214yes—
1145C22×C4#281214yes—
1146C22×C4#284614yes—
1147C22×C4#284614yes—
1148C22×C4#284612yes—
1149C22×C4#284612yes—
1150C22×C4#284714yes—
1151C22×C4#284714yes—
1152C22×C4C22×#12011yescharacteristic
1153C22×C4C22×#12011yescharacteristic
1154C22×C4C22×#12011yescharacteristic
1155C22×C4C22×#12011yescharacteristic
1156C22×C4C22×#12011yescharacteristic
1157C22×C4C22×#12011yescharacteristic
1158C22×C4C22×#12011yescharacteristic
1159C22×C4C22×#12011yescharacteristic
1160C22×C4C22×#12011yescharacteristic
1161C22×C4C22×#12011yescharacteristic
1162C22×C4C22×#12011yescharacteristic
1163C22×C4C22×#12011yescharacteristic
1164C22×C4C22×#12011yescharacteristic
1165C22×C4C22×#12011yescharacteristic
1166C22×C4C22×#12111yescharacteristic
1167C22×C4C22×#12111yescharacteristic
1168C22×C4C22×#12111yescharacteristic
1169C22×C4C22×#12111yescharacteristic
1170C22×C4C22×#12111yescharacteristic
1171C22×C4C22×#12111yescharacteristic
1172C22×C4C22×#12111yescharacteristic
1173C22×C4C22×#12111yescharacteristic
1174C22×C4C2×#52511yescharacteristic
1175C22×C4C2×#52511yescharacteristic
1176C22×C4C2×#52511yescharacteristic
1177C22×C4C22×#12711yescharacteristic
1178C22×C4C22×#12711yescharacteristic
1179C22×C4C22×#12711yescharacteristic
1180C22×C4C2×#53411yescharacteristic
1181C22×C4C2×#53411yescharacteristic
1182C22×C4C2×#53411yescharacteristic
1183C22×C4C2×#53411yescharacteristic
1184C22×C4C2×#53411yescharacteristic
1185C22×C4C2×#53411yescharacteristic
1186C22×C4C2×#53411yescharacteristic
1187C22×C4C2×#53411yescharacteristic
1188C22×C4C2×#53411yescharacteristic
1189C22×C4C2×#53411yescharacteristic
1190C22×C4C2×#53411yescharacteristic
1191C22×C4C2×#53411yescharacteristic
1192C22×C4C2×#53411yescharacteristic
1193C22×C4C2×#53411yescharacteristic
1194C22×C4C2×#53411yescharacteristic
1195C22×C4C2×#53411yescharacteristic
1196C22×C4C2×#53411yescharacteristic
1197C22×C4C2×#53411yescharacteristic
1198C22×C4C2×#53411yescharacteristic
1199C22×C4C2×#53511yescharacteristic
1200C22×C4C2×#53511yescharacteristic
1201C22×C4C2×#53511yescharacteristic
1202C22×C4C2×#53511yescharacteristic
1203C22×C4C2×#53511yescharacteristic
1204C22×C4C2×#53511yescharacteristic
1205C22×C4C2×#53511yescharacteristic
1206C22×C4C2×#53511yescharacteristic
1207C22×C4C2×#53511yescharacteristic
1208C22×C4C2×#53511yescharacteristic
1209C22×C4C2×#53511yescharacteristic
1210C22×C4C2×#53511yescharacteristic
1211C22×C4C2×#53511yescharacteristic
1212C22×C4C2×#53511yescharacteristic
1213C22×C4C2×#53511yescharacteristic
1214C22×C4C2×#53811yescharacteristic
1215C22×C4C2×#53811yescharacteristic
1216C22×C4C2×#53811yescharacteristic
1217C22×C4C2×#53811yescharacteristic
1218C22×C4C2×#53811yescharacteristic
1219C22×C4C2×#53811yescharacteristic
1220C22×C4C2×D4211yescharacteristic
1221C22×C4C2×D4211yescharacteristic
1222C22×C4C2×D4211yescharacteristic
1223C22×C4C2×D4211yescharacteristic
1224C22×C4C2×D4211yescharacteristic
1225C22×C4C2×D4211yescharacteristic
1226C22×C4C2×D4211yescharacteristic
1227C22×C4C2×D4211yescharacteristic
1228C22×C4C2×D4211yescharacteristic
1229C22×C4C2×D4211yescharacteristic
1230C22×C4C2×D4211yescharacteristic
1231C22×C4C2×D4211yescharacteristic
1232C22×C4C2×D4211yescharacteristic
1233C22×C4C2×D4211yescharacteristic
1234C22×C4C2×D4211yescharacteristic
1235C22×C4C2×D4211yescharacteristic
1236C22×C4C2×D4211yescharacteristic
1237C22×C4C2×D4211yescharacteristic
1238C22×C4C2×D4211yescharacteristic
1239C22×C4C2×D4211yescharacteristic
1240C22×C4C2×D4211yescharacteristic
1241C22×C4C2×D4211yescharacteristic
1242C22×C4C2×D4211yescharacteristic
1243C22×C4C2×D4211yescharacteristic
1244C22×C4C2×D4211yescharacteristic
1245C22×C4C2×D4211yescharacteristic
1246C22×C4C2×D4211yescharacteristic
1247C22×C4C2×D4211yescharacteristic
1248C22×C4C2×D4211yescharacteristic
1249C22×C4C2×D4211yescharacteristic
1250C22×C4C2×D4211yescharacteristic
1251C22×C4C2×D4211yescharacteristic
1252C22×C4C2×D4211yescharacteristic
1253C22×C4C2×D4211yescharacteristic
1254C22×C4C2×D4211yescharacteristic
1255C22×C4C2×D4211yescharacteristic
1256C22×C4C2×D4211yescharacteristic
1257C22×C4C2×D4211yescharacteristic
1258C22×C4C2×D4211yescharacteristic
1259C22×C4C2×D4211yescharacteristic
1260C22×C4C2×D4211yescharacteristic
1261C22×C4C2×D4211yescharacteristic
1262C22×C4C2×#54611yescharacteristic
1263C22×C4C2×#54611yescharacteristic
1264C22×C4C2×#54611yescharacteristic
1265C22×C4C2×#54611yescharacteristic
1266C22×C4C2×#54611yescharacteristic
1267C22×C4C2×#54611yescharacteristic
1268C22×C4C2×#54611yescharacteristic
1269C22×C4C2×#54611yescharacteristic
1270C22×C4C2×#54611yescharacteristic
1271C22×C4C2×#54611yescharacteristic
1272C22×C4C2×#54611yescharacteristic
1273C22×C4C2×#54611yescharacteristic
1274C22×C4C2×#54611yescharacteristic
1275C22×C4C2×#54611yescharacteristic
1276C22×C4C2×#54611yescharacteristic
1277C22×C4C2×#54611yescharacteristic
1278C22×C4C2×#54611yescharacteristic
1279C22×C4C2×#54611yescharacteristic
1280C22×C4C2×#54611yescharacteristic
1281C22×C4C2×#54611yescharacteristic
1282C22×C4C2×#54611yescharacteristic
1283C22×C4C2×#54611yescharacteristic
1284C22×C4C2×#56011yescharacteristic
1285C22×C4C2×#56011yescharacteristic
1286C22×C4C2×#56011yescharacteristic
1287C22×C4C2×#56011yescharacteristic
1288C22×C4C2×#56011yescharacteristic
1289C22×C4C2×#56011yescharacteristic
1290C22×C4C2×H(3,𝔽4)11yescharacteristic
1291C22×C4C2×H(3,𝔽4)11yescharacteristic
1292C23#1471512yes—
1293C23#1471512yes—
1294C23#1471514yes—
1295C23#1471514yes—
1296C23#1471512yes—
1297C23#1471514yes—
1298C23#1471514yes—
1299C23#1471514yes—
1300C23#1471514yes—
1301C23#1471512yes—
1302C23#1471614yes—
1303C23#1471614yes—
1304C23#1525712yes—
1305C23#1525714yes—
1306C23#1525714yes—
1307C23#1525714yes—
1308C23#1525712yes—
1309C23#1525712yes—
1310C23#1525714yes—
1311C23#1525714yes—
1312C23#1525714yes—
1313C23#1525712yes—
1314C23#1525814yes—
1315C23#1525814yes—
1316C23#1526714yes—
1317C23#1526714yes—
1318C23#1526714yes—
1319C23#1526714yes—
1320C23#1594712yes—
1321C23#1594712yes—
1322C23#1594712yes—
1323C23#1594712yes—
1324C23#1624914yes—
1325C23#1624914yes—
1326C23#1624914yes—
1327C23#1624914yes—
1328C23#2388218yes—
1329C23C22×#39211yescharacteristic
1330C23C2×#261311yescharacteristic
1331C23C2×#240311yescharacteristic
1332C23C2×#240311yescharacteristic
1333C23C2×#240311yescharacteristic
1334C23C2×#240311yescharacteristic
1335C23C2×#240311yescharacteristic
1336C23C2×#240311yescharacteristic
1337C23C2×#240311yescharacteristic
1338C23C2×#240311yescharacteristic
1339C23C2×#240311yescharacteristic
1340C23C2×#241011yescharacteristic
1341C23C2×#241011yescharacteristic
1342C23C2×#241011yescharacteristic
1343C23C2×#241011yescharacteristic
1344C23C2×#241011yescharacteristic
1345C23C2×#241011yescharacteristic
1346C23C2×#242411yescharacteristic
1347C23C2×#242411yescharacteristic
1348C23C2×#240811yescharacteristic
1349C23C2×#240811yescharacteristic
1350C23C2×#240811yescharacteristic
1351C23C2×#240811yescharacteristic
1352C23C2×#243311yescharacteristic
1353C23C2×#243311yescharacteristic
1354C23C2×#240411yescharacteristic
1355C23C2×#284611yescharacteristic
1356C23C2×#266811yescharacteristic
1357C23C2×#266811yescharacteristic
1358C23C2×#266911yescharacteristic
1359C23C2×#266911yescharacteristic
1360C23C2×#267811yescharacteristic
1361C23C2×#267811yescharacteristic
1362C23C2×#267911yescharacteristic
1363C23C2×#267911yescharacteristic
1364C2×C4#1471514yes—
1365C2×C4#1471514yes—
1366C2×C4#1471512yes—
1367C2×C4#1471512yes—
1368C2×C4#1471514yes—
1369C2×C4#1471514yes—
1370C2×C4#1471514yes—
1371C2×C4#1471512yes—
1372C2×C4#1471512yes—
1373C2×C4#1471514yes—
1374C2×C4#1471514yes—
1375C2×C4#1471514yes—
1376C2×C4#1471514yes—
1377C2×C4#1471514yes—
1378C2×C4#1471514yes—
1379C2×C4#1471514yes—
1380C2×C4#1471514yes—
1381C2×C4#1471514yes—
1382C2×C4#1471614yes—
1383C2×C4#1471614yes—
1384C2×C4#1471614yes—
1385C2×C4#1471614yes—
1386C2×C4#1471614yes—
1387C2×C4#1471614yes—
1388C2×C4#1471614yes—
1389C2×C4#1471614yes—
1390C2×C4#1471614yes—
1391C2×C4#1471614yes—
1392C2×C4#1525712yes—
1393C2×C4#1525712yes—
1394C2×C4#1525714yes—
1395C2×C4#1525714yes—
1396C2×C4#1525714yes—
1397C2×C4#1525712yes—
1398C2×C4#1525712yes—
1399C2×C4#1525714yes—
1400C2×C4#1525714yes—
1401C2×C4#1525714yes—
1402C2×C4#1525714yes—
1403C2×C4#1525714yes—
1404C2×C4#1525714yes—
1405C2×C4#1525714yes—
1406C2×C4#1525714yes—
1407C2×C4#1525714yes—
1408C2×C4#1525714yes—
1409C2×C4#1525714yes—
1410C2×C4#1525814yes—
1411C2×C4#1525814yes—
1412C2×C4#1525814yes—
1413C2×C4#1525814yes—
1414C2×C4#1525814yes—
1415C2×C4#1525814yes—
1416C2×C4#1525814yes—
1417C2×C4#1525814yes—
1418C2×C4#1525814yes—
1419C2×C4#1525814yes—
1420C2×C4#1526714yes—
1421C2×C4#1526714yes—
1422C2×C4#1526714yes—
1423C2×C4#1526714yes—
1424C2×C4#1526714yes—
1425C2×C4#1526714yes—
1426C2×C4#1526714yes—
1427C2×C4#1526714yes—
1428C2×C4#1526714yes—
1429C2×C4#1526714yes—
1430C2×C4#1526714yes—
1431C2×C4#1526714yes—
1432C2×C4#1526714yes—
1433C2×C4#1526714yes—
1434C2×C4#1526714yes—
1435C2×C4#1526714yes—
1436C2×C4#1526714yes—
1437C2×C4#1526714yes—
1438C2×C4#1526714yes—
1439C2×C4#1526714yes—
1440C2×C4#1594712yes—
1441C2×C4#1594712yes—
1442C2×C4#1594712yes—
1443C2×C4#1594712yes—
1444C2×C4#1624914yes—
1445C2×C4#1624914yes—
1446C2×C4#1624914yes—
1447C2×C4#1624914yes—
1448C2×C4#1624914yes—
1449C2×C4#1624914yes—
1450C2×C4#1624914yes—
1451C2×C4#1624914yes—
1452C2×C4#1624914yes—
1453C2×C4#1624914yes—
1454C2×C4#1624914yes—
1455C2×C4#1624914yes—
1456C2×C4#1624914yes—
1457C2×C4#1624914yes—
1458C2×C4#1624914yes—
1459C2×C4#1624914yes—
1460C2×C4#1624914yes—
1461C2×C4#1624914yes—
1462C2×C4#1624914yes—
1463C2×C4#1624914yes—
1464C2×C4C22×#39211yescharacteristic
1465C2×C4C22×#39211yescharacteristic
1466C2×C4C2×#261311yescharacteristic
1467C2×C4C2×#261311yescharacteristic
1468C2×C4C2×#261311yescharacteristic
1469C2×C4C2×#261311yescharacteristic
1470C2×C4C2×#261311yescharacteristic
1471C2×C4C2×#261711yescharacteristic
1472C2×C4C2×#261711yescharacteristic
1473C2×C4C2×#261711yescharacteristic
1474C2×C4C2×#240311yescharacteristic
1475C2×C4C2×#240311yescharacteristic
1476C2×C4C2×#240311yescharacteristic
1477C2×C4C2×#240311yescharacteristic
1478C2×C4C2×#240311yescharacteristic
1479C2×C4C2×#240311yescharacteristic
1480C2×C4C2×#240311yescharacteristic
1481C2×C4C2×#240311yescharacteristic
1482C2×C4C2×#240311yescharacteristic
1483C2×C4C2×#240311yescharacteristic
1484C2×C4C2×#240311yescharacteristic
1485C2×C4C2×#240311yescharacteristic
1486C2×C4C2×#241011yescharacteristic
1487C2×C4C2×#241011yescharacteristic
1488C2×C4C2×#241011yescharacteristic
1489C2×C4C2×#241011yescharacteristic
1490C2×C4C2×#241011yescharacteristic
1491C2×C4C2×#241011yescharacteristic
1492C2×C4C2×#241011yescharacteristic
1493C2×C4C2×#241011yescharacteristic
1494C2×C4C2×#241011yescharacteristic
1495C2×C4C2×#241011yescharacteristic
1496C2×C4C2×#241011yescharacteristic
1497C2×C4C2×#241011yescharacteristic
1498C2×C4C2×#241011yescharacteristic
1499C2×C4C2×#241011yescharacteristic
1500C2×C4C2×#241011yescharacteristic
1501C2×C4C2×#241011yescharacteristic
1502C2×C4C2×#241011yescharacteristic
1503C2×C4C2×#241011yescharacteristic
1504C2×C4C2×#242411yescharacteristic
1505C2×C4C2×#242411yescharacteristic
1506C2×C4C2×#242411yescharacteristic
1507C2×C4C2×#242411yescharacteristic
1508C2×C4C2×#242411yescharacteristic
1509C2×C4C2×#242411yescharacteristic
1510C2×C4C2×#242411yescharacteristic
1511C2×C4C2×#242411yescharacteristic
1512C2×C4C2×#242411yescharacteristic
1513C2×C4C2×#242411yescharacteristic
1514C2×C4C2×#240811yescharacteristic
1515C2×C4C2×#240811yescharacteristic
1516C2×C4C2×#240811yescharacteristic
1517C2×C4C2×#240811yescharacteristic
1518C2×C4C2×#240811yescharacteristic
1519C2×C4C2×#240811yescharacteristic
1520C2×C4C2×#240811yescharacteristic
1521C2×C4C2×#240811yescharacteristic
1522C2×C4C2×#243311yescharacteristic
1523C2×C4C2×#243311yescharacteristic
1524C2×C4C2×#243311yescharacteristic
1525C2×C4C2×#243311yescharacteristic
1526C2×C4C2×#243311yescharacteristic
1527C2×C4C2×#243311yescharacteristic
1528C2×C4C2×#243311yescharacteristic
1529C2×C4C2×#243311yescharacteristic
1530C2×C4C2×#243311yescharacteristic
1531C2×C4C2×#243311yescharacteristic
1532C2×C4C2×#243311yescharacteristic
1533C2×C4C2×#243311yescharacteristic
1534C2×C4C2×#243311yescharacteristic
1535C2×C4C2×#240411yescharacteristic
1536C2×C4C2×#240411yescharacteristic
1537C2×C4C2×#253911yescharacteristic
1538C2×C4C2×#253911yescharacteristic
1539C2×C4C2×#253911yescharacteristic
1540C2×C4C2×#284611yescharacteristic
1541C2×C4C2×#284711yescharacteristic
1542C2×C4C2×#281211yescharacteristic
1543C2×C4C2×#281211yescharacteristic
1544C2×C4C2×#266811yescharacteristic
1545C2×C4C2×#266811yescharacteristic
1546C2×C4C2×#266811yescharacteristic
1547C2×C4C2×#266811yescharacteristic
1548C2×C4C2×#266911yescharacteristic
1549C2×C4C2×#266911yescharacteristic
1550C2×C4C2×#266911yescharacteristic
1551C2×C4C2×#266911yescharacteristic
1552C2×C4C2×#266911yescharacteristic
1553C2×C4C2×#266911yescharacteristic
1554C2×C4C2×#266911yescharacteristic
1555C2×C4C2×#266911yescharacteristic
1556C2×C4C2×#266911yescharacteristic
1557C2×C4C2×#266911yescharacteristic
1558C2×C4C2×#266911yescharacteristic
1559C2×C4C2×#266911yescharacteristic
1560C2×C4C2×#266911yescharacteristic
1561C2×C4C2×#266911yescharacteristic
1562C2×C4C2×#266911yescharacteristic
1563C2×C4C2×#266911yescharacteristic
1564C2×C4C2×#267011yescharacteristic
1565C2×C4C2×#267011yescharacteristic
1566C2×C4C2×#267011yescharacteristic
1567C2×C4C2×#267011yescharacteristic
1568C2×C4C2×#267011yescharacteristic
1569C2×C4C2×#267011yescharacteristic
1570C2×C4C2×#267811yescharacteristic
1571C2×C4C2×#267811yescharacteristic
1572C2×C4C2×#267811yescharacteristic
1573C2×C4C2×#267811yescharacteristic
1574C2×C4C2×#267811yescharacteristic
1575C2×C4C2×#267811yescharacteristic
1576C2×C4C2×#267811yescharacteristic
1577C2×C4C2×#267811yescharacteristic
1578C2×C4C2×#267811yescharacteristic
1579C2×C4C2×#267811yescharacteristic
1580C2×C4C2×#267911yescharacteristic
1581C2×C4C2×#267911yescharacteristic
1582C2×C4C2×#267911yescharacteristic
1583C2×C4C2×#267911yescharacteristic
1584C22#15668414yes—
1585C22#15668414yes—
1586C22#15668414yes—
1587C22#15668414yes—
1588C22#39410218yes—
1589C22#41759718yes—
1590C22#44949618yes—
1591C22C2×#1471511yescharacteristic
1592C22C2×#1471511yescharacteristic
1593C22C2×#1471511yescharacteristic
1594C22C2×#1471511yescharacteristic
1595C22C2×#1471611yescharacteristic
1596C22C2×#1525711yescharacteristic
1597C22C2×#1525711yescharacteristic
1598C22C2×#1525711yescharacteristic
1599C22C2×#1525711yescharacteristic
1600C22C2×#1525811yescharacteristic
1601C22C2×#1526711yescharacteristic
1602C22C2×#1526711yescharacteristic
1603C22C2×#1594711yescharacteristic
1604C22C2×#1624911yescharacteristic
1605C22C2×#1624911yescharacteristic
1606C22C2×#2388214yes—
1607C4#15668414yes—
1608C4#15668414yes—
1609C4#15668414yes—
1610C4#15668414yes—
1611C4C2×#1471511yescharacteristic
1612C4C2×#1471511yescharacteristic
1613C4C2×#1471611yescharacteristic
1614C4C2×#1471611yescharacteristic
1615C4C2×#1525711yescharacteristic
1616C4C2×#1525711yescharacteristic
1617C4C2×#1525811yescharacteristic
1618C4C2×#1525811yescharacteristic
1619C4C2×#1526711yescharacteristic
1620C4C2×#1526711yescharacteristic
1621C4C2×#1526711yescharacteristic
1622C4C2×#1526711yescharacteristic
1623C4C2×#1624911yescharacteristic
1624C4C2×#1624911yescharacteristic
1625C4C2×#1624911yescharacteristic
1626C4C2×#1624911yescharacteristic
1627C2C2×#39410212yes—
1628C2C2×#41759712yes—
1629C2C2×#44949612yes—
1630C2#7223673718yesdirect product factor
1631C2C2×#15668411yescharacteristic
subgroupG/H
center, socleC24#2403
commutator, Frattini, cosocleC24×C4C25
LCSG ▷ C24×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#10993C2semidirect
2. C2×#123600C2semidirect
3. C22×#11030C2semidirect
4. C22×#10987C2semidirect
5. C2×#123605C2semidirect
6. C22×#11012C2semidirect
7. C22×#10984C2semidirect
8. C22×#23400C2semidirect
9. C2×#6431707C2semidirect
10. C22×#23443C2semidirect
11. C2×#123531C2semidirect
12. C22×#10994C2semidirect
13. C22×#20598C2semidirect
14. C22×#35222C2semidirect
15. #72236737C2direct (N × H)
16. C23×#3003C2semidirect
20. C22×#3449C22semidirect
25. C22×#3003C22semidirect
26. C22×#2879C22semidirect
29. C23×#410C22semidirect
30. C23×#410C22semidirect
31. C22×#2896C22semidirect
32. C23×#413C22semidirect
33. C23×#421C22semidirect
40. C2×#35222C22semidirect
45. C2×#23443C22semidirect
46. C2×#23400C22semidirect
47. #6431707C22semidirect
48. C2×#20598C22semidirect
49. C23×#344C22semidirect
50. C23×#344C22semidirect
51. C22×#1740C22semidirect
52. C2×#20347C22semidirect
53. C22×#1733C22semidirect
54. C22×#1733C22semidirect
55. C22×#1733C22semidirect
56. C23×H(3,ℤ/4)C22semidirect
57. C23×H(3,ℤ/4)C22semidirect
58. C2×#11030C22semidirect
59. C2×#11012C22semidirect
60. C2×#10994C22semidirect
61. C2×#10993C22semidirect
62. C2×#10987C22semidirect
63. C2×#10984C22semidirect
64. #123605C22semidirect
65. #123600C22semidirect
66. #123531C22semidirect
69. C25×D4D4semidirect
74. C23×AGL(1,ℤ/8)D4semidirect
75. C23×AGL(1,ℤ/8)D4semidirect
78. C24×SD16D4semidirect
79. C24×D8D4semidirect
84. C2×#3449C23semidirect
85. C22×#535D4semidirect
86. C22×#535D4semidirect
89. C23×#127D4semidirect
90. C23×#124D4semidirect
92. C22×#525D4semidirect
96. C23×#121D4semidirect
104. C22×#421C23semidirect
105. C2×#2896C23semidirect
106. C22×#418D4semidirect
107. C22×#418D4semidirect
108. C22×#418D4semidirect
109. C22×#418D4semidirect
116. C23×#102D4semidirect
117. C22×#413C23semidirect
118. C22×#410C23semidirect
119. C22×#410C23semidirect
120. C2×#2879C23semidirect
121. C22×#407D4semidirect
124. C2×#2309D4semidirect
125. C2×#2309D4semidirect
128. C2×#2280D4semidirect
129. C2×#2280D4semidirect
132. C22×#344C23semidirect
133. C22×#344C23semidirect
134. C2×#1740C23semidirect
135. #20347C23semidirect
136. C2×#1733C23semidirect
137. C2×#1733C23semidirect
138. C2×#1733C23semidirect
139. C22×H(3,ℤ/4)C23semidirect
140. C22×H(3,ℤ/4)C23semidirect
171. C24×D4C2×D4semidirect
187. C22×AGL(1,ℤ/8)C2×D4semidirect
188. C23×SD16C2×D4semidirect
189. C23×D8C2×D4semidirect
204. C22×#127C2×D4semidirect
205. C22×#124C2×D4semidirect
206. C2×#525C2×D4semidirect
208. C22×#121C2×D4semidirect
236. C2×#418C2×D4semidirect
237. C2×#418C2×D4semidirect
238. C2×#418C2×D4semidirect
239. C22×#102C2×D4semidirect
240. C2×#407C2×D4semidirect
241. #2309C2×D4semidirect
242. #2309C2×D4semidirect
243. #2280C2×D4semidirect
244. #2280C2×D4semidirect
251. C22×#41#120semidirect
255. C23×Q8#120semidirect
273. C23×D4#120semidirect
362. C22×M16#120semidirect
363. C22×M16#120semidirect
370. C23×C8#120semidirect
376. C2×#117#120semidirect
377. C2×#117#120semidirect
391. C22×C4⋊C4#120semidirect
422. C22×Q8C2×#120semidirect
435. C22×D4C2×#120semidirect
726. C2×M16C2×#120semidirect
727. C22×C8C2×#120semidirect
728. #117C2×#120semidirect
730. C2×C4⋊C4C2×#120semidirect
1630. C2#72236737direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#109932
C2×#1236002
C22×#110302
C22×#109872
C2×#1236052
C22×#110122
C22×#109842
C22×#234002
C2×#64317072
C22×#234432
C2×#1235312
C22×#109942
C22×#205982
C22×#352222
#722367372
C23×#30032