Finite Group Databasebeta

← #62013

Subgroups — #62013

Order 256.

895 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#3518C211yesmaximal, characteristic, complemented
3#3402C211yesmaximal, characteristic, complemented
4#3401C211yesmaximal, characteristic, complemented
5#3375C211yesmaximal, characteristic, complemented
6#3369C211yesmaximal, characteristic, complemented
7#3321C211yesmaximal, characteristic, complemented
8#3319C211yesmaximal, characteristic, complemented
9#3313C211yesmaximal, characteristic, complemented
10#3311C211yesmaximal, characteristic, complemented
11#3304C211yesmaximal, characteristic, complemented
12#3302C211yesmaximal, characteristic, complemented
13#3285C211yesmaximal, characteristic, complemented
14#3282C211yesmaximal, characteristic, complemented
15#3271C211yesmaximal, characteristic, complemented
16#3270C211yesmaximal, characteristic, complemented
17#3269C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3258C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3216C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3126C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3044C211yesmaximal, characteristic, complemented
29#3043C211yesmaximal, characteristic, complemented
30#3035C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C2×#135C2211yescharacteristic, complemented
36C22×Q16C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic
38#562—21no—
39#560—21no—
40#559C2211yescharacteristic
41Q82C2211yescharacteristic, complemented
42#556—21no—
43#556—21no—
44#556—21no—
45#556C2211yescharacteristic
46#556C2211yescharacteristic
47#556C2211yescharacteristic, complemented
48#556C2211yescharacteristic, complemented
49#555—21no—
50#555C2211yescharacteristic
51#553—21no—
52#551—21no—
53#550C2211yescharacteristic
54D4×Q8C2211yescharacteristic
55#548C2211yescharacteristic
56#548C2211yescharacteristic
57#548C2211yescharacteristic
58#548C2211yescharacteristic, complemented
59#547C2211yescharacteristic
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#542—21no—
63#542—21no—
64#542C2211yescharacteristic
65#542C2211yescharacteristic, complemented
66#541C2211yescharacteristic
67#540—21no—
68#540C2211yescharacteristic
69#539—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic
73#535C2211yescharacteristic
74#533—21no—
75#533C2211yescharacteristic, complemented
76#532C2211yescharacteristic
77#529—21no—
78#529C2211yescharacteristic
79#529C2211yescharacteristic
80#519C2211yescharacteristic
81#519C2211yescharacteristic, complemented
82C4×#41C2211yescharacteristic, complemented
83#497C2211yescharacteristic
84#497C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#496C2211yescharacteristic
87#495C2211yescharacteristic
88#495C2211yescharacteristic
89#489C2211yescharacteristic
90#489C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic, complemented
93#487C2211yescharacteristic, complemented
94#486C2211yescharacteristic
95#485C2211yescharacteristic
96#485C2211yescharacteristic
97#485C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#482C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#477C2211yescharacteristic, complemented
106#476C2211yescharacteristic
107#475C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#474C2211yescharacteristic
110#474C2211yescharacteristic, complemented
111#470C2211yescharacteristic
112#469C2211yescharacteristic, complemented
113#468C2211yescharacteristic
114#468C2211yescharacteristic
115#467C2211yescharacteristic
116#467C2211yescharacteristic, complemented
117#467C2211yescharacteristic, complemented
118#466C2211yescharacteristic
119#465C2211yescharacteristic
120#465C2211yescharacteristic
121#465C2211yescharacteristic
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic
131#464C2211yescharacteristic, complemented
132#464C2211yescharacteristic, complemented
133#464C2211yescharacteristic, complemented
134#463C2211yescharacteristic
135#463C2211yescharacteristic
136#463C2211yescharacteristic
137#463C2211yescharacteristic, complemented
138#463C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#462C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#462C2211yescharacteristic, complemented
145#461C2211yescharacteristic
146#461C2211yescharacteristic, complemented
147#460C2211yescharacteristic
148#460C2211yescharacteristic
149#460C2211yescharacteristic
150#460C2211yescharacteristic
151#460C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#452C2211yescharacteristic, complemented
160#451C2211yescharacteristic
161#451C2211yescharacteristic
162#451C2211yescharacteristic, complemented
163#450C2211yescharacteristic
164#449C2211yescharacteristic
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#448C2211yescharacteristic
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic, complemented
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×Q16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic
184C4×SD16C2211yescharacteristic, 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#419C2211yescharacteristic, complemented
198#418C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic
201#416C2211yescharacteristic
202#416C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213#137—42no—
214#135—42no—
215#135—42no—
216C2×Q16—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
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×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258#127—21no—
259#127C2311yescharacteristic
260#127C2311yescharacteristic
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126—21no—
270#126—21no—
271#126—21no—
272#126—21no—
273#126—21no—
274#126D411yescharacteristic
275#126D411yescharacteristic
276#125—21no—
277#125—21no—
278#125—21no—
279#125D411yescharacteristic
280#125C2311yescharacteristic
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
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#124C2311yescharacteristic
299#124C2311yescharacteristic
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#123D411yescharacteristic
314#123D411yescharacteristic
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8D411yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
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#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121D411yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
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×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×Q8C2311yescharacteristic
377C4×Q8C2311yescharacteristic
378C4×Q8C2311yescharacteristic
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×D4—21no—
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
402#117—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—21no—
411#117—21no—
412#117C2311yescharacteristic
413#117C2311yescharacteristic
414#117C2311yescharacteristic
415#117C2311yescharacteristic
416#117C2311yescharacteristic
417C2×C4⋊C4—21no—
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—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8C2×D411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×Q8C2411yescharacteristic
513C2×Q8C2411yescharacteristic
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—41no—
530C2×D4—41no—
531C2×D4C2×D411yescharacteristic
532C2×D4C2×D411yescharacteristic
533C2×D4C2×D411yescharacteristic
534C2×D4C2411yescharacteristic
535C2×D4C2411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
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—22no—
557Q16—22no—
558Q16—22no—
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—41no—
578D8—41no—
579D8—41no—
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⋊C4C2×D411yescharacteristic
624C4⋊C4C2×D411yescharacteristic
625C4⋊C4C2×D411yescharacteristic
626C4⋊C4C2×D411yescharacteristic
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2411yescharacteristic
634C4⋊C4C2411yescharacteristic
635C4⋊C4C2411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
674C22⋊C4C2×D411yescharacteristic
675C22⋊C4C2×D411yescharacteristic
676C22⋊C4C2×D411yescharacteristic
677C22⋊C4C2×D411yescharacteristic
678C22⋊C4C2×D411yescharacteristic
679C22⋊C4C2×D411yescharacteristic
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
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—41no—
725Q8—42no—
726Q8—42no—
727Q8—81no—
728Q8—81no—
729Q8—81no—
730Q8—81no—
731Q8H(5,𝔽2)12yes—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—42no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
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—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
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—41no—
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—22no—
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—81no—
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. #3518C2semidirect
3. #3402C2semidirect
4. #3401C2semidirect
5. #3375C2semidirect
6. #3369C2semidirect
7. #3321C2semidirect
8. #3319C2semidirect
9. #3313C2semidirect
10. #3311C2semidirect
11. #3304C2semidirect
12. #3302C2semidirect
13. #3285C2semidirect
14. #3282C2semidirect
15. #3271C2semidirect
16. #3270C2semidirect
17. #3269C2semidirect
18. #3266C2semidirect
19. #3258C2semidirect
20. #3257C2semidirect
21. #3248C2semidirect
22. #3225C2semidirect
23. #3224C2semidirect
24. #3216C2semidirect
25. #3127C2semidirect
26. #3126C2semidirect
27. #3111C2semidirect
28. #3044C2semidirect
29. #3043C2semidirect
30. #3035C2semidirect
31. #2992C2semidirect
35. C2×#135C22semidirect
36. C22×Q16C22semidirect
41. Q82C22semidirect
47. #556C22semidirect
48. #556C22semidirect
58. #548C22semidirect
65. #542C22semidirect
75. #533C22semidirect
81. #519C22semidirect
82. C4×#41C22semidirect
84. #497C22semidirect
85. #497C22semidirect
92. #489C22semidirect
93. #487C22semidirect
97. #485C22semidirect
100. #482C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #477C22semidirect
107. #475C22semidirect
108. #475C22semidirect
110. #474C22semidirect
112. #469C22semidirect
116. #467C22semidirect
117. #467C22semidirect
122. #465C22semidirect
131. #464C22semidirect
132. #464C22semidirect
133. #464C22semidirect
137. #463C22semidirect
138. #463C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
142. #462C22semidirect
143. #462C22semidirect
144. #462C22semidirect
146. #461C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #452C22semidirect
162. #451C22semidirect
168. #448C22semidirect
169. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #441C22semidirect
179. #440C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×Q16C22semidirect
184. C4×SD16C22semidirect
188. #435C22semidirect
190. C8×D4C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
197. #419C22semidirect
202. #416C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35182
#34022
#34012
#33752
#33692
#33212
#33192
#33132
#33112
#33042
#33022
#32852
#32822
#32712
#32702
#32692
#32662
#32582
#32572
#32482
#32252
#32242
#32162
#31272
#31262
#31112
#30442
#30432
#30352
#29922