Finite Group Databasebeta

← #61455

Subgroups — #61455

Order 256.

923 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3482C211yesmaximal, characteristic, complemented
2#3475C211yesmaximal, characteristic, complemented
3#3402C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3376C211yesmaximal, characteristic, complemented
7#3348C211yesmaximal, characteristic, complemented
8#3343C211yesmaximal, characteristic, complemented
9#3336C211yesmaximal, characteristic, complemented
10#3321C211yesmaximal, characteristic, complemented
11#3315C211yesmaximal, characteristic, complemented
12#3312C211yesmaximal, characteristic, complemented
13#3306C211yesmaximal, characteristic, complemented
14#3300C211yesmaximal, characteristic, complemented
15#3296C211yesmaximal, characteristic, complemented
16#3282C211yesmaximal, characteristic, complemented
17#3269C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3183C211yesmaximal, characteristic, complemented
20#3181C211yesmaximal, characteristic, complemented
21#3181C211yesmaximal, characteristic, complemented
22#3117C211yesmaximal, characteristic, complemented
23#3116C211yesmaximal, characteristic, complemented
24#3114C211yesmaximal, characteristic, complemented
25#3113C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#2970C211yesmaximal, characteristic, complemented
29C4×#137C211yesmaximal, characteristic, complemented
30#2943C211yesmaximal, characteristic, complemented
31C2×#440C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#135C2211yescharacteristic
34C22×SD16C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556—21no—
37#556C2211yescharacteristic
38#556C2211yescharacteristic, complemented
39#555C2211yescharacteristic
40#554C2211yescharacteristic
41#553—21no—
42#552—21no—
43#552—21no—
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51D4×Q8C2211yescharacteristic
52#548C2211yescharacteristic
53#548C2211yescharacteristic, complemented
54#547—21no—
55#547C2211yescharacteristic
56#547C2211yescharacteristic
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#533—21no—
60#533C2211yescharacteristic
61#533C2211yescharacteristic, complemented
62#529—21no—
63#529—21no—
64#529—21no—
65#529—21no—
66#529C2211yescharacteristic
67#529C2211yescharacteristic
68#529C2211yescharacteristic
69#529C2211yescharacteristic, complemented
70#525—21no—
71C4×#41—21no—
72C4×#41C2211yescharacteristic
73C4×#41C2211yescharacteristic
74C4×#41C2211yescharacteristic
75C4×#41C2211yescharacteristic, complemented
76C2×C4×Q8C2211yescharacteristic
77C2×C4×Q8C2211yescharacteristic, complemented
78C2×C4×D4C2211yescharacteristic
79C2×#117—21no—
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#497C2211yescharacteristic
84#497C2211yescharacteristic, complemented
85#495C2211yescharacteristic
86#491C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#489C2211yescharacteristic
89#489C2211yescharacteristic, complemented
90#488C2211yescharacteristic
91#488C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#483C2211yescharacteristic
98#483C2211yescharacteristic
99#483C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic
103#480C2211yescharacteristic
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic, complemented
112#477C2211yescharacteristic, complemented
113#476C2211yescharacteristic
114#475C2211yescharacteristic, complemented
115#475C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#469C2211yescharacteristic
118#468C2211yescharacteristic
119#468C2211yescharacteristic, complemented
120#467C2211yescharacteristic
121#467C2211yescharacteristic
122#467C2211yescharacteristic, complemented
123#467C2211yescharacteristic, complemented
124#465C2211yescharacteristic
125#465C2211yescharacteristic
126#465C2211yescharacteristic
127#465C2211yescharacteristic
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#462C2211yescharacteristic, complemented
139#461C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic
143#452C2211yescharacteristic, complemented
144#451C2211yescharacteristic
145#451C2211yescharacteristic
146#451C2211yescharacteristic, complemented
147#450C2211yescharacteristic
148#449C2211yescharacteristic
149#449C2211yescharacteristic
150#448C2211yescharacteristic
151#447C2211yescharacteristic
152#446C2211yescharacteristic, complemented
153#446C2211yescharacteristic, complemented
154#442C2211yescharacteristic
155#442C2211yescharacteristic
156#442C2211yescharacteristic
157#441C2211yescharacteristic, complemented
158#441C2211yescharacteristic, complemented
159#441C2211yescharacteristic, complemented
160#441C2211yescharacteristic, complemented
161#441C2211yescharacteristic, complemented
162#441C2211yescharacteristic, complemented
163#441C2211yescharacteristic, complemented
164#440C2211yescharacteristic
165#440C2211yescharacteristic
166#440C2211yescharacteristic
167#440C2211yescharacteristic
168#440C2211yescharacteristic
169#440C2211yescharacteristic
170#440C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×Q16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic
181C4×SD16C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic
187C8×D4C2211yescharacteristic
188#432C2211yescharacteristic
189#432C2211yescharacteristic, complemented
190#432C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193C2×#107C2211yescharacteristic
194#419C2211yescharacteristic, complemented
195#417C2211yescharacteristic
196#416C2211yescharacteristic
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic
199C2×#102C2211yescharacteristic
200C4×M16C2211yescharacteristic, complemented
201C2×#97C2211yescharacteristic
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41D411yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4—21no—
212#137—24no—
213#135—24no—
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×Q16C2311yescharacteristic
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×SD16—24no—
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×M16C2311yescharacteristic
232C2×M16C2311yescharacteristic
233C22×C8C2311yescharacteristic
234C22×C8C2311yescharacteristic
235C22×C8C2311yescharacteristic
236C22×C8C2311yescharacteristic
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241C4⋊Q8C2311yescharacteristic
242C4⋊Q8C2311yescharacteristic
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124C2311yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
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—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121C2311yescharacteristic
316#121C2311yescharacteristic
317#121C2311yescharacteristic
318#121C2311yescharacteristic
319#120—21no—
320#120—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8D411yescharacteristic
329C4×Q8C2311yescharacteristic
330C4×Q8C2311yescharacteristic
331C4×Q8C2311yescharacteristic
332C4×Q8C2311yescharacteristic
333C4×Q8C2311yescharacteristic
334C4×Q8C2311yescharacteristic
335C4×Q8C2311yescharacteristic
336C4×Q8C2311yescharacteristic
337C4×Q8C2311yescharacteristic
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
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×D4D411yescharacteristic
358C4×D4D411yescharacteristic
359C4×D4D411yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371#117—21no—
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#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117D411yescharacteristic
388#117D411yescharacteristic
389#117D411yescharacteristic
390#117C2311yescharacteristic
391#117C2311yescharacteristic
392#117C2311yescharacteristic
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×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C2311yescharacteristic
409C2×C42C2311yescharacteristic
410C2×C42C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
418#107C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476#97C2311yescharacteristic
477#97C2311yescharacteristic
478#97C2311yescharacteristic
479C4×C8C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C24—21no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—42no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—44no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8C2×D411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
503C2×Q8C2411yescharacteristic
504C2×D4—22no—
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—41no—
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2411yescharacteristic
518C2×D4C2411yescharacteristic
519C2×D4C2411yescharacteristic
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—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—44no—
537C22×C4C2×D411yescharacteristic
538C22×C4C2×D411yescharacteristic
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2×D411yescharacteristic
543C22×C4C2411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546Q16—22no—
547Q16—22no—
548Q16—22no—
549Q16—41no—
550Q16—41no—
551Q16—41no—
552SD16—22no—
553SD16—22no—
554SD16—22no—
555SD16—22no—
556SD16—22no—
557SD16—41no—
558SD16—41no—
559SD16#4114yescomplemented
560D8—22no—
561D8—41no—
562M16—22no—
563M16—41no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
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⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊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—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42C2×D411yescharacteristic
680C42C2×D411yescharacteristic
681C42C2×D411yescharacteristic
682C42C2×D411yescharacteristic
683C42C2×D411yescharacteristic
684C42C2×D411yescharacteristic
685C42C2411yescharacteristic
686C42C2411yescharacteristic
687C42C2411yescharacteristic
688C42C2411yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—42no—
693C23—42no—
694C23—81no—
695C23C22×D411yescharacteristic
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—42no—
709Q8—42no—
710Q8—42no—
711Q8—81no—
712Q8C2×#4112yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—81no—
728D4—81no—
729D4C2×#4112yes—
730C2×C4—22no—
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—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—81no—
770C2×C4—81no—
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×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C2511yescharacteristic
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C8C2×#4112yes—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—22no—
798C22—21no—
799C22—21no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—84no—
809C22#57512yes—
810C22C23×D411yescharacteristic
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—22no—
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—
835C4C22×#4111yescharacteristic
836C4#58511yescharacteristic
837C2—22no—
838C2—41no—
839C2—41no—
840C2—42no—
841C2—81no—
842C2—81no—
843C2D4×#4111yescharacteristic
844C2C2×#57511yescharacteristic
845C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3482C2semidirect
2. #3475C2semidirect
3. #3402C2semidirect
4. #3388C2semidirect
5. #3377C2semidirect
6. #3376C2semidirect
7. #3348C2semidirect
8. #3343C2semidirect
9. #3336C2semidirect
10. #3321C2semidirect
11. #3315C2semidirect
12. #3312C2semidirect
13. #3306C2semidirect
14. #3300C2semidirect
15. #3296C2semidirect
16. #3282C2semidirect
17. #3269C2semidirect
18. #3266C2semidirect
19. #3183C2semidirect
20. #3181C2semidirect
21. #3181C2semidirect
22. #3117C2semidirect
23. #3116C2semidirect
24. #3114C2semidirect
25. #3113C2semidirect
26. #3111C2semidirect
27. #3111C2semidirect
28. #2970C2semidirect
29. C4×#137C2semidirect
30. #2943C2semidirect
31. C2×#440C2semidirect
35. #557C22semidirect
38. #556C22semidirect
48. #552C22semidirect
53. #548C22semidirect
61. #533C22semidirect
69. #529C22semidirect
75. C4×#41C22semidirect
77. C2×C4×Q8C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #499C22semidirect
84. #497C22semidirect
86. #491C22semidirect
87. #491C22semidirect
89. #489C22semidirect
91. #488C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #484C22semidirect
101. #482C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
107. #479C22semidirect
111. #478C22semidirect
112. #477C22semidirect
114. #475C22semidirect
115. #475C22semidirect
116. #470C22semidirect
119. #468C22semidirect
122. #467C22semidirect
123. #467C22semidirect
131. #464C22semidirect
136. #462C22semidirect
137. #462C22semidirect
138. #462C22semidirect
143. #452C22semidirect
146. #451C22semidirect
152. #446C22semidirect
153. #446C22semidirect
157. #441C22semidirect
158. #441C22semidirect
159. #441C22semidirect
160. #441C22semidirect
161. #441C22semidirect
162. #441C22semidirect
163. #441C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. #440C22semidirect
178. C4×Q16C22semidirect
179. C4×Q16C22semidirect
184. #435C22semidirect
185. #435C22semidirect
189. #432C22semidirect
190. #432C22semidirect
191. #428C22semidirect
192. #427C22semidirect
194. #419C22semidirect
197. #416C22semidirect
200. C4×M16C22semidirect
202. C2×#97C22semidirect
559. SD16#41semidirect

Maximal subgroups

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

subgroupindex
#34822
#34752
#34022
#33882
#33772
#33762
#33482
#33432
#33362
#33212
#33152
#33122
#33062
#33002
#32962
#32822
#32692
#32662
#31832
#31812
#31172
#31162
#31142
#31132
#31112
#29702
C4×#1372
#29432
C2×#4402