Finite Group Databasebeta

← #6502415

Subgroups — #6502415

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35152C211yesmaximal, characteristic
2#34421C211yesmaximal, characteristic, complemented
3#29253C211yesmaximal, characteristic, complemented
4#29251C211yesmaximal, characteristic, complemented
5#27594C211yesmaximal, characteristic, complemented
6#27593C211yesmaximal, characteristic, complemented
7#27210C211yesmaximal, characteristic, complemented
8#27207C211yesmaximal, characteristic, complemented
9#27194C211yesmaximal, characteristic, complemented
10#27191C211yesmaximal, characteristic, complemented
11#26717C211yesmaximal, characteristic, complemented
12#26716C211yesmaximal, characteristic, complemented
13#26701C211yesmaximal, characteristic, complemented
14#26700C211yesmaximal, characteristic, complemented
15#26605C211yesmaximal, characteristic, complemented
16#26604C211yesmaximal, characteristic, complemented
17#26589C211yesmaximal, characteristic, complemented
18#26588C211yesmaximal, characteristic, complemented
19#26181C211yesmaximal, characteristic, complemented
20#26175C211yesmaximal, characteristic, complemented
21#26165C211yesmaximal, characteristic, complemented
22#26159C211yesmaximal, characteristic, complemented
23#24220C211yesmaximal, characteristic
24#24220C211yesmaximal, characteristic
25#23944C211yesmaximal, characteristic, complemented
26#23942C211yesmaximal, characteristic, complemented
27#22048C211yesmaximal, characteristic, complemented
28#22042C211yesmaximal, characteristic, complemented
29#21915C211yesmaximal, characteristic, complemented
30#21453C211yesmaximal, characteristic, complemented
31C4×#450C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47#2849—21no—
48#2849—21no—
49#2622—21no—
50#2622—21no—
51#2447C2211yescharacteristic
52#2447C2211yescharacteristic
53#2447C2211yescharacteristic
54#2447C2211yescharacteristic
55#2445C2211yescharacteristic
56#2445C2211yescharacteristic
57#2445C2211yescharacteristic
58#2445C2211yescharacteristic
59#2422—21no—
60#2422—21no—
61#2420—21no—
62#2420—21no—
63#2382—21no—
64#2382—21no—
65#2370—21no—
66#2370—21no—
67#2370C2211yescharacteristic, complemented
68#2370C2211yescharacteristic, complemented
69#2365C2211yescharacteristic, complemented
70#2365C2211yescharacteristic, complemented
71#2355C2211yescharacteristic, complemented
72#2355C2211yescharacteristic, complemented
73#2351C2211yescharacteristic, complemented
74#2351C2211yescharacteristic, complemented
75#2334—21no—
76#2334—21no—
77#2334—21no—
78#2334—21no—
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2317C2211yescharacteristic
82#2314C2211yescharacteristic
83#2311C2211yescharacteristic
84#2309C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87#2297C2211yescharacteristic
88#2296C2211yescharacteristic
89#2097C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2026C2211yescharacteristic, complemented
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic, complemented
113#2016C2211yescharacteristic, complemented
114#2015C2211yescharacteristic
115#2015C2211yescharacteristic
116#2014C2211yescharacteristic
117#2014C2211yescharacteristic
118#2013C2211yescharacteristic
119#2013C2211yescharacteristic
120#2013C2211yescharacteristic, complemented
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1982C2211yescharacteristic
124#1982C2211yescharacteristic
125#1973C2211yescharacteristic, complemented
126#1971C2211yescharacteristic, complemented
127#1969C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1936C2211yescharacteristic, complemented
130#1935C2211yescharacteristic, complemented
131#1934C2211yescharacteristic, complemented
132#1933C2211yescharacteristic, complemented
133#1928C2211yescharacteristic, complemented
134#1928C2211yescharacteristic, complemented
135#1927C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1916C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic, complemented
162#1880C2211yescharacteristic, complemented
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1873C2211yescharacteristic
174#1873C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1818C2211yescharacteristic
190#1818C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214#541—24no—
215#541—24no—
216#535—42no—
217#535—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—42no—
247C2×C4×D4—42no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#464—42no—
259#464—42no—
260#460—42no—
261#460—42no—
262#452—24no—
263#452—24no—
264#450—24no—
265#450—24no—
266#440—42no—
267#440—42no—
268C4×SD16—42no—
269C4×SD16—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389D411yescharacteristic
367#389D411yescharacteristic
368#389D411yescharacteristic
369#389D411yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385D411yescharacteristic
419#385D411yescharacteristic
420#385D411yescharacteristic
421#385D411yescharacteristic
422#384—21no—
423#384C2311yescharacteristic
424#382—21no—
425#382—21no—
426#382—21no—
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#381—21no—
433#381—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439#379—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—44no—
528C23×C4—82no—
529C23×C4—82no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—22no—
566C4⋊Q8—22no—
567#127—22no—
568#127—22no—
569#127—41no—
570#127—41no—
571#126—28no—
572#126—28no—
573#125—28no—
574#125—28no—
575#125—22no—
576#125—22no—
577#124—22no—
578#124—22no—
579#124—41no—
580#124—41no—
581#123—82no—
582#123—82no—
583#123—82no—
584#123—82no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8#4114yes—
588C22⋊Q8#4114yes—
589#121—44no—
590#121—44no—
591#120—44no—
592#120—44no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
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—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—44no—
614C4×D4—44no—
615#117—22no—
616#117—22no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621C2×C4⋊C4—21no—
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⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
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×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773#97—41no—
774#97—41no—
775C4×C8—41no—
776C4×C8—41no—
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#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819C24—24no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830#41—82no—
831#41—82no—
832#41—82no—
833#41—82no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8C2×#4112yes—
851C2×Q8C2×#4112yes—
852C2×D4—24no—
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—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
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—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4H(5,𝔽2)12yes—
891C2×D4H(5,𝔽2)12yes—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—816no—
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C2×#4112yes—
948C22×C4C2×#4112yes—
949C22×C4C2511yescharacteristic
950Q16—82no—
951Q16—82no—
952SD16—44no—
953SD16—44no—
954SD16—44no—
955SD16—44no—
956SD16—82no—
957SD16—82no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
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—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4C2×#4112yes—
1036C4⋊C4C2×#4112yes—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—24no—
1071C42—24no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—41no—
1085C42—41no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—22no—
1105C23—48no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23#52512yes—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—22no—
1136Q8—22no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145D4—22no—
1146D4—22no—
1147D4—22no—
1148D4—22no—
1149D4—48no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—84no—
1159D4—162no—
1160D4—162no—
1161D4—162no—
1162D4—162no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—82no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4#52512yes—
1252C2×C4#57712yes—
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4#58511yescharacteristic
1258C2×C4#58511yescharacteristic
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—816no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22C2×#52511yescharacteristic
1297C22#348411yescharacteristic
1298C22#348711yescharacteristic
1299C22C2×#57711yescharacteristic
1300C22#358411yescharacteristic
1301C22#358511yescharacteristic
1302C22#358611yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—42no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4#351311yescharacteristic
1330C4#351311yescharacteristic
1331C4#351311yescharacteristic
1332C4#351311yescharacteristic
1333C2—42no—
1334C2—82no—
1335C2—82no—
1336C2—161no—
1337C2#3535611yescharacteristic
1338C2#6057211yescharacteristic
1339C2#6057611yescharacteristic
1340C2#6161011yescharacteristic
1341C2#6161311yescharacteristic
1342C2#6191111yescharacteristic
1343C2#6191911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34421C2semidirect
3. #29253C2semidirect
4. #29251C2semidirect
5. #27594C2semidirect
6. #27593C2semidirect
7. #27210C2semidirect
8. #27207C2semidirect
9. #27194C2semidirect
10. #27191C2semidirect
11. #26717C2semidirect
12. #26716C2semidirect
13. #26701C2semidirect
14. #26700C2semidirect
15. #26605C2semidirect
16. #26604C2semidirect
17. #26589C2semidirect
18. #26588C2semidirect
19. #26181C2semidirect
20. #26175C2semidirect
21. #26165C2semidirect
22. #26159C2semidirect
25. #23944C2semidirect
26. #23942C2semidirect
27. #22048C2semidirect
28. #22042C2semidirect
29. #21915C2semidirect
30. #21453C2semidirect
31. C4×#450C2semidirect
67. #2370C22semidirect
68. #2370C22semidirect
69. #2365C22semidirect
70. #2365C22semidirect
71. #2355C22semidirect
72. #2355C22semidirect
73. #2351C22semidirect
74. #2351C22semidirect
89. #2097C22semidirect
92. #2092C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
99. #2072C22semidirect
100. #2071C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2066C22semidirect
104. #2066C22semidirect
109. #2026C22semidirect
112. #2025C22semidirect
113. #2016C22semidirect
120. #2013C22semidirect
125. #1973C22semidirect
126. #1971C22semidirect
127. #1969C22semidirect
128. #1968C22semidirect
129. #1936C22semidirect
130. #1935C22semidirect
131. #1934C22semidirect
132. #1933C22semidirect
133. #1928C22semidirect
134. #1928C22semidirect
135. #1927C22semidirect
136. #1927C22semidirect
139. #1926C22semidirect
140. #1926C22semidirect
143. #1925C22semidirect
144. #1925C22semidirect
145. #1921C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
152. #1917C22semidirect
153. #1916C22semidirect
154. #1916C22semidirect
155. #1916C22semidirect
156. #1916C22semidirect
161. #1880C22semidirect
162. #1880C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
177. #1865C22semidirect
178. #1865C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect

Maximal subgroups

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

subgroupindex
#351522
#344212
#292532
#292512
#275942
#275932
#272102
#272072
#271942
#271912
#267172
#267162
#267012
#267002
#266052
#266042
#265892
#265882
#261812
#261752
#261652
#261592
#242202
#239442
#239422
#220482
#220422
#219152
#214532
C4×#4502