Finite Group Databasebeta

← #62009

Subgroups — #62009

Order 256.

948 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543C211yesmaximal, characteristic, complemented
2#3516C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3397C211yesmaximal, characteristic, complemented
5#3371C211yesmaximal, characteristic, complemented
6#3368C211yesmaximal, characteristic, complemented
7#3318C211yesmaximal, characteristic, complemented
8#3317C211yesmaximal, characteristic, complemented
9#3314C211yesmaximal, characteristic, complemented
10#3310C211yesmaximal, characteristic, complemented
11#3297C211yesmaximal, characteristic, complemented
12#3295C211yesmaximal, characteristic, complemented
13#3282C211yesmaximal, characteristic, complemented
14D4×SD16C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3266C211yesmaximal, characteristic, complemented
17#3265C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3250C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3222C211yesmaximal, characteristic, complemented
24#3217C211yesmaximal, characteristic, complemented
25#3126C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3117C211yesmaximal, characteristic, complemented
28#3045C211yesmaximal, characteristic, complemented
29#3043C211yesmaximal, characteristic, complemented
30C2×#460C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic, complemented
35C22×SD16C2211yescharacteristic, complemented
36C22×SD16C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic, complemented
38#560—21no—
39#560—21no—
40#559C2211yescharacteristic
41#557C2211yescharacteristic, complemented
42#556—21no—
43#556C2211yescharacteristic, complemented
44#554—21no—
45#554C2211yescharacteristic, complemented
46#553—21no—
47#553C2211yescharacteristic, complemented
48#552—21no—
49#552C2211yescharacteristic, complemented
50#550C2211yescharacteristic
51#550C2211yescharacteristic
52D4×Q8C2211yescharacteristic, complemented
53#548C2211yescharacteristic, complemented
54#548C2211yescharacteristic, complemented
55#546—21no—
56#546C2211yescharacteristic
57#546C2211yescharacteristic
58D42—21no—
59D42C2211yescharacteristic
60D42C2211yescharacteristic
61D42C2211yescharacteristic
62#542—21no—
63#542C2211yescharacteristic, complemented
64#541—21no—
65#541C2211yescharacteristic, complemented
66#540—21no—
67#540C2211yescharacteristic
68#540C2211yescharacteristic
69#535—21no—
70#535C2211yescharacteristic
71#535C2211yescharacteristic
72#534—21no—
73#534—21no—
74C2×#127C2211yescharacteristic
75#529—21no—
76#529—21no—
77#529C2211yescharacteristic
78#529C2211yescharacteristic
79#529C2211yescharacteristic, complemented
80#520C2211yescharacteristic, complemented
81#519C2211yescharacteristic, complemented
82C2×C4×Q8C2211yescharacteristic, complemented
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#496C2211yescharacteristic, complemented
86#496C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic, complemented
89#490C2211yescharacteristic
90#490C2211yescharacteristic, complemented
91#490C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#486C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#482C2211yescharacteristic, complemented
97#482C2211yescharacteristic, complemented
98#481C2211yescharacteristic
99#481C2211yescharacteristic, complemented
100#480C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#478C2211yescharacteristic, complemented
106#478C2211yescharacteristic, complemented
107#478C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#476C2211yescharacteristic, complemented
110#474C2211yescharacteristic, complemented
111#469C2211yescharacteristic, complemented
112#468C2211yescharacteristic, complemented
113#468C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic, complemented
116#466C2211yescharacteristic
117#466C2211yescharacteristic, complemented
118#465C2211yescharacteristic
119#465C2211yescharacteristic, complemented
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#463C2211yescharacteristic, complemented
131#463C2211yescharacteristic, complemented
132#463C2211yescharacteristic, complemented
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#461C2211yescharacteristic, complemented
136#461C2211yescharacteristic, complemented
137#460C2211yescharacteristic
138#460C2211yescharacteristic
139#460C2211yescharacteristic, complemented
140#460C2211yescharacteristic, complemented
141#460C2211yescharacteristic, complemented
142#460C2211yescharacteristic, complemented
143#460C2211yescharacteristic, complemented
144#460C2211yescharacteristic, complemented
145#460C2211yescharacteristic, complemented
146#460C2211yescharacteristic, complemented
147#460C2211yescharacteristic, complemented
148#460C2211yescharacteristic, complemented
149#460C2211yescharacteristic, complemented
150#459C2211yescharacteristic, complemented
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#450C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#450C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#450C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic
166#448C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#447C2211yescharacteristic, complemented
169#447C2211yescharacteristic, complemented
170#447C2211yescharacteristic, complemented
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177#440C2211yescharacteristic, complemented
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187#435C2211yescharacteristic, complemented
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic, complemented
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#418C2211yescharacteristic, complemented
198#417C2211yescharacteristic, complemented
199#416C2211yescharacteristic, complemented
200C2×#102C2211yescharacteristic, complemented
201C2×#102C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4C2311yescharacteristic
215C22×D4C2311yescharacteristic
216C22×D4C2311yescharacteristic
217C22×D4C2311yescharacteristic
218#137—42no—
219AGL(1,ℤ/8)—42no—
220#135—42no—
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×SD16—42no—
225C2×SD16—42no—
226C2×SD16—42no—
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×SD16C2311yescharacteristic
239C2×SD16C2311yescharacteristic
240C2×SD16C2311yescharacteristic
241C2×SD16C2311yescharacteristic
242C2×SD16C2311yescharacteristic
243C2×D8C2311yescharacteristic
244C2×D8C2311yescharacteristic
245C2×D8C2311yescharacteristic
246C2×D8C2311yescharacteristic
247C2×D8C2311yescharacteristic
248C2×M16C2311yescharacteristic
249C2×M16C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C22×C8C2311yescharacteristic
252C22×C8C2311yescharacteristic
253C22×C8C2311yescharacteristic
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258#127—21no—
259#127—21no—
260#127—21no—
261#127C2311yescharacteristic
262#127C2311yescharacteristic
263#127C2311yescharacteristic
264#127C2311yescharacteristic
265#127C2311yescharacteristic
266#127C2311yescharacteristic
267#126—21no—
268#126—21no—
269#126—21no—
270#126—21no—
271#126—21no—
272#126—21no—
273#126—21no—
274#126—21no—
275#126—21no—
276#126D411yescharacteristic
277#126D411yescharacteristic
278#125—21no—
279#125—21no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125D411yescharacteristic
285#125C2311yescharacteristic
286#125C2311yescharacteristic
287#125C2311yescharacteristic
288#124—21no—
289#124—21no—
290#124—21no—
291#124—21no—
292#124D411yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#124C2311yescharacteristic
297#124C2311yescharacteristic
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123D411yescharacteristic
312#123D411yescharacteristic
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8D411yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121D411yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351#121C2311yescharacteristic
352#121C2311yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#120—21no—
357#120—21no—
358#120—21no—
359#120—21no—
360#120—21no—
361#120—21no—
362#120—21no—
363#120—21no—
364#120—21no—
365#120—21no—
366#120—21no—
367#120—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×Q8C2311yescharacteristic
377C4×Q8C2311yescharacteristic
378C4×Q8C2311yescharacteristic
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402C4×D4C2311yescharacteristic
403C4×D4C2311yescharacteristic
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—21no—
411#117C2311yescharacteristic
412#117C2311yescharacteristic
413#117C2311yescharacteristic
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C2311yescharacteristic
417C2×C4⋊C4C2311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C42—21no—
421C2×C42C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
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
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478#97C2311yescharacteristic
479#97C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488#41—22no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—82no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8C2×D411yescharacteristic
503C2×Q8C2411yescharacteristic
504C2×Q8C2411yescharacteristic
505C2×Q8C2411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C2×D4C2×D411yescharacteristic
547C2×D4C2×D411yescharacteristic
548C2×D4C2×D411yescharacteristic
549C2×D4C2411yescharacteristic
550C2×D4C2411yescharacteristic
551C2×D4C2411yescharacteristic
552C2×D4C2411yescharacteristic
553C2×D4C2411yescharacteristic
554C2×D4C2411yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4C2×D411yescharacteristic
570C22×C4C2×D411yescharacteristic
571C22×C4C2411yescharacteristic
572C22×C4C2411yescharacteristic
573C22×C4C2411yescharacteristic
574Q16—22no—
575Q16—41no—
576Q16—41no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582SD16—41no—
583SD16—41no—
584SD16—41no—
585SD16—41no—
586SD16—41no—
587SD16—41no—
588SD16—41no—
589SD16—41no—
590SD16—41no—
591SD16—41no—
592SD16—41no—
593D8—41no—
594D8—41no—
595D8—41no—
596D8—41no—
597D8—41no—
598M16—41no—
599M16—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8C2411yescharacteristic
605C2×C8C2411yescharacteristic
606C2×C8C2411yescharacteristic
607C2×C8C2411yescharacteristic
608C2×C8C2411yescharacteristic
609C2×C8C2411yescharacteristic
610C2×C8C2411yescharacteristic
611C2×C8C2411yescharacteristic
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2×D411yescharacteristic
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2×D411yescharacteristic
645C4⋊C4C2×D411yescharacteristic
646C4⋊C4C2×D411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
650C4⋊C4C2411yescharacteristic
651C4⋊C4C2411yescharacteristic
652C4⋊C4C2411yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C22⋊C4C2×D411yescharacteristic
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42C2×D411yescharacteristic
704C42C2×D411yescharacteristic
705C42C2411yescharacteristic
706C42C2411yescharacteristic
707C42C2411yescharacteristic
708C42C2411yescharacteristic
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—42no—
716C23—42no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23C22×D411yescharacteristic
728C23C22×D411yescharacteristic
729C23C22×D411yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—21no—
734Q8—21no—
735Q8—21no—
736Q8—21no—
737Q8—41no—
738Q8—42no—
739Q8—42no—
740Q8—81no—
741Q8H(5,𝔽2)12yes—
742D4—22no—
743D4—22no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—41no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—81no—
766D4—81no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4C22×D411yescharacteristic
816C2×C4C22×D411yescharacteristic
817C2×C4C22×D411yescharacteristic
818C2×C4C22×D411yescharacteristic
819C2×C4C22×D411yescharacteristic
820C2×C4C22×D411yescharacteristic
821C2×C4C22×D411yescharacteristic
822C2×C4C22×D411yescharacteristic
823C2×C4C22×D411yescharacteristic
824C2×C4C22×D411yescharacteristic
825C2×C4C22×D411yescharacteristic
826C2×C4C2511yescharacteristic
827C8—21no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—21no—
832C8—21no—
833C8—21no—
834C8—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—162no—
862C22—162no—
863C22—162no—
864C22—162no—
865C22#57712yes—
866C22C23×D411yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—22no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4C2×H(5,𝔽2)11yescharacteristic
889C4#58511yescharacteristic
890C2—22no—
891C2—41no—
892C2—41no—
893C2—81no—
894C2—81no—
895C2—81no—
896C2—81no—
897C2—81no—
898C2—81no—
899C2#348811yescharacteristic
900C2C2×#57711yescharacteristic
901C2#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. #3543C2semidirect
2. #3516C2semidirect
3. #3401C2semidirect
4. #3397C2semidirect
5. #3371C2semidirect
6. #3368C2semidirect
7. #3318C2semidirect
8. #3317C2semidirect
9. #3314C2semidirect
10. #3310C2semidirect
11. #3297C2semidirect
12. #3295C2semidirect
13. #3282C2semidirect
14. D4×SD16C2semidirect
15. #3271C2semidirect
16. #3266C2semidirect
17. #3265C2semidirect
18. #3265C2semidirect
19. #3260C2semidirect
20. #3257C2semidirect
21. #3250C2semidirect
22. #3224C2semidirect
23. #3222C2semidirect
24. #3217C2semidirect
25. #3126C2semidirect
26. #3119C2semidirect
27. #3117C2semidirect
28. #3045C2semidirect
29. #3043C2semidirect
30. C2×#460C2semidirect
31. #2992C2semidirect
32. C2×#137C22semidirect
33. C2×AGL(1,ℤ/8)C22semidirect
34. C2×#135C22semidirect
35. C22×SD16C22semidirect
36. C22×SD16C22semidirect
37. C22×SD16C22semidirect
41. #557C22semidirect
43. #556C22semidirect
45. #554C22semidirect
47. #553C22semidirect
49. #552C22semidirect
52. D4×Q8C22semidirect
53. #548C22semidirect
54. #548C22semidirect
63. #542C22semidirect
65. #541C22semidirect
79. #529C22semidirect
80. #520C22semidirect
81. #519C22semidirect
82. C2×C4×Q8C22semidirect
83. #497C22semidirect
85. #496C22semidirect
86. #496C22semidirect
87. #495C22semidirect
88. #492C22semidirect
90. #490C22semidirect
91. #490C22semidirect
92. #489C22semidirect
93. #488C22semidirect
94. #486C22semidirect
95. #484C22semidirect
96. #482C22semidirect
97. #482C22semidirect
99. #481C22semidirect
100. #480C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
105. #478C22semidirect
106. #478C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #476C22semidirect
110. #474C22semidirect
111. #469C22semidirect
112. #468C22semidirect
113. #468C22semidirect
114. #468C22semidirect
115. #467C22semidirect
117. #466C22semidirect
119. #465C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #463C22semidirect
131. #463C22semidirect
132. #463C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #461C22semidirect
136. #461C22semidirect
139. #460C22semidirect
140. #460C22semidirect
141. #460C22semidirect
142. #460C22semidirect
143. #460C22semidirect
144. #460C22semidirect
145. #460C22semidirect
146. #460C22semidirect
147. #460C22semidirect
148. #460C22semidirect
149. #460C22semidirect
150. #459C22semidirect
151. #459C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #451C22semidirect
157. #450C22semidirect
158. #450C22semidirect
159. #450C22semidirect
160. #450C22semidirect
161. #450C22semidirect
162. #449C22semidirect
163. #449C22semidirect
164. #449C22semidirect
166. #448C22semidirect
167. #448C22semidirect
168. #447C22semidirect
169. #447C22semidirect
170. #447C22semidirect
171. #446C22semidirect
172. #446C22semidirect
173. #442C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #440C22semidirect
177. #440C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×SD16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
184. C4×D8C22semidirect
185. #435C22semidirect
186. #435C22semidirect
187. #435C22semidirect
188. #435C22semidirect
189. C8×D4C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #432C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
197. #418C22semidirect
198. #417C22semidirect
199. #416C22semidirect
200. C2×#102C22semidirect
201. C2×#102C22semidirect
202. C2×#102C22semidirect

Maximal subgroups

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

subgroupindex
#35432
#35162
#34012
#33972
#33712
#33682
#33182
#33172
#33142
#33102
#32972
#32952
#32822
D4×SD162
#32712
#32662
#32652
#32602
#32572
#32502
#32242
#32222
#32172
#31262
#31192
#31172
#30452
#30432
C2×#4602
#29922