Finite Group Databasebeta

← #62613

Subgroups — #62613

Order 256.

863 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#3562C211yesmaximal, characteristic, complemented
2#3559C211yesmaximal, characteristic, complemented
3#3376C211yesmaximal, characteristic, complemented
4#3370C211yesmaximal, characteristic, complemented
5#3361C211yesmaximal, characteristic, complemented
6#3360C211yesmaximal, characteristic, complemented
7#3332C211yesmaximal, characteristic, complemented
8#3330C211yesmaximal, characteristic, complemented
9#3326C211yesmaximal, characteristic, complemented
10#3326C211yesmaximal, characteristic, complemented
11#3322C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3309C211yesmaximal, characteristic, complemented
14#3308C211yesmaximal, characteristic, complemented
15#3307C211yesmaximal, characteristic, complemented
16#3306C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3297C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3232C211yesmaximal, characteristic, complemented
22#3221C211yesmaximal, characteristic, complemented
23#3220C211yesmaximal, characteristic, complemented
24#3207C211yesmaximal, characteristic, complemented
25#3176C211yesmaximal, characteristic, complemented
26#3174C211yesmaximal, characteristic, complemented
27#3171C211yesmaximal, characteristic, complemented
28#3142C211yesmaximal, characteristic, complemented
29#3137C211yesmaximal, characteristic, complemented
30#3136C211yesmaximal, characteristic, complemented
31#2969C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#562—21no—
35#560—21no—
36#559C2211yescharacteristic
37#556C2211yescharacteristic
38#554C2211yescharacteristic, complemented
39#554C2211yescharacteristic, complemented
40#553—21no—
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#551—21no—
46#550C2211yescharacteristic
47#548C2211yescharacteristic
48#548C2211yescharacteristic
49#547—21no—
50#547—21no—
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic, complemented
58#541C2211yescharacteristic
59#540—21no—
60#540C2211yescharacteristic
61#540C2211yescharacteristic
62#540C2211yescharacteristic, complemented
63#539—21no—
64#539—21no—
65#539—21no—
66#539—21no—
67#538—21no—
68#538—21no—
69#537—21no—
70#536C2211yescharacteristic
71#535C2211yescharacteristic
72#532C2211yescharacteristic
73#532C2211yescharacteristic, complemented
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76C2×#125C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#499C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#496C2211yescharacteristic
81#493C2211yescharacteristic
82#492C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#491C2211yescharacteristic, complemented
86#490C2211yescharacteristic
87#490C2211yescharacteristic
88#490C2211yescharacteristic
89#490C2211yescharacteristic, complemented
90#489C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#488C2211yescharacteristic, complemented
100#488C2211yescharacteristic, complemented
101#487C2211yescharacteristic, complemented
102#487C2211yescharacteristic, complemented
103#486C2211yescharacteristic
104#486C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#484C2211yescharacteristic
108#484C2211yescharacteristic, complemented
109#483C2211yescharacteristic
110#483C2211yescharacteristic, complemented
111#482C2211yescharacteristic
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic
114#481C2211yescharacteristic, complemented
115#480C2211yescharacteristic
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#479C2211yescharacteristic, complemented
120#479C2211yescharacteristic, complemented
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#469C2211yescharacteristic
130#469C2211yescharacteristic
131#469C2211yescharacteristic
132#469C2211yescharacteristic, complemented
133#468C2211yescharacteristic
134#468C2211yescharacteristic
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#466C2211yescharacteristic
138#466C2211yescharacteristic, complemented
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#463C2211yescharacteristic
142#463C2211yescharacteristic
143#463C2211yescharacteristic
144#463C2211yescharacteristic
145#463C2211yescharacteristic
146#463C2211yescharacteristic
147#463C2211yescharacteristic, complemented
148#463C2211yescharacteristic, complemented
149#461C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#459C2211yescharacteristic
152#459C2211yescharacteristic
153#449C2211yescharacteristic
154#449C2211yescharacteristic
155#449C2211yescharacteristic
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#448C2211yescharacteristic, complemented
162#448C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170#440C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic, complemented
174C4×SD16C2211yescharacteristic, complemented
175C4×D8C2211yescharacteristic
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#436C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#419C2211yescharacteristic, complemented
189#418C2211yescharacteristic
190#417C2211yescharacteristic
191#417C2211yescharacteristic
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic
197#416C2211yescharacteristic
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237#127—21no—
238#127C2311yescharacteristic
239#127C2311yescharacteristic
240#127C2311yescharacteristic
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126D411yescharacteristic
251#126D411yescharacteristic
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125D411yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124D411yescharacteristic
271#124C2311yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
275#124C2311yescharacteristic
276#123—21no—
277#123—21no—
278#123—21no—
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#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⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8D411yescharacteristic
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#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121D411yescharacteristic
345#121C2311yescharacteristic
346#121C2311yescharacteristic
347#121C2311yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#120—21no—
355#120—21no—
356#120—21no—
357#120—21no—
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
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×D4—21no—
373C4×D4—21no—
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386#117—21no—
387#117—21no—
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#102C2311yescharacteristic
441#102C2311yescharacteristic
442#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
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
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×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—82no—
488#41—82no—
489#41—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8C2×D411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
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—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2411yescharacteristic
526C2×D4C2411yescharacteristic
527C2×D4C2411yescharacteristic
528C2×D4C2411yescharacteristic
529C2×D4C2411yescharacteristic
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×C4—21no—
548C22×C4C2×D411yescharacteristic
549C22×C4C2×D411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559D8—41no—
560D8—41no—
561D8—41no—
562D8—41no—
563D8—41no—
564D8—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568M16—41no—
569C2×C8—41no—
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⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
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⋊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—
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692C23C22×D411yescharacteristic
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—41no—
700Q8—81no—
701Q8—81no—
702Q8—81no—
703Q8—81no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—42no—
718D4—42no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
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—41no—
755C2×C4—41no—
756C2×C4—42no—
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×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
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×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C2511yescharacteristic
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—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—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—162no—
819C22C23×D411yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4#58511yescharacteristic
843C4#58511yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—81no—
848C2—81no—
849C2—81no—
850C2—81no—
851C2—81no—
852C2#350011yescharacteristic
853C2#358411yescharacteristic
854C2#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. #3562C2semidirect
2. #3559C2semidirect
3. #3376C2semidirect
4. #3370C2semidirect
5. #3361C2semidirect
6. #3360C2semidirect
7. #3332C2semidirect
8. #3330C2semidirect
9. #3326C2semidirect
10. #3326C2semidirect
11. #3322C2semidirect
12. #3322C2semidirect
13. #3309C2semidirect
14. #3308C2semidirect
15. #3307C2semidirect
16. #3306C2semidirect
17. #3301C2semidirect
18. #3297C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3232C2semidirect
22. #3221C2semidirect
23. #3220C2semidirect
24. #3207C2semidirect
25. #3176C2semidirect
26. #3174C2semidirect
27. #3171C2semidirect
28. #3142C2semidirect
29. #3137C2semidirect
30. #3136C2semidirect
31. #2969C2semidirect
38. #554C22semidirect
39. #554C22semidirect
44. #553C22semidirect
53. #547C22semidirect
57. #544C22semidirect
62. #540C22semidirect
73. #532C22semidirect
76. C2×#125C22semidirect
77. #501C22semidirect
78. #499C22semidirect
79. #499C22semidirect
82. #492C22semidirect
83. #491C22semidirect
84. #491C22semidirect
85. #491C22semidirect
89. #490C22semidirect
99. #488C22semidirect
100. #488C22semidirect
101. #487C22semidirect
102. #487C22semidirect
108. #484C22semidirect
110. #483C22semidirect
112. #482C22semidirect
114. #481C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #479C22semidirect
120. #479C22semidirect
124. #478C22semidirect
125. #477C22semidirect
127. #475C22semidirect
128. #474C22semidirect
132. #469C22semidirect
135. #468C22semidirect
136. #468C22semidirect
138. #466C22semidirect
147. #463C22semidirect
148. #463C22semidirect
149. #461C22semidirect
150. #461C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #448C22semidirect
162. #448C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
168. #442C22semidirect
169. #440C22semidirect
170. #440C22semidirect
171. C4×SD16C22semidirect
172. C4×SD16C22semidirect
173. C4×SD16C22semidirect
174. C4×SD16C22semidirect
178. C4×D8C22semidirect
181. #436C22semidirect
183. #435C22semidirect
186. #433C22semidirect
187. #431C22semidirect
188. #419C22semidirect
194. #417C22semidirect
195. #417C22semidirect
198. C2×#103C22semidirect
201. #405C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35592
#33762
#33702
#33612
#33602
#33322
#33302
#33262
#33222
#33092
#33082
#33072
#33062
#33012
#32972
#32422
#32412
#32322
#32212
#32202
#32072
#31762
#31742
#31712
#31422
#31372
#31362
#29692