Finite Group Databasebeta

← C22×#394102 #72315008

Subgroups — C22×#394102 #72315008

Order 2048.

At least 7992 conjugacy classes of subgroups; only the 11912 normal subgroups are shown.

The subgroup lattice has 947 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10993C211yesmaximal, characteristic, complemented
2C22×#10785C211yesmaximal, characteristic, complemented
3C22×#11004C211yesmaximal, characteristic, complemented
4C22×#10987C211yesmaximal, characteristic, complemented
5C22×#23400C211yesmaximal, characteristic, complemented
6C22×#23443C211yesmaximal, characteristic, complemented
7C22×#10994C211yesmaximal, characteristic, complemented
8C22×#20598C211yesmaximal, characteristic, complemented
9C22×#60367C211yesmaximal, characteristic, complemented
10C23×#1795C211yesmaximal, characteristic, complemented
11C23×#1904C211yesmaximal, characteristic, complemented
12C23×#2008C211yesmaximal, characteristic, complemented
13C23×#2010C211yesmaximal, characteristic, complemented
14C23×#3003C211yesmaximal, characteristic, complemented
15C23×#3484C211yesmaximal, characteristic, complemented
16C2×#394102C2148yesmaximal, direct product factor
17C24×H(5,𝔽2)C2211yescharacteristic
18C26×D4C2211yescharacteristic
19C23×#575C2211yescharacteristic, complemented
20C24×AGL(1,ℤ/8)C2211yescharacteristic
21C24×AGL(1,ℤ/8)C2211yescharacteristic, complemented
22C22×#3484C22124yescomplemented
23C22×#3449C2211yescharacteristic, complemented
24C23×#535C2211yescharacteristic
25C23×#535C2211yescharacteristic
26C23×#525C2211yescharacteristic
27C23×#525C2211yescharacteristic
28C23×#525C2211yescharacteristic, complemented
29C23×#518C2211yescharacteristic
30C2×#60367C22124yescomplemented
31C22×#3003C22124yescomplemented
32C22×#2879C2211yescharacteristic, complemented
33C23×#407C2211yescharacteristic, complemented
34C23×#407C2211yescharacteristic, complemented
35C23×#410C2211yescharacteristic, complemented
36C23×#410C2211yescharacteristic, complemented
37C22×#2896C2211yescharacteristic, complemented
38C23×#413C2211yescharacteristic, complemented
39C23×#421C2211yescharacteristic, complemented
40C23×#421C2211yescharacteristic, complemented
41C23×#421C2211yescharacteristic, complemented
42C23×#418C2211yescharacteristic
43C23×#418C2211yescharacteristic
44C23×#418C2211yescharacteristic
45C23×#418C2211yescharacteristic, complemented
46C23×#418C2211yescharacteristic, complemented
47C23×#418C2211yescharacteristic, complemented
48C22×#2280C2211yescharacteristic, complemented
49C2×#23443C22124yescomplemented
50C22×#2010C22124yescomplemented
51C22×#2008C22124yescomplemented
52C2×#23400C22124yescomplemented
53C22×#1904C22124yescomplemented
54C22×#1795C22124yescomplemented
55C2×#20598C22124yescomplemented
56C23×#344C2211yescharacteristic, complemented
57C23×#344C2211yescharacteristic, complemented
58C22×#1740C2211yescharacteristic, complemented
59C22×#1733C2211yescharacteristic, complemented
60C23×H(3,ℤ/4)C2211yescharacteristic, complemented
61C23×H(3,ℤ/4)C2211yescharacteristic, complemented
62#394102C221256yesdirect product factor
63C2×#11004C22124yescomplemented
64C2×#10994C22124yescomplemented
65C2×#10993C22124yescomplemented
66C2×#10987C22124yescomplemented
67C2×#10785C22124yescomplemented
68C23×H(5,𝔽2)D4112yescomplemented
69C23×H(5,𝔽2)C23112yes—
70C24×#41D412yescomplemented
71C24×#41C2311yescharacteristic
72C24×#41C2311yescharacteristic
73C24×#41C2311yescharacteristic
74C25×D4D412yescomplemented
75C25×D4D4116yescomplemented
76C25×D4C23112yes—
77C25×D4C2311yescharacteristic
78C25×D4C2311yescharacteristic
79C26×C4C2311yescharacteristic
80C22×#575C23112yescomplemented
81C23×AGL(1,ℤ/8)D4112yescomplemented
82C23×AGL(1,ℤ/8)C23112yes—
83C23×AGL(1,ℤ/8)C23112yescomplemented
84C24×SD16D412yescomplemented
85C24×D8D412yescomplemented
86C24×M16C2311yescharacteristic
87C24×M16C2311yescharacteristic
88C24×M16C2311yescharacteristic
89C24×M16C2311yescharacteristic
90C2×#3484C23164yescomplemented
91C2×#3449C23112yescomplemented
92C22×#535D4116yescomplemented
93C22×#535D4112yescomplemented
94C22×#535C23112yes—
95C22×#535C23112yes—
96C23×#127D412yescomplemented
97C23×#124D412yescomplemented
98C22×#525D4112yes—
99C22×#525D4116yescomplemented
100C22×#525C23112yes—
101C22×#525C23112yes—
102C22×#525C23112yescomplemented
103C23×#123D412yes—
104C23×#120D412yes—
105C22×#518D4116yescomplemented
106C22×#518C23112yes—
107C23×#117C2311yescharacteristic
108C23×#117C2311yescharacteristic
109C23×#117C2311yescharacteristic
110C23×#117C2311yescharacteristic
111C23×#117C2311yescharacteristic
112#60367C23164yescomplemented
113C2×#3003C23164yescomplemented
114C22×#421C23112yescomplemented
115C22×#421C23112yescomplemented
116C22×#421C23112yescomplemented
117C2×#2896C23112yescomplemented
118C22×#418D4116yescomplemented
119C22×#418D4112yescomplemented
120C22×#418C23112yes—
121C22×#418C23112yes—
122C22×#418C23112yes—
123C22×#418C23112yescomplemented
124C22×#418C23112yescomplemented
125C22×#418C23112yescomplemented
126C23×#102D414yescomplemented
127C22×#413C23112yescomplemented
128C22×#410C23112yescomplemented
129C22×#410C23112yescomplemented
130C2×#2879C23112yescomplemented
131C22×#407C23112yescomplemented
132C22×#407C23112yescomplemented
133C2×#2280C23112yescomplemented
134#23443C23164yescomplemented
135C2×#2010C23164yescomplemented
136C2×#2008C23164yescomplemented
137#23400C23164yescomplemented
138C2×#1904C23164yescomplemented
139C2×#1795C23164yescomplemented
140#20598C23164yescomplemented
141C22×#344C23112yescomplemented
142C22×#344C23112yescomplemented
143C2×#1740C23112yescomplemented
144C2×#1733C23112yescomplemented
145C22×H(3,ℤ/4)C23112yescomplemented
146C22×H(3,ℤ/4)C23112yescomplemented
147#11004C23164yescomplemented
148#10994C23164yescomplemented
149#10993C23164yescomplemented
150#10987C23164yescomplemented
151#10785C23164yescomplemented
152C27C2×D411yescharacteristic
153C22×H(5,𝔽2)C2×D4148yescomplemented
154C22×H(5,𝔽2)C24116yes—
155C23×#41C2×D418yes—
156C23×#41C2×D418yes—
157C23×#41C2×D416yes—
158C23×#41C2×D416yes—
159C23×#41C2×D416yes—
160C23×#41C2×D416yes—
161C23×#41C2×D4124yescomplemented
162C23×#41C2×D416yescomplemented
163C23×#41C2416yes—
164C23×#41C2416yes—
165C23×#41C2416yes—
166C24×Q8C2×D411yescharacteristic
167C24×Q8C2×D411yescharacteristic
168C24×Q8C2×D411yescharacteristic, complemented
169C24×D4C2×D412yes—
170C24×D4C2×D411yescharacteristic
171C24×D4C2×D412yes—
172C24×D4C2×D418yes—
173C24×D4C2×D416yes—
174C24×D4C2×D418yes—
175C24×D4C2×D411yescharacteristic
176C24×D4C2×D412yes—
177C24×D4C2×D412yes—
178C24×D4C2×D416yes—
179C24×D4C2×D418yes—
180C24×D4C2×D416yes—
181C24×D4C2×D412yes—
182C24×D4C2×D418yes—
183C24×D4C2×D416yes—
184C24×D4C2×D418yes—
185C24×D4C2×D411yescharacteristic, complemented
186C24×D4C2×D4196yescomplemented
187C24×D4C2×D4124yescomplemented
188C24×D4#4118yes—
189C24×D4C2416yes—
190C24×D4C24116yes—
191C24×D4C2416yes—
192C25×C4C2×D411yescharacteristic
193C25×C4C2×D416yes—
194C25×C4C2×D418yes—
195C25×C4C2×D418yes—
196C25×C4C2×D412yes—
197C25×C4C2416yes—
198C25×C4C2411yescharacteristic
199C2×#575C24116yescomplemented
200C22×AGL(1,ℤ/8)C2×D4148yescomplemented
201C22×AGL(1,ℤ/8)C24116yes—
202C22×AGL(1,ℤ/8)C24116yescomplemented
203C23×SD16C2×D4124yescomplemented
204C23×D8C2×D4124yescomplemented
205C23×M16C2×D418yescomplemented
206C23×M16C2×D416yescomplemented
207C23×M16C2×D416yescomplemented
208C23×M16C2416yes—
209C23×M16C2416yes—
210C23×M16C2416yes—
211C23×M16C2416yes—
212C24×C8C2×D412yescomplemented
213C24×C8C2×D412yescomplemented
214#3449C24116yescomplemented
215C2×#535C2×D4196yescomplemented
216C2×#535C2×D4148yescomplemented
217C2×#535C24116yes—
218C2×#535C24116yes—
219C22×#127C2×D4124yescomplemented
220C22×#124C2×D4124yescomplemented
221C2×#525C2×D4148yes—
222C2×#525C2×D4196yescomplemented
223C2×#525C24116yes—
224C2×#525C24116yes—
225C2×#525C24116yescomplemented
226C22×#123C2×D4124yes—
227C22×#120C2×D4124yes—
228C2×#518C2×D4196yescomplemented
229C2×#518C24116yes—
230C22×#117C2×D416yes—
231C22×#117C2×D418yes—
232C22×#117C2×D418yes—
233C22×#117C2×D418yes—
234C22×#117C2×D418yes—
235C22×#117C2×D416yes—
236C22×#117C2×D418yescomplemented
237C22×#117C2×D416yescomplemented
238C22×#117C2416yes—
239C22×#117C2416yes—
240C22×#117C2416yes—
241C22×#117C2416yes—
242C22×#117C2416yes—
243C23×C4⋊C4C2×D412yescomplemented
244C23×C22⋊C4C2×D412yes—
245C23×C42C2×D412yes—
246C2×#421C24116yescomplemented
247C2×#421C24116yescomplemented
248C2×#421C24116yescomplemented
249#2896C24116yescomplemented
250C2×#418C2×D4196yescomplemented
251C2×#418C2×D4148yescomplemented
252C2×#418C24116yes—
253C2×#418C24116yes—
254C2×#418C24116yes—
255C2×#418C24116yescomplemented
256C2×#418C24116yescomplemented
257C2×#418C24116yescomplemented
258C22×#102C2×D4148yescomplemented
259C2×#413C24116yescomplemented
260C2×#410C24116yescomplemented
261C2×#410C24116yescomplemented
262#2879C24116yescomplemented
263C2×#407C24116yescomplemented
264C2×#407C24116yescomplemented
265#2280C24116yescomplemented
266C2×#344C24116yescomplemented
267C2×#344C24116yescomplemented
268#1740C24116yescomplemented
269#1733C24116yescomplemented
270C2×H(3,ℤ/4)C24116yescomplemented
271C2×H(3,ℤ/4)C24116yescomplemented
272C26#12018yes—
273C26#12012yes—
274C26C22×D416yes—
275C26C22×D411yescharacteristic
276C22×#41#120148yes—
277C22×#41#120124yes—
278C22×#41C22×D4124yes—
279C22×#41C22×D4124yes—
280C22×#41C22×D4112yes—
281C22×#41C22×D4112yes—
282C22×#41C22×D4112yes—
283C22×#41C22×D4112yes—
284C22×#41C22×D4132yescomplemented
285C22×#41C22×D4112yescomplemented
286C22×#41C2514yes—
287C22×#41C2514yes—
288C22×#41C2514yes—
289C23×Q8#12018yes—
290C23×Q8#12016yes—
291C23×Q8C22×D416yes—
292C23×Q8C22×D416yes—
293C23×Q8C22×D416yescomplemented
294C23×D4#120112yes—
295C23×D4#12016yes—
296C23×D4#120116yes—
297C23×D4#120148yes—
298C23×D4#12018yes—
299C23×D4#120116yes—
300C23×D4#120148yes—
301C23×D4#120116yes—
302C23×D4#120148yes—
303C23×D4#12014yes—
304C23×D4#120112yes—
305C23×D4#120112yes—
306C23×D4#120112yes—
307C23×D4#120124yes—
308C23×D4#121116yes—
309C23×D4#121148yes—
310C23×D4#121116yes—
311C23×D4#121148yes—
312C23×D4#121116yes—
313C23×D4#121148yes—
314C23×D4#127116yes—
315C23×D4#127148yes—
316C23×D4C22×D4112yes—
317C23×D4C22×D416yes—
318C23×D4C22×D4112yes—
319C23×D4C22×D4124yes—
320C23×D4C22×D4112yes—
321C23×D4C22×D4124yes—
322C23×D4C22×D416yes—
323C23×D4C22×D4112yes—
324C23×D4C22×D4112yes—
325C23×D4C22×D4112yes—
326C23×D4C22×D4112yes—
327C23×D4C22×D4124yes—
328C23×D4C22×D4112yes—
329C23×D4C22×D4124yes—
330C23×D4C22×D4112yes—
331C23×D4C22×D4124yes—
332C23×D4C22×D416yescomplemented
333C23×D4C22×D4164yescomplemented
334C23×D4C22×D4132yescomplemented
335C23×D4C2×#41124yes—
336C23×D4C2514yes—
337C23×D4C2514yes—
338C24×C4#12012yes—
339C24×C4#12018yes—
340C24×C4#120148yes—
341C24×C4#120112yes—
342C24×C4C22×D416yes—
343C24×C4C22×D4112yes—
344C24×C4C22×D4124yes—
345C24×C4C22×D4124yes—
346C24×C4C22×D4112yes—
347C24×C4C22×D411yescharacteristic
348C24×C4C22×D413yes—
349C24×C4C22×D414yes—
350C24×C4C22×D413yes—
351C24×C4C22×D414yes—
352C24×C4C22×D411yescharacteristic
353C24×C4C22×D413yes—
354C24×C4C22×D414yes—
355C24×C4C22×D414yes—
356C24×C4C22×D411yescharacteristic
357C24×C4C22×D413yes—
358C24×C4C22×D411yescharacteristic
359C24×C4C22×D414yes—
360C24×C4C22×D413yes—
361C24×C4C2×#4114yes—
362C24×C4H(5,𝔽2)14yes—
363C24×C4H(5,𝔽2)11yescharacteristic
364C24×C4H(5,𝔽2)11yescharacteristic
365C24×C4H(5,𝔽2)14yes—
366C24×C4H(5,𝔽2)13yes—
367C24×C4H(5,𝔽2)13yes—
368C24×C4C2514yes—
369C24×C4C2513yes—
370C22×SD16C22×D4132yescomplemented
371C22×D8C22×D4132yescomplemented
372C22×M16C22×D4124yescomplemented
373C22×M16C22×D4112yescomplemented
374C22×M16C22×D4112yescomplemented
375C22×M16C2514yes—
376C22×M16C2514yes—
377C22×M16C2514yes—
378C22×M16C2514yes—
379C23×C8C22×D4112yescomplemented
380C23×C8C22×D4112yescomplemented
381#535C22×D4164yescomplemented
382C2×#127C22×D4132yescomplemented
383C2×#124C22×D4132yescomplemented
384#525C22×D4164yescomplemented
385C2×#123C22×D4132yes—
386C2×#120C22×D4132yes—
387#518C22×D4164yescomplemented
388C2×#117#120148yes—
389C2×#117#120148yes—
390C2×#117C22×D4124yes—
391C2×#117C22×D4124yes—
392C2×#117C22×D4112yes—
393C2×#117C22×D4124yes—
394C2×#117C22×D4124yes—
395C2×#117C22×D4112yes—
396C2×#117C22×D4124yescomplemented
397C2×#117C22×D4112yescomplemented
398C2×#117C2514yes—
399C2×#117C2514yes—
400C2×#117C2514yes—
401C2×#117C2514yes—
402C2×#117C2514yes—
403C22×C4⋊C4C22×D4112yescomplemented
404C22×C22⋊C4#120116yes—
405C22×C22⋊C4C22×D4112yes—
406C22×C42#120116yes—
407C22×C42C22×D4112yes—
408#418C22×D4164yescomplemented
409C2×#102C22×D4164yescomplemented
410C25C2×#12011yescharacteristic
411C25C2×#120112yes—
412C25C2×#120124yes—
413C25C2×#12013yes—
414C25C2×#12014yes—
415C25C2×#12014yes—
416C25D4211yescharacteristic
417C25D4211yescharacteristic
418C25D4213yes—
419C25D4213yes—
420C25D4214yes—
421C25#54614yes—
422C25C23×D414yes—
423C25C23×D413yes—
424C2×#41C2×#120148yes—
425C2×#41C23×D418yes—
426C2×#41C23×D418yes—
427C22×Q8C2×#120124yes—
428C22×Q8C2×#120112yes—
429C22×Q8C23×D414yes—
430C22×Q8C23×D414yes—
431C22×Q8C23×D414yescomplemented
432C22×D4#392132yes—
433C22×D4#392196yes—
434C22×D4#392196yes—
435C22×D4#392196yes—
436C22×D4#3921192yes—
437C22×D4C2×#120124yes—
438C22×D4C2×#120112yes—
439C22×D4C2×#120148yes—
440C22×D4C2×#120124yes—
441C22×D4C2×#120148yes—
442C22×D4C2×#120148yes—
443C22×D4C2×#120148yes—
444C22×D4C2×#120148yes—
445C22×D4C2×#120124yes—
446C22×D4C2×#120124yes—
447C22×D4C2×#120148yes—
448C22×D4C2×#120124yes—
449C22×D4C2×#120124yes—
450C22×D4C2×#121148yes—
451C22×D4C2×#121148yes—
452C22×D4C2×#121148yes—
453C22×D4C2×#121148yes—
454C22×D4C2×#121148yes—
455C22×D4C2×#121148yes—
456C22×D4C2×#127148yes—
457C22×D4C2×#127148yes—
458C22×D4C23×D414yes—
459C22×D4C23×D418yes—
460C22×D4C23×D414yes—
461C22×D4C23×D418yes—
462C22×D4C23×D418yes—
463C22×D4C23×D418yes—
464C22×D4C23×D418yes—
465C22×D4C23×D418yes—
466C22×D4C23×D418yes—
467C22×D4C23×D418yes—
468C22×D4C23×D418yes—
469C22×D4C23×D418yes—
470C22×D4C23×D414yescomplemented
471C22×D4C22×#4118yes—
472C23×C4C2×#120112yes—
473C23×C4C2×#120124yes—
474C23×C4C2×#120124yes—
475C23×C4C2×#120148yes—
476C23×C4C2×#12013yes—
477C23×C4C2×#12013yes—
478C23×C4C2×#12016yes—
479C23×C4C2×#120112yes—
480C23×C4C2×#120112yes—
481C23×C4C2×#12014yes—
482C23×C4C2×#120112yes—
483C23×C4C2×#12014yes—
484C23×C4C2×#12014yes—
485C23×C4C2×#120112yes—
486C23×C4C2×#120112yes—
487C23×C4C2×#12014yes—
488C23×C4C2×#120112yes—
489C23×C4C2×#12014yes—
490C23×C4C2×#12013yes—
491C23×C4C2×#12013yes—
492C23×C4C2×#12013yes—
493C23×C4C2×#120112yes—
494C23×C4C2×#12016yes—
495C23×C4C2×#12011yescharacteristic
496C23×C4C2×#12114yes—
497C23×C4C2×#121112yes—
498C23×C4C2×#12114yes—
499C23×C4C2×#12114yes—
500C23×C4C2×#121112yes—
501C23×C4C2×#121112yes—
502C23×C4C2×#12714yes—
503C23×C4C2×#127112yes—
504C23×C4#53414yes—
505C23×C4#53414yes—
506C23×C4#534112yes—
507C23×C4#534112yes—
508C23×C4#53413yes—
509C23×C4#534112yes—
510C23×C4#53413yes—
511C23×C4#53416yes—
512C23×C4#53414yes—
513C23×C4#53413yes—
514C23×C4#53411yescharacteristic
515C23×C4#535112yes—
516C23×C4#53514yes—
517C23×C4#53514yes—
518C23×C4#535112yes—
519C23×C4D4213yes—
520C23×C4D4216yes—
521C23×C4D4213yes—
522C23×C4D4214yes—
523C23×C4D42112yes—
524C23×C4D4214yes—
525C23×C4D4213yes—
526C23×C4D42112yes—
527C23×C4D4213yes—
528C23×C4D4216yes—
529C23×C4D4213yes—
530C23×C4D4211yescharacteristic
531C23×C4D4213yes—
532C23×C4D42112yes—
533C23×C4D4216yes—
534C23×C4D4213yes—
535C23×C4D4214yes—
536C23×C4D42112yes—
537C23×C4D42112yes—
538C23×C4D4214yes—
539C23×C4D4214yes—
540C23×C4D42112yes—
541C23×C4D4214yes—
542C23×C4D42112yes—
543C23×C4D4213yes—
544C23×C4D42112yes—
545C23×C4D4213yes—
546C23×C4D4213yes—
547C23×C4D4216yes—
548C23×C4D4214yes—
549C23×C4D4211yescharacteristic
550C23×C4#546112yes—
551C23×C4#54614yes—
552C23×C4#546112yes—
553C23×C4#54614yes—
554C23×C4#546112yes—
555C23×C4#54614yes—
556C23×C4#546112yes—
557C23×C4C23×D418yes—
558C23×C4C23×D418yes—
559C23×C4C23×D418yes—
560C23×C4C23×D414yes—
561C23×C4C23×D413yes—
562C23×C4C23×D413yes—
563C23×C4C23×D416yes—
564C23×C4C23×D416yes—
565C23×C4C23×D413yes—
566C23×C4C23×D413yes—
567C23×C4C23×D416yes—
568C23×C4C23×D416yes—
569C23×C4C23×D413yes—
570C23×C4C23×D413yes—
571C23×C4C23×D413yes—
572C23×C4C23×D413yes—
573C23×C4C23×D416yes—
574C23×C4C23×D413yes—
575C23×C4C22×#4116yes—
576C23×C4C2×H(5,𝔽2)16yes—
577C23×C4C2×H(5,𝔽2)13yes—
578C23×C4C2×H(5,𝔽2)13yes—
579C23×C4C2×H(5,𝔽2)16yes—
580C23×C4C2×H(5,𝔽2)13yes—
581C23×C4C2×H(5,𝔽2)13yes—
582C23×C4C2611yescharacteristic
583C2×M16C23×D418yescomplemented
584C22×C8C23×D418yescomplemented
585C22×C8C23×D418yescomplemented
586#117C2×#120148yes—
587#117C2×#120148yes—
588#117C23×D418yes—
589#117C23×D418yes—
590#117C23×D418yes—
591#117C23×D418yes—
592#117C23×D418yescomplemented
593C2×C4⋊C4C23×D418yescomplemented
594C2×C22⋊C4C2×#120148yes—
595C2×C22⋊C4C23×D418yes—
596C2×C42C2×#120148yes—
597C2×C42C23×D418yes—
598C24#240313yes—
599C24#240313yes—
600C24#240314yes—
601C24#240313yes—
602C24#2403112yes—
603C24#240316yes—
604C24#240311yescharacteristic
605C24#240814yes—
606C24#2408112yes—
607C24#241014yes—
608C24#241014yes—
609C24#2410112yes—
610C24#2410112yes—
611C24#243314yes—
612C24#2433112yes—
613C24#284614yes—
614C24#2846112yes—
615C24C22×#12013yes—
616C24C22×#12018yes—
617C24C22×#12018yes—
618C24C22×#12013yes—
619C24C22×#12016yes—
620C24C22×#12016yes—
621C24C2×D4213yes—
622C24C2×D4213yes—
623C24C2×D4213yes—
624C24C2×D4213yes—
625C24C2×D4216yes—
626C24C2×#54616yes—
627C24C24×D411yescharacteristic
628C2×Q8C22×#12018yes—
629C2×D4C2×#392196yes—
630C2×D4C2×#392196yes—
631C2×D4C2×#392196yes—
632C2×D4C2×#392196yes—
633C2×D4C22×#120116yes—
634C2×D4C22×#12018yes—
635C2×D4C22×#120116yes—
636C2×D4C22×#120116yes—
637C2×D4C22×#120116yes—
638C2×D4C22×#121116yes—
639C2×D4C22×#121116yes—
640C2×D4C22×#121116yes—
641C2×D4C22×#127116yes—
642C22×C4C2×#39214yes—
643C22×C4C2×#392112yes—
644C22×C4C2×#392112yes—
645C22×C4C2×#392112yes—
646C22×C4C2×#392124yes—
647C22×C4#240314yes—
648C22×C4#240314yes—
649C22×C4#2403112yes—
650C22×C4#2403112yes—
651C22×C4#2403112yes—
652C22×C4#2403112yes—
653C22×C4#2403112yes—
654C22×C4#2403124yes—
655C22×C4#2403112yes—
656C22×C4#2403124yes—
657C22×C4#240313yes—
658C22×C4#2403112yes—
659C22×C4#240313yes—
660C22×C4#240316yes—
661C22×C4#240313yes—
662C22×C4#2403112yes—
663C22×C4#240313yes—
664C22×C4#240316yes—
665C22×C4#240316yes—
666C22×C4#2403124yes—
667C22×C4#240316yes—
668C22×C4#240316yes—
669C22×C4#240316yes—
670C22×C4#240814yes—
671C22×C4#2408112yes—
672C22×C4#2408112yes—
673C22×C4#2408112yes—
674C22×C4#2408124yes—
675C22×C4#2408112yes—
676C22×C4#2408112yes—
677C22×C4#2408124yes—
678C22×C4#241014yes—
679C22×C4#241014yes—
680C22×C4#2410112yes—
681C22×C4#2410112yes—
682C22×C4#2410112yes—
683C22×C4#2410112yes—
684C22×C4#2410112yes—
685C22×C4#2410124yes—
686C22×C4#2410112yes—
687C22×C4#2410124yes—
688C22×C4#2410112yes—
689C22×C4#2410112yes—
690C22×C4#2410112yes—
691C22×C4#2410124yes—
692C22×C4#2410112yes—
693C22×C4#2410124yes—
694C22×C4#243314yes—
695C22×C4#2433112yes—
696C22×C4#2433112yes—
697C22×C4#2433112yes—
698C22×C4#2433124yes—
699C22×C4#2433112yes—
700C22×C4#2433112yes—
701C22×C4#2433124yes—
702C22×C4#261314yes—
703C22×C4#2613112yes—
704C22×C4#2613112yes—
705C22×C4#2613112yes—
706C22×C4#2613124yes—
707C22×C4#2846112yes—
708C22×C4#2846112yes—
709C22×C4#2846124yes—
710C22×C4C22×#12018yes—
711C22×C4C22×#12018yes—
712C22×C4C22×#12013yes—
713C22×C4C22×#12013yes—
714C22×C4C22×#12016yes—
715C22×C4C22×#12016yes—
716C22×C4C22×#12016yes—
717C22×C4C22×#12016yes—
718C22×C4C22×#12016yes—
719C22×C4C22×#12016yes—
720C22×C4C22×#12016yes—
721C22×C4C22×#12016yes—
722C22×C4C22×#12016yes—
723C22×C4C22×#12016yes—
724C22×C4C22×#12013yes—
725C22×C4C22×#12016yes—
726C22×C4C22×#12013yes—
727C22×C4C22×#12013yes—
728C22×C4C22×#12013yes—
729C22×C4C22×#12016yes—
730C22×C4C22×#12116yes—
731C22×C4C22×#12116yes—
732C22×C4C22×#12116yes—
733C22×C4C22×#12116yes—
734C22×C4C22×#12116yes—
735C22×C4C22×#12116yes—
736C22×C4C22×#12716yes—
737C22×C4C22×#12716yes—
738C22×C4C2×#53416yes—
739C22×C4C2×#53416yes—
740C22×C4C2×#53416yes—
741C22×C4C2×#53416yes—
742C22×C4C2×#53413yes—
743C22×C4C2×#53416yes—
744C22×C4C2×#53413yes—
745C22×C4C2×#53413yes—
746C22×C4C2×#53416yes—
747C22×C4C2×#53413yes—
748C22×C4C2×#53516yes—
749C22×C4C2×#53516yes—
750C22×C4C2×#53516yes—
751C22×C4C2×#53516yes—
752C22×C4C2×D4213yes—
753C22×C4C2×D4213yes—
754C22×C4C2×D4216yes—
755C22×C4C2×D4216yes—
756C22×C4C2×D4213yes—
757C22×C4C2×D4213yes—
758C22×C4C2×D4216yes—
759C22×C4C2×D4213yes—
760C22×C4C2×D4216yes—
761C22×C4C2×D4213yes—
762C22×C4C2×D4213yes—
763C22×C4C2×D4213yes—
764C22×C4C2×D4216yes—
765C22×C4C2×D4216yes—
766C22×C4C2×D4216yes—
767C22×C4C2×D4216yes—
768C22×C4C2×D4216yes—
769C22×C4C2×D4216yes—
770C22×C4C2×D4216yes—
771C22×C4C2×D4216yes—
772C22×C4C2×D4216yes—
773C22×C4C2×D4216yes—
774C22×C4C2×D4213yes—
775C22×C4C2×D4213yes—
776C22×C4C2×D4216yes—
777C22×C4C2×D4213yes—
778C22×C4C2×D4213yes—
779C22×C4C2×#54616yes—
780C22×C4C2×#54616yes—
781C22×C4C2×#54616yes—
782C22×C4C2×#54616yes—
783C22×C4C2×#54616yes—
784C22×C4C2×#54616yes—
785C22×C4C2×#54616yes—
786C22×C4C24×D411yescharacteristic
787C22×C4C24×D411yescharacteristic
788C22×C4C24×D411yescharacteristic
789C22×C4C24×D411yescharacteristic
790C22×C4C24×D411yescharacteristic
791C22×C4C24×D411yescharacteristic
792C22×C4C24×D411yescharacteristic
793C22×C4C24×D411yescharacteristic
794C22×C4C24×D411yescharacteristic
795C22×C4C23×#4111yescharacteristic
796C22×C4C22×H(5,𝔽2)11yescharacteristic
797C22×C4C22×H(5,𝔽2)11yescharacteristic
798C22×C4C22×H(5,𝔽2)11yescharacteristic
799C22×C4C22×H(5,𝔽2)11yescharacteristic
800C22⋊C4C22×#120116yes—
801C42C22×#120116yes—
802C23#14715112yes—
803C23#14715112yes—
804C23#14715112yes—
805C23#14715124yes—
806C23#1471514yes—
807C23#2388218yes—
808C23C2×#240313yes—
809C23C2×#240313yes—
810C23C2×#240316yes—
811C23C2×#240313yes—
812C23C2×#240316yes—
813C23C2×#240313yes—
814C23C2×#241016yes—
815C23C2×#241016yes—
816C23C2×#241016yes—
817C23C2×#241016yes—
818C23C2×#240816yes—
819C23C2×#240816yes—
820C23C2×#243316yes—
821C23C2×#243316yes—
822C23C2×#284616yes—
823C23C2×#284616yes—
824C23C23×#12011yescharacteristic
825C23C23×#12011yescharacteristic
826C23C23×#12011yescharacteristic
827C23C22×D4211yescharacteristic
828C23C22×D4211yescharacteristic
829C23C22×D4211yescharacteristic
830C23C22×#54611yescharacteristic
831D4C22×#392132yes—
832C2×C4#14715112yes—
833C2×C4#14715112yes—
834C2×C4#14715112yes—
835C2×C4#14715112yes—
836C2×C4#14715124yes—
837C2×C4#14715124yes—
838C2×C4#14715124yes—
839C2×C4#14715124yes—
840C2×C4#14715124yes—
841C2×C4#14715124yes—
842C2×C4C22×#39216yes—
843C2×C4C22×#39216yes—
844C2×C4C22×#39216yes—
845C2×C4C22×#39216yes—
846C2×C4C2×#261316yes—
847C2×C4C2×#261316yes—
848C2×C4C2×#261316yes—
849C2×C4C2×#261316yes—
850C2×C4C2×#240316yes—
851C2×C4C2×#240316yes—
852C2×C4C2×#240316yes—
853C2×C4C2×#240316yes—
854C2×C4C2×#240316yes—
855C2×C4C2×#240316yes—
856C2×C4C2×#240316yes—
857C2×C4C2×#240316yes—
858C2×C4C2×#240313yes—
859C2×C4C2×#240316yes—
860C2×C4C2×#240313yes—
861C2×C4C2×#240313yes—
862C2×C4C2×#240316yes—
863C2×C4C2×#240313yes—
864C2×C4C2×#241016yes—
865C2×C4C2×#241016yes—
866C2×C4C2×#241016yes—
867C2×C4C2×#241016yes—
868C2×C4C2×#241016yes—
869C2×C4C2×#241016yes—
870C2×C4C2×#241016yes—
871C2×C4C2×#241016yes—
872C2×C4C2×#241016yes—
873C2×C4C2×#241016yes—
874C2×C4C2×#241016yes—
875C2×C4C2×#241016yes—
876C2×C4C2×#240816yes—
877C2×C4C2×#240816yes—
878C2×C4C2×#240816yes—
879C2×C4C2×#240816yes—
880C2×C4C2×#240816yes—
881C2×C4C2×#240816yes—
882C2×C4C2×#243316yes—
883C2×C4C2×#243316yes—
884C2×C4C2×#243316yes—
885C2×C4C2×#243316yes—
886C2×C4C2×#243316yes—
887C2×C4C2×#243316yes—
888C2×C4C2×#284616yes—
889C2×C4C2×#284616yes—
890C2×C4C23×#12011yescharacteristic
891C2×C4C23×#12011yescharacteristic
892C2×C4C23×#12011yescharacteristic
893C2×C4C23×#12011yescharacteristic
894C2×C4C23×#12011yescharacteristic
895C2×C4C23×#12011yescharacteristic
896C2×C4C23×#12111yescharacteristic
897C2×C4C23×#12111yescharacteristic
898C2×C4C23×#12111yescharacteristic
899C2×C4C23×#12711yescharacteristic
900C2×C4C22×#53411yescharacteristic
901C2×C4C22×#53411yescharacteristic
902C2×C4C22×#53411yescharacteristic
903C2×C4C22×#53411yescharacteristic
904C2×C4C22×#53511yescharacteristic
905C2×C4C22×#53511yescharacteristic
906C2×C4C22×D4211yescharacteristic
907C2×C4C22×D4211yescharacteristic
908C2×C4C22×D4211yescharacteristic
909C2×C4C22×D4211yescharacteristic
910C2×C4C22×D4211yescharacteristic
911C2×C4C22×D4211yescharacteristic
912C2×C4C22×D4211yescharacteristic
913C2×C4C22×D4211yescharacteristic
914C2×C4C22×D4211yescharacteristic
915C2×C4C22×#54611yescharacteristic
916C2×C4C22×#54611yescharacteristic
917C2×C4C22×#54611yescharacteristic
918C22#394102116yesdirect product factor
919C22C2×#1471516yes—
920C22C2×#1471516yes—
921C22C2×#1471516yes—
922C22C2×#1471516yes—
923C22C2×#23882112yes—
924C22C22×#240311yescharacteristic
925C22C22×#240311yescharacteristic
926C22C22×#241011yescharacteristic
927C22C22×#241011yescharacteristic
928C22C22×#240811yescharacteristic
929C22C22×#243311yescharacteristic
930C22C22×#284611yescharacteristic
931C4C2×#1471516yes—
932C4C2×#1471516yes—
933C4C2×#1471516yes—
934C4C2×#1471516yes—
935C4C23×#39211yescharacteristic
936C4C22×#261311yescharacteristic
937C4C22×#240311yescharacteristic
938C4C22×#240311yescharacteristic
939C4C22×#241011yescharacteristic
940C4C22×#241011yescharacteristic
941C4C22×#240811yescharacteristic
942C4C22×#243311yescharacteristic
943C2C2×#394102112yesdirect product factor
944C2C22×#2388212yes—
945C2C22×#1471511yescharacteristic
subgroupG/H
center, socleC24#2403
commutator, Frattini, cosocleC23×C4C26
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#10993C2semidirect
2. C22×#10785C2semidirect
3. C22×#11004C2semidirect
4. C22×#10987C2semidirect
5. C22×#23400C2semidirect
6. C22×#23443C2semidirect
7. C22×#10994C2semidirect
8. C22×#20598C2semidirect
9. C22×#60367C2semidirect
10. C23×#1795C2semidirect
11. C23×#1904C2semidirect
12. C23×#2008C2semidirect
13. C23×#2010C2semidirect
14. C23×#3003C2semidirect
15. C23×#3484C2semidirect
16. C2×#394102C2direct (N × H)
19. C23×#575C22semidirect
21. C24×AGL(1,ℤ/8)C22semidirect
22. C22×#3484C22semidirect
23. C22×#3449C22semidirect
28. C23×#525C22semidirect
30. C2×#60367C22semidirect
31. C22×#3003C22semidirect
32. C22×#2879C22semidirect
33. C23×#407C22semidirect
34. C23×#407C22semidirect
35. C23×#410C22semidirect
36. C23×#410C22semidirect
37. C22×#2896C22semidirect
38. C23×#413C22semidirect
39. C23×#421C22semidirect
40. C23×#421C22semidirect
41. C23×#421C22semidirect
45. C23×#418C22semidirect
46. C23×#418C22semidirect
47. C23×#418C22semidirect
48. C22×#2280C22semidirect
49. C2×#23443C22semidirect
50. C22×#2010C22semidirect
51. C22×#2008C22semidirect
52. C2×#23400C22semidirect
53. C22×#1904C22semidirect
54. C22×#1795C22semidirect
55. C2×#20598C22semidirect
56. C23×#344C22semidirect
57. C23×#344C22semidirect
58. C22×#1740C22semidirect
59. C22×#1733C22semidirect
60. C23×H(3,ℤ/4)C22semidirect
61. C23×H(3,ℤ/4)C22semidirect
62. #394102C22direct (N × H)
63. C2×#11004C22semidirect
64. C2×#10994C22semidirect
65. C2×#10993C22semidirect
66. C2×#10987C22semidirect
67. C2×#10785C22semidirect
68. C23×H(5,𝔽2)D4semidirect
70. C24×#41D4semidirect
74. C25×D4D4semidirect
75. C25×D4D4semidirect
80. C22×#575C23semidirect
81. C23×AGL(1,ℤ/8)D4semidirect
83. C23×AGL(1,ℤ/8)C23semidirect
84. C24×SD16D4semidirect
85. C24×D8D4semidirect
90. C2×#3484C23semidirect
91. C2×#3449C23semidirect
92. C22×#535D4semidirect
93. C22×#535D4semidirect
96. C23×#127D4semidirect
97. C23×#124D4semidirect
99. C22×#525D4semidirect
102. C22×#525C23semidirect
105. C22×#518D4semidirect
112. #60367C23semidirect
113. C2×#3003C23semidirect
114. C22×#421C23semidirect
115. C22×#421C23semidirect
116. C22×#421C23semidirect
117. C2×#2896C23semidirect
118. C22×#418D4semidirect
119. C22×#418D4semidirect
123. C22×#418C23semidirect
124. C22×#418C23semidirect
125. C22×#418C23semidirect
126. C23×#102D4semidirect
127. C22×#413C23semidirect
128. C22×#410C23semidirect
129. C22×#410C23semidirect
130. C2×#2879C23semidirect
131. C22×#407C23semidirect
132. C22×#407C23semidirect
133. C2×#2280C23semidirect
134. #23443C23semidirect
135. C2×#2010C23semidirect
136. C2×#2008C23semidirect
137. #23400C23semidirect
138. C2×#1904C23semidirect
139. C2×#1795C23semidirect
140. #20598C23semidirect
141. C22×#344C23semidirect
142. C22×#344C23semidirect
143. C2×#1740C23semidirect
144. C2×#1733C23semidirect
145. C22×H(3,ℤ/4)C23semidirect
146. C22×H(3,ℤ/4)C23semidirect
147. #11004C23semidirect
148. #10994C23semidirect
149. #10993C23semidirect
150. #10987C23semidirect
151. #10785C23semidirect
153. C22×H(5,𝔽2)C2×D4semidirect
161. C23×#41C2×D4semidirect
162. C23×#41C2×D4semidirect
168. C24×Q8C2×D4semidirect
185. C24×D4C2×D4semidirect
186. C24×D4C2×D4semidirect
187. C24×D4C2×D4semidirect
199. C2×#575C24semidirect
200. C22×AGL(1,ℤ/8)C2×D4semidirect
202. C22×AGL(1,ℤ/8)C24semidirect
203. C23×SD16C2×D4semidirect
204. C23×D8C2×D4semidirect
205. C23×M16C2×D4semidirect
206. C23×M16C2×D4semidirect
207. C23×M16C2×D4semidirect
212. C24×C8C2×D4semidirect
213. C24×C8C2×D4semidirect
214. #3449C24semidirect
215. C2×#535C2×D4semidirect
216. C2×#535C2×D4semidirect
219. C22×#127C2×D4semidirect
220. C22×#124C2×D4semidirect
222. C2×#525C2×D4semidirect
225. C2×#525C24semidirect
228. C2×#518C2×D4semidirect
236. C22×#117C2×D4semidirect
237. C22×#117C2×D4semidirect
243. C23×C4⋊C4C2×D4semidirect
246. C2×#421C24semidirect
247. C2×#421C24semidirect
248. C2×#421C24semidirect
249. #2896C24semidirect
250. C2×#418C2×D4semidirect
251. C2×#418C2×D4semidirect
255. C2×#418C24semidirect
256. C2×#418C24semidirect
257. C2×#418C24semidirect
258. C22×#102C2×D4semidirect
259. C2×#413C24semidirect
260. C2×#410C24semidirect
261. C2×#410C24semidirect
262. #2879C24semidirect
263. C2×#407C24semidirect
264. C2×#407C24semidirect
265. #2280C24semidirect
266. C2×#344C24semidirect
267. C2×#344C24semidirect
268. #1740C24semidirect
269. #1733C24semidirect
270. C2×H(3,ℤ/4)C24semidirect
271. C2×H(3,ℤ/4)C24semidirect
284. C22×#41C22×D4semidirect
285. C22×#41C22×D4semidirect
293. C23×Q8C22×D4semidirect
332. C23×D4C22×D4semidirect
333. C23×D4C22×D4semidirect
334. C23×D4C22×D4semidirect
370. C22×SD16C22×D4semidirect
371. C22×D8C22×D4semidirect
372. C22×M16C22×D4semidirect
373. C22×M16C22×D4semidirect
374. C22×M16C22×D4semidirect
379. C23×C8C22×D4semidirect
380. C23×C8C22×D4semidirect
381. #535C22×D4semidirect
382. C2×#127C22×D4semidirect
383. C2×#124C22×D4semidirect
384. #525C22×D4semidirect
387. #518C22×D4semidirect
396. C2×#117C22×D4semidirect
397. C2×#117C22×D4semidirect
403. C22×C4⋊C4C22×D4semidirect
408. #418C22×D4semidirect
409. C2×#102C22×D4semidirect
431. C22×Q8C23×D4semidirect
470. C22×D4C23×D4semidirect
583. C2×M16C23×D4semidirect
584. C22×C8C23×D4semidirect
585. C22×C8C23×D4semidirect
592. #117C23×D4semidirect
593. C2×C4⋊C4C23×D4semidirect
918. C22#394102direct (N × H)
943. C2C2×#394102direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#109932
C22×#107852
C22×#110042
C22×#109872
C22×#234002
C22×#234432
C22×#109942
C22×#205982
C22×#603672
C23×#17952
C23×#19042
C23×#20082
C23×#20102
C23×#30032
C23×#34842
C2×#3941022