Finite Group Databasebeta

← #61520

Subgroups — #61520

Order 256.

913 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3523C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic
3#3400C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3372C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3343C211yesmaximal, characteristic, complemented
9#3336C211yesmaximal, characteristic, complemented
10#3320C211yesmaximal, characteristic, complemented
11#3312C211yesmaximal, characteristic, complemented
12#3311C211yesmaximal, characteristic, complemented
13#3310C211yesmaximal, characteristic, complemented
14#3298C211yesmaximal, characteristic, complemented
15#3296C211yesmaximal, characteristic, complemented
16D4×SD16C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3181C211yesmaximal, characteristic, complemented
20#3178C211yesmaximal, characteristic, complemented
21#3174C211yesmaximal, characteristic, complemented
22#3126C211yesmaximal, characteristic, complemented
23#3123C211yesmaximal, characteristic, complemented
24#3121C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3108C211yesmaximal, characteristic, complemented
27#3101C211yesmaximal, characteristic, complemented
28#2968C211yesmaximal, characteristic, complemented
29#2949C211yesmaximal, characteristic, complemented
30#2947C211yesmaximal, characteristic, complemented
31C2×#440C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C22×SD16C2211yescharacteristic
34C22×SD16C2211yescharacteristic
35#559C2211yescharacteristic
36#557—21no—
37#557C2211yescharacteristic, complemented
38#557C2211yescharacteristic, complemented
39#556—21no—
40#556C2211yescharacteristic, complemented
41#554C2211yescharacteristic
42#553—21no—
43#553C2211yescharacteristic
44#552—21no—
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51D4×Q8C2211yescharacteristic
52D4×Q8C2211yescharacteristic, complemented
53D4×Q8C2211yescharacteristic, complemented
54#547C2211yescharacteristic
55#546—21no—
56#546C2211yescharacteristic
57#546C2211yescharacteristic
58D42C2211yescharacteristic
59#542C2211yescharacteristic
60#541—21no—
61#541—21no—
62#541C2211yescharacteristic, complemented
63#541C2211yescharacteristic, complemented
64#540C2211yescharacteristic
65#539—21no—
66#538—21no—
67#533—21no—
68#533C2211yescharacteristic, complemented
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525—21no—
73C2×#123—21no—
74#520C2211yescharacteristic
75#519C2211yescharacteristic, complemented
76#519C2211yescharacteristic, complemented
77#518C2211yescharacteristic
78C2×C4×Q8C2211yescharacteristic, complemented
79C2×C4×D4C2211yescharacteristic
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#497C2211yescharacteristic, complemented
85#492C2211yescharacteristic
86#491C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#490C2211yescharacteristic
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#487C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#480C2211yescharacteristic
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic, complemented
112#477C2211yescharacteristic, complemented
113#476C2211yescharacteristic
114#476C2211yescharacteristic, complemented
115#475C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#468C2211yescharacteristic
118#468C2211yescharacteristic, complemented
119#468C2211yescharacteristic, complemented
120#467C2211yescharacteristic, complemented
121#467C2211yescharacteristic, complemented
122#467C2211yescharacteristic, complemented
123#465C2211yescharacteristic
124#465C2211yescharacteristic
125#465C2211yescharacteristic
126#465C2211yescharacteristic, complemented
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#462C2211yescharacteristic, complemented
133#461C2211yescharacteristic
134#461C2211yescharacteristic
135#461C2211yescharacteristic
136#461C2211yescharacteristic, complemented
137#461C2211yescharacteristic, complemented
138#460C2211yescharacteristic
139#460C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#451C2211yescharacteristic, complemented
143#451C2211yescharacteristic, complemented
144#450C2211yescharacteristic
145#450C2211yescharacteristic
146#450C2211yescharacteristic
147#450C2211yescharacteristic
148#448C2211yescharacteristic
149#448C2211yescharacteristic
150#448C2211yescharacteristic, complemented
151#448C2211yescharacteristic, complemented
152#446C2211yescharacteristic, complemented
153#446C2211yescharacteristic, complemented
154#441C2211yescharacteristic, complemented
155#441C2211yescharacteristic, complemented
156#441C2211yescharacteristic, complemented
157#440C2211yescharacteristic
158#440C2211yescharacteristic
159#440C2211yescharacteristic
160#440C2211yescharacteristic
161#440C2211yescharacteristic
162#440C2211yescharacteristic
163#440C2211yescharacteristic, complemented
164#440C2211yescharacteristic, complemented
165#440C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×Q16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic
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
197C2×#103C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C22×Q8C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4—21no—
212#137—24no—
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×Q16C2311yescharacteristic
217C2×SD16—24no—
218C2×SD16—24no—
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C2×M16C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C22×C8C2311yescharacteristic
235C22×C8C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243C4⋊Q8C2311yescharacteristic
244C4⋊Q8C2311yescharacteristic
245C4⋊Q8C2311yescharacteristic
246#127C2311yescharacteristic
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#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126D411yescharacteristic
260#126D411yescharacteristic
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125D411yescharacteristic
275#125C2311yescharacteristic
276#125C2311yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#124—21no—
280#124—21no—
281#124—21no—
282#124D411yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
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#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123D411yescharacteristic
300#123D411yescharacteristic
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⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8D411yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121D411yescharacteristic
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×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
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×D4—21no—
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#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#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
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—
483#41—22no—
484#41—41no—
485#41—82no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8C2×D411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×D4—22no—
504C2×D4—22no—
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—41no—
515C2×D4—41no—
516C2×D4—82no—
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
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—82no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544Q16—22no—
545Q16—22no—
546Q16—41no—
547Q16—41no—
548SD16—22no—
549SD16—22no—
550SD16—22no—
551SD16—22no—
552SD16—22no—
553SD16—22no—
554SD16—22no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559SD16#4114yescomplemented
560M16—22no—
561M16—41no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
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⋊C4—21no—
612C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
622C4⋊C4C2×D411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
629C4⋊C4C2411yescharacteristic
630C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C42—21no—
669C42—21no—
670C42—21no—
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—42no—
693C23—42no—
694C23—42no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23C22×D411yescharacteristic
699C23C22×D411yescharacteristic
700C23C22×D411yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—41no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—81no—
716Q8C2×#4112yes—
717D4—22no—
718D4—22no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—41no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4C2×#4112yes—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
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—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—81no—
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×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C2511yescharacteristic
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C8C2×#4112yes—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—22no—
798C22—21no—
799C22—21no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—84no—
809C22—162no—
810C22#57712yes—
811C22C23×D411yescharacteristic
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—22no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4C22×#4111yescharacteristic
837C4#58511yescharacteristic
838C2—22no—
839C2—41no—
840C2—41no—
841C2—42no—
842C2—81no—
843C2—81no—
844C2D4×#4111yescharacteristic
845C2C2×#57711yescharacteristic
846C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3513C2
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. #3523C2semidirect
3. #3400C2semidirect
4. #3388C2semidirect
5. #3372C2semidirect
6. #3371C2semidirect
7. #3350C2semidirect
8. #3343C2semidirect
9. #3336C2semidirect
10. #3320C2semidirect
11. #3312C2semidirect
12. #3311C2semidirect
13. #3310C2semidirect
14. #3298C2semidirect
15. #3296C2semidirect
16. D4×SD16C2semidirect
17. #3266C2semidirect
18. #3266C2semidirect
19. #3181C2semidirect
20. #3178C2semidirect
21. #3174C2semidirect
22. #3126C2semidirect
23. #3123C2semidirect
24. #3121C2semidirect
25. #3120C2semidirect
26. #3108C2semidirect
27. #3101C2semidirect
28. #2968C2semidirect
29. #2949C2semidirect
30. #2947C2semidirect
31. C2×#440C2semidirect
37. #557C22semidirect
38. #557C22semidirect
40. #556C22semidirect
48. #552C22semidirect
52. D4×Q8C22semidirect
53. D4×Q8C22semidirect
62. #541C22semidirect
63. #541C22semidirect
68. #533C22semidirect
75. #519C22semidirect
76. #519C22semidirect
78. C2×C4×Q8C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #499C22semidirect
83. #497C22semidirect
84. #497C22semidirect
86. #491C22semidirect
87. #491C22semidirect
89. #489C22semidirect
90. #488C22semidirect
91. #487C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #484C22semidirect
96. #483C22semidirect
97. #483C22semidirect
98. #483C22semidirect
99. #483C22semidirect
101. #482C22semidirect
102. #482C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
108. #479C22semidirect
111. #478C22semidirect
112. #477C22semidirect
114. #476C22semidirect
115. #475C22semidirect
116. #470C22semidirect
118. #468C22semidirect
119. #468C22semidirect
120. #467C22semidirect
121. #467C22semidirect
122. #467C22semidirect
126. #465C22semidirect
127. #465C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
132. #462C22semidirect
136. #461C22semidirect
137. #461C22semidirect
142. #451C22semidirect
143. #451C22semidirect
150. #448C22semidirect
151. #448C22semidirect
152. #446C22semidirect
153. #446C22semidirect
154. #441C22semidirect
155. #441C22semidirect
156. #441C22semidirect
163. #440C22semidirect
164. #440C22semidirect
165. #440C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. #440C22semidirect
170. C4×Q16C22semidirect
171. C4×Q16C22semidirect
172. C4×Q16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. C4×SD16C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
187. C8×D4C22semidirect
188. #433C22semidirect
189. #433C22semidirect
190. #431C22semidirect
191. #428C22semidirect
192. #427C22semidirect
193. C2×#107C22semidirect
194. #419C22semidirect
197. C2×#103C22semidirect
198. C2×#103C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C2×#97C22semidirect
559. SD16#41semidirect

Maximal subgroups

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

subgroupindex
#35232
#35132
#34002
#33882
#33722
#33712
#33502
#33432
#33362
#33202
#33122
#33112
#33102
#32982
#32962
D4×SD162
#32662
#31812
#31782
#31742
#31262
#31232
#31212
#31202
#31082
#31012
#29682
#29492
#29472
C2×#4402