Finite Group Databasebeta

← #62175

Subgroups — #62175

Order 256.

858 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3381C211yesmaximal, characteristic, complemented
5#3371C211yesmaximal, characteristic, complemented
6#3361C211yesmaximal, characteristic, complemented
7#3354C211yesmaximal, characteristic, complemented
8#3351C211yesmaximal, characteristic, complemented
9#3351C211yesmaximal, characteristic, complemented
10#3349C211yesmaximal, characteristic, complemented
11#3343C211yesmaximal, characteristic, complemented
12#3339C211yesmaximal, characteristic, complemented
13#3324C211yesmaximal, characteristic, complemented
14#3323C211yesmaximal, characteristic, complemented
15#3322C211yesmaximal, characteristic, complemented
16#3319C211yesmaximal, characteristic, complemented
17#3318C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3256C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3241C211yesmaximal, characteristic, complemented
24#3233C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3105C211yesmaximal, characteristic, complemented
28#3083C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3077C211yesmaximal, characteristic, complemented
31#2993C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#559C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556—21no—
37#556C2211yescharacteristic
38#555C2211yescharacteristic, complemented
39#554C2211yescharacteristic
40#554C2211yescharacteristic, complemented
41#553—21no—
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51#547C2211yescharacteristic
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#542C2211yescharacteristic, complemented
63#541—21no—
64#540C2211yescharacteristic
65#539—21no—
66#539—21no—
67#538—21no—
68#533C2211yescharacteristic, complemented
69#529C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic, complemented
72#525—21no—
73C2×#123—21no—
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C2×C4×D4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#489C2211yescharacteristic, complemented
85#488C2211yescharacteristic, complemented
86#488C2211yescharacteristic, complemented
87#488C2211yescharacteristic, complemented
88#486C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic, complemented
94#483C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#482C2211yescharacteristic
97#482C2211yescharacteristic
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic
103#481C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic, complemented
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#478C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#477C2211yescharacteristic, complemented
124#477C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic
127#476C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic
132#474C2211yescharacteristic
133#474C2211yescharacteristic
134#474C2211yescharacteristic, complemented
135#474C2211yescharacteristic, complemented
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic, complemented
138#469C2211yescharacteristic
139#469C2211yescharacteristic, complemented
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic, complemented
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#466C2211yescharacteristic
147#466C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#464C2211yescharacteristic, complemented
152#463C2211yescharacteristic
153#463C2211yescharacteristic, complemented
154#463C2211yescharacteristic, complemented
155#463C2211yescharacteristic, complemented
156#463C2211yescharacteristic, complemented
157#460C2211yescharacteristic
158#459C2211yescharacteristic
159#452C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#441C2211yescharacteristic, complemented
170#440C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#436C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#428C2211yescharacteristic, complemented
190#428C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193C2×#107C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#418C2211yescharacteristic
199#418C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C22×D4—21no—
206C22×D4C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4—21no—
209C2×Q16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×D8C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231#127C2311yescharacteristic
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#126—21no—
245#126D411yescharacteristic
246#126D411yescharacteristic
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125D411yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124D411yescharacteristic
270#124C2311yescharacteristic
271#124C2311yescharacteristic
272#124C2311yescharacteristic
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—
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#123D411yescharacteristic
293#123D411yescharacteristic
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8D411yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
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#121—21no—
325#121D411yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
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
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480#41—22no—
481#41—41no—
482#41—82no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
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—41no—
506C2×D4—41no—
507C2×D4—82no—
508C2×D4C2×D411yescharacteristic
509C2×D4C2×D411yescharacteristic
510C2×D4C2×D411yescharacteristic
511C2×D4C2411yescharacteristic
512C2×D4C2411yescharacteristic
513C2×D4C2411yescharacteristic
514C2×D4C2411yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
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—82no—
532C22×C4C2×D411yescharacteristic
533C22×C4C2×D411yescharacteristic
534C22×C4C2411yescharacteristic
535C22×C4C2411yescharacteristic
536C22×C4C2411yescharacteristic
537Q16—41no—
538SD16—22no—
539SD16—41no—
540SD16—41no—
541SD16—41no—
542D8—22no—
543D8—41no—
544D8—41no—
545M16—41no—
546M16—41no—
547M16—41no—
548M16—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23C22×D411yescharacteristic
683C23C22×D411yescharacteristic
684C23C22×D411yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—41no—
690Q8—81no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694Q8—81no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D4—81no—
715D4—81no—
716D4—81no—
717D42−1+412yes—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
760C2×C4C22×D411yescharacteristic
761C2×C4C22×D411yescharacteristic
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C2511yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—84no—
796C22—162no—
797C22C23×D411yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4C2×2−1+411yescharacteristic
822C4#58511yescharacteristic
823C2—41no—
824C2—41no—
825C2—41no—
826C2—42no—
827C2—81no—
828C2—81no—
829C2—81no—
830C2#348911yescharacteristic
831C2#358411yescharacteristic
832C2#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. #3565C2semidirect
2. #3513C2semidirect
3. #3389C2semidirect
4. #3381C2semidirect
5. #3371C2semidirect
6. #3361C2semidirect
7. #3354C2semidirect
8. #3351C2semidirect
9. #3351C2semidirect
10. #3349C2semidirect
11. #3343C2semidirect
12. #3339C2semidirect
13. #3324C2semidirect
14. #3323C2semidirect
15. #3322C2semidirect
16. #3319C2semidirect
17. #3318C2semidirect
18. #3296C2semidirect
19. #3262C2semidirect
20. #3257C2semidirect
21. #3256C2semidirect
22. #3244C2semidirect
23. #3241C2semidirect
24. #3233C2semidirect
25. #3125C2semidirect
26. #3118C2semidirect
27. #3105C2semidirect
28. #3083C2semidirect
29. #3081C2semidirect
30. #3077C2semidirect
31. #2993C2semidirect
35. #557C22semidirect
38. #555C22semidirect
40. #554C22semidirect
44. #553C22semidirect
47. #552C22semidirect
48. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
61. #542C22semidirect
62. #542C22semidirect
68. #533C22semidirect
71. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #499C22semidirect
81. #499C22semidirect
82. #498C22semidirect
84. #489C22semidirect
85. #488C22semidirect
86. #488C22semidirect
87. #488C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #484C22semidirect
94. #483C22semidirect
95. #483C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
103. #481C22semidirect
104. #481C22semidirect
105. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
116. #478C22semidirect
117. #478C22semidirect
118. #478C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #478C22semidirect
122. #478C22semidirect
123. #477C22semidirect
124. #477C22semidirect
125. #477C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #475C22semidirect
134. #474C22semidirect
135. #474C22semidirect
136. #474C22semidirect
137. #470C22semidirect
139. #469C22semidirect
142. #468C22semidirect
143. #468C22semidirect
144. #468C22semidirect
145. #467C22semidirect
147. #466C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #464C22semidirect
153. #463C22semidirect
154. #463C22semidirect
155. #463C22semidirect
156. #463C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
169. #441C22semidirect
170. #440C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
177. C4×D8C22semidirect
178. C4×D8C22semidirect
180. #436C22semidirect
181. #436C22semidirect
183. #435C22semidirect
184. C8×D4C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #431C22semidirect
188. #428C22semidirect
189. #428C22semidirect
190. #428C22semidirect
191. #428C22semidirect
192. #427C22semidirect
193. C2×#107C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. #423C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35132
#33892
#33812
#33712
#33612
#33542
#33512
#33492
#33432
#33392
#33242
#33232
#33222
#33192
#33182
#32962
#32622
#32572
#32562
#32442
#32412
#32332
#31252
#31182
#31052
#30832
#30812
#30772
#29932