Finite Group Databasebeta

← #62077

Subgroups — #62077

Order 256.

888 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3562C211yesmaximal, characteristic
2#3523C211yesmaximal, characteristic, complemented
3#3400C211yesmaximal, characteristic, complemented
4#3398C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3323C211yesmaximal, characteristic, complemented
9#3317C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3313C211yesmaximal, characteristic, complemented
12#3311C211yesmaximal, characteristic, complemented
13#3278C211yesmaximal, characteristic, complemented
14#3276C211yesmaximal, characteristic, complemented
15#3270C211yesmaximal, characteristic, complemented
16#3270C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3261C211yesmaximal, characteristic, complemented
20#3260C211yesmaximal, characteristic, complemented
21#3252C211yesmaximal, characteristic, complemented
22#3223C211yesmaximal, characteristic, complemented
23#3222C211yesmaximal, characteristic, complemented
24#3216C211yesmaximal, characteristic, complemented
25#3127C211yesmaximal, characteristic, complemented
26#3126C211yesmaximal, characteristic, complemented
27#3117C211yesmaximal, characteristic, complemented
28#3044C211yesmaximal, characteristic, complemented
29#3043C211yesmaximal, characteristic, complemented
30#3037C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic
34C2×#137C2211yescharacteristic
35C2×#137C2211yescharacteristic, complemented
36C22×Q16C2211yescharacteristic, complemented
37C22×SD16C2211yescharacteristic
38#562—21no—
39#560—21no—
40#559C2211yescharacteristic
41#557—21no—
42#557C2211yescharacteristic, complemented
43#557C2211yescharacteristic, complemented
44#556—21no—
45#556C2211yescharacteristic
46#556C2211yescharacteristic
47#553—21no—
48#552—21no—
49#552—21no—
50#552C2211yescharacteristic
51#552C2211yescharacteristic, complemented
52#551—21no—
53#550C2211yescharacteristic
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic
56D4×Q8C2211yescharacteristic, complemented
57#548C2211yescharacteristic
58#548C2211yescharacteristic
59#547C2211yescharacteristic
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#541—21no—
63#541—21no—
64#541C2211yescharacteristic
65#541C2211yescharacteristic
66#541C2211yescharacteristic, complemented
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
82C2×C4×Q8C2211yescharacteristic, 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
96#485C2211yescharacteristic
97#484C2211yescharacteristic, complemented
98#482C2211yescharacteristic
99#482C2211yescharacteristic, complemented
100#481C2211yescharacteristic
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#479C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#478C2211yescharacteristic
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#476C2211yescharacteristic
111#470C2211yescharacteristic
112#470C2211yescharacteristic
113#470C2211yescharacteristic, complemented
114#470C2211yescharacteristic, complemented
115#468C2211yescharacteristic
116#468C2211yescharacteristic
117#468C2211yescharacteristic
118#468C2211yescharacteristic, complemented
119#467C2211yescharacteristic
120#467C2211yescharacteristic
121#465C2211yescharacteristic
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic
124#464C2211yescharacteristic
125#464C2211yescharacteristic
126#464C2211yescharacteristic
127#464C2211yescharacteristic
128#464C2211yescharacteristic
129#464C2211yescharacteristic
130#464C2211yescharacteristic
131#464C2211yescharacteristic
132#464C2211yescharacteristic
133#464C2211yescharacteristic, complemented
134#464C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#462C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#462C2211yescharacteristic, complemented
139#462C2211yescharacteristic, complemented
140#462C2211yescharacteristic, complemented
141#462C2211yescharacteristic, complemented
142#462C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#461C2211yescharacteristic
145#461C2211yescharacteristic
146#461C2211yescharacteristic, complemented
147#460C2211yescharacteristic
148#460C2211yescharacteristic
149#460C2211yescharacteristic
150#460C2211yescharacteristic
151#460C2211yescharacteristic
152#460C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic
162#451C2211yescharacteristic
163#451C2211yescharacteristic, complemented
164#451C2211yescharacteristic, complemented
165#451C2211yescharacteristic, complemented
166#450C2211yescharacteristic
167#450C2211yescharacteristic
168#448C2211yescharacteristic
169#448C2211yescharacteristic
170#448C2211yescharacteristic, complemented
171#446C2211yescharacteristic, complemented
172#446C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#441C2211yescharacteristic, complemented
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic, complemented
181C4×Q16C2211yescharacteristic, complemented
182C4×Q16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic
184C4×SD16C2211yescharacteristic, complemented
185#436C2211yescharacteristic
186#436C2211yescharacteristic, complemented
187#435C2211yescharacteristic
188#435C2211yescharacteristic
189#435C2211yescharacteristic
190#435C2211yescharacteristic, complemented
191#433C2211yescharacteristic
192#433C2211yescharacteristic, complemented
193#432C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#418C2211yescharacteristic
199#417C2211yescharacteristic
200#417C2211yescharacteristic, complemented
201#416C2211yescharacteristic
202#416C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212#137—42no—
213#137—42no—
214#137—42no—
215#137—42no—
216C2×Q16—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×Q16C2311yescharacteristic
227C2×Q16C2311yescharacteristic
228C2×Q16C2311yescharacteristic
229C2×SD16—42no—
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×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C2×M16C2311yescharacteristic
245C2×M16C2311yescharacteristic
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#125—21no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125—21no—
285#125—21no—
286#125—21no—
287#125—21no—
288#125—21no—
289#125—21no—
290#125D411yescharacteristic
291#125C2311yescharacteristic
292#125C2311yescharacteristic
293#125C2311yescharacteristic
294#124—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124D411yescharacteristic
299#124C2311yescharacteristic
300#124C2311yescharacteristic
301#124C2311yescharacteristic
302#124C2311yescharacteristic
303#124C2311yescharacteristic
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#123—21no—
316#123—21no—
317#123D411yescharacteristic
318#123D411yescharacteristic
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⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8D411yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
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×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×Q8C2311yescharacteristic
377C4×Q8C2311yescharacteristic
378C4×Q8C2311yescharacteristic
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
383C4×Q8C2311yescharacteristic
384C4×Q8C2311yescharacteristic
385C4×Q8C2311yescharacteristic
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×D4—21no—
395C4×D4—21no—
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#117C2311yescharacteristic
412#117C2311yescharacteristic
413#117C2311yescharacteristic
414#117C2311yescharacteristic
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
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#103C2311yescharacteristic
459#103C2311yescharacteristic
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—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8C2×D411yescharacteristic
507C2×Q8C2411yescharacteristic
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—41no—
527C2×D4—41no—
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551Q16—22no—
552Q16—22no—
553Q16—22no—
554Q16—41no—
555Q16—41no—
556Q16—41no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561Q16—41no—
562Q16—41no—
563SD16—22no—
564SD16—22no—
565SD16—22no—
566SD16—41no—
567SD16—41no—
568SD16—41no—
569SD16—41no—
570SD16—41no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575M16—41no—
576M16—41no—
577M16—41no—
578M16—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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
682C42—21no—
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—81no—
707C23—81no—
708C23—81no—
709C23C22×D411yescharacteristic
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712Q8—21no—
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—42no—
727Q8—42no—
728Q8—42no—
729Q8—42no—
730Q8—81no—
731Q8H(5,𝔽2)12yes—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753C2×C4—21no—
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×C4C22×D411yescharacteristic
787C2×C4C22×D411yescharacteristic
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C2511yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—162no—
825C22C23×D411yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—22no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4C2×H(5,𝔽2)11yescharacteristic
851C4#58511yescharacteristic
852C2—41no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2#348811yescharacteristic
859C2#358611yescharacteristic
860C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3562C2
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
2. #3523C2semidirect
3. #3400C2semidirect
4. #3398C2semidirect
5. #3377C2semidirect
6. #3371C2semidirect
7. #3327C2semidirect
8. #3323C2semidirect
9. #3317C2semidirect
10. #3315C2semidirect
11. #3313C2semidirect
12. #3311C2semidirect
13. #3278C2semidirect
14. #3276C2semidirect
15. #3270C2semidirect
16. #3270C2semidirect
17. #3266C2semidirect
18. #3266C2semidirect
19. #3261C2semidirect
20. #3260C2semidirect
21. #3252C2semidirect
22. #3223C2semidirect
23. #3222C2semidirect
24. #3216C2semidirect
25. #3127C2semidirect
26. #3126C2semidirect
27. #3117C2semidirect
28. #3044C2semidirect
29. #3043C2semidirect
30. #3037C2semidirect
31. #2995C2semidirect
35. C2×#137C22semidirect
36. C22×Q16C22semidirect
42. #557C22semidirect
43. #557C22semidirect
51. #552C22semidirect
56. D4×Q8C22semidirect
66. #541C22semidirect
75. #533C22semidirect
81. #519C22semidirect
82. C2×C4×Q8C22semidirect
86. #497C22semidirect
87. #494C22semidirect
89. #491C22semidirect
92. #489C22semidirect
97. #484C22semidirect
99. #482C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #479C22semidirect
105. #479C22semidirect
106. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
113. #470C22semidirect
114. #470C22semidirect
118. #468C22semidirect
122. #465C22semidirect
133. #464C22semidirect
134. #464C22semidirect
135. #462C22semidirect
136. #462C22semidirect
137. #462C22semidirect
138. #462C22semidirect
139. #462C22semidirect
140. #462C22semidirect
141. #462C22semidirect
142. #462C22semidirect
143. #462C22semidirect
146. #461C22semidirect
159. #452C22semidirect
160. #452C22semidirect
163. #451C22semidirect
164. #451C22semidirect
165. #451C22semidirect
170. #448C22semidirect
171. #446C22semidirect
172. #446C22semidirect
173. #441C22semidirect
174. #441C22semidirect
175. #441C22semidirect
176. #441C22semidirect
180. #440C22semidirect
181. C4×Q16C22semidirect
182. C4×Q16C22semidirect
184. C4×SD16C22semidirect
186. #436C22semidirect
190. #435C22semidirect
192. #433C22semidirect
193. #432C22semidirect
195. #424C22semidirect
196. #423C22semidirect
197. #419C22semidirect
200. #417C22semidirect

Maximal subgroups

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

subgroupindex
#35622
#35232
#34002
#33982
#33772
#33712
#33272
#33232
#33172
#33152
#33132
#33112
#32782
#32762
#32702
#32662
#32612
#32602
#32522
#32232
#32222
#32162
#31272
#31262
#31172
#30442
#30432
#30372
#29952