Finite Group Databasebeta

← #61747

Subgroups — #61747

Order 256.

867 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3492C211yesmaximal, characteristic, complemented
3#3353C211yesmaximal, characteristic, complemented
4#3352C211yesmaximal, characteristic, complemented
5#3349C211yesmaximal, characteristic, complemented
6#3346C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3343C211yesmaximal, characteristic, complemented
9#3339C211yesmaximal, characteristic, complemented
10#3338C211yesmaximal, characteristic, complemented
11#3330C211yesmaximal, characteristic, complemented
12#3327C211yesmaximal, characteristic, complemented
13#3320C211yesmaximal, characteristic, complemented
14#3316C211yesmaximal, characteristic, complemented
15#3315C211yesmaximal, characteristic, complemented
16#3308C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3299C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3242C211yesmaximal, characteristic, complemented
21#3203C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3196C211yesmaximal, characteristic, complemented
24#3191C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3098C211yesmaximal, characteristic, complemented
28#3097C211yesmaximal, characteristic, complemented
29#3092C211yesmaximal, characteristic, complemented
30C2×#484C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#556C2211yescharacteristic
35#554—21no—
36#554—21no—
37#554C2211yescharacteristic
38#554C2211yescharacteristic
39#554C2211yescharacteristic
40#553—21no—
41#553—21no—
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49D4×Q8C2211yescharacteristic
50#548C2211yescharacteristic
51#548C2211yescharacteristic
52#547—21no—
53#547C2211yescharacteristic
54#547C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#542—21no—
58#542C2211yescharacteristic
59#541C2211yescharacteristic
60#539—21no—
61#539—21no—
62#539—21no—
63#538—21no—
64#538—21no—
65#537C2211yescharacteristic
66#537C2211yescharacteristic
67#536C2211yescharacteristic
68#525—21no—
69#525—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic
73C2×C22⋊Q8C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C22×C4⋊C4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#491C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#487C2211yescharacteristic, complemented
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic
95#484C2211yescharacteristic
96#484C2211yescharacteristic
97#484C2211yescharacteristic
98#484C2211yescharacteristic
99#484C2211yescharacteristic
100#484C2211yescharacteristic
101#484C2211yescharacteristic
102#484C2211yescharacteristic
103#484C2211yescharacteristic
104#484C2211yescharacteristic, complemented
105#484C2211yescharacteristic, complemented
106#484C2211yescharacteristic, complemented
107#483C2211yescharacteristic
108#483C2211yescharacteristic
109#483C2211yescharacteristic, complemented
110#482C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic, complemented
113#482C2211yescharacteristic, complemented
114#481C2211yescharacteristic
115#481C2211yescharacteristic
116#481C2211yescharacteristic
117#480C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#477C2211yescharacteristic, complemented
129#477C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic
134#470C2211yescharacteristic
135#470C2211yescharacteristic, complemented
136#468C2211yescharacteristic
137#468C2211yescharacteristic
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic
142#467C2211yescharacteristic, complemented
143#467C2211yescharacteristic, complemented
144#466C2211yescharacteristic
145#466C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#462C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#451C2211yescharacteristic
159#451C2211yescharacteristic, complemented
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic, complemented
163#448C2211yescharacteristic
164#448C2211yescharacteristic, complemented
165#441C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic
174#436C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic
178#435C2211yescharacteristic
179C8×D4C2211yescharacteristic
180C8×D4C2211yescharacteristic
181#433C2211yescharacteristic
182#433C2211yescharacteristic
183#428C2211yescharacteristic
184#428C2211yescharacteristic
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188C2×#107C2211yescharacteristic
189C2×#107C2211yescharacteristic
190C2×#107C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#103C2211yescharacteristic
197C2×#103C2211yescharacteristic
198C2×#103C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C23×C4—21no—
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
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#126—21no—
246#126—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124C2311yescharacteristic
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123D411yescharacteristic
283#123D411yescharacteristic
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—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⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8D411yescharacteristic
304C22⋊Q8D411yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
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#121D411yescharacteristic
331#121D411yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#121C2311yescharacteristic
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24C2×D411yescharacteristic
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—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8C2×D411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×Q8C2411yescharacteristic
502C2×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2411yescharacteristic
521C2×D4C2411yescharacteristic
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—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—82no—
543C22×C4C2×D411yescharacteristic
544C22×C4C2×D411yescharacteristic
545C22×C4C2×D411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551Q16—41no—
552Q16—41no—
553Q16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558D8—41no—
559M16—41no—
560M16—41no—
561M16—41no—
562M16—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
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
628C4⋊C4C2411yescharacteristic
629C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—22no—
683C23—21no—
684C23—21no—
685C23—41no—
686C23—41no—
687C23C22×D411yescharacteristic
688C23C22×D411yescharacteristic
689C23C22×D411yescharacteristic
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—41no—
701Q8—81no—
702Q8—81no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706D4—22no—
707D4—22no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
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—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
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×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×C4C2511yescharacteristic
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—44no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22#57812yes—
812C22C23×D411yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4#58511yescharacteristic
837C4#58511yescharacteristic
838C2—22no—
839C2—41no—
840C2—41no—
841C2—41no—
842C2—41no—
843C2—81no—
844C2—81no—
845C2#348511yescharacteristic
846C2C2×#57811yescharacteristic
847C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3541C2semidirect
2. #3492C2semidirect
3. #3353C2semidirect
4. #3352C2semidirect
5. #3349C2semidirect
6. #3346C2semidirect
7. #3346C2semidirect
8. #3343C2semidirect
9. #3339C2semidirect
10. #3338C2semidirect
11. #3330C2semidirect
12. #3327C2semidirect
13. #3320C2semidirect
14. #3316C2semidirect
15. #3315C2semidirect
16. #3308C2semidirect
17. #3301C2semidirect
18. #3299C2semidirect
19. #3243C2semidirect
20. #3242C2semidirect
21. #3203C2semidirect
22. #3201C2semidirect
23. #3196C2semidirect
24. #3191C2semidirect
25. #3124C2semidirect
26. #3120C2semidirect
27. #3098C2semidirect
28. #3097C2semidirect
29. #3092C2semidirect
30. C2×#484C2semidirect
31. #2976C2semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #491C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #487C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
104. #484C22semidirect
105. #484C22semidirect
106. #484C22semidirect
109. #483C22semidirect
112. #482C22semidirect
113. #482C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #477C22semidirect
129. #477C22semidirect
130. #475C22semidirect
131. #474C22semidirect
132. #474C22semidirect
135. #470C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
142. #467C22semidirect
143. #467C22semidirect
145. #466C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #463C22semidirect
151. #462C22semidirect
152. #461C22semidirect
157. #452C22semidirect
159. #451C22semidirect
162. #449C22semidirect
164. #448C22semidirect
165. #441C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×Q16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
190. C2×#107C22semidirect
191. #419C22semidirect
194. #417C22semidirect
195. #416C22semidirect
198. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#34922
#33532
#33522
#33492
#33462
#33432
#33392
#33382
#33302
#33272
#33202
#33162
#33152
#33082
#33012
#32992
#32432
#32422
#32032
#32012
#31962
#31912
#31242
#31202
#30982
#30972
#30922
C2×#4842
#29762