Finite Group Databasebeta

← #61472

Subgroups — #61472

Order 256.

920 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3516C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3394C211yesmaximal, characteristic, complemented
4#3381C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3337C211yesmaximal, characteristic, complemented
8#3337C211yesmaximal, characteristic, complemented
9#3335C211yesmaximal, characteristic, complemented
10#3326C211yesmaximal, characteristic, complemented
11#3323C211yesmaximal, characteristic, complemented
12#3318C211yesmaximal, characteristic, complemented
13#3314C211yesmaximal, characteristic, complemented
14#3312C211yesmaximal, characteristic, complemented
15#3308C211yesmaximal, characteristic, complemented
16#3282C211yesmaximal, characteristic, complemented
17#3282C211yesmaximal, characteristic, complemented
18D4×SD16C211yesmaximal, characteristic, complemented
19#3174C211yesmaximal, characteristic, complemented
20#3173C211yesmaximal, characteristic, complemented
21#3168C211yesmaximal, characteristic, complemented
22#3121C211yesmaximal, characteristic, complemented
23#3120C211yesmaximal, characteristic, complemented
24#3119C211yesmaximal, characteristic, complemented
25#3118C211yesmaximal, characteristic, complemented
26#3117C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#2966C211yesmaximal, characteristic, complemented
29#2952C211yesmaximal, characteristic, complemented
30#2949C211yesmaximal, characteristic, complemented
31C2×C4×SD16C211yesmaximal, characteristic, complemented
32C2×#135C2211yescharacteristic
33C22×SD16C2211yescharacteristic
34C22×SD16C2211yescharacteristic
35#559C2211yescharacteristic
36#557C2211yescharacteristic, complemented
37#556—21no—
38#556C2211yescharacteristic, complemented
39#554—21no—
40#554C2211yescharacteristic
41#554C2211yescharacteristic, complemented
42#553—21no—
43#553—21no—
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#552—21no—
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51D4×Q8C2211yescharacteristic
52#548C2211yescharacteristic, complemented
53#548C2211yescharacteristic, complemented
54#547C2211yescharacteristic
55#546—21no—
56#546C2211yescharacteristic
57#546C2211yescharacteristic
58D42C2211yescharacteristic
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#541—21no—
63#541C2211yescharacteristic, complemented
64#540C2211yescharacteristic
65#539—21no—
66#538—21no—
67#529—21no—
68#529—21no—
69#529C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic, complemented
72#525—21no—
73C2×#123—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76#519C2211yescharacteristic, complemented
77#518C2211yescharacteristic
78C2×C4×Q8C2211yescharacteristic, complemented
79C2×C4×D4C2211yescharacteristic
80#499C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#495C2211yescharacteristic, complemented
84#495C2211yescharacteristic, complemented
85#492C2211yescharacteristic
86#491C2211yescharacteristic, complemented
87#490C2211yescharacteristic
88#489C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#481C2211yescharacteristic
101#481C2211yescharacteristic, complemented
102#480C2211yescharacteristic, complemented
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic, complemented
111#478C2211yescharacteristic, complemented
112#477C2211yescharacteristic, complemented
113#476C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#474C2211yescharacteristic
116#470C2211yescharacteristic, complemented
117#469C2211yescharacteristic
118#468C2211yescharacteristic, complemented
119#468C2211yescharacteristic, complemented
120#467C2211yescharacteristic, complemented
121#466C2211yescharacteristic
122#465C2211yescharacteristic
123#465C2211yescharacteristic
124#465C2211yescharacteristic, complemented
125#465C2211yescharacteristic, complemented
126#465C2211yescharacteristic, complemented
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic, complemented
135#463C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#461C2211yescharacteristic
138#460C2211yescharacteristic
139#459C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#451C2211yescharacteristic, complemented
143#451C2211yescharacteristic, complemented
144#450C2211yescharacteristic
145#450C2211yescharacteristic
146#449C2211yescharacteristic, complemented
147#449C2211yescharacteristic, complemented
148#448C2211yescharacteristic
149#448C2211yescharacteristic
150#447C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153C8×Q8C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#442C2211yescharacteristic, complemented
157#441C2211yescharacteristic, complemented
158#441C2211yescharacteristic, complemented
159#441C2211yescharacteristic, complemented
160#440C2211yescharacteristic
161#440C2211yescharacteristic
162#440C2211yescharacteristic, complemented
163#440C2211yescharacteristic, complemented
164#440C2211yescharacteristic, complemented
165#440C2211yescharacteristic, complemented
166C4×Q16C2211yescharacteristic, complemented
167C4×SD16C2211yescharacteristic
168C4×SD16C2211yescharacteristic
169C4×SD16C2211yescharacteristic
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×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×D8C2211yescharacteristic, complemented
182#436C2211yescharacteristic, complemented
183#435C2211yescharacteristic
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic
186C8×D4C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic, complemented
188#433C2211yescharacteristic, complemented
189#433C2211yescharacteristic, complemented
190#432C2211yescharacteristic, complemented
191#427C2211yescharacteristic, complemented
192C2×#106C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#419C2211yescharacteristic, complemented
195#418C2211yescharacteristic
196#417C2211yescharacteristic
197#417C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C2×C4×C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4—21no—
212#135—24no—
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C2×M16C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C22×C8C2311yescharacteristic
235C22×C8C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242#127C2311yescharacteristic
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126D411yescharacteristic
256#126D411yescharacteristic
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125D411yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124D411yescharacteristic
275#124C2311yescharacteristic
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#123—21no—
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#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123D411yescharacteristic
296#123D411yescharacteristic
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8D411yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
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#121—21no—
326#121D411yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×D4—21no—
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×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C2311yescharacteristic
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#106C2311yescharacteristic
418#106C2311yescharacteristic
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#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
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
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C4×C8C2311yescharacteristic
479C4×C8C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C24—21no—
482C24—21no—
483#41—22no—
484#41—22no—
485#41—41no—
486#41—41no—
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×Q8C2411yescharacteristic
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—41no—
516C2×D4—41no—
517C2×D4—82no—
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
523C2×D4C2411yescharacteristic
524C2×D4C2411yescharacteristic
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
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—82no—
544C22×C4C2×D411yescharacteristic
545C22×C4C2×D411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549Q16—22no—
550Q16—41no—
551Q16—41no—
552SD16—22no—
553SD16—22no—
554SD16—22no—
555SD16—22no—
556SD16—22no—
557SD16—22no—
558SD16—22no—
559SD16—41no—
560SD16—41no—
561SD16#4114yescomplemented
562D8—22no—
563D8—41no—
564D8—41no—
565M16—41no—
566M16—41no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—41no—
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42C2×D411yescharacteristic
684C42C2×D411yescharacteristic
685C42C2411yescharacteristic
686C42C2411yescharacteristic
687C42C2411yescharacteristic
688C42C2411yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23C22×D411yescharacteristic
700C23C22×D411yescharacteristic
701C23C22×D411yescharacteristic
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—21no—
708Q8—21no—
709Q8—41no—
710Q8—42no—
711Q8—42no—
712Q8—81no—
713Q8—81no—
714Q8C2×#4112yes—
715D4—22no—
716D4—22no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—41no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4C2×#4112yes—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C22×D411yescharacteristic
787C2×C4C2511yescharacteristic
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8C2×#4112yes—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—84no—
817C22—162no—
818C22#57712yes—
819C22C23×D411yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—22no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4C22×#4111yescharacteristic
844C4#58511yescharacteristic
845C2—22no—
846C2—41no—
847C2—41no—
848C2—42no—
849C2—81no—
850C2—81no—
851C2—81no—
852C2D4×#4111yescharacteristic
853C2C2×#57711yescharacteristic
854C2#358411yescharacteristic
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. #3516C2semidirect
2. #3513C2semidirect
3. #3394C2semidirect
4. #3381C2semidirect
5. #3376C2semidirect
6. #3371C2semidirect
7. #3337C2semidirect
8. #3337C2semidirect
9. #3335C2semidirect
10. #3326C2semidirect
11. #3323C2semidirect
12. #3318C2semidirect
13. #3314C2semidirect
14. #3312C2semidirect
15. #3308C2semidirect
16. #3282C2semidirect
17. #3282C2semidirect
18. D4×SD16C2semidirect
19. #3174C2semidirect
20. #3173C2semidirect
21. #3168C2semidirect
22. #3121C2semidirect
23. #3120C2semidirect
24. #3119C2semidirect
25. #3118C2semidirect
26. #3117C2semidirect
27. #3114C2semidirect
28. #2966C2semidirect
29. #2952C2semidirect
30. #2949C2semidirect
31. C2×C4×SD16C2semidirect
36. #557C22semidirect
38. #556C22semidirect
41. #554C22semidirect
48. #552C22semidirect
52. #548C22semidirect
53. #548C22semidirect
61. #542C22semidirect
63. #541C22semidirect
71. #529C22semidirect
75. #520C22semidirect
76. #519C22semidirect
78. C2×C4×Q8C22semidirect
80. #499C22semidirect
81. #499C22semidirect
82. #498C22semidirect
83. #495C22semidirect
84. #495C22semidirect
86. #491C22semidirect
88. #489C22semidirect
89. #489C22semidirect
90. #488C22semidirect
91. #488C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #483C22semidirect
97. #483C22semidirect
99. #482C22semidirect
101. #481C22semidirect
102. #480C22semidirect
103. #480C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
110. #478C22semidirect
111. #478C22semidirect
112. #477C22semidirect
113. #476C22semidirect
114. #475C22semidirect
116. #470C22semidirect
118. #468C22semidirect
119. #468C22semidirect
120. #467C22semidirect
124. #465C22semidirect
125. #465C22semidirect
126. #465C22semidirect
127. #465C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
134. #463C22semidirect
135. #463C22semidirect
136. #462C22semidirect
142. #451C22semidirect
143. #451C22semidirect
146. #449C22semidirect
147. #449C22semidirect
152. #446C22semidirect
153. C8×Q8C22semidirect
156. #442C22semidirect
157. #441C22semidirect
158. #441C22semidirect
159. #441C22semidirect
162. #440C22semidirect
163. #440C22semidirect
164. #440C22semidirect
165. #440C22semidirect
166. C4×Q16C22semidirect
173. C4×SD16C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. C4×D8C22semidirect
182. #436C22semidirect
184. #435C22semidirect
186. C8×D4C22semidirect
187. C8×D4C22semidirect
188. #433C22semidirect
189. #433C22semidirect
190. #432C22semidirect
191. #427C22semidirect
192. C2×#106C22semidirect
193. C2×#106C22semidirect
194. #419C22semidirect
197. #417C22semidirect
198. C2×#103C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C2×C4×C8C22semidirect
561. SD16#41semidirect

Maximal subgroups

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

subgroupindex
#35162
#35132
#33942
#33812
#33762
#33712
#33372
#33352
#33262
#33232
#33182
#33142
#33122
#33082
#32822
D4×SD162
#31742
#31732
#31682
#31212
#31202
#31192
#31182
#31172
#31142
#29662
#29522
#29492
C2×C4×SD162