Finite Group Databasebeta

← #61521

Subgroups — #61521

Order 256.

943 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3519C211yesmaximal, characteristic, complemented
2#3516C211yesmaximal, characteristic, complemented
3#3397C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3368C211yesmaximal, characteristic, complemented
7#3348C211yesmaximal, characteristic, complemented
8#3346C211yesmaximal, characteristic, complemented
9#3339C211yesmaximal, characteristic, complemented
10#3321C211yesmaximal, characteristic, complemented
11#3320C211yesmaximal, characteristic, complemented
12#3318C211yesmaximal, characteristic, complemented
13#3310C211yesmaximal, characteristic, complemented
14#3301C211yesmaximal, characteristic, complemented
15#3295C211yesmaximal, characteristic, complemented
16D4×SD16C211yesmaximal, characteristic, complemented
17#3265C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3180C211yesmaximal, characteristic, complemented
20#3179C211yesmaximal, characteristic, complemented
21#3174C211yesmaximal, characteristic, complemented
22#3126C211yesmaximal, characteristic, complemented
23#3123C211yesmaximal, characteristic, complemented
24#3119C211yesmaximal, characteristic, complemented
25#3118C211yesmaximal, characteristic, complemented
26#3105C211yesmaximal, characteristic, complemented
27#3103C211yesmaximal, characteristic, complemented
28#2968C211yesmaximal, characteristic, complemented
29#2949C211yesmaximal, characteristic, complemented
30#2946C211yesmaximal, characteristic, complemented
31C2×#440C211yesmaximal, characteristic, complemented
32C2×AGL(1,ℤ/8)C2211yescharacteristic
33C22×SD16C2211yescharacteristic
34C22×SD16C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556—21no—
37#556C2211yescharacteristic, complemented
38#555C2211yescharacteristic
39#554—21no—
40#554C2211yescharacteristic
41#554C2211yescharacteristic, complemented
42#553—21no—
43#553—21no—
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic, complemented
47#552—21no—
48#552C2211yescharacteristic, complemented
49#550C2211yescharacteristic
50D4×Q8C2211yescharacteristic, complemented
51#548C2211yescharacteristic, complemented
52#548C2211yescharacteristic, complemented
53#546—21no—
54#546—21no—
55#546—21no—
56D42C2211yescharacteristic
57D42C2211yescharacteristic
58D42C2211yescharacteristic
59#542—21no—
60#542C2211yescharacteristic, complemented
61#541—21no—
62#541C2211yescharacteristic, complemented
63#540C2211yescharacteristic
64#540C2211yescharacteristic
65#538—21no—
66#538—21no—
67#532C2211yescharacteristic
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic, complemented
72#525—21no—
73C2×#121—21no—
74#520C2211yescharacteristic, complemented
75#519C2211yescharacteristic, complemented
76#518C2211yescharacteristic
77#518C2211yescharacteristic
78C2×C4×Q8C2211yescharacteristic, complemented
79C2×C4×D4C2211yescharacteristic
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#496C2211yescharacteristic, complemented
84#496C2211yescharacteristic, complemented
85#492C2211yescharacteristic, complemented
86#491C2211yescharacteristic, complemented
87#490C2211yescharacteristic, complemented
88#490C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#486C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#482C2211yescharacteristic, complemented
97#482C2211yescharacteristic, complemented
98#482C2211yescharacteristic, complemented
99#481C2211yescharacteristic, complemented
100#481C2211yescharacteristic, complemented
101#481C2211yescharacteristic, complemented
102#481C2211yescharacteristic, complemented
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#478C2211yescharacteristic
108#478C2211yescharacteristic
109#478C2211yescharacteristic, complemented
110#478C2211yescharacteristic, complemented
111#478C2211yescharacteristic, complemented
112#476C2211yescharacteristic
113#475C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#474C2211yescharacteristic, complemented
116#469C2211yescharacteristic, complemented
117#468C2211yescharacteristic, complemented
118#468C2211yescharacteristic, complemented
119#468C2211yescharacteristic, complemented
120#466C2211yescharacteristic, complemented
121#466C2211yescharacteristic, complemented
122#466C2211yescharacteristic, complemented
123#465C2211yescharacteristic, complemented
124#465C2211yescharacteristic, complemented
125#465C2211yescharacteristic, complemented
126#465C2211yescharacteristic, complemented
127#465C2211yescharacteristic, complemented
128#463C2211yescharacteristic
129#463C2211yescharacteristic
130#463C2211yescharacteristic, complemented
131#463C2211yescharacteristic, complemented
132#461C2211yescharacteristic
133#461C2211yescharacteristic, complemented
134#460C2211yescharacteristic, complemented
135#460C2211yescharacteristic, complemented
136#460C2211yescharacteristic, complemented
137#460C2211yescharacteristic, complemented
138#460C2211yescharacteristic, complemented
139#459C2211yescharacteristic, complemented
140#450C2211yescharacteristic
141#450C2211yescharacteristic
142#450C2211yescharacteristic
143#450C2211yescharacteristic
144#449C2211yescharacteristic, complemented
145#449C2211yescharacteristic, complemented
146#448C2211yescharacteristic, complemented
147#448C2211yescharacteristic, complemented
148#448C2211yescharacteristic, complemented
149#448C2211yescharacteristic, complemented
150#447C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153#446C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic, complemented
156#442C2211yescharacteristic, complemented
157#440C2211yescharacteristic
158#440C2211yescharacteristic
159#440C2211yescharacteristic
160#440C2211yescharacteristic
161#440C2211yescharacteristic
162#440C2211yescharacteristic, complemented
163#440C2211yescharacteristic, complemented
164#440C2211yescharacteristic, complemented
165#440C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic, complemented
174C4×SD16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×D8C2211yescharacteristic
180C4×D8C2211yescharacteristic, complemented
181C4×D8C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic, complemented
188#433C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#431C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193C2×#107C2211yescharacteristic, complemented
194#419C2211yescharacteristic, complemented
195#418C2211yescharacteristic
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C2311yescharacteristic
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4—21no—
215AGL(1,ℤ/8)—24no—
216C2×SD16—24no—
217C2×SD16—24no—
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233C2×D8C2311yescharacteristic
234C2×M16C2311yescharacteristic
235C2×M16C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C22×C8C2311yescharacteristic
238C22×C8C2311yescharacteristic
239C22×C8C2311yescharacteristic
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8C2311yescharacteristic
243C4⋊Q8C2311yescharacteristic
244C4⋊Q8C2311yescharacteristic
245#127C2311yescharacteristic
246#127C2311yescharacteristic
247#127C2311yescharacteristic
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126D411yescharacteristic
259#126D411yescharacteristic
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125D411yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124D411yescharacteristic
278#124C2311yescharacteristic
279#124C2311yescharacteristic
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123D411yescharacteristic
291#123D411yescharacteristic
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8D411yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121D411yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#120—21no—
335#120—21no—
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396#117C2311yescharacteristic
397#117C2311yescharacteristic
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C2311yescharacteristic
402C2×C4⋊C4C2311yescharacteristic
403C2×C4⋊C4C2311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
418#107C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#102C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476#97C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C4×C8C2311yescharacteristic
479C4×C8C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C24—21no—
482C24—21no—
483C24—21no—
484#41—22no—
485#41—41no—
486#41—82no—
487#41—82no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8C2×D411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4—82no—
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C2×D4C2411yescharacteristic
534C2×D4C2411yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—82no—
554C22×C4C2×D411yescharacteristic
555C22×C4C2×D411yescharacteristic
556C22×C4C2411yescharacteristic
557C22×C4C2411yescharacteristic
558C22×C4C2411yescharacteristic
559SD16—22no—
560SD16—22no—
561SD16—22no—
562SD16—22no—
563SD16—22no—
564SD16—22no—
565SD16—22no—
566SD16—41no—
567SD16—41no—
568SD16—41no—
569SD16—41no—
570SD16#4114yescomplemented
571D8—22no—
572D8—22no—
573D8—41no—
574D8—41no—
575M16—22no—
576M16—41no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2×D411yescharacteristic
622C4⋊C4C2×D411yescharacteristic
623C4⋊C4C2×D411yescharacteristic
624C4⋊C4C2×D411yescharacteristic
625C4⋊C4C2×D411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
629C4⋊C4C2411yescharacteristic
630C4⋊C4C2411yescharacteristic
631C4⋊C4C2411yescharacteristic
632C4⋊C4C2411yescharacteristic
633C4⋊C4C2411yescharacteristic
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C22⋊C4C2×D411yescharacteristic
672C22⋊C4C2×D411yescharacteristic
673C22⋊C4C2×D411yescharacteristic
674C22⋊C4C2×D411yescharacteristic
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42C2×D411yescharacteristic
687C42C2×D411yescharacteristic
688C42C2411yescharacteristic
689C42C2411yescharacteristic
690C42C2411yescharacteristic
691C42C2411yescharacteristic
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
705C23—81no—
706C23C22×D411yescharacteristic
707C23C22×D411yescharacteristic
708C23C22×D411yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—21no—
713Q8—21no—
714Q8—41no—
715Q8—42no—
716Q8—42no—
717Q8—81no—
718Q8—81no—
719Q8C2×#4112yes—
720D4—22no—
721D4—22no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—21no—
726D4—21no—
727D4—21no—
728D4—21no—
729D4—21no—
730D4—21no—
731D4—41no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4C2×#4112yes—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C2511yescharacteristic
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8C2×#4112yes—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—84no—
832C22—162no—
833C22—162no—
834C22#57712yes—
835C22C23×D411yescharacteristic
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—22no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4C22×#4111yescharacteristic
859C4#58511yescharacteristic
860C2—22no—
861C2—41no—
862C2—41no—
863C2—42no—
864C2—81no—
865C2—81no—
866C2—81no—
867C2—81no—
868C2D4×#4111yescharacteristic
869C2C2×#57711yescharacteristic
870C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3519C2semidirect
2. #3516C2semidirect
3. #3397C2semidirect
4. #3388C2semidirect
5. #3376C2semidirect
6. #3368C2semidirect
7. #3348C2semidirect
8. #3346C2semidirect
9. #3339C2semidirect
10. #3321C2semidirect
11. #3320C2semidirect
12. #3318C2semidirect
13. #3310C2semidirect
14. #3301C2semidirect
15. #3295C2semidirect
16. D4×SD16C2semidirect
17. #3265C2semidirect
18. #3265C2semidirect
19. #3180C2semidirect
20. #3179C2semidirect
21. #3174C2semidirect
22. #3126C2semidirect
23. #3123C2semidirect
24. #3119C2semidirect
25. #3118C2semidirect
26. #3105C2semidirect
27. #3103C2semidirect
28. #2968C2semidirect
29. #2949C2semidirect
30. #2946C2semidirect
31. C2×#440C2semidirect
35. #557C22semidirect
37. #556C22semidirect
41. #554C22semidirect
46. #553C22semidirect
48. #552C22semidirect
50. D4×Q8C22semidirect
51. #548C22semidirect
52. #548C22semidirect
60. #542C22semidirect
62. #541C22semidirect
71. #529C22semidirect
74. #520C22semidirect
75. #519C22semidirect
78. C2×C4×Q8C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #499C22semidirect
83. #496C22semidirect
84. #496C22semidirect
85. #492C22semidirect
86. #491C22semidirect
87. #490C22semidirect
88. #490C22semidirect
89. #489C22semidirect
90. #488C22semidirect
91. #486C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #484C22semidirect
96. #482C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #481C22semidirect
100. #481C22semidirect
101. #481C22semidirect
102. #481C22semidirect
103. #480C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
109. #478C22semidirect
110. #478C22semidirect
111. #478C22semidirect
113. #475C22semidirect
114. #475C22semidirect
115. #474C22semidirect
116. #469C22semidirect
117. #468C22semidirect
118. #468C22semidirect
119. #468C22semidirect
120. #466C22semidirect
121. #466C22semidirect
122. #466C22semidirect
123. #465C22semidirect
124. #465C22semidirect
125. #465C22semidirect
126. #465C22semidirect
127. #465C22semidirect
130. #463C22semidirect
131. #463C22semidirect
133. #461C22semidirect
134. #460C22semidirect
135. #460C22semidirect
136. #460C22semidirect
137. #460C22semidirect
138. #460C22semidirect
139. #459C22semidirect
144. #449C22semidirect
145. #449C22semidirect
146. #448C22semidirect
147. #448C22semidirect
148. #448C22semidirect
149. #448C22semidirect
152. #446C22semidirect
153. #446C22semidirect
155. #442C22semidirect
156. #442C22semidirect
162. #440C22semidirect
163. #440C22semidirect
164. #440C22semidirect
165. #440C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. #440C22semidirect
173. C4×SD16C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
180. C4×D8C22semidirect
181. C4×D8C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. C8×D4C22semidirect
187. C8×D4C22semidirect
188. #433C22semidirect
189. #433C22semidirect
190. #431C22semidirect
191. #428C22semidirect
192. #427C22semidirect
193. C2×#107C22semidirect
194. #419C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C2×#97C22semidirect
570. SD16#41semidirect

Maximal subgroups

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

subgroupindex
#35192
#35162
#33972
#33882
#33762
#33682
#33482
#33462
#33392
#33212
#33202
#33182
#33102
#33012
#32952
D4×SD162
#32652
#31802
#31792
#31742
#31262
#31232
#31192
#31182
#31052
#31032
#29682
#29492
#29462
C2×#4402