Finite Group Databasebeta

← #61529

Subgroups — #61529

Order 256.

923 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3521C211yesmaximal, characteristic, complemented
2#3514C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3384C211yesmaximal, characteristic, complemented
5#3370C211yesmaximal, characteristic, complemented
6#3367C211yesmaximal, characteristic, complemented
7#3349C211yesmaximal, characteristic, complemented
8#3347C211yesmaximal, characteristic, complemented
9#3340C211yesmaximal, characteristic, complemented
10#3319C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3311C211yesmaximal, characteristic, complemented
13#3310C211yesmaximal, characteristic, complemented
14#3303C211yesmaximal, characteristic, complemented
15#3297C211yesmaximal, characteristic, complemented
16#3280C211yesmaximal, characteristic, complemented
17#3267C211yesmaximal, characteristic, complemented
18#3264C211yesmaximal, characteristic, complemented
19#3180C211yesmaximal, characteristic, complemented
20#3178C211yesmaximal, characteristic, complemented
21#3173C211yesmaximal, characteristic, complemented
22#3124C211yesmaximal, characteristic, complemented
23#3123C211yesmaximal, characteristic, complemented
24#3118C211yesmaximal, characteristic, complemented
25#3118C211yesmaximal, characteristic, complemented
26#3106C211yesmaximal, characteristic, complemented
27#3102C211yesmaximal, characteristic, complemented
28#2968C211yesmaximal, characteristic, complemented
29#2948C211yesmaximal, characteristic, complemented
30#2946C211yesmaximal, characteristic, complemented
31#2943C211yesmaximal, characteristic, complemented
32C2×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#135C2211yescharacteristic
34C22×D8C2211yescharacteristic
35#559C2211yescharacteristic, complemented
36#556C2211yescharacteristic
37#556C2211yescharacteristic, complemented
38#556C2211yescharacteristic, complemented
39#555C2211yescharacteristic
40#555C2211yescharacteristic, complemented
41#554C2211yescharacteristic, complemented
42#553—21no—
43#553C2211yescharacteristic, complemented
44#552—21no—
45#552C2211yescharacteristic
46#551—21no—
47#551—21no—
48#551—21no—
49#551—21no—
50D4×Q8C2211yescharacteristic, complemented
51#548—21no—
52#547C2211yescharacteristic, complemented
53#546—21no—
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#546C2211yescharacteristic, complemented
57#546C2211yescharacteristic, complemented
58D42C2211yescharacteristic
59#542C2211yescharacteristic
60#542C2211yescharacteristic, complemented
61#542C2211yescharacteristic, complemented
62#541C2211yescharacteristic, complemented
63#539—21no—
64#538—21no—
65#538—21no—
66#538—21no—
67#532C2211yescharacteristic, complemented
68#529—21no—
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic, complemented
72C2×#126—21no—
73C2×#124—21no—
74#520C2211yescharacteristic, complemented
75#518C2211yescharacteristic
76#518C2211yescharacteristic, complemented
77#518C2211yescharacteristic, complemented
78C4×#41C2211yescharacteristic, complemented
79C4×#41C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#495C2211yescharacteristic, complemented
86#490C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic, complemented
91#487C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#480C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#478C2211yescharacteristic, complemented
106#478C2211yescharacteristic, complemented
107#478C2211yescharacteristic, complemented
108#477C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#476C2211yescharacteristic, complemented
111#476C2211yescharacteristic, complemented
112#476C2211yescharacteristic, complemented
113#474C2211yescharacteristic, complemented
114#474C2211yescharacteristic, complemented
115#474C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#470C2211yescharacteristic, complemented
118#469C2211yescharacteristic
119#468C2211yescharacteristic
120#467C2211yescharacteristic, complemented
121#466C2211yescharacteristic, complemented
122#466C2211yescharacteristic, complemented
123#465C2211yescharacteristic
124#465C2211yescharacteristic, complemented
125#465C2211yescharacteristic, complemented
126#465C2211yescharacteristic, complemented
127#465C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic, complemented
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#463C2211yescharacteristic, complemented
136#461C2211yescharacteristic, complemented
137#461C2211yescharacteristic, complemented
138#460C2211yescharacteristic, complemented
139#459C2211yescharacteristic
140#452C2211yescharacteristic, complemented
141#452C2211yescharacteristic, complemented
142#450C2211yescharacteristic
143#450C2211yescharacteristic
144#450C2211yescharacteristic, complemented
145#450C2211yescharacteristic, complemented
146#449C2211yescharacteristic
147#449C2211yescharacteristic
148#449C2211yescharacteristic, complemented
149#449C2211yescharacteristic, complemented
150#447C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153#446C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#442C2211yescharacteristic
157#442C2211yescharacteristic, complemented
158#442C2211yescharacteristic, complemented
159#442C2211yescharacteristic, complemented
160#442C2211yescharacteristic, complemented
161#441C2211yescharacteristic, complemented
162#441C2211yescharacteristic, complemented
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×SD16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic, complemented
174C4×SD16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic
179C4×D8C2211yescharacteristic, complemented
180C4×D8C2211yescharacteristic, complemented
181C4×D8C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic
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
193#427C2211yescharacteristic, complemented
194#418C2211yescharacteristic
195#418C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic, complemented
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8—21no—
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212AGL(1,ℤ/8)—24no—
213#135—24no—
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×D8—24no—
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×D8C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C2×M16C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C22×C8C2311yescharacteristic
235C22×C8C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
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#126—21no—
256#126—21no—
257#126D411yescharacteristic
258#126D411yescharacteristic
259#125—21no—
260#125—21no—
261#125—21no—
262#125D411yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124D411yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#124C2311yescharacteristic
280#124C2311yescharacteristic
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⋊Q8D411yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#120—21no—
332#120—21no—
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
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×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—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—22no—
486#41—22no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—82no—
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—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—82no—
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2411yescharacteristic
525C2×D4C2411yescharacteristic
526C2×D4C2411yescharacteristic
527C2×D4C2411yescharacteristic
528C2×D4C2411yescharacteristic
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—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4C2×D411yescharacteristic
548C22×C4C2×D411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552Q16—22no—
553Q16—41no—
554SD16—22no—
555SD16—22no—
556SD16—22no—
557SD16—22no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561SD16—41no—
562D8—22no—
563D8—22no—
564D8—22no—
565D8—22no—
566D8—41no—
567D8#4114yescomplemented
568M16—22no—
569M16—41no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
580C2×C8C2411yescharacteristic
581C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
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⋊C4—21no—
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
671C22⋊C4C2×D411yescharacteristic
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—21no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23C22×D411yescharacteristic
704C23C22×D411yescharacteristic
705C23C22×D411yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—41no—
713Q8—42no—
714Q8—81no—
715Q8—81no—
716Q8—81no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4C2×#4112yes—
743D4C2×#4112yes—
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—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
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×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C22×D411yescharacteristic
787C2×C4C22×D411yescharacteristic
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C2511yescharacteristic
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—21no—
798C8—21no—
799C8—21no—
800C8C2×#4112yes—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—162no—
826C22—162no—
827C22—162no—
828C22C23×D411yescharacteristic
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4C22×#4111yescharacteristic
852C4#58511yescharacteristic
853C2—41no—
854C2—41no—
855C2—41no—
856C2—42no—
857C2—42no—
858C2—81no—
859C2—81no—
860C2—81no—
861C2D4×#4111yescharacteristic
862C2#358411yescharacteristic
863C2#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. #3521C2semidirect
2. #3514C2semidirect
3. #3401C2semidirect
4. #3384C2semidirect
5. #3370C2semidirect
6. #3367C2semidirect
7. #3349C2semidirect
8. #3347C2semidirect
9. #3340C2semidirect
10. #3319C2semidirect
11. #3311C2semidirect
12. #3311C2semidirect
13. #3310C2semidirect
14. #3303C2semidirect
15. #3297C2semidirect
16. #3280C2semidirect
17. #3267C2semidirect
18. #3264C2semidirect
19. #3180C2semidirect
20. #3178C2semidirect
21. #3173C2semidirect
22. #3124C2semidirect
23. #3123C2semidirect
24. #3118C2semidirect
25. #3118C2semidirect
26. #3106C2semidirect
27. #3102C2semidirect
28. #2968C2semidirect
29. #2948C2semidirect
30. #2946C2semidirect
31. #2943C2semidirect
35. #559C22semidirect
37. #556C22semidirect
38. #556C22semidirect
40. #555C22semidirect
41. #554C22semidirect
43. #553C22semidirect
50. D4×Q8C22semidirect
52. #547C22semidirect
56. #546C22semidirect
57. #546C22semidirect
60. #542C22semidirect
61. #542C22semidirect
62. #541C22semidirect
67. #532C22semidirect
71. #529C22semidirect
74. #520C22semidirect
76. #518C22semidirect
77. #518C22semidirect
78. C4×#41C22semidirect
79. C4×#41C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #498C22semidirect
83. #497C22semidirect
85. #495C22semidirect
86. #490C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #489C22semidirect
90. #488C22semidirect
91. #487C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #484C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #480C22semidirect
104. #479C22semidirect
105. #478C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #477C22semidirect
109. #477C22semidirect
110. #476C22semidirect
111. #476C22semidirect
112. #476C22semidirect
113. #474C22semidirect
114. #474C22semidirect
115. #474C22semidirect
116. #470C22semidirect
117. #470C22semidirect
120. #467C22semidirect
121. #466C22semidirect
122. #466C22semidirect
124. #465C22semidirect
125. #465C22semidirect
126. #465C22semidirect
127. #465C22semidirect
128. #464C22semidirect
129. #464C22semidirect
132. #463C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #463C22semidirect
136. #461C22semidirect
137. #461C22semidirect
138. #460C22semidirect
140. #452C22semidirect
141. #452C22semidirect
144. #450C22semidirect
145. #450C22semidirect
148. #449C22semidirect
149. #449C22semidirect
152. #446C22semidirect
153. #446C22semidirect
157. #442C22semidirect
158. #442C22semidirect
159. #442C22semidirect
160. #442C22semidirect
161. #441C22semidirect
162. #441C22semidirect
163. #440C22semidirect
164. #440C22semidirect
165. #440C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. #440C22semidirect
170. C4×Q16C22semidirect
171. C4×SD16C22semidirect
172. C4×SD16C22semidirect
173. C4×SD16C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
179. C4×D8C22semidirect
180. C4×D8C22semidirect
181. C4×D8C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. C8×D4C22semidirect
187. C8×D4C22semidirect
188. #433C22semidirect
189. #433C22semidirect
190. #431C22semidirect
191. #428C22semidirect
192. #427C22semidirect
193. #427C22semidirect
195. #418C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. #416C22semidirect
199. C2×#102C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C2×#97C22semidirect
567. D8#41semidirect

Maximal subgroups

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

subgroupindex
#35212
#35142
#34012
#33842
#33702
#33672
#33492
#33472
#33402
#33192
#33112
#33102
#33032
#32972
#32802
#32672
#32642
#31802
#31782
#31732
#31242
#31232
#31182
#31062
#31022
#29682
#29482
#29462
#29432