Finite Group Databasebeta

← #72317072

Subgroups — #72317072

Order 2048.

At least 21356 conjugacy classes of subgroups; only the 4120 normal subgroups are shown.

The subgroup lattice has 3213 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#353426C211yesmaximal, characteristic, complemented
2C2×#353460C211yesmaximal, characteristic, complemented
3C2×#123608C211yesmaximal, characteristic, complemented
4#72317054C211yesmaximal, characteristic, complemented
5C2×#357515C211yesmaximal, characteristic, complemented
6#72317045C211yesmaximal, characteristic, complemented
7C22×#11036C211yesmaximal, characteristic, complemented
8C2×#124024C211yesmaximal, characteristic, complemented
9C2×#124020C211yesmaximal, characteristic, complemented
10C22×#11006C211yesmaximal, characteristic, complemented
11C2×#123600C211yesmaximal, characteristic, complemented
12C22×#11012C211yesmaximal, characteristic, complemented
13C22×#60426C211yesmaximal, characteristic
14C22×#11041C211yesmaximal, characteristic, complemented
15C2×#123557C211yesmaximal, characteristic, complemented
16C23×#575C2211yescharacteristic
17C24×AGL(1,ℤ/8)C2211yescharacteristic
18C23×#535C2211yescharacteristic
19C22×#3428C2211yescharacteristic
20C2×#60426C418yescomplemented
21C22×#2905C2211yescharacteristic
22C23×#410C2211yescharacteristic
23C22×#2896C2211yescharacteristic
24C23×#417C2211yescharacteristic
25C23×#421C2211yescharacteristic
26C23×#421C2211yescharacteristic
27C23×#421C2211yescharacteristic
28C23×#418C2211yescharacteristic
29C23×#418C2211yescharacteristic
30C23×#418C2211yescharacteristic
31C22×#2311C2211yescharacteristic
32C22×#2309C2211yescharacteristic
33C22×#2297C2211yescharacteristic
34C22×#2297C2211yescharacteristic
35C23×#390C2211yescharacteristic
36C23×#344C2211yescharacteristic
37C23×#344C2211yescharacteristic
38C22×#1742C2211yescharacteristic
39C22×#1740C2211yescharacteristic
40C22×#1740C2211yescharacteristic
41C22×#1736C2211yescharacteristic
42C22×#1736C2211yescharacteristic
43C22×#1736C2211yescharacteristic
44C22×#1733C2211yescharacteristic
45C23×H(3,ℤ/4)C2211yescharacteristic
46C23×H(3,ℤ/4)C2211yescharacteristic
47C22×#1728C2211yescharacteristic
48C22×#1728C2211yescharacteristic
49C2×#13795C2211yescharacteristic
50C2×#13756C2211yescharacteristic
51C2×#13756C2211yescharacteristic
52C24×#41C2311yescharacteristic
53C24×#41C2311yescharacteristic
54C25×D4C2311yescharacteristic
55C22×#575C2×C414yes—
56C22×#575D414yes—
57C22×#575D414yes—
58C23×AGL(1,ℤ/8)C2×C414yes—
59C23×AGL(1,ℤ/8)D414yes—
60C24×SD16D412yes—
61C24×D8D412yes—
62C24×M16C2311yescharacteristic
63C24×M16C2311yescharacteristic
64C24×M16C2311yescharacteristic
65C24×M16C2311yescharacteristic
66C22×#535C2×C414yes—
67C22×#535D414yes—
68C23×#127D412yes—
69C23×#124D412yes—
70C2×#3428C2×C414yes—
71C2×#3428D414yes—
72C2×#3428D414yes—
73C23×#117C2311yescharacteristic
74C23×#117C2311yescharacteristic
75C23×#117C2311yescharacteristic
76C23×#117C2311yescharacteristic
77C23×#117C2311yescharacteristic
78C23×#117C2311yescharacteristic
79C24×C4⋊C4C2311yescharacteristic
80C24×C42C2311yescharacteristic
81C2×#2905C2×C414yes—
82C2×#2905D414yes—
83C2×#2905D414yes—
84C22×#421D414yescomplemented
85C2×#2896C2×C414yes—
86C2×#2896D414yes—
87C2×#2896D414yes—
88C22×#417D414yescomplemented
89C22×#418C2×C414yes—
90C22×#418D414yes—
91C23×#102D414yes—
92C22×#410D414yescomplemented
93C2×#2297D414yescomplemented
94C2×#1742D414yes—
95C2×#1740D414yes—
96C2×C4⋊#95D414yes—
97C2×C22⋊#95D414yes—
98C23×#41C22×C412yes—
99C23×#41C22×C412yes—
100C23×#41C2×D412yes—
101C23×#41C2×D412yes—
102C23×#41C2×D412yes—
103C23×#41C2×D412yes—
104C23×#41C2×D412yes—
105C23×#41C2×D412yes—
106C23×#41C2×D412yes—
107C23×#41C2×D412yes—
108C23×#41C2×D412yes—
109C23×#41C2×D412yes—
110C23×#41C2×D412yes—
111C23×#41C2×D412yes—
112C23×#41C2×D412yes—
113C23×#41C2×D412yes—
114C23×#41#4112yes—
115C23×#41#4112yes—
116C23×#41#4112yes—
117C23×#41#4112yes—
118C24×Q8C2×D411yescharacteristic
119C24×Q8C2×D411yescharacteristic
120C24×D4C22×C412yes—
121C24×D4C2×D412yes—
122C24×D4C2×D412yes—
123C24×D4C2×D412yes—
124C24×D4C2×D412yes—
125C24×D4C2×D412yes—
126C24×D4C2×D411yescharacteristic
127C24×D4C2×D412yes—
128C24×D4C2×D411yescharacteristic
129C25×C4C2×D412yes—
130C25×C4C2411yescharacteristic
131C2×#575C22⋊C4116yescomplemented
132C23×SD16C22⋊C418yescomplemented
133C23×D8C22⋊C418yescomplemented
134C23×M16C22×C412yes—
135C23×M16C22×C412yes—
136C23×M16C2×D412yes—
137C23×M16C2×D412yes—
138C23×M16C2×D412yes—
139C23×M16C2×D412yes—
140C23×M16C2×D412yes—
141C23×M16C2×D412yes—
142C23×M16C2×D412yes—
143C23×M16C2×D412yes—
144C23×M16C2×D412yes—
145C23×M16C2×D412yes—
146C23×M16C2×D412yes—
147C23×M16C2×D412yes—
148C23×M16C2×D412yes—
149C23×M16C2×D412yes—
150C23×M16#4112yes—
151C23×M16#4112yes—
152C24×C8C2×D412yes—
153C24×C8C2×D412yes—
154C22×#127C22⋊C418yescomplemented
155C22×#124C22⋊C418yescomplemented
156#3428C22⋊C4116yescomplemented
157C22×#117C22×C412yes—
158C22×#117C22×C412yes—
159C22×#117C2×D412yes—
160C22×#117C2×D412yes—
161C22×#117C2×D412yes—
162C22×#117C2×D412yes—
163C22×#117C2×D412yes—
164C22×#117C2×D412yes—
165C22×#117C2×D412yes—
166C22×#117C2×D412yes—
167C22×#117C2×D412yes—
168C22×#117C2×D412yes—
169C22×#117C2×D412yes—
170C22×#117C2×D412yes—
171C22×#117C2×D412yes—
172C22×#117C2×D412yes—
173C22×#117C2×D412yes—
174C22×#117C2×D412yes—
175C22×#117C2×D412yes—
176C22×#117C2×D412yes—
177C22×#117#4112yes—
178C22×#117#4112yes—
179C22×#117#4112yes—
180C22×#117#4112yes—
181C22×#117#4112yes—
182C22×#117#4112yes—
183C22×#117#4112yes—
184C22×#117#4112yes—
185C23×C4⋊C4C2×D412yes—
186C23×C4⋊C4C2×D412yes—
187C23×C4⋊C4C2×D412yes—
188C23×C4⋊C4C2×D412yes—
189C23×C4⋊C4#4112yes—
190C23×C22⋊C4C2×D412yes—
191C23×C22⋊C4C2×D412yes—
192C23×C42C2×D412yes—
193C23×C42C2×D412yes—
194C23×C42C2×D412yes—
195C23×C42#4112yes—
196#2905C22⋊C4116yescomplemented
197#2896C22⋊C4116yescomplemented
198C22×#102C22⋊C4116yescomplemented
199C26C22×D411yescharacteristic
200C22×#41C2×C22⋊C414yes—
201C22×#41C2×C22⋊C414yes—
202C22×#41C2×C22⋊C414yes—
203C22×#41C2×C22⋊C414yes—
204C22×#41C4×D414yes—
205C22×#41C4×D414yes—
206C22×#41C4×D414yes—
207C22×#41C4×D414yes—
208C22×#41#12014yes—
209C22×#41#12014yes—
210C22×#41#12014yes—
211C22×#41#12014yes—
212C22×#41#12014yes—
213C22×#41#12014yes—
214C22×#41#12014yes—
215C22×#41#12114yes—
216C22×#41#12114yes—
217C22×#41#12114yes—
218C22×#41#12114yes—
219C22×#41#12114yes—
220C22×#41#12114yes—
221C22×#41#12114yes—
222C22×#41#12114yes—
223C22×#41#12114yes—
224C22×#41#12114yes—
225C22×#41#12314yes—
226C22×#41#12314yes—
227C22×#41#12314yes—
228C22×#41#12414yes—
229C22×#41#12414yes—
230C22×#41#12714yes—
231C22×#41#12714yes—
232C23×Q8C2×C22⋊C412yes—
233C23×Q8C2×C22⋊C412yes—
234C23×Q8#12012yes—
235C23×Q8#12012yes—
236C23×Q8#12012yes—
237C23×Q8#12012yes—
238C23×Q8#12012yes—
239C23×Q8#12112yes—
240C23×Q8#12112yes—
241C23×Q8#12312yes—
242C23×D4C2×C22⋊C414yes—
243C23×D4C2×C22⋊C414yes—
244C23×D4C2×C22⋊C414yes—
245C23×D4C2×C22⋊C412yes—
246C23×D4C2×C22⋊C412yes—
247C23×D4#12014yes—
248C23×D4#12014yes—
249C23×D4#12014yes—
250C23×D4#12014yes—
251C23×D4#12012yes—
252C23×D4#12012yes—
253C23×D4#12012yes—
254C23×D4#12012yes—
255C23×D4#12012yes—
256C23×D4#12112yes—
257C23×D4#12112yes—
258C23×D4#12312yes—
259C24×C4#12014yes—
260C24×C4#12114yes—
261C24×C4C23×C411yescharacteristic
262C24×C4C22×D411yescharacteristic
263C24×C4C22×D411yescharacteristic
264C24×C4C22×D411yescharacteristic
265C24×C4C22×D411yescharacteristic
266C24×C4C22×D411yescharacteristic
267C24×C4C22×D411yescharacteristic
268C24×C4C22×D411yescharacteristic
269C24×C4C22×D411yescharacteristic
270C24×C4C22×D411yescharacteristic
271C24×C4C22×D411yescharacteristic
272C24×C4C22×D411yescharacteristic
273C24×C4C22×D411yescharacteristic
274C24×C4C22×D411yescharacteristic
275C24×C4C22×D411yescharacteristic
276C24×C4C22×D411yescharacteristic
277C24×C4C22×D411yescharacteristic
278C24×C4C22×D411yescharacteristic
279C24×C4C22×D411yescharacteristic
280C24×C4C22×D411yescharacteristic
281C24×C4C22×D411yescharacteristic
282C24×C4C22×D411yescharacteristic
283C24×C4C2×#4111yescharacteristic
284C24×C4C2×#4111yescharacteristic
285C24×C4C2×#4111yescharacteristic
286C24×C4C2×#4111yescharacteristic
287C24×C4C2×#4111yescharacteristic
288C24×C4C2×#4111yescharacteristic
289C24×C4C2×#4111yescharacteristic
290C24×C4C2×#4111yescharacteristic
291C24×C4C2×#4111yescharacteristic
292C24×C4C2×#4111yescharacteristic
293C24×C4C2×#4111yescharacteristic
294C24×C4C2×#4111yescharacteristic
295C24×C4C2×#4111yescharacteristic
296C24×C4C2×#4111yescharacteristic
297C24×C4C2×#4111yescharacteristic
298C24×C4C2×#4111yescharacteristic
299C24×C4H(5,𝔽2)11yescharacteristic
300C24×C4H(5,𝔽2)11yescharacteristic
301C24×C4H(5,𝔽2)11yescharacteristic
302C24×C4H(5,𝔽2)11yescharacteristic
303C24×C4H(5,𝔽2)11yescharacteristic
304C24×C4H(5,𝔽2)11yescharacteristic
305C24×C4H(5,𝔽2)11yescharacteristic
306C24×C4H(5,𝔽2)11yescharacteristic
307C24×C4H(5,𝔽2)11yescharacteristic
308C24×C4H(5,𝔽2)11yescharacteristic
309C24×C4H(5,𝔽2)11yescharacteristic
310C24×C4H(5,𝔽2)11yescharacteristic
311C24×C4H(5,𝔽2)11yescharacteristic
312C24×C4H(5,𝔽2)11yescharacteristic
313C24×C4H(5,𝔽2)11yescharacteristic
314C24×C4H(5,𝔽2)11yescharacteristic
315C24×C4H(5,𝔽2)11yescharacteristic
316C24×C4H(5,𝔽2)11yescharacteristic
317C24×C4H(5,𝔽2)11yescharacteristic
318C24×C4H(5,𝔽2)11yescharacteristic
319C24×C42−1+411yescharacteristic
320C24×C42−1+411yescharacteristic
321C24×C42−1+411yescharacteristic
322C24×C42−1+411yescharacteristic
323C22×M16C2×C22⋊C414yes—
324C22×M16C2×C22⋊C414yes—
325C22×M16C2×C22⋊C414yes—
326C22×M16C2×C22⋊C414yes—
327C22×M16#12014yes—
328C22×M16#12014yes—
329C22×M16#12014yes—
330C22×M16#12014yes—
331C22×M16#12114yes—
332C22×M16#12114yes—
333C23×C8C2×C22⋊C414yes—
334C23×C8C2×C22⋊C414yes—
335C23×C8#12014yes—
336C23×C8#12014yes—
337C23×C8#12014yes—
338C23×C8#12014yes—
339C2×#117C2×C22⋊C414yes—
340C2×#117C2×C22⋊C414yes—
341C2×#117C2×C22⋊C414yes—
342C2×#117C2×C22⋊C414yes—
343C2×#117C4×D414yes—
344C2×#117C4×D414yes—
345C2×#117#12014yes—
346C2×#117#12014yes—
347C2×#117#12014yes—
348C2×#117#12014yes—
349C2×#117#12014yes—
350C2×#117#12114yes—
351C2×#117#12114yes—
352C2×#117#12114yes—
353C2×#117#12114yes—
354C2×#117#12114yes—
355C2×#117#12114yes—
356C2×#117#12314yes—
357C2×#117#12314yes—
358C2×#117#12314yes—
359C2×#117#12414yes—
360C2×#117#12414yes—
361C22×C4⋊C4C2×C22⋊C414yes—
362C22×C4⋊C4C4×D414yes—
363C22×C4⋊C4#12014yes—
364C22×C4⋊C4#12014yes—
365C22×C4⋊C4#12014yes—
366C22×C4⋊C4#12114yes—
367C22×C4⋊C4#12114yes—
368C22×C4⋊C4#12114yes—
369C22×C4⋊C4#12114yes—
370C22×C4⋊C4#12714yes—
371C22×C22⋊C4C4×D414yes—
372C22×C22⋊C4#12014yes—
373C22×C22⋊C4#12114yes—
374C22×C22⋊C4#12114yes—
375C22×C22⋊C4#12114yes—
376C22×C22⋊C4#12114yes—
377C22×C22⋊C4#12714yes—
378C22×C42C2×C22⋊C414yes—
379C22×C42#12014yes—
380C22×C42#12014yes—
381C22×C42#12114yes—
382C22×C42#12114yes—
383C22×C42#12114yes—
384C22×C42#12314yes—
385C25C2×C4×D411yescharacteristic
386C25C2×#12011yescharacteristic
387C25C2×#12011yescharacteristic
388C25C2×#12111yescharacteristic
389C25C2×#12111yescharacteristic
390C25C2×#12111yescharacteristic
391C25C2×#12111yescharacteristic
392C25C2×#12111yescharacteristic
393C25#52511yescharacteristic
394C25#52511yescharacteristic
395C25C2×#12711yescharacteristic
396C25#53511yescharacteristic
397C25#53511yescharacteristic
398C25#53711yescharacteristic
399C25#53711yescharacteristic
400C25D4211yescharacteristic
401C25D4211yescharacteristic
402C25D4211yescharacteristic
403C25D4211yescharacteristic
404C25D4211yescharacteristic
405C25D4211yescharacteristic
406C25D4211yescharacteristic
407C25D4211yescharacteristic
408C25D4211yescharacteristic
409C25D4211yescharacteristic
410C25#54611yescharacteristic
411C25#54611yescharacteristic
412C25#54811yescharacteristic
413C25#54811yescharacteristic
414C25#55011yescharacteristic
415C25#55011yescharacteristic
416C2×#41#38618yes—
417C2×#41#38618yes—
418C2×#41#39018yes—
419C2×#41#39018yes—
420C2×#41#39218yes—
421C2×#41#39218yes—
422C2×#41#39418yes—
423C2×#41#39418yes—
424C22×Q8#37914yes—
425C22×Q8#37914yes—
426C22×Q8#38614yes—
427C22×Q8#38614yes—
428C22×Q8#39214yes—
429C22×Q8#39214yes—
430C22×Q8#39414yes—
431C22×Q8#39414yes—
432C22×D4#37918yes—
433C22×D4#37914yes—
434C22×D4#37914yes—
435C22×D4#38614yes—
436C22×D4#38614yes—
437C22×D4#39214yes—
438C22×D4#39214yes—
439C22×D4#39414yes—
440C22×D4#39414yes—
441C23×C4#38618yes—
442C23×C4#39218yes—
443C23×C4#39218yes—
444C23×C4C22×C22⋊C411yescharacteristic
445C23×C4C22×C22⋊C411yescharacteristic
446C23×C4C22×C22⋊C411yescharacteristic
447C23×C4C22×C22⋊C411yescharacteristic
448C23×C4C22×C22⋊C411yescharacteristic
449C23×C4C22×C22⋊C411yescharacteristic
450C23×C4C22×C22⋊C411yescharacteristic
451C23×C4C2×C4×D411yescharacteristic
452C23×C4C2×C4×D411yescharacteristic
453C23×C4C2×C4×D411yescharacteristic
454C23×C4C2×C4×D411yescharacteristic
455C23×C4C2×C4×D411yescharacteristic
456C23×C4C2×C4×D411yescharacteristic
457C23×C4C2×C4×D411yescharacteristic
458C23×C4C4×#4111yescharacteristic
459C23×C4C4×#4111yescharacteristic
460C23×C4C4×#4111yescharacteristic
461C23×C4C4×#4111yescharacteristic
462C23×C4#51811yescharacteristic
463C23×C4#51811yescharacteristic
464C23×C4#51811yescharacteristic
465C23×C4#51811yescharacteristic
466C23×C4#51811yescharacteristic
467C23×C4#51811yescharacteristic
468C23×C4#51811yescharacteristic
469C23×C4#51811yescharacteristic
470C23×C4#52011yescharacteristic
471C23×C4#52011yescharacteristic
472C23×C4#52011yescharacteristic
473C23×C4#52011yescharacteristic
474C23×C4C2×#12011yescharacteristic
475C23×C4C2×#12011yescharacteristic
476C23×C4C2×#12011yescharacteristic
477C23×C4C2×#12011yescharacteristic
478C23×C4C2×#12011yescharacteristic
479C23×C4C2×#12011yescharacteristic
480C23×C4C2×#12011yescharacteristic
481C23×C4C2×#12011yescharacteristic
482C23×C4C2×#12011yescharacteristic
483C23×C4C2×#12011yescharacteristic
484C23×C4C2×#12011yescharacteristic
485C23×C4C2×#12011yescharacteristic
486C23×C4C2×#12011yescharacteristic
487C23×C4C2×#12011yescharacteristic
488C23×C4C2×#12011yescharacteristic
489C23×C4C2×#12011yescharacteristic
490C23×C4C2×#12011yescharacteristic
491C23×C4C2×#12011yescharacteristic
492C23×C4C2×#12011yescharacteristic
493C23×C4C2×#12011yescharacteristic
494C23×C4C2×#12011yescharacteristic
495C23×C4C2×#12011yescharacteristic
496C23×C4C2×#12011yescharacteristic
497C23×C4C2×#12011yescharacteristic
498C23×C4C2×#12011yescharacteristic
499C23×C4C2×#12011yescharacteristic
500C23×C4C2×#12011yescharacteristic
501C23×C4C2×#12011yescharacteristic
502C23×C4C2×#12011yescharacteristic
503C23×C4C2×#12011yescharacteristic
504C23×C4C2×#12011yescharacteristic
505C23×C4C2×#12011yescharacteristic
506C23×C4C2×#12011yescharacteristic
507C23×C4C2×#12011yescharacteristic
508C23×C4C2×#12111yescharacteristic
509C23×C4C2×#12111yescharacteristic
510C23×C4C2×#12111yescharacteristic
511C23×C4C2×#12111yescharacteristic
512C23×C4C2×#12111yescharacteristic
513C23×C4C2×#12111yescharacteristic
514C23×C4C2×#12111yescharacteristic
515C23×C4C2×#12111yescharacteristic
516C23×C4C2×#12111yescharacteristic
517C23×C4C2×#12111yescharacteristic
518C23×C4C2×#12111yescharacteristic
519C23×C4C2×#12111yescharacteristic
520C23×C4C2×#12111yescharacteristic
521C23×C4C2×#12111yescharacteristic
522C23×C4C2×#12111yescharacteristic
523C23×C4C2×#12111yescharacteristic
524C23×C4C2×#12111yescharacteristic
525C23×C4C2×#12111yescharacteristic
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1064C22×C8#37918yes—
1065C22×C8#37918yes—
1066C2×C4⋊C4#37918yes—
1067C2×C4⋊C4#38618yes—
1068C2×C4⋊C4#39018yes—
1069C2×C4⋊C4#39218yes—
1070C2×C4⋊C4#39418yes—
1071C2×C22⋊C4#38618yes—
1072C2×C22⋊C4#39018yes—
1073C2×C22⋊C4#39218yes—
1074C2×C22⋊C4#39418yes—
1075C2×C42#37918yes—
1076C2×C42#38618yes—
1077C2×C42#39418yes—
1078C2×C42#39418yes—
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1085C24#232411yescharacteristic
1086C24D4×C22⋊C411yescharacteristic
1087C24D4×C22⋊C411yescharacteristic
1088C24D4×C22⋊C411yescharacteristic
1089C24D4×C22⋊C411yescharacteristic
1090C24#236111yescharacteristic
1091C24#236111yescharacteristic
1092C24#236311yescharacteristic
1093C24#236311yescharacteristic
1094C24C2×#39211yescharacteristic
1095C24C2×#39211yescharacteristic
1096C24C2×#39211yescharacteristic
1097C24C2×#39411yescharacteristic
1098C24#240311yescharacteristic
1099C24#240311yescharacteristic
1100C24#240311yescharacteristic
1101C24#240311yescharacteristic
1102C24#240311yescharacteristic
1103C24#240311yescharacteristic
1104C24#240311yescharacteristic
1105C24#240311yescharacteristic
1106C24#240711yescharacteristic
1107C24#240711yescharacteristic
1108C24#240711yescharacteristic
1109C24#240711yescharacteristic
1110C24#240811yescharacteristic
1111C24#240811yescharacteristic
1112C24#240811yescharacteristic
1113C24#240811yescharacteristic
1114C24#240811yescharacteristic
1115C24#240811yescharacteristic
1116C24#240811yescharacteristic
1117C24#240811yescharacteristic
1118C24#241011yescharacteristic
1119C24#241011yescharacteristic
1120C24#241011yescharacteristic
1121C24#241011yescharacteristic
1122C24#241011yescharacteristic
1123C24#241011yescharacteristic
1124C24#241011yescharacteristic
1125C24#241011yescharacteristic
1126C24#241011yescharacteristic
1127C24#241011yescharacteristic
1128C24#241011yescharacteristic
1129C24#241011yescharacteristic
1130C24#241411yescharacteristic
1131C24#241411yescharacteristic
1132C24#241411yescharacteristic
1133C24#241411yescharacteristic
1134C24#241611yescharacteristic
1135C24#241611yescharacteristic
1136C24#241611yescharacteristic
1137C24#241611yescharacteristic
1138C24#241611yescharacteristic
1139C24#241611yescharacteristic
1140C24#241611yescharacteristic
1141C24#241611yescharacteristic
1142C24#242411yescharacteristic
1143C24#242411yescharacteristic
1144C24#242411yescharacteristic
1145C24#242411yescharacteristic
1146C24#242411yescharacteristic
1147C24#242411yescharacteristic
1148C24#242411yescharacteristic
1149C24#242411yescharacteristic
1150C24#242611yescharacteristic
1151C24#242611yescharacteristic
1152C24#242711yescharacteristic
1153C24#242711yescharacteristic
1154C24#242811yescharacteristic
1155C24#242811yescharacteristic
1156C24#242811yescharacteristic
1157C24#242811yescharacteristic
1158C24#242811yescharacteristic
1159C24#242811yescharacteristic
1160C24#242811yescharacteristic
1161C24#242811yescharacteristic
1162C24#243111yescharacteristic
1163C24#243111yescharacteristic
1164C24#243311yescharacteristic
1165C24#243311yescharacteristic
1166C24#243311yescharacteristic
1167C24#243311yescharacteristic
1168C24#243311yescharacteristic
1169C24#243611yescharacteristic
1170C24#244311yescharacteristic
1171C24#244311yescharacteristic
1172C24#244311yescharacteristic
1173C24#244311yescharacteristic
1174C24#245611yescharacteristic
1175C24#245611yescharacteristic
1176C24#245611yescharacteristic
1177C24#245611yescharacteristic
1178C24#246411yescharacteristic
1179C24#246411yescharacteristic
1180C24#246411yescharacteristic
1181C24#246411yescharacteristic
1182C24#253511yescharacteristic
1183C24#253511yescharacteristic
1184C24#253711yescharacteristic
1185C24#253711yescharacteristic
1186C24#254011yescharacteristic
1187C24#254011yescharacteristic
1188C24#254011yescharacteristic
1189C24#254011yescharacteristic
1190C24#254111yescharacteristic
1191C24#254111yescharacteristic
1192C24#254111yescharacteristic
1193C24#254111yescharacteristic
1194C24#261511yescharacteristic
1195C24#261511yescharacteristic
1196C24#261911yescharacteristic
1197C24#262011yescharacteristic
1198C24#266911yescharacteristic
1199C24#266911yescharacteristic
1200C24#266911yescharacteristic
1201C24#266911yescharacteristic
1202C24#267111yescharacteristic
1203C24#267111yescharacteristic
1204C24#267111yescharacteristic
1205C24#267111yescharacteristic
1206C24#267311yescharacteristic
1207C24#267311yescharacteristic
1208C24#267311yescharacteristic
1209C24#267311yescharacteristic
1210C24#267511yescharacteristic
1211C24#267511yescharacteristic
1212C24#267511yescharacteristic
1213C24#267511yescharacteristic
1214C24#267611yescharacteristic
1215C24#267611yescharacteristic
1216C24#267611yescharacteristic
1217C24#267611yescharacteristic
1218C24#267811yescharacteristic
1219C24#267811yescharacteristic
1220C24#267811yescharacteristic
1221C24#267811yescharacteristic
1222C24#268111yescharacteristic
1223C24#268111yescharacteristic
1224C24#268111yescharacteristic
1225C24#268111yescharacteristic
1226C24#268211yescharacteristic
1227C24#268211yescharacteristic
1228C24#268211yescharacteristic
1229C24#268211yescharacteristic
1230C24#284711yescharacteristic
1231C24#284711yescharacteristic
1232C24#285011yescharacteristic
1233C24#285611yescharacteristic
1234C2×Q8#143818yescomplemented
1235C2×D4#143818yescomplemented
1236C22×C4#1438116yes—
1237C22×C4C2×#37911yescharacteristic
1238C22×C4C2×#37911yescharacteristic
1239C22×C4C2×#37911yescharacteristic
1240C22×C4C2×#37911yescharacteristic
1241C22×C4C2×#37911yescharacteristic
1242C22×C4C2×#37911yescharacteristic
1243C22×C4C2×#37911yescharacteristic
1244C22×C4C2×#38611yescharacteristic
1245C22×C4C2×#38611yescharacteristic
1246C22×C4C2×#38611yescharacteristic
1247C22×C4C2×#38611yescharacteristic
1248C22×C4C2×#38611yescharacteristic
1249C22×C4C2×#38611yescharacteristic
1250C22×C4C2×#39011yescharacteristic
1251C22×C4C2×#39011yescharacteristic
1252C22×C4C2×#39011yescharacteristic
1253C22×C4#229711yescharacteristic
1254C22×C4#229711yescharacteristic
1255C22×C4#229711yescharacteristic
1256C22×C4#229711yescharacteristic
1257C22×C4#229711yescharacteristic
1258C22×C4#229711yescharacteristic
1259C22×C4C4×#12111yescharacteristic
1260C22×C4C4×#12111yescharacteristic
1261C22×C4C4×#12111yescharacteristic
1262C22×C4C4×#12111yescharacteristic
1263C22×C4C4×#12111yescharacteristic
1264C22×C4C4×#12111yescharacteristic
1265C22×C4#230811yescharacteristic
1266C22×C4#230811yescharacteristic
1267C22×C4#230811yescharacteristic
1268C22×C4#230811yescharacteristic
1269C22×C4#230811yescharacteristic
1270C22×C4#230811yescharacteristic
1271C22×C4#230811yescharacteristic
1272C22×C4#230811yescharacteristic
1273C22×C4#230911yescharacteristic
1274C22×C4#230911yescharacteristic
1275C22×C4#230911yescharacteristic
1276C22×C4#230911yescharacteristic
1277C22×C4#231111yescharacteristic
1278C22×C4#231111yescharacteristic
1279C22×C4#231111yescharacteristic
1280C22×C4#231111yescharacteristic
1281C22×C4#231111yescharacteristic
1282C22×C4#231111yescharacteristic
1283C22×C4#232411yescharacteristic
1284C22×C4#232411yescharacteristic
1285C22×C4#232411yescharacteristic
1286C22×C4#232411yescharacteristic
1287C22×C4#232411yescharacteristic
1288C22×C4#232411yescharacteristic
1289C22×C4#232511yescharacteristic
1290C22×C4#232511yescharacteristic
1291C22×C4#232511yescharacteristic
1292C22×C4#232511yescharacteristic
1293C22×C4#232511yescharacteristic
1294C22×C4#232511yescharacteristic
1295C22×C4#232511yescharacteristic
1296C22×C4#232511yescharacteristic
1297C22×C4#233311yescharacteristic
1298C22×C4#233311yescharacteristic
1299C22×C4#233311yescharacteristic
1300C22×C4#233311yescharacteristic
1301C22×C4#233311yescharacteristic
1302C22×C4#233311yescharacteristic
1303C22×C4#233311yescharacteristic
1304C22×C4#233311yescharacteristic
1305C22×C4D4×C22⋊C411yescharacteristic
1306C22×C4D4×C22⋊C411yescharacteristic
1307C22×C4D4×C22⋊C411yescharacteristic
1308C22×C4D4×C22⋊C411yescharacteristic
1309C22×C4D4×C22⋊C411yescharacteristic
1310C22×C4D4×C22⋊C411yescharacteristic
1311C22×C4D4×C22⋊C411yescharacteristic
1312C22×C4D4×C22⋊C411yescharacteristic
1313C22×C4D4×C22⋊C411yescharacteristic
1314C22×C4D4×C22⋊C411yescharacteristic
1315C22×C4D4×C22⋊C411yescharacteristic
1316C22×C4D4×C22⋊C411yescharacteristic
1317C22×C4D4×C22⋊C411yescharacteristic
1318C22×C4D4×C22⋊C411yescharacteristic
1319C22×C4D4×C22⋊C411yescharacteristic
1320C22×C4D4×C22⋊C411yescharacteristic
1321C22×C4D4×C22⋊C411yescharacteristic
1322C22×C4D4×C22⋊C411yescharacteristic
1323C22×C4D4×C22⋊C411yescharacteristic
1324C22×C4D4×C22⋊C411yescharacteristic
1325C22×C4D4×C22⋊C411yescharacteristic
1326C22×C4D4×C22⋊C411yescharacteristic
1327C22×C4D4×C22⋊C411yescharacteristic
1328C22×C4D4×C22⋊C411yescharacteristic
1329C22×C4D4×C22⋊C411yescharacteristic
1330C22×C4D4×C22⋊C411yescharacteristic
1331C22×C4D4×C22⋊C411yescharacteristic
1332C22×C4D4×C22⋊C411yescharacteristic
1333C22×C4#233911yescharacteristic
1334C22×C4#233911yescharacteristic
1335C22×C4#233911yescharacteristic
1336C22×C4#233911yescharacteristic
1337C22×C4#233911yescharacteristic
1338C22×C4#233911yescharacteristic
1339C22×C4#233911yescharacteristic
1340C22×C4#233911yescharacteristic
1341C22×C4#233911yescharacteristic
1342C22×C4#233911yescharacteristic
1343C22×C4#233911yescharacteristic
1344C22×C4#233911yescharacteristic
1345C22×C4#234111yescharacteristic
1346C22×C4#234111yescharacteristic
1347C22×C4#234111yescharacteristic
1348C22×C4#234111yescharacteristic
1349C22×C4#236111yescharacteristic
1350C22×C4#236111yescharacteristic
1351C22×C4#236111yescharacteristic
1352C22×C4#236111yescharacteristic
1353C22×C4#236111yescharacteristic
1354C22×C4#236111yescharacteristic
1355C22×C4#236311yescharacteristic
1356C22×C4#236311yescharacteristic
1357C22×C4#236311yescharacteristic
1358C22×C4#236311yescharacteristic
1359C22×C4#236311yescharacteristic
1360C22×C4#236311yescharacteristic
1361C22×C4#236411yescharacteristic
1362C22×C4#236411yescharacteristic
1363C22×C4#236411yescharacteristic
1364C22×C4#236411yescharacteristic
1365C22×C4#236411yescharacteristic
1366C22×C4#236411yescharacteristic
1367C22×C4#236411yescharacteristic
1368C22×C4#236411yescharacteristic
1369C22×C4#237711yescharacteristic
1370C22×C4#237711yescharacteristic
1371C22×C4#237711yescharacteristic
1372C22×C4#237711yescharacteristic
1373C22×C4#237711yescharacteristic
1374C22×C4#237711yescharacteristic
1375C22×C4#237711yescharacteristic
1376C22×C4#237711yescharacteristic
1377C22×C4C2×#39211yescharacteristic
1378C22×C4C2×#39211yescharacteristic
1379C22×C4C2×#39211yescharacteristic
1380C22×C4C2×#39211yescharacteristic
1381C22×C4C2×#39211yescharacteristic
1382C22×C4C2×#39411yescharacteristic
1383C22×C4C2×#39411yescharacteristic
1384C22×C4C2×#39411yescharacteristic
1385C22×C4C2×#39411yescharacteristic
1386C22×C4C2×#39411yescharacteristic
1387C22×C4C2×#39411yescharacteristic
1388C22×C4C2×#39411yescharacteristic
1389C22×C4#238811yescharacteristic
1390C22×C4#238811yescharacteristic
1391C22×C4#238811yescharacteristic
1392C22×C4#238811yescharacteristic
1393C22×C4#238811yescharacteristic
1394C22×C4#238811yescharacteristic
1395C22×C4#238811yescharacteristic
1396C22×C4#238811yescharacteristic
1397C22×C4#240311yescharacteristic
1398C22×C4#240311yescharacteristic
1399C22×C4#240311yescharacteristic
1400C22×C4#240311yescharacteristic
1401C22×C4#240311yescharacteristic
1402C22×C4#240311yescharacteristic
1403C22×C4#240311yescharacteristic
1404C22×C4#240311yescharacteristic
1405C22×C4#240311yescharacteristic
1406C22×C4#240311yescharacteristic
1407C22×C4#240311yescharacteristic
1408C22×C4#240311yescharacteristic
1409C22×C4#240311yescharacteristic
1410C22×C4#240311yescharacteristic
1411C22×C4#240311yescharacteristic
1412C22×C4#240311yescharacteristic
1413C22×C4#240311yescharacteristic
1414C22×C4#240311yescharacteristic
1415C22×C4#240311yescharacteristic
1416C22×C4#240311yescharacteristic
1417C22×C4#240311yescharacteristic
1418C22×C4#240311yescharacteristic
1419C22×C4#240311yescharacteristic
1420C22×C4#240311yescharacteristic
1421C22×C4#240411yescharacteristic
1422C22×C4#240411yescharacteristic
1423C22×C4#240411yescharacteristic
1424C22×C4#240411yescharacteristic
1425C22×C4#240411yescharacteristic
1426C22×C4#240411yescharacteristic
1427C22×C4#240411yescharacteristic
1428C22×C4#240411yescharacteristic
1429C22×C4#240411yescharacteristic
1430C22×C4#240411yescharacteristic
1431C22×C4#240411yescharacteristic
1432C22×C4#240411yescharacteristic
1433C22×C4#240511yescharacteristic
1434C22×C4#240511yescharacteristic
1435C22×C4#240511yescharacteristic
1436C22×C4#240511yescharacteristic
1437C22×C4#240511yescharacteristic
1438C22×C4#240511yescharacteristic
1439C22×C4#240511yescharacteristic
1440C22×C4#240511yescharacteristic
1441C22×C4#240511yescharacteristic
1442C22×C4#240511yescharacteristic
1443C22×C4#240511yescharacteristic
1444C22×C4#240511yescharacteristic
1445C22×C4#240511yescharacteristic
1446C22×C4#240511yescharacteristic
1447C22×C4#240511yescharacteristic
1448C22×C4#240511yescharacteristic
1449C22×C4#240511yescharacteristic
1450C22×C4#240511yescharacteristic
1451C22×C4#240511yescharacteristic
1452C22×C4#240511yescharacteristic
1453C22×C4#240511yescharacteristic
1454C22×C4#240511yescharacteristic
1455C22×C4#240511yescharacteristic
1456C22×C4#240511yescharacteristic
1457C22×C4#240511yescharacteristic
1458C22×C4#240511yescharacteristic
1459C22×C4#240511yescharacteristic
1460C22×C4#240511yescharacteristic
1461C22×C4#240511yescharacteristic
1462C22×C4#240511yescharacteristic
1463C22×C4#240511yescharacteristic
1464C22×C4#240511yescharacteristic
1465C22×C4#240611yescharacteristic
1466C22×C4#240611yescharacteristic
1467C22×C4#240611yescharacteristic
1468C22×C4#240611yescharacteristic
1469C22×C4#240611yescharacteristic
1470C22×C4#240611yescharacteristic
1471C22×C4#240611yescharacteristic
1472C22×C4#240611yescharacteristic
1473C22×C4#240611yescharacteristic
1474C22×C4#240611yescharacteristic
1475C22×C4#240611yescharacteristic
1476C22×C4#240611yescharacteristic
1477C22×C4#240711yescharacteristic
1478C22×C4#240711yescharacteristic
1479C22×C4#240711yescharacteristic
1480C22×C4#240711yescharacteristic
1481C22×C4#240711yescharacteristic
1482C22×C4#240711yescharacteristic
1483C22×C4#240711yescharacteristic
1484C22×C4#240711yescharacteristic
1485C22×C4#240711yescharacteristic
1486C22×C4#240711yescharacteristic
1487C22×C4#240711yescharacteristic
1488C22×C4#240711yescharacteristic
1489C22×C4#240711yescharacteristic
1490C22×C4#240711yescharacteristic
1491C22×C4#240711yescharacteristic
1492C22×C4#240711yescharacteristic
1493C22×C4#240711yescharacteristic
1494C22×C4#240711yescharacteristic
1495C22×C4#240711yescharacteristic
1496C22×C4#240711yescharacteristic
1497C22×C4#240711yescharacteristic
1498C22×C4#240711yescharacteristic
1499C22×C4#240711yescharacteristic
1500C22×C4#240711yescharacteristic
1501C22×C4#240711yescharacteristic
1502C22×C4#240711yescharacteristic
1503C22×C4#240711yescharacteristic
1504C22×C4#240711yescharacteristic
1505C22×C4#240811yescharacteristic
1506C22×C4#240811yescharacteristic
1507C22×C4#240811yescharacteristic
1508C22×C4#240811yescharacteristic
1509C22×C4#240811yescharacteristic
1510C22×C4#240811yescharacteristic
1511C22×C4#240811yescharacteristic
1512C22×C4#240811yescharacteristic
1513C22×C4#240811yescharacteristic
1514C22×C4#240811yescharacteristic
1515C22×C4#240811yescharacteristic
1516C22×C4#240811yescharacteristic
1517C22×C4#240811yescharacteristic
1518C22×C4#240811yescharacteristic
1519C22×C4#240811yescharacteristic
1520C22×C4#240811yescharacteristic
1521C22×C4#240811yescharacteristic
1522C22×C4#240811yescharacteristic
1523C22×C4#240811yescharacteristic
1524C22×C4#240811yescharacteristic
1525C22×C4#240811yescharacteristic
1526C22×C4#240811yescharacteristic
1527C22×C4#240811yescharacteristic
1528C22×C4#240811yescharacteristic
1529C22×C4#240811yescharacteristic
1530C22×C4#240811yescharacteristic
1531C22×C4#240811yescharacteristic
1532C22×C4#240811yescharacteristic
1533C22×C4#240811yescharacteristic
1534C22×C4#240811yescharacteristic
1535C22×C4#240811yescharacteristic
1536C22×C4#240811yescharacteristic
1537C22×C4#241011yescharacteristic
1538C22×C4#241011yescharacteristic
1539C22×C4#241011yescharacteristic
1540C22×C4#241011yescharacteristic
1541C22×C4#241011yescharacteristic
1542C22×C4#241011yescharacteristic
1543C22×C4#241011yescharacteristic
1544C22×C4#241011yescharacteristic
1545C22×C4#241011yescharacteristic
1546C22×C4#241011yescharacteristic
1547C22×C4#241011yescharacteristic
1548C22×C4#241011yescharacteristic
1549C22×C4#241011yescharacteristic
1550C22×C4#241011yescharacteristic
1551C22×C4#241011yescharacteristic
1552C22×C4#241011yescharacteristic
1553C22×C4#241011yescharacteristic
1554C22×C4#241011yescharacteristic
1555C22×C4#241011yescharacteristic
1556C22×C4#241011yescharacteristic
1557C22×C4#241011yescharacteristic
1558C22×C4#241011yescharacteristic
1559C22×C4#241011yescharacteristic
1560C22×C4#241011yescharacteristic
1561C22×C4#241011yescharacteristic
1562C22×C4#241011yescharacteristic
1563C22×C4#241011yescharacteristic
1564C22×C4#241011yescharacteristic
1565C22×C4#241011yescharacteristic
1566C22×C4#241011yescharacteristic
1567C22×C4#241011yescharacteristic
1568C22×C4#241011yescharacteristic
1569C22×C4#241011yescharacteristic
1570C22×C4#241011yescharacteristic
1571C22×C4#241011yescharacteristic
1572C22×C4#241011yescharacteristic
1573C22×C4#241011yescharacteristic
1574C22×C4#241011yescharacteristic
1575C22×C4#241011yescharacteristic
1576C22×C4#241011yescharacteristic
1577C22×C4#241011yescharacteristic
1578C22×C4#241011yescharacteristic
1579C22×C4#241011yescharacteristic
1580C22×C4#241011yescharacteristic
1581C22×C4#241011yescharacteristic
1582C22×C4#241011yescharacteristic
1583C22×C4#241011yescharacteristic
1584C22×C4#241011yescharacteristic
1585C22×C4#241011yescharacteristic
1586C22×C4#241011yescharacteristic
1587C22×C4#241011yescharacteristic
1588C22×C4#241011yescharacteristic
1589C22×C4#241011yescharacteristic
1590C22×C4#241011yescharacteristic
1591C22×C4#241011yescharacteristic
1592C22×C4#241011yescharacteristic
1593C22×C4#241011yescharacteristic
1594C22×C4#241011yescharacteristic
1595C22×C4#241011yescharacteristic
1596C22×C4#241011yescharacteristic
1597C22×C4#241011yescharacteristic
1598C22×C4#241011yescharacteristic
1599C22×C4#241011yescharacteristic
1600C22×C4#241011yescharacteristic
1601C22×C4#241011yescharacteristic
1602C22×C4#241011yescharacteristic
1603C22×C4#241011yescharacteristic
1604C22×C4#241011yescharacteristic
1605C22×C4#241411yescharacteristic
1606C22×C4#241411yescharacteristic
1607C22×C4#241411yescharacteristic
1608C22×C4#241411yescharacteristic
1609C22×C4#241411yescharacteristic
1610C22×C4#241411yescharacteristic
1611C22×C4#241411yescharacteristic
1612C22×C4#241411yescharacteristic
1613C22×C4#241411yescharacteristic
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2012C22×C4#255911yescharacteristic
2013C22×C4#255911yescharacteristic
2014C22×C4#255911yescharacteristic
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3163C22#39402412yes—
3164C22#39408014yes—
3165C22#41767012yes—
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3167C22#41830614yes—
3168C22#41843012yes—
3169C22#41843212yes—
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3203C2#7223955211yescharacteristic
3204C2#7223956212yes—
3205C2#7231674812yes—
3206C2#7231678112yes—
3207C2#7231686912yes—
3208C2#7231698012yes—
3209C2#7231698212yes—
3210C2#7231701011yescharacteristic
3211C2#7231701711yescharacteristic
subgroupG/H
center, socleC24#2403
commutatorC24×C4C23×C4
Frattini, cosocleC25×C4C24
prime radicalC22×#60426C2
LCSG ▷ C24×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C25×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#353426C2semidirect
2. C2×#353460C2semidirect
3. C2×#123608C2semidirect
4. #72317054C2semidirect
5. C2×#357515C2semidirect
6. #72317045C2semidirect
7. C22×#11036C2semidirect
8. C2×#124024C2semidirect
9. C2×#124020C2semidirect
10. C22×#11006C2semidirect
11. C2×#123600C2semidirect
12. C22×#11012C2semidirect
14. C22×#11041C2semidirect
15. C2×#123557C2semidirect
20. C2×#60426C4semidirect
84. C22×#421D4semidirect
88. C22×#417D4semidirect
92. C22×#410D4semidirect
93. C2×#2297D4semidirect
131. C2×#575C22⋊C4semidirect
132. C23×SD16C22⋊C4semidirect
133. C23×D8C22⋊C4semidirect
154. C22×#127C22⋊C4semidirect
155. C22×#124C22⋊C4semidirect
156. #3428C22⋊C4semidirect
196. #2905C22⋊C4semidirect
197. #2896C22⋊C4semidirect
198. C22×#102C22⋊C4semidirect
1234. C2×Q8#1438semidirect
1235. C2×D4#1438semidirect

Maximal subgroups

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

subgroupindex
C2×#3534262
C2×#3534602
C2×#1236082
#723170542
C2×#3575152
#723170452
C22×#110362
C2×#1240242
C2×#1240202
C22×#110062
C2×#1236002
C22×#110122
C22×#604262
C22×#110412
C2×#1235572