Finite Group Databasebeta

← #72330328

Subgroups — #72330328

Order 1024.

At least 6324 conjugacy classes of subgroups; only the 1697 normal subgroups are shown.

The subgroup lattice has 684 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#2410C211yesmaximal, characteristic, complemented
2C22×#2410C211yesmaximal, characteristic, complemented
3C23×#392C211yesmaximal, characteristic, complemented
4C2×#15263C212yesmaximal, complemented
5C2×#14724C211yesmaximal, characteristic, complemented
6C2×#14715C211yesmaximal, characteristic, complemented
7C2×#14127C211yesmaximal, characteristic, complemented
8C2×#13867C211yesmaximal, characteristic, complemented
9C2×#13867C211yesmaximal, characteristic, complemented
10#158823C212yesmaximal, complemented
11#158820C212yesmaximal, complemented
12#156827C212yesmaximal, complemented
13#156706C212yesmaximal, complemented
14#156706C212yesmaximal, complemented
15#156686C212yesmaximal, complemented
16#155065C212yesmaximal, complemented
17#154208C211yesmaximal, characteristic, complemented
18#154196C211yesmaximal, characteristic, complemented
19#154195C211yesmaximal, characteristic, complemented
20#154195C211yesmaximal, characteristic, complemented
21#154195C211yesmaximal, characteristic, complemented
22#154194C211yesmaximal, characteristic, complemented
23#153851C211yesmaximal, characteristic, complemented
24C25×D4C2211yescharacteristic
25C25×D4C2211yescharacteristic
26C25×D4C2211yescharacteristic
27C23×#121C2211yescharacteristic, complemented
28C23×#121C2212yescomplemented
29C23×#121C2211yescharacteristic, complemented
30C23×#120C2211yescharacteristic
31C23×#120C2211yescharacteristic
32C23×#120C2211yescharacteristic
33C24×C22⋊C4C2211yescharacteristic
34C24×C22⋊C4C2211yescharacteristic
35C24×C22⋊C4C2211yescharacteristic
36C24×C22⋊C4C2211yescharacteristic
37C24×C22⋊C4C2211yescharacteristic
38C22×#394C2212yescomplemented
39C22×#394C2211yescharacteristic, complemented
40C22×#394C2211yescharacteristic, complemented
41C22×#394C2212yescomplemented
42C22×#394C2212yescomplemented
43C22×#392C2212yes—
44C22×#392C2212yes—
45C22×#392C2212yes—
46C22×#392C2212yes—
47C22×#392C2211yescharacteristic, complemented
48C22×#392C2212yescomplemented
49C22×#392C2211yescharacteristic, complemented
50C22×#392C2212yescomplemented
51C22×#392C2212yescomplemented
52C22×#386C2211yescharacteristic
53C22×#386C2211yescharacteristic
54C22×#386C2211yescharacteristic
55C22×#386C2211yescharacteristic
56C22×#386C2211yescharacteristic, complemented
57C22×#386C2212yescomplemented
58C22×#386C2211yescharacteristic, complemented
59C22×#386C2212yescomplemented
60C22×#386C2212yescomplemented
61C22×#386C2212yescomplemented
62C22×#386C2212yescomplemented
63C22×#385C2211yescharacteristic
64C22×#385C2211yescharacteristic
65C22×#385C2211yescharacteristic
66C22×#385C2212yescomplemented
67C22×#379C2211yescharacteristic
68C22×#379C2211yescharacteristic
69C22×#379C2211yescharacteristic
70C22×#379C2211yescharacteristic
71C22×#379C2211yescharacteristic
72C22×#379C2211yescharacteristic
73C22×#379C2211yescharacteristic
74C23×#95C2211yescharacteristic
75C2×#1441C2212yescomplemented
76C2×#1439C2212yescomplemented
77C2×#1439C2212yescomplemented
78C2×#1439C2212yescomplemented
79C2×#1439C2212yescomplemented
80C2×#1439C2212yescomplemented
81C2×#1438C2212yescomplemented
82C2×#1438C2212yescomplemented
83C2×#1438C2212yescomplemented
84C2×#1438C2212yescomplemented
85C2×#1438C2212yescomplemented
86C2×#1438C2212yescomplemented
87C2×#1438C2212yescomplemented
88C2×#1438C2212yescomplemented
89C2×#1438C2212yescomplemented
90C2×#1438C2212yescomplemented
91C2×#1438C2212yescomplemented
92C2×#1438C2212yescomplemented
93C2×#1438C2212yescomplemented
94C2×#1438C2212yescomplemented
95C2×C22⋊#95C2211yescharacteristic
96C2×C22⋊#95C2211yescharacteristic
97C2×C22⋊#95C2211yescharacteristic
98C2×C22⋊#95C2211yescharacteristic
99C2×C22⋊#95C2211yescharacteristic
100C2×C22⋊#95C2211yescharacteristic
101C2×C22⋊#95C2211yescharacteristic
102C2×C22⋊#95C2211yescharacteristic
103C2×C22⋊#95C2211yescharacteristic
104C2×C22⋊#95C2212yescomplemented
105C2×C22⋊#95C2212yescomplemented
106C2×C22⋊#95C2212yescomplemented
107#7557C2212yescomplemented
108#7557C2212yescomplemented
109#7557C2212yescomplemented
110#7556C2212yescomplemented
111#7556C2212yescomplemented
112#7555C2212yescomplemented
113#7555C2212yescomplemented
114#7555C2212yescomplemented
115#7555C2212yescomplemented
116#7555C2212yescomplemented
117#7555C2212yescomplemented
118#7555C2212yescomplemented
119#7555C2212yescomplemented
120#7555C2212yescomplemented
121#7555C2212yescomplemented
122#7555C2212yescomplemented
123C27C2311yescharacteristic
124C27C2311yescharacteristic
125C27C2311yescharacteristic
126C24×D4D418yescomplemented
127C24×D4C2311yescharacteristic
128C24×D4C2311yescharacteristic
129C24×D4C2312yes—
130C24×D4C2312yes—
131C24×D4C2311yescharacteristic
132C24×D4C2312yes—
133C24×D4C2311yescharacteristic
134C24×D4C2312yes—
135C24×D4C2311yescharacteristic
136C24×D4C2311yescharacteristic
137C24×D4C2312yes—
138C24×D4C2311yescharacteristic
139C24×D4C2311yescharacteristic
140C24×D4C2311yescharacteristic
141C25×C4C2311yescharacteristic
142C25×C4C2311yescharacteristic
143C25×C4C2311yescharacteristic
144C25×C4C2311yescharacteristic
145C25×C4C2312yes—
146C25×C4C2311yescharacteristic
147C25×C4C2311yescharacteristic
148C22×#120D418yescomplemented
149C23×C4⋊C4C2311yescharacteristic
150C23×C4⋊C4C2311yescharacteristic
151C23×C4⋊C4C2312yes—
152C23×C4⋊C4C2312yes—
153C23×C22⋊C4C2311yescharacteristic
154C23×C22⋊C4C2311yescharacteristic
155C23×C22⋊C4C2311yescharacteristic
156C23×C22⋊C4C2311yescharacteristic
157C23×C22⋊C4C2311yescharacteristic
158C23×C22⋊C4C2311yescharacteristic
159C23×C22⋊C4C2311yescharacteristic
160C23×C22⋊C4C2311yescharacteristic
161C23×C22⋊C4C2311yescharacteristic
162C23×C22⋊C4C2312yes—
163C23×C22⋊C4C2312yes—
164C23×C22⋊C4C2311yescharacteristic
165C23×C22⋊C4C2312yes—
166C23×C22⋊C4C2311yescharacteristic
167C23×C22⋊C4C2311yescharacteristic
168C23×C22⋊C4C2312yes—
169C23×C22⋊C4C2312yes—
170C23×C22⋊C4C2312yes—
171C23×C22⋊C4C2312yes—
172C23×C22⋊C4C2312yes—
173C23×C22⋊C4C2312yes—
174C23×C22⋊C4C2312yes—
175C23×C22⋊C4C2312yes—
176C23×C22⋊C4C2312yes—
177C23×C22⋊C4C2312yes—
178C23×C22⋊C4C2312yes—
179C23×C22⋊C4C2311yescharacteristic
180C23×C22⋊C4C2311yescharacteristic
181C23×C22⋊C4C2311yescharacteristic
182C23×C22⋊C4C2311yescharacteristic
183C23×C22⋊C4C2312yes—
184C23×C22⋊C4C2312yes—
185C23×C22⋊C4C2312yes—
186C23×C22⋊C4C2312yes—
187C23×C22⋊C4C2312yes—
188C23×C22⋊C4C2312yes—
189C23×C22⋊C4C2312yes—
190C23×C22⋊C4C2311yescharacteristic
191C23×C22⋊C4C2311yescharacteristic
192C23×C22⋊C4C2312yes—
193C23×C22⋊C4C2311yescharacteristic
194C23×C22⋊C4C2312yes—
195C2×#392D4116yescomplemented
196C2×#385D418yescomplemented
197C2×#379D418yescomplemented
198C2×#379D418yescomplemented
199C2×#379D418yescomplemented
200C22×#95C2311yescharacteristic
201C22×#95C2311yescharacteristic
202C22×#95C2312yes—
203C22×#95C2311yescharacteristic
204C22×#95C2311yescharacteristic
205C22×#95C2312yes—
206C22×#95C2312yes—
207C22×#95C2312yes—
208C22×#95C2312yes—
209C22×#95C2312yes—
210C22×#95C2312yes—
211C22×#95C2312yes—
212C22×#95C2312yes—
213C22×#95C2312yes—
214C22×#95C2312yes—
215C22×#95C2312yes—
216C22×#95C2312yes—
217C22×#95C2312yes—
218C22×#95C2312yes—
219C22×#95C2312yes—
220C22×#95C2312yes—
221C22×#95C2312yes—
222C22×#95C2312yes—
223C22×#95C2312yes—
224C22×#95C2312yes—
225C22×#95C2312yes—
226C22×#95C2312yes—
227C22×#95C2312yes—
228C22×#95C2312yes—
229C26C2×D414yes—
230C26C2×D414yes—
231C26C2×D414yes—
232C26C2×D414yes—
233C26C2×D414yes—
234C26C2×D414yes—
235C26#4114yes—
236C26C2411yescharacteristic
237C26C2411yescharacteristic
238C26C2411yescharacteristic
239C26C2412yes—
240C26C2411yescharacteristic
241C26C2411yescharacteristic
242C26C2411yescharacteristic
243C23×D4C2×D414yes—
244C23×D4C2×D418yes—
245C23×D4C2×D418yes—
246C23×D4C2×D414yes—
247C23×D4C2×D414yes—
248C23×D4C2×D418yes—
249C23×D4C2×D414yes—
250C23×D4C2×D414yes—
251C23×D4C2×D414yescomplemented
252C23×D4C2×D414yescomplemented
253C24×C4C2×D414yes—
254C24×C4C2×D414yes—
255C24×C4#4114yes—
256C24×C4C2412yes—
257C24×C4C2411yescharacteristic
258C24×C4C2412yes—
259C24×C4C2412yes—
260C24×C4C2411yescharacteristic
261C24×C4C2411yescharacteristic
262C24×C4C2411yescharacteristic
263C24×C4C2411yescharacteristic
264C24×C4C2412yes—
265C24×C4C2411yescharacteristic
266C24×C4C2411yescharacteristic
267C24×C4C2411yescharacteristic
268C24×C4C2412yes—
269C24×C4C2412yes—
270C24×C4C2412yes—
271C24×C4C2411yescharacteristic
272C22×C4⋊C4C2×D418yescomplemented
273C22×C22⋊C4C2×D414yes—
274C22×C22⋊C4C2×D414yes—
275C22×C22⋊C4C2×D414yes—
276C22×C22⋊C4C2×D414yes—
277C22×C22⋊C4C2×D418yes—
278C22×C22⋊C4C2×D418yes—
279C22×C22⋊C4C2×D414yes—
280C22×C22⋊C4C2×D414yes—
281C22×C22⋊C4C2×D414yes—
282C22×C22⋊C4C2×D414yes—
283C22×C22⋊C4C2×D414yes—
284C22×C22⋊C4C2×D418yes—
285C22×C22⋊C4C2×D414yescomplemented
286C22×C22⋊C4C2×D418yescomplemented
287C22×C22⋊C4C2×D414yescomplemented
288C22×C22⋊C4C2×D414yescomplemented
289C22×C22⋊C4C2×D418yescomplemented
290C22×C22⋊C4C2×D414yescomplemented
291C22×C22⋊C4C2×D414yescomplemented
292C22×C22⋊C4C2×D418yescomplemented
293C22×C22⋊C4C2×D418yescomplemented
294C22×C22⋊C4C2×D414yescomplemented
295C22×C22⋊C4#4114yes—
296C2×#95C2×D418yes—
297C2×#95C2×D418yescomplemented
298C25#120116yes—
299C25#121116yescomplemented
300C25C22×D412yes—
301C25C22×D412yes—
302C25C22×D412yes—
303C25C22×D412yes—
304C25C22×D412yes—
305C25C22×D412yes—
306C25C22×D414yes—
307C25C22×D414yes—
308C25C22×D412yes—
309C25C22×D412yes—
310C25C22×D414yes—
311C25C22×D412yes—
312C25C22×D412yes—
313C25C22×D414yes—
314C25C22×D412yes—
315C25C22×D412yes—
316C25C22×D412yes—
317C25C22×D412yes—
318C25C22×D412yes—
319C25C22×D412yes—
320C25C22×D412yes—
321C25C2×#4112yes—
322C25C2×#4112yes—
323C25C2×#4112yes—
324C25C2×#4112yes—
325C25C2×#4112yes—
326C25H(5,𝔽2)14yes—
327C25H(5,𝔽2)14yes—
328C25H(5,𝔽2)14yes—
329C25H(5,𝔽2)12yes—
330C25H(5,𝔽2)12yes—
331C25H(5,𝔽2)12yes—
332C25H(5,𝔽2)12yes—
333C25H(5,𝔽2)12yes—
334C252−1+412yes—
335C25C2511yescharacteristic
336C22×D4#120116yescomplemented
337C23×C4C22×D414yes—
338C23×C4C22×D414yes—
339C23×C4C22×D412yes—
340C23×C4C22×D412yes—
341C23×C4C22×D414yes—
342C23×C4C22×D412yes—
343C23×C4C22×D412yes—
344C23×C4C22×D412yes—
345C23×C4C22×D412yes—
346C23×C4C22×D412yes—
347C23×C4C22×D412yes—
348C23×C4C22×D412yes—
349C23×C4C22×D412yes—
350C23×C4C22×D412yes—
351C23×C4C22×D412yes—
352C23×C4C22×D414yes—
353C23×C4C22×D414yes—
354C23×C4C22×D414yes—
355C23×C4C22×D412yes—
356C23×C4C22×D414yes—
357C23×C4C22×D414yes—
358C23×C4C22×D414yes—
359C23×C4C2×#4114yes—
360C23×C4C2×#4114yes—
361C23×C4H(5,𝔽2)14yes—
362C23×C4H(5,𝔽2)14yes—
363C23×C4H(5,𝔽2)14yes—
364C2×C22⋊C4#120116yes—
365C2×C22⋊C4#121116yescomplemented
366C24C2×#12014yes—
367C24C2×#12014yes—
368C24C2×#12014yes—
369C24C2×#12014yes—
370C24C2×#12014yes—
371C24C2×#12014yes—
372C24C2×#12114yes—
373C24C2×#12114yes—
374C24C2×#12114yes—
375C24C2×#12114yes—
376C24#52514yes—
377C24#53214yes—
378C24#53414yes—
379C24#53414yes—
380C24#53414yes—
381C24#53414yes—
382C24#53514yes—
383C24#53714yes—
384C24#53714yes—
385C24#53714yes—
386C24#53814yes—
387C24#54014yes—
388C24#54014yes—
389C24D4218yes—
390C24D4218yes—
391C24D4218yes—
392C24D4218yes—
393C24D4214yes—
394C24D4214yes—
395C24D4214yes—
396C24D4214yes—
397C24D4214yes—
398C24D4214yes—
399C24D4214yes—
400C24#54618yes—
401C24#54614yes—
402C24#54614yes—
403C24#54614yes—
404C24#54614yes—
405C24#54614yes—
406C24#54614yes—
407C24#54714yes—
408C24#54714yes—
409C24#54814yes—
410C24#55014yes—
411C24#55314yes—
412C24#56014yes—
413C24#56214yes—
414C24C23×D411yescharacteristic
415C24C23×D411yescharacteristic
416C24C23×D411yescharacteristic
417C24C23×D411yescharacteristic
418C24C23×D411yescharacteristic
419C24C23×D412yes—
420C24C23×D411yescharacteristic
421C24C22×#4111yescharacteristic
422C24C22×#4111yescharacteristic
423C24C22×#4111yescharacteristic
424C24C2×H(5,𝔽2)11yescharacteristic
425C24C2×H(5,𝔽2)11yescharacteristic
426C24C2×H(5,𝔽2)11yescharacteristic
427C24C2×H(5,𝔽2)11yescharacteristic
428C24C2×H(5,𝔽2)12yes—
429C24C2×H(5,𝔽2)12yes—
430C24C2×H(5,𝔽2)12yes—
431C24C2×H(5,𝔽2)11yescharacteristic
432C24C2×H(5,𝔽2)12yes—
433C24C2×H(5,𝔽2)12yes—
434C24C2×H(5,𝔽2)12yes—
435C24C2×2−1+411yescharacteristic
436C24#58512yes—
437C22×C4C2×#12014yes—
438C22×C4C2×#12014yes—
439C22×C4C2×#12014yes—
440C22×C4C2×#12118yes—
441C22×C4#53414yes—
442C22×C4D4218yes—
443C22×C4#54618yes—
444C23#240318yes—
445C23#240318yes—
446C23#240718yes—
447C23#240818yes—
448C23#241018yes—
449C23#241018yescomplemented
450C23#241618yes—
451C23#242418yes—
452C23#242818yes—
453C23#243018yes—
454C23#246418yes—
455C23#267118yes—
456C23#267118yes—
457C23#267318yes—
458C23#267518yes—
459C23#267618yes—
460C23#268818yes—
461C23C22×#12011yescharacteristic
462C23C22×#12011yescharacteristic
463C23C22×#12011yescharacteristic
464C23C22×#12111yescharacteristic
465C23C22×#12111yescharacteristic
466C23C2×#52511yescharacteristic
467C23C2×#53211yescharacteristic
468C23C2×#53411yescharacteristic
469C23C2×#53411yescharacteristic
470C23C2×#53411yescharacteristic
471C23C2×#53411yescharacteristic
472C23C2×#53411yescharacteristic
473C23C2×#53511yescharacteristic
474C23C2×#53711yescharacteristic
475C23C2×#53711yescharacteristic
476C23C2×#53711yescharacteristic
477C23C2×#53811yescharacteristic
478C23C2×#54011yescharacteristic
479C23C2×#54011yescharacteristic
480C23C2×D4212yes—
481C23C2×D4211yescharacteristic
482C23C2×D4211yescharacteristic
483C23C2×D4212yes—
484C23C2×D4212yes—
485C23C2×D4212yes—
486C23C2×D4212yes—
487C23C2×D4211yescharacteristic
488C23C2×D4211yescharacteristic
489C23C2×D4211yescharacteristic
490C23C2×D4211yescharacteristic
491C23C2×D4211yescharacteristic
492C23C2×#54612yes—
493C23C2×#54612yes—
494C23C2×#54611yescharacteristic
495C23C2×#54611yescharacteristic
496C23C2×#54611yescharacteristic
497C23C2×#54611yescharacteristic
498C23C2×#54611yescharacteristic
499C23C2×#54611yescharacteristic
500C23C2×#54711yescharacteristic
501C23C2×#54711yescharacteristic
502C23C2×#54811yescharacteristic
503C23C2×#55011yescharacteristic
504C23D4×#4112yes—
505C23C2×#55311yescharacteristic
506C23#348412yes—
507C23#348411yescharacteristic
508C23#348412yes—
509C23#348411yescharacteristic
510C23#348412yes—
511C23#348411yescharacteristic
512C23#348412yes—
513C23#348412yes—
514C23#348412yes—
515C23#348412yes—
516C23#348412yes—
517C23#348412yes—
518C23#348412yes—
519C23#348412yes—
520C23#348412yes—
521C23#348412yes—
522C23#348412yes—
523C23#348511yescharacteristic
524C23#348812yes—
525C23#348912yes—
526C23#349012yes—
527C23#349012yes—
528C23#349012yes—
529C23#349412yes—
530C23#349612yes—
531C23#349612yes—
532C23#349612yes—
533C23#349612yes—
534C23#349812yes—
535C23#350512yes—
536C23#350812yes—
537C23#351912yes—
538C23#351912yes—
539C23#351912yes—
540C23C2×#56011yescharacteristic
541C23C2×#56211yescharacteristic
542C23#353212yes—
543C23#353212yes—
544C23#353212yes—
545C23#353212yes—
546C23#353212yes—
547C23#353212yes—
548C23#353412yes—
549C23#353412yes—
550C23#353412yes—
551C23#353412yes—
552C23#353612yes—
553C23#353612yes—
554C23#353612yes—
555C23#354212yes—
556C23#354312yes—
557C23#354312yes—
558C23#354312yes—
559C23#354312yes—
560C22#15263116yescomplemented
561C22C2×#240311yescharacteristic
562C22C2×#240311yescharacteristic
563C22C2×#241011yescharacteristic
564C22C2×#241011yescharacteristic
565C22C2×#242411yescharacteristic
566C22C2×#240811yescharacteristic
567C22C2×#241611yescharacteristic
568C22C2×#246411yescharacteristic
569C22C2×#242811yescharacteristic
570C22C2×#240711yescharacteristic
571C22C2×#243011yescharacteristic
572C22#3498011yescharacteristic
573C22#3498011yescharacteristic
574C22#3498111yescharacteristic
575C22#3534611yescharacteristic
576C22#3534711yescharacteristic
577C22#3534811yescharacteristic
578C22#3535811yescharacteristic
579C22#3568012yes—
580C22#3568112yes—
581C22#3569112yes—
582C22#3569412yes—
583C22D4×#12011yescharacteristic
584C22D4×#12012yes—
585C22D4×#12011yescharacteristic
586C22D4×#12112yes—
587C22#3609812yes—
588C22#3612312yes—
589C22#3615211yescharacteristic
590C22#3621311yescharacteristic
591C22#3711711yescharacteristic
592C22#3723211yescharacteristic
593C22#3743611yescharacteristic
594C22#3764412yes—
595C22#3764411yescharacteristic
596C22#3764411yescharacteristic
597C22#3764411yescharacteristic
598C22#3764611yescharacteristic
599C22#3766012yes—
600C22#3767312yes—
601C22#3767312yes—
602C22#3767312yes—
603C22#3767412yes—
604C22#3769412yes—
605C22#3772212yes—
606C22#3783211yescharacteristic
607C22#3783411yescharacteristic
608C22#3803611yescharacteristic
609C22#3803611yescharacteristic
610C22#3891611yescharacteristic
611C22#3933611yescharacteristic
612C22#3933811yescharacteristic
613C22#3946411yescharacteristic
614C22#4048412yes—
615C22#4053712yes—
616C22#4058612yes—
617C22#4058612yes—
618C22#4058612yes—
619C22#4059012yes—
620C22#4064212yes—
621C22#4073012yes—
622C22#4299612yes—
623C22#4299612yes—
624C22#4299612yes—
625C22#4299612yes—
626C22#4299712yes—
627C22#4299712yes—
628C22#4300212yes—
629C22#4307912yes—
630C22#4309512yes—
631C22#4309512yes—
632C22#4309912yes—
633C22#4317312yes—
634C22#4388612yes—
635C22#4388712yes—
636C22#4544312yes—
637C22#4632412yes—
638C22C2×#267111yescharacteristic
639C22C2×#267111yescharacteristic
640C22C2×#267311yescharacteristic
641C22C2×#267511yescharacteristic
642C22C2×#267611yescharacteristic
643C22C2×#268811yescharacteristic
644C22#5231612yes—
645C22#5239812yes—
646C22#5899012yes—
647C22#5899012yes—
648C22#5899012yes—
649C22#5899012yes—
650C22#5899012yes—
651C22#5899112yes—
652C22#5899112yes—
653C22#5899112yes—
654C22#5899612yes—
655C22#5901512yes—
656C22#5912312yes—
657C22#5912312yes—
658C22#5912412yes—
659C22#5914212yes—
660C2C2×#1526311yescharacteristic
661C2#64765611yescharacteristic
662C2#64804211yescharacteristic
663C2#64840311yescharacteristic
664C2#64903411yescharacteristic
665C2#68620011yescharacteristic
666C2#68691811yescharacteristic
667C2#68695011yescharacteristic
668C2#69545811yescharacteristic
669C2#75928811yescharacteristic
670C2#76334111yescharacteristic
671C2#77376212yes—
672C2#77399012yes—
673C2#77403812yes—
674C2#77847412yes—
675C2#84673711yescharacteristic
676C2#84679711yescharacteristic
677C2#91860911yescharacteristic
678C2#91867311yescharacteristic
679C2#99098212yes—
680C2#99158912yes—
681C2#100721412yes—
682C2#100723812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC25C25
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#2410C2semidirect
2. C22×#2410C2semidirect
3. C23×#392C2semidirect
4. C2×#15263C2semidirect
5. C2×#14724C2semidirect
6. C2×#14715C2semidirect
7. C2×#14127C2semidirect
8. C2×#13867C2semidirect
9. C2×#13867C2semidirect
10. #158823C2semidirect
11. #158820C2semidirect
12. #156827C2semidirect
13. #156706C2semidirect
14. #156706C2semidirect
15. #156686C2semidirect
16. #155065C2semidirect
17. #154208C2semidirect
18. #154196C2semidirect
19. #154195C2semidirect
20. #154195C2semidirect
21. #154195C2semidirect
22. #154194C2semidirect
23. #153851C2semidirect
27. C23×#121C22semidirect
28. C23×#121C22semidirect
29. C23×#121C22semidirect
38. C22×#394C22semidirect
39. C22×#394C22semidirect
40. C22×#394C22semidirect
41. C22×#394C22semidirect
42. C22×#394C22semidirect
47. C22×#392C22semidirect
48. C22×#392C22semidirect
49. C22×#392C22semidirect
50. C22×#392C22semidirect
51. C22×#392C22semidirect
56. C22×#386C22semidirect
57. C22×#386C22semidirect
58. C22×#386C22semidirect
59. C22×#386C22semidirect
60. C22×#386C22semidirect
61. C22×#386C22semidirect
62. C22×#386C22semidirect
66. C22×#385C22semidirect
75. C2×#1441C22semidirect
76. C2×#1439C22semidirect
77. C2×#1439C22semidirect
78. C2×#1439C22semidirect
79. C2×#1439C22semidirect
80. C2×#1439C22semidirect
81. C2×#1438C22semidirect
82. C2×#1438C22semidirect
83. C2×#1438C22semidirect
84. C2×#1438C22semidirect
85. C2×#1438C22semidirect
86. C2×#1438C22semidirect
87. C2×#1438C22semidirect
88. C2×#1438C22semidirect
89. C2×#1438C22semidirect
90. C2×#1438C22semidirect
91. C2×#1438C22semidirect
92. C2×#1438C22semidirect
93. C2×#1438C22semidirect
94. C2×#1438C22semidirect
104. C2×C22⋊#95C22semidirect
105. C2×C22⋊#95C22semidirect
106. C2×C22⋊#95C22semidirect
107. #7557C22semidirect
108. #7557C22semidirect
109. #7557C22semidirect
110. #7556C22semidirect
111. #7556C22semidirect
112. #7555C22semidirect
113. #7555C22semidirect
114. #7555C22semidirect
115. #7555C22semidirect
116. #7555C22semidirect
117. #7555C22semidirect
118. #7555C22semidirect
119. #7555C22semidirect
120. #7555C22semidirect
121. #7555C22semidirect
122. #7555C22semidirect
126. C24×D4D4semidirect
148. C22×#120D4semidirect
195. C2×#392D4semidirect
196. C2×#385D4semidirect
197. C2×#379D4semidirect
198. C2×#379D4semidirect
199. C2×#379D4semidirect
251. C23×D4C2×D4semidirect
252. C23×D4C2×D4semidirect
272. C22×C4⋊C4C2×D4semidirect
285. C22×C22⋊C4C2×D4semidirect
286. C22×C22⋊C4C2×D4semidirect
287. C22×C22⋊C4C2×D4semidirect
288. C22×C22⋊C4C2×D4semidirect
289. C22×C22⋊C4C2×D4semidirect
290. C22×C22⋊C4C2×D4semidirect
291. C22×C22⋊C4C2×D4semidirect
292. C22×C22⋊C4C2×D4semidirect
293. C22×C22⋊C4C2×D4semidirect
294. C22×C22⋊C4C2×D4semidirect
297. C2×#95C2×D4semidirect
299. C25#121semidirect
336. C22×D4#120semidirect
365. C2×C22⋊C4#121semidirect
449. C23#2410semidirect
560. C22#15263semidirect

Maximal subgroups

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

subgroupindex
C22×#24102
C23×#3922
C2×#152632
C2×#147242
C2×#147152
C2×#141272
C2×#138672
#1588232
#1588202
#1568272
#1567062
#1566862
#1550652
#1542082
#1541962
#1541952
#1541942
#1538512