Finite Group Databasebeta

← #61925

Subgroups — #61925

Order 256.

832 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3555C211yesmaximal, characteristic, complemented
2#3510C211yesmaximal, characteristic, complemented
3#3402C211yesmaximal, characteristic, complemented
4#3402C211yesmaximal, characteristic, complemented
5#3401C211yesmaximal, characteristic, complemented
6#3401C211yesmaximal, characteristic, complemented
7#3400C211yesmaximal, characteristic, complemented
8#3398C211yesmaximal, characteristic, complemented
9#3394C211yesmaximal, characteristic, complemented
10#3393C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3376C211yesmaximal, characteristic, complemented
13#3375C211yesmaximal, characteristic, complemented
14#3371C211yesmaximal, characteristic, complemented
15#3370C211yesmaximal, characteristic, complemented
16#3369C211yesmaximal, characteristic, complemented
17#3365C211yesmaximal, characteristic, complemented
18#3364C211yesmaximal, characteristic, complemented
19#3225C211yesmaximal, characteristic, complemented
20#3224C211yesmaximal, characteristic
21#3223C211yesmaximal, characteristic, complemented
22#3222C211yesmaximal, characteristic, complemented
23#3215C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3123C211yesmaximal, characteristic, complemented
27#3121C211yesmaximal, characteristic, complemented
28#3118C211yesmaximal, characteristic, complemented
29#3111C211yesmaximal, characteristic, complemented
30#3107C211yesmaximal, characteristic, complemented
31#2985C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic
35#559C2211yescharacteristic
36#559C2211yescharacteristic
37#559C2211yescharacteristic
38Q82C2211yescharacteristic, complemented
39#557C2211yescharacteristic, complemented
40#557C2211yescharacteristic, complemented
41#557C2211yescharacteristic, complemented
42#556—21no—
43#556C2211yescharacteristic
44#556C2211yescharacteristic
45#556C2211yescharacteristic
46#556C2211yescharacteristic
47#556C2211yescharacteristic, complemented
48#556C2211yescharacteristic, complemented
49#556C2211yescharacteristic, complemented
50#554C2211yescharacteristic, complemented
51#552—21no—
52#551—21no—
53#551—21no—
54#551—21no—
55#551—21no—
56#544—21no—
57#542—21no—
58#542—21no—
59#542C2211yescharacteristic
60#542C2211yescharacteristic
61#541—21no—
62#541—21no—
63#541—21no—
64#541C2211yescharacteristic
65#541C2211yescharacteristic
66#536C2211yescharacteristic
67#535C2211yescharacteristic
68#533C2211yescharacteristic
69#533C2211yescharacteristic
70#529—21no—
71#529—21no—
72#529C2211yescharacteristic
73C2×#124C2211yescharacteristic
74#519C2211yescharacteristic
75#518C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#497C2211yescharacteristic
78#497C2211yescharacteristic
79#497C2211yescharacteristic
80#497C2211yescharacteristic, complemented
81#497C2211yescharacteristic, complemented
82#496C2211yescharacteristic
83#495C2211yescharacteristic
84#495C2211yescharacteristic
85#495C2211yescharacteristic
86#495C2211yescharacteristic, complemented
87#494C2211yescharacteristic, complemented
88#492C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic
93#489C2211yescharacteristic
94#489C2211yescharacteristic, complemented
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic, complemented
99#487C2211yescharacteristic, complemented
100#486C2211yescharacteristic
101#485C2211yescharacteristic
102#485C2211yescharacteristic
103#485C2211yescharacteristic
104#482C2211yescharacteristic
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic, complemented
111#477C2211yescharacteristic, complemented
112#476C2211yescharacteristic
113#475C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#474C2211yescharacteristic
116#474C2211yescharacteristic, complemented
117#464C2211yescharacteristic
118#464C2211yescharacteristic
119#464C2211yescharacteristic
120#464C2211yescharacteristic
121#464C2211yescharacteristic
122#464C2211yescharacteristic
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#463C2211yescharacteristic
137#463C2211yescharacteristic, complemented
138#463C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#462C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#462C2211yescharacteristic, complemented
145#461C2211yescharacteristic
146#461C2211yescharacteristic
147#461C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#460C2211yescharacteristic
150#460C2211yescharacteristic
151#460C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#451C2211yescharacteristic
157#451C2211yescharacteristic
158#451C2211yescharacteristic
159#450C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#446C2211yescharacteristic, complemented
168#446C2211yescharacteristic, complemented
169#446C2211yescharacteristic, complemented
170#446C2211yescharacteristic, complemented
171C8×Q8C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#441C2211yescharacteristic, complemented
178#441C2211yescharacteristic, complemented
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic
182#440C2211yescharacteristic, complemented
183#440C2211yescharacteristic, complemented
184#440C2211yescharacteristic, complemented
185C4×Q16C2211yescharacteristic, complemented
186C4×Q16C2211yescharacteristic, complemented
187C4×Q16C2211yescharacteristic, complemented
188C4×Q16C2211yescharacteristic, complemented
189C4×Q16C2211yescharacteristic, complemented
190C4×SD16C2211yescharacteristic
191C4×SD16C2211yescharacteristic
192C4×SD16C2211yescharacteristic
193C4×SD16C2211yescharacteristic, complemented
194C4×SD16C2211yescharacteristic, complemented
195C4×SD16C2211yescharacteristic, complemented
196C4×D8C2211yescharacteristic
197#433C2211yescharacteristic
198#433C2211yescharacteristic
199#433C2211yescharacteristic
200#433C2211yescharacteristic
201#432C2211yescharacteristic
202#431C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C22×Q8C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C2×Q16C2311yescharacteristic
207C2×Q16C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×D8C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D411yescharacteristic
236C4⋊Q8D411yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243C4⋊Q8C2311yescharacteristic
244C4⋊Q8C2311yescharacteristic
245#127C2311yescharacteristic
246#127C2311yescharacteristic
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#125—21no—
280#125D411yescharacteristic
281#125D411yescharacteristic
282#125C2311yescharacteristic
283#125C2311yescharacteristic
284#125C2311yescharacteristic
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124—21no—
290#124—21no—
291#124—21no—
292#124—21no—
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
297#124C2311yescharacteristic
298#124C2311yescharacteristic
299#124C2311yescharacteristic
300#124C2311yescharacteristic
301#124C2311yescharacteristic
302#124C2311yescharacteristic
303#124C2311yescharacteristic
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123—21no—
316#123—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8D411yescharacteristic
333C22⋊Q8D411yescharacteristic
334C22⋊Q8D411yescharacteristic
335C22⋊Q8D411yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339#121—21no—
340#121—21no—
341#121C2311yescharacteristic
342#120—21no—
343#120—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117C2311yescharacteristic
401#117C2311yescharacteristic
402#117C2311yescharacteristic
403C2×C4⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
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#103C2311yescharacteristic
447#103C2311yescharacteristic
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
466#97C2311yescharacteristic
467#97C2311yescharacteristic
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—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8C2×D411yescharacteristic
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2×D411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
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—41no—
505C2×D4—41no—
506C2×D4C2411yescharacteristic
507C2×D4C2411yescharacteristic
508C2×D4C2411yescharacteristic
509C2×D4C2411yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C2×D411yescharacteristic
522C22×C4C2×D411yescharacteristic
523C22×C4C2411yescharacteristic
524Q16—41no—
525Q16—41no—
526Q16—41no—
527Q16—41no—
528Q16—41no—
529Q16—41no—
530Q16—41no—
531Q16—41no—
532Q16—41no—
533SD16—41no—
534SD16—41no—
535SD16—41no—
536SD16—41no—
537SD16—41no—
538SD16—41no—
539SD16—41no—
540SD16—41no—
541SD16—41no—
542SD16—41no—
543SD16—41no—
544SD16—41no—
545D8—41no—
546D8—41no—
547D8—41no—
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
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⋊C4—21no—
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⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
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⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42C2×D411yescharacteristic
672C42C2×D411yescharacteristic
673C42C2411yescharacteristic
674C42C2411yescharacteristic
675C42C2411yescharacteristic
676C42C2411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—42no—
684C23—81no—
685C23—81no—
686C23C22×D411yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—42no—
704Q8—81no—
705Q8—81no—
706Q8—81no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—42no—
716D4—42no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
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—42no—
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×C4C22×D411yescharacteristic
750C2×C4C22×D411yescharacteristic
751C2×C4C22×D411yescharacteristic
752C2×C4C22×D411yescharacteristic
753C2×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
763C8—21no—
764C8—21no—
765C8—21no—
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—162no—
787C22C23×D411yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4#58511yescharacteristic
814C4#58511yescharacteristic
815C2—41no—
816C2—81no—
817C2—81no—
818C2—81no—
819C2—81no—
820C2#348711yescharacteristic
821C2#358411yescharacteristic
822C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3224C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3555C2semidirect
2. #3510C2semidirect
3. #3402C2semidirect
4. #3402C2semidirect
5. #3401C2semidirect
6. #3401C2semidirect
7. #3400C2semidirect
8. #3398C2semidirect
9. #3394C2semidirect
10. #3393C2semidirect
11. #3377C2semidirect
12. #3376C2semidirect
13. #3375C2semidirect
14. #3371C2semidirect
15. #3370C2semidirect
16. #3369C2semidirect
17. #3365C2semidirect
18. #3364C2semidirect
19. #3225C2semidirect
21. #3223C2semidirect
22. #3222C2semidirect
23. #3215C2semidirect
24. #3211C2semidirect
25. #3127C2semidirect
26. #3123C2semidirect
27. #3121C2semidirect
28. #3118C2semidirect
29. #3111C2semidirect
30. #3107C2semidirect
31. #2985C2semidirect
38. Q82C22semidirect
39. #557C22semidirect
40. #557C22semidirect
41. #557C22semidirect
47. #556C22semidirect
48. #556C22semidirect
49. #556C22semidirect
50. #554C22semidirect
80. #497C22semidirect
81. #497C22semidirect
86. #495C22semidirect
87. #494C22semidirect
89. #491C22semidirect
94. #489C22semidirect
98. #488C22semidirect
99. #487C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
110. #478C22semidirect
111. #477C22semidirect
113. #475C22semidirect
114. #475C22semidirect
116. #474C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
137. #463C22semidirect
138. #463C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
142. #462C22semidirect
143. #462C22semidirect
144. #462C22semidirect
147. #461C22semidirect
148. #461C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #446C22semidirect
168. #446C22semidirect
169. #446C22semidirect
170. #446C22semidirect
171. C8×Q8C22semidirect
172. C8×Q8C22semidirect
174. #442C22semidirect
175. #441C22semidirect
176. #441C22semidirect
177. #441C22semidirect
178. #441C22semidirect
182. #440C22semidirect
183. #440C22semidirect
184. #440C22semidirect
185. C4×Q16C22semidirect
186. C4×Q16C22semidirect
187. C4×Q16C22semidirect
188. C4×Q16C22semidirect
189. C4×Q16C22semidirect
193. C4×SD16C22semidirect
194. C4×SD16C22semidirect
195. C4×SD16C22semidirect

Maximal subgroups

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

subgroupindex
#35552
#35102
#34022
#34012
#34002
#33982
#33942
#33932
#33772
#33762
#33752
#33712
#33702
#33692
#33652
#33642
#32252
#32242
#32232
#32222
#32152
#32112
#31272
#31232
#31212
#31182
#31112
#31072
#29852