Finite Group Databasebeta

← #62012

Subgroups — #62012

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3562C211yesmaximal, characteristic, complemented
2#3515C211yesmaximal, characteristic, complemented
3#3400C211yesmaximal, characteristic, complemented
4#3398C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3370C211yesmaximal, characteristic, complemented
7#3317C211yesmaximal, characteristic, complemented
8#3316C211yesmaximal, characteristic, complemented
9#3315C211yesmaximal, characteristic, complemented
10#3314C211yesmaximal, characteristic, complemented
11#3300C211yesmaximal, characteristic, complemented
12#3296C211yesmaximal, characteristic, complemented
13#3284C211yesmaximal, characteristic, complemented
14#3283C211yesmaximal, characteristic, complemented
15#3269C211yesmaximal, characteristic, complemented
16#3269C211yesmaximal, characteristic, complemented
17#3267C211yesmaximal, characteristic, complemented
18#3267C211yesmaximal, characteristic, complemented
19#3261C211yesmaximal, characteristic, complemented
20#3260C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3223C211yesmaximal, characteristic, complemented
23#3222C211yesmaximal, characteristic, complemented
24#3216C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3045C211yesmaximal, characteristic, complemented
30#3035C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic
36C2×#135C2211yescharacteristic
37C2×#135C2211yescharacteristic, complemented
38#562—21no—
39#560—21no—
40#559C2211yescharacteristic
41#557C2211yescharacteristic, complemented
42#556C2211yescharacteristic
43#554C2211yescharacteristic
44#554C2211yescharacteristic, complemented
45#553—21no—
46#553—21no—
47#552—21no—
48#552—21no—
49#552—21no—
50#552C2211yescharacteristic
51#552C2211yescharacteristic, complemented
52#551—21no—
53#550C2211yescharacteristic
54#548C2211yescharacteristic
55#548C2211yescharacteristic
56#547C2211yescharacteristic
57#547C2211yescharacteristic
58#547C2211yescharacteristic
59#547C2211yescharacteristic, complemented
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#541C2211yescharacteristic
63#541C2211yescharacteristic
64#541C2211yescharacteristic, complemented
65#540—21no—
66#540C2211yescharacteristic
67#539—21no—
68#539—21no—
69#539—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic
73#535C2211yescharacteristic
74#533C2211yescharacteristic, complemented
75#532C2211yescharacteristic
76#529—21no—
77#529C2211yescharacteristic
78#529C2211yescharacteristic
79C2×#125—21no—
80#520C2211yescharacteristic
81#520C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic, complemented
83#497C2211yescharacteristic
84#497C2211yescharacteristic
85#497C2211yescharacteristic
86#497C2211yescharacteristic, complemented
87#494C2211yescharacteristic, complemented
88#492C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic, complemented
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#485C2211yescharacteristic, complemented
96#484C2211yescharacteristic
97#483C2211yescharacteristic
98#482C2211yescharacteristic
99#481C2211yescharacteristic, complemented
100#480C2211yescharacteristic
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#478C2211yescharacteristic
107#478C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#475C2211yescharacteristic, complemented
110#474C2211yescharacteristic
111#470C2211yescharacteristic
112#470C2211yescharacteristic
113#468C2211yescharacteristic
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic
116#467C2211yescharacteristic
117#467C2211yescharacteristic, complemented
118#467C2211yescharacteristic, complemented
119#465C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic
128#464C2211yescharacteristic
129#464C2211yescharacteristic, complemented
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#462C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#461C2211yescharacteristic
143#461C2211yescharacteristic
144#461C2211yescharacteristic, complemented
145#461C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#460C2211yescharacteristic
148#460C2211yescharacteristic
149#460C2211yescharacteristic
150#460C2211yescharacteristic
151#459C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#452C2211yescharacteristic, complemented
162#452C2211yescharacteristic, complemented
163#452C2211yescharacteristic, complemented
164#451C2211yescharacteristic, complemented
165#451C2211yescharacteristic, complemented
166#450C2211yescharacteristic
167#450C2211yescharacteristic
168#449C2211yescharacteristic
169#449C2211yescharacteristic
170#449C2211yescharacteristic, complemented
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic
178#440C2211yescharacteristic, complemented
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic, complemented
185#435C2211yescharacteristic
186#435C2211yescharacteristic
187#435C2211yescharacteristic
188#435C2211yescharacteristic, complemented
189C8×D4C2211yescharacteristic
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#417C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic, complemented
201C2×#103C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213AGL(1,ℤ/8)—42no—
214#135—42no—
215#135—42no—
216#135—42no—
217#135—42no—
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8C2311yescharacteristic
249C4⋊Q8C2311yescharacteristic
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254#127—21no—
255#127C2311yescharacteristic
256#127C2311yescharacteristic
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#126D411yescharacteristic
269#126D411yescharacteristic
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#125—21no—
281#125—21no—
282#125—21no—
283#125D411yescharacteristic
284#125C2311yescharacteristic
285#125C2311yescharacteristic
286#125C2311yescharacteristic
287#124—21no—
288#124—21no—
289#124—21no—
290#124D411yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#124C2311yescharacteristic
294#124C2311yescharacteristic
295#124C2311yescharacteristic
296#123—21no—
297#123—21no—
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#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123D411yescharacteristic
316#123D411yescharacteristic
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⋊Q8D411yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
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#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121D411yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#120—21no—
359#120—21no—
360#120—21no—
361#120—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
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#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#103C2311yescharacteristic
457#103C2311yescharacteristic
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—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8C2×D411yescharacteristic
504C2×Q8C2411yescharacteristic
505C2×Q8C2411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
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—41no—
526C2×D4—41no—
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C2×D4C2411yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C2×D411yescharacteristic
552C22×C4C2×D411yescharacteristic
553C22×C4C2411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556Q16—41no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561Q16—41no—
562Q16—41no—
563Q16—41no—
564Q16—41no—
565SD16—22no—
566SD16—22no—
567SD16—22no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577D8—22no—
578D8—22no—
579D8—22no—
580M16—41no—
581M16—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C2×C8C2411yescharacteristic
590C2×C8C2411yescharacteristic
591C2×C8C2411yescharacteristic
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
678C22⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42C2×D411yescharacteristic
698C42C2×D411yescharacteristic
699C42C2411yescharacteristic
700C42C2411yescharacteristic
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712C23C22×D411yescharacteristic
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—41no—
726Q8—81no—
727Q8—81no—
728D4—21no—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4H(5,𝔽2)12yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C2511yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—162no—
833C22C23×D411yescharacteristic
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4C2×H(5,𝔽2)11yescharacteristic
858C4#58511yescharacteristic
859C2—41no—
860C2—41no—
861C2—41no—
862C2—42no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2#348811yescharacteristic
867C2#358411yescharacteristic
868C2#358611yescharacteristic
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. #3562C2semidirect
2. #3515C2semidirect
3. #3400C2semidirect
4. #3398C2semidirect
5. #3376C2semidirect
6. #3370C2semidirect
7. #3317C2semidirect
8. #3316C2semidirect
9. #3315C2semidirect
10. #3314C2semidirect
11. #3300C2semidirect
12. #3296C2semidirect
13. #3284C2semidirect
14. #3283C2semidirect
15. #3269C2semidirect
16. #3269C2semidirect
17. #3267C2semidirect
18. #3267C2semidirect
19. #3261C2semidirect
20. #3260C2semidirect
21. #3248C2semidirect
22. #3223C2semidirect
23. #3222C2semidirect
24. #3216C2semidirect
25. #3120C2semidirect
26. #3119C2semidirect
27. #3111C2semidirect
28. #3046C2semidirect
29. #3045C2semidirect
30. #3035C2semidirect
31. #2992C2semidirect
32. C2×#137C22semidirect
37. C2×#135C22semidirect
41. #557C22semidirect
44. #554C22semidirect
51. #552C22semidirect
59. #547C22semidirect
64. #541C22semidirect
74. #533C22semidirect
81. #520C22semidirect
82. C4×#41C22semidirect
86. #497C22semidirect
87. #494C22semidirect
89. #491C22semidirect
92. #489C22semidirect
95. #485C22semidirect
99. #481C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
105. #479C22semidirect
107. #478C22semidirect
108. #478C22semidirect
109. #475C22semidirect
114. #468C22semidirect
117. #467C22semidirect
118. #467C22semidirect
122. #465C22semidirect
129. #464C22semidirect
134. #463C22semidirect
135. #462C22semidirect
136. #462C22semidirect
137. #462C22semidirect
138. #462C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
144. #461C22semidirect
145. #461C22semidirect
146. #461C22semidirect
161. #452C22semidirect
162. #452C22semidirect
163. #452C22semidirect
164. #451C22semidirect
165. #451C22semidirect
170. #449C22semidirect
171. #446C22semidirect
172. #446C22semidirect
175. #441C22semidirect
176. #441C22semidirect
178. #440C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
183. C4×SD16C22semidirect
184. C4×D8C22semidirect
188. #435C22semidirect
190. C8×D4C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
200. #416C22semidirect
201. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35152
#34002
#33982
#33762
#33702
#33172
#33162
#33152
#33142
#33002
#32962
#32842
#32832
#32692
#32672
#32612
#32602
#32482
#32232
#32222
#32162
#31202
#31192
#31112
#30462
#30452
#30352
#29922