Finite Group Databasebeta

← #6998932

Subgroups — #6998932

Order 512.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44872C211yesmaximal, characteristic
2#42905C211yesmaximal, characteristic, complemented
3#31801C211yesmaximal, characteristic, complemented
4#31463C211yesmaximal, characteristic, complemented
5#31403C211yesmaximal, characteristic, complemented
6#31314C211yesmaximal, characteristic, complemented
7#31004C211yesmaximal, characteristic, complemented
8#30988C211yesmaximal, characteristic, complemented
9#30876C211yesmaximal, characteristic, complemented
10#30802C211yesmaximal, characteristic, complemented
11#29116C211yesmaximal, characteristic, complemented
12#29064C211yesmaximal, characteristic, complemented
13#29024C211yesmaximal, characteristic, complemented
14#29006C211yesmaximal, characteristic, complemented
15#27755C211yesmaximal, characteristic, complemented
16#27520C211yesmaximal, characteristic, complemented
17#27273C211yesmaximal, characteristic, complemented
18#27038C211yesmaximal, characteristic, complemented
19#26768C211yesmaximal, characteristic, complemented
20#26686C211yesmaximal, characteristic, complemented
21#26630C211yesmaximal, characteristic, complemented
22#26498C211yesmaximal, characteristic, complemented
23#26175C211yesmaximal, characteristic, complemented
24#25685C211yesmaximal, characteristic, complemented
25#24252C211yesmaximal, characteristic, complemented
26#24044C211yesmaximal, characteristic, complemented
27#23582C211yesmaximal, characteristic, complemented
28#23301C211yesmaximal, characteristic, complemented
29#23010C211yesmaximal, characteristic, complemented
30#22864C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#418C2211yescharacteristic
45#2837—21no—
46#2798—21no—
47#2785—21no—
48#2777—21no—
49#2767—21no—
50#2703—21no—
51#2678—21no—
52#2678—21no—
53#2668—21no—
54#2666—21no—
55#2650—21no—
56#2628C2211yescharacteristic, complemented
57#2596—21no—
58#2571C2211yescharacteristic, complemented
59#2541C2211yescharacteristic
60#2539—21no—
61#2536C2211yescharacteristic
62#2508C2211yescharacteristic, complemented
63#2497C2211yescharacteristic, complemented
64#2495C2211yescharacteristic, complemented
65#2490C2211yescharacteristic
66#2485C2211yescharacteristic
67#2464—21no—
68#2454C2211yescharacteristic
69#2451C2211yescharacteristic, complemented
70#2445C2211yescharacteristic
71#2439C2211yescharacteristic, complemented
72#2433C2211yescharacteristic
73#2433C2211yescharacteristic
74#2428C2211yescharacteristic
75#2423C2211yescharacteristic, complemented
76#2421C2211yescharacteristic, complemented
77#2414C2211yescharacteristic
78#2410—21no—
79#2408—21no—
80#2395C2211yescharacteristic
81#2366C2211yescharacteristic
82#2363C2211yescharacteristic
83#2362C2211yescharacteristic, complemented
84#2351C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2323C2211yescharacteristic, complemented
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2092C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic, complemented
110#2041C2211yescharacteristic, complemented
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic, complemented
113#2034C2211yescharacteristic, complemented
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic, complemented
118#2033C2211yescharacteristic, complemented
119#2026C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic, complemented
123#2014C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#2000C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1982C2211yescharacteristic, complemented
130#1973C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic, complemented
133#1961C2211yescharacteristic
134#1961C2211yescharacteristic
135#1961C2211yescharacteristic, complemented
136#1957C2211yescharacteristic, complemented
137#1955C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1942C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1936C2211yescharacteristic, complemented
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic, complemented
164#1894C2211yescharacteristic, complemented
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic, complemented
167#1880C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211D42—42no—
212D42—42no—
213#540—42no—
214#540—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C22⋊C4—21no—
255#501—42no—
256#486—42no—
257#482—42no—
258#460—24no—
259#460—42no—
260#450—24no—
261#450—24no—
262#440—42no—
263#440—42no—
264C4×SD16—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400D411yescharacteristic
331#399—21no—
332#399—21no—
333#399—21no—
334#399D411yescharacteristic
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398D411yescharacteristic
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394D411yescharacteristic
360#394D411yescharacteristic
361#393—21no—
362#393—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#384C2311yescharacteristic
435#383—21no—
436#382—21no—
437#382—21no—
438#382—21no—
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#380—21no—
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450#379—21no—
451#379—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—44no—
524C22×D4—82no—
525C22×D4—82no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16#4114yes—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#127—22no—
563#127—22no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#127—41no—
569#127—41no—
570#125—22no—
571#125—41no—
572#123—44no—
573#123—44no—
574#123—82no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—44no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—44no—
587#121—44no—
588#121—41no—
589#121—41no—
590#121—82no—
591#121—82no—
592#121—82no—
593#120—44no—
594#120—44no—
595#120—82no—
596#120—82no—
597#120—82no—
598#120—82no—
599C4×Q8—22no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—82no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—41no—
769#97—41no—
770#97—41no—
771#97—41no—
772C4×C8—41no—
773C4×C8—41no—
774C4×C8—41no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8C2×#4112yes—
843C2×D4—24no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—816no—
919C2×D4C2×#4112yes—
920C2×D4H(5,𝔽2)12yes—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C2511yescharacteristic
970SD16—44no—
971SD16—44no—
972SD16—44no—
973SD16—82no—
974M16—82no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8C2×#4112yes—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4H(5,𝔽2)12yes—
1048C22⋊C4—24no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—84no—
1153C23—84no—
1154C23—84no—
1155C23—84no—
1156C23—84no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23C23×D411yescharacteristic
1167Q8—22no—
1168Q8—22no—
1169Q8—41no—
1170Q8—41no—
1171Q8—162no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—44no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—84no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4#57712yes—
1287C2×C4C22×#4111yescharacteristic
1288C2×C4C2×H(5,𝔽2)11yescharacteristic
1289C2×C4C2×H(5,𝔽2)11yescharacteristic
1290C2×C4#58511yescharacteristic
1291C2×C4#58511yescharacteristic
1292C2×C4#58511yescharacteristic
1293C8—22no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C22—41no—
1302C22—41no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—42no—
1319C22—41no—
1320C22—41no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—168no—
1344C22—168no—
1345C22D4×#4111yescharacteristic
1346C22#348411yescharacteristic
1347C22#350011yescharacteristic
1348C22C2×#57711yescharacteristic
1349C22#358511yescharacteristic
1350C22#358511yescharacteristic
1351C22#358511yescharacteristic
1352C4—22no—
1353C4—41no—
1354C4—41no—
1355C4—42no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4#350511yescharacteristic
1377C4#351311yescharacteristic
1378C4#356011yescharacteristic
1379C4#356211yescharacteristic
1380C2—81no—
1381C2—81no—
1382C2—82no—
1383C2—82no—
1384C2—161no—
1385C2—161no—
1386C2#4300811yescharacteristic
1387C2#6150411yescharacteristic
1388C2#6154311yescharacteristic
1389C2#6164411yescharacteristic
1390C2#6168911yescharacteristic
1391C2#6256411yescharacteristic
1392C2#6259611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44872C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42905C2semidirect
3. #31801C2semidirect
4. #31463C2semidirect
5. #31403C2semidirect
6. #31314C2semidirect
7. #31004C2semidirect
8. #30988C2semidirect
9. #30876C2semidirect
10. #30802C2semidirect
11. #29116C2semidirect
12. #29064C2semidirect
13. #29024C2semidirect
14. #29006C2semidirect
15. #27755C2semidirect
16. #27520C2semidirect
17. #27273C2semidirect
18. #27038C2semidirect
19. #26768C2semidirect
20. #26686C2semidirect
21. #26630C2semidirect
22. #26498C2semidirect
23. #26175C2semidirect
24. #25685C2semidirect
25. #24252C2semidirect
26. #24044C2semidirect
27. #23582C2semidirect
28. #23301C2semidirect
29. #23010C2semidirect
30. #22864C2semidirect
31. #22052C2semidirect
34. C2×#501C22semidirect
35. C2×#486C22semidirect
42. C2×#440C22semidirect
43. C2×C4×SD16C22semidirect
56. #2628C22semidirect
58. #2571C22semidirect
62. #2508C22semidirect
63. #2497C22semidirect
64. #2495C22semidirect
69. #2451C22semidirect
71. #2439C22semidirect
75. #2423C22semidirect
76. #2421C22semidirect
83. #2362C22semidirect
84. #2351C22semidirect
86. #2323C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2092C22semidirect
91. #2086C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
95. #2073C22semidirect
96. #2073C22semidirect
97. #2073C22semidirect
99. #2068C22semidirect
100. #2067C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
104. #2059C22semidirect
109. #2041C22semidirect
110. #2041C22semidirect
112. #2034C22semidirect
113. #2034C22semidirect
117. #2033C22semidirect
118. #2033C22semidirect
119. #2026C22semidirect
121. #2023C22semidirect
122. #2014C22semidirect
123. #2014C22semidirect
126. #2000C22semidirect
127. #2000C22semidirect
128. #1991C22semidirect
129. #1982C22semidirect
132. #1968C22semidirect
135. #1961C22semidirect
136. #1957C22semidirect
138. #1949C22semidirect
139. #1943C22semidirect
140. #1942C22semidirect
142. #1936C22semidirect
143. #1936C22semidirect
144. #1936C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
149. #1934C22semidirect
152. #1925C22semidirect
153. #1924C22semidirect
154. #1924C22semidirect
155. #1923C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
163. #1895C22semidirect
164. #1894C22semidirect
166. #1880C22semidirect
167. #1880C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
170. #1877C22semidirect
171. #1875C22semidirect
172. #1873C22semidirect
174. #1865C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
184. #1825C22semidirect
185. #1825C22semidirect
187. #1802C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
195. #1763C22semidirect
196. #1762C22semidirect
197. C4×#102C22semidirect
198. C4×#102C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#448722
#429052
#318012
#314632
#314032
#313142
#310042
#309882
#308762
#308022
#291162
#290642
#290242
#290062
#277552
#275202
#272732
#270382
#267682
#266862
#266302
#264982
#261752
#256852
#242522
#240442
#235822
#233012
#230102
#228642
#220522