Finite Group Databasebeta

← #61790

Subgroups — #61790

Order 256.

853 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic, complemented
2#3512C211yesmaximal, characteristic, complemented
3#3355C211yesmaximal, characteristic, complemented
4#3352C211yesmaximal, characteristic, complemented
5#3351C211yesmaximal, characteristic, complemented
6#3351C211yesmaximal, characteristic, complemented
7#3339C211yesmaximal, characteristic, complemented
8#3337C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3336C211yesmaximal, characteristic, complemented
11#3327C211yesmaximal, characteristic, complemented
12#3326C211yesmaximal, characteristic, complemented
13#3323C211yesmaximal, characteristic, complemented
14#3322C211yesmaximal, characteristic, complemented
15#3301C211yesmaximal, characteristic, complemented
16#3300C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3232C211yesmaximal, characteristic, complemented
20#3232C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3102C211yesmaximal, characteristic, complemented
26#3102C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3097C211yesmaximal, characteristic, complemented
30#3096C211yesmaximal, characteristic, complemented
31#2979C211yesmaximal, characteristic, complemented
32#563—21no—
33#560—21no—
34#555—21no—
35#553—21no—
36#553—21no—
37#553—21no—
38#553—21no—
39#553C2211yescharacteristic
40#553C2211yescharacteristic
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic, complemented
44#553C2211yescharacteristic, complemented
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic, complemented
50#552C2211yescharacteristic, complemented
51#551—21no—
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#541—21no—
57#540—21no—
58#540—21no—
59#540—21no—
60#538—21no—
61#538—21no—
62#537C2211yescharacteristic
63#537C2211yescharacteristic
64#537C2211yescharacteristic
65#537C2211yescharacteristic, complemented
66#536C2211yescharacteristic
67#535C2211yescharacteristic
68#532C2211yescharacteristic
69#529—21no—
70#529—21no—
71#529C2211yescharacteristic
72#529C2211yescharacteristic
73C2×#125C2211yescharacteristic, complemented
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76C4×#41C2211yescharacteristic, complemented
77#499C2211yescharacteristic, complemented
78#499C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#488C2211yescharacteristic
82#488C2211yescharacteristic
83#488C2211yescharacteristic
84#488C2211yescharacteristic
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic
99#483C2211yescharacteristic, complemented
100#483C2211yescharacteristic, complemented
101#483C2211yescharacteristic, complemented
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic
110#482C2211yescharacteristic, complemented
111#481C2211yescharacteristic
112#481C2211yescharacteristic
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#480C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, complemented
125#479C2211yescharacteristic, complemented
126#479C2211yescharacteristic, complemented
127#478C2211yescharacteristic
128#478C2211yescharacteristic
129#478C2211yescharacteristic
130#478C2211yescharacteristic
131#478C2211yescharacteristic, complemented
132#478C2211yescharacteristic, complemented
133#470C2211yescharacteristic
134#470C2211yescharacteristic, complemented
135#469C2211yescharacteristic
136#469C2211yescharacteristic
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic
142#467C2211yescharacteristic, complemented
143#466C2211yescharacteristic
144#466C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic
165C4×Q16C2211yescharacteristic, complemented
166C4×Q16C2211yescharacteristic, complemented
167C4×SD16C2211yescharacteristic
168C4×SD16C2211yescharacteristic
169C4×SD16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×D8C2211yescharacteristic
172C4×D8C2211yescharacteristic
173#436C2211yescharacteristic
174#436C2211yescharacteristic
175#436C2211yescharacteristic, complemented
176#436C2211yescharacteristic, complemented
177C8×D4C2211yescharacteristic
178C8×D4C2211yescharacteristic
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#431C2211yescharacteristic, complemented
182#431C2211yescharacteristic, complemented
183#428C2211yescharacteristic
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202#408C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8D411yescharacteristic
228#127—21no—
229#127D411yescharacteristic
230#126—21no—
231#126—21no—
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#124—21no—
259#124—21no—
260#124—21no—
261#124—21no—
262#124D411yescharacteristic
263#124D411yescharacteristic
264#124C2311yescharacteristic
265#124C2311yescharacteristic
266#123—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8C2311yescharacteristic
291C22⋊Q8C2311yescharacteristic
292C22⋊Q8C2311yescharacteristic
293C22⋊Q8C2311yescharacteristic
294C22⋊Q8C2311yescharacteristic
295C22⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300#121—21no—
301#121—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
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#121D411yescharacteristic
323#121D411yescharacteristic
324#121D411yescharacteristic
325#121D411yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340C4×Q8—21no—
341C4×Q8—21no—
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×D4—21no—
363C4×D4—21no—
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
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#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
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8C2×D411yescharacteristic
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
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—41no—
512C2×D4—41no—
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2411yescharacteristic
524C2×D4C2411yescharacteristic
525C2×D4C2411yescharacteristic
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×C4C2×D411yescharacteristic
543C22×C4C2×D411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549Q16—41no—
550Q16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555D8—41no—
556D8—41no—
557M16—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23C22×D411yescharacteristic
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688C23C22×D411yescharacteristic
689C23C22×D411yescharacteristic
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—42no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
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—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
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×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—162no—
813C22C23×D411yescharacteristic
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4#58511yescharacteristic
837C4#58511yescharacteristic
838C2—41no—
839C2—41no—
840C2—41no—
841C2—41no—
842C2—41no—
843C2—81no—
844C2—81no—
845C2—81no—
846C2#348511yescharacteristic
847C2#358411yescharacteristic
848C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3551C2semidirect
2. #3512C2semidirect
3. #3355C2semidirect
4. #3352C2semidirect
5. #3351C2semidirect
6. #3351C2semidirect
7. #3339C2semidirect
8. #3337C2semidirect
9. #3337C2semidirect
10. #3336C2semidirect
11. #3327C2semidirect
12. #3326C2semidirect
13. #3323C2semidirect
14. #3322C2semidirect
15. #3301C2semidirect
16. #3300C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3232C2semidirect
20. #3232C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3201C2semidirect
24. #3198C2semidirect
25. #3102C2semidirect
26. #3102C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3097C2semidirect
30. #3096C2semidirect
31. #2979C2semidirect
43. #553C22semidirect
44. #553C22semidirect
49. #552C22semidirect
50. #552C22semidirect
65. #537C22semidirect
73. C2×#125C22semidirect
75. #520C22semidirect
76. C4×#41C22semidirect
77. #499C22semidirect
78. #499C22semidirect
79. #499C22semidirect
80. #499C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #484C22semidirect
97. #484C22semidirect
99. #483C22semidirect
100. #483C22semidirect
101. #483C22semidirect
102. #483C22semidirect
110. #482C22semidirect
115. #481C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #479C22semidirect
126. #479C22semidirect
131. #478C22semidirect
132. #478C22semidirect
134. #470C22semidirect
140. #468C22semidirect
142. #467C22semidirect
148. #465C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
163. #448C22semidirect
165. C4×Q16C22semidirect
166. C4×Q16C22semidirect
169. C4×SD16C22semidirect
170. C4×SD16C22semidirect
175. #436C22semidirect
176. #436C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #431C22semidirect
182. #431C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #419C22semidirect
197. C2×#103C22semidirect
201. #408C22semidirect
202. #408C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#35122
#33552
#33522
#33512
#33392
#33372
#33362
#33272
#33262
#33232
#33222
#33012
#33002
#32972
#32962
#32322
#32042
#32032
#32012
#31982
#31022
#30992
#30982
#30972
#30962
#29792