Finite Group Databasebeta

← #6856559

Subgroups — #6856559

Order 512.

1237 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39753C211yesmaximal, characteristic, complemented
2#35175C211yesmaximal, characteristic
3#33197C211yesmaximal, characteristic
4#32336C211yesmaximal, characteristic, complemented
5#32328C211yesmaximal, characteristic, complemented
6#32322C211yesmaximal, characteristic, complemented
7#32314C211yesmaximal, characteristic, complemented
8#31478C211yesmaximal, characteristic
9#31470C211yesmaximal, characteristic
10#31466C211yesmaximal, characteristic
11#31458C211yesmaximal, characteristic
12#29874C211yesmaximal, characteristic
13#29874C211yesmaximal, characteristic
14#29291C211yesmaximal, characteristic, complemented
15#29282C211yesmaximal, characteristic, complemented
16#29281C211yesmaximal, characteristic, complemented
17#29229C211yesmaximal, characteristic, complemented
18#29228C211yesmaximal, characteristic, complemented
19#29225C211yesmaximal, characteristic, complemented
20#28808C211yesmaximal, characteristic, complemented
21#28802C211yesmaximal, characteristic, complemented
22#27743C211yesmaximal, characteristic
23#27739C211yesmaximal, characteristic
24#26290C211yesmaximal, characteristic, complemented
25#26289C211yesmaximal, characteristic, complemented
26#25003C211yesmaximal, characteristic
27#25002C211yesmaximal, characteristic
28#22824C211yesmaximal, characteristic, complemented
29#22123C211yesmaximal, characteristic
30#22123C211yesmaximal, characteristic
31#21617C211yesmaximal, characteristic
32C2×#478C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×#476C2211yescharacteristic
35#2868C2211yescharacteristic
36#2855—21no—
37#2851—21no—
38#2791—21no—
39#2791—21no—
40#2713—21no—
41#2713—21no—
42#2667—21no—
43#2665—21no—
44#2660C2211yescharacteristic
45#2660C2211yescharacteristic
46#2589—21no—
47#2587—21no—
48#2584C2211yescharacteristic
49#2580C2211yescharacteristic
50#2574—21no—
51#2571C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2566C2211yescharacteristic
55#2565—21no—
56#2556—21no—
57#2552C2211yescharacteristic
58#2552C2211yescharacteristic
59#2552C2211yescharacteristic
60#2550—21no—
61#2550C2211yescharacteristic
62#2508C2211yescharacteristic
63#2506—21no—
64#2506C2211yescharacteristic
65#2454C2211yescharacteristic
66#2452C2211yescharacteristic
67#2451—21no—
68#2355C2211yescharacteristic
69Q8×C4⋊C4C2211yescharacteristic
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2331C2211yescharacteristic
73#2330C2211yescharacteristic
74#2319C2211yescharacteristic
75#2319C2211yescharacteristic
76C4×#125C2211yescharacteristic
77C4×#125C2211yescharacteristic
78#2295C2211yescharacteristic
79C42×D4C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2100C2211yescharacteristic
92#2100C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2099C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2071C2211yescharacteristic
113#2071C2211yescharacteristic
114#2071C2211yescharacteristic
115#2071C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2057C2211yescharacteristic
120#1993C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1992C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1988C2211yescharacteristic
133#1988C2211yescharacteristic
134#1988C2211yescharacteristic
135#1987C2211yescharacteristic
136#1987C2211yescharacteristic
137#1985C2211yescharacteristic
138#1985C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1948C2211yescharacteristic
145#1948C2211yescharacteristic
146#1948C2211yescharacteristic
147#1948C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1941C2211yescharacteristic
151#1941C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1920C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1917C2211yescharacteristic
175#1917C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1842C2211yescharacteristic
181#1836C2211yescharacteristic
182#1836C2211yescharacteristic
183#1836C2211yescharacteristic
184#1836C2211yescharacteristic
185#1835C2211yescharacteristic
186#1834C2211yescharacteristic
187#1832C2211yescharacteristic
188#1832C2211yescharacteristic
189#1804C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1768C2211yescharacteristic
199#1768C2211yescharacteristic
200#1767C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C22×C42—21no—
222#478—24no—
223#476—24no—
224#476—24no—
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#97C2311yescharacteristic
254C2×#97C2311yescharacteristic
255C2×#97C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259#400—21no—
260#400—21no—
261#400—21no—
262#400—21no—
263#400—21no—
264#400—21no—
265#399—21no—
266#399—21no—
267#398—21no—
268#398—21no—
269#398—21no—
270#398—21no—
271#398—21no—
272#398—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#396—21no—
284#396—21no—
285#396—21no—
286#396—21no—
287#395—21no—
288#395—21no—
289#395—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#393—21no—
294#393—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391D411yescharacteristic
304#391D411yescharacteristic
305#390C2311yescharacteristic
306#390C2311yescharacteristic
307#390C2311yescharacteristic
308#390C2311yescharacteristic
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389D411yescharacteristic
322#389D411yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387D411yescharacteristic
364#387D411yescharacteristic
365#387D411yescharacteristic
366#387D411yescharacteristic
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#384—21no—
374#384—21no—
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#384C2311yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#382—21no—
385#382—21no—
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#381—21no—
394#381—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4—21no—
419C4×C22⋊C4—21no—
420#376C2311yescharacteristic
421#376C2311yescharacteristic
422C43C2311yescharacteristic
423#340C2311yescharacteristic
424#340C2311yescharacteristic
425#340C2311yescharacteristic
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2×D411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—22no—
502C4⋊Q8—41no—
503C4⋊Q8—82no—
504C4⋊Q8—82no—
505#125—22no—
506#125—22no—
507#125—22no—
508#125—22no—
509#125—22no—
510#125—41no—
511#125—82no—
512#125—82no—
513#125—82no—
514#125—82no—
515C22⋊Q8—82no—
516C4×Q8—22no—
517C4×Q8—22no—
518C4×Q8—82no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—41no—
524C4×D4#4114yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—82no—
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626#107—22no—
627#107—22no—
628#107—41no—
629#107—41no—
630#106—22no—
631#106—22no—
632#106—22no—
633#106—22no—
634#106—22no—
635#106—22no—
636#106—41no—
637#106—41no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—22no—
642C4⋊C8—22no—
643C4⋊C8—22no—
644C4⋊C8—41no—
645C4⋊C8—41no—
646#102—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—41no—
653#102—41no—
654#97—22no—
655#97—22no—
656#97—41no—
657#97—41no—
658C4×C8—41no—
659C4×C8—41no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704#95C2×D411yescharacteristic
705#95C2×D411yescharacteristic
706#95C2×D411yescharacteristic
707#95C2×D411yescharacteristic
708#95C2×D411yescharacteristic
709#95C2×D411yescharacteristic
710#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715C24—21no—
716C2×Q8—22no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8—81no—
723C2×Q8—81no—
724C2×Q8—81no—
725C2×Q8—81no—
726C2×Q8—81no—
727C2×Q8—81no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4C2×#4112yes—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—24no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—81no—
754C22×C4—81no—
755C22×C4—81no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C2511yescharacteristic
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—41no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4C2×#4112yes—
878C4⋊C42−1+412yes—
879C22⋊C4—24no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—81no—
883C22⋊C4—81no—
884C22⋊C4—81no—
885C22⋊C4—81no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—41no—
902C42—41no—
903C42—41no—
904C42—42no—
905C42—42no—
906C42—42no—
907C42—81no—
908C42—81no—
909C42—81no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42C2×#4112yes—
916C422−1+412yes—
917C422−1+412yes—
918C422−1+412yes—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23C23×D411yescharacteristic
927Q8—44no—
928Q8—162no—
929Q8—162no—
930Q8—162no—
931D4—22no—
932D4—22no—
933D4—41no—
934D4—41no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—84no—
1018C2×C4—84no—
1019C2×C4—84no—
1020C2×C4#53612yes—
1021C2×C4#53612yes—
1022C2×C4#54812yes—
1023C2×C4#54812yes—
1024C2×C4#57712yes—
1025C2×C4C22×#4111yescharacteristic
1026C2×C4C2×2−1+411yescharacteristic
1027C2×C4C2×2−1+411yescharacteristic
1028C2×C4C2×2−1+411yescharacteristic
1029C2×C4C2×2−1+411yescharacteristic
1030C2×C4#58511yescharacteristic
1031C8—41no—
1032C8—41no—
1033C8—41no—
1034C8—41no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C8—41no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22C2×#53611yescharacteristic
1047C22C2×#54811yescharacteristic
1048C22#348911yescharacteristic
1049C22C2×#57711yescharacteristic
1050C22#358511yescharacteristic
1051C22#358511yescharacteristic
1052C22#358611yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—22no—
1058C4—41no—
1059C4—41no—
1060C4—41no—
1061C4—42no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4#350711yescharacteristic
1083C4#350911yescharacteristic
1084C4#355511yescharacteristic
1085C4#355611yescharacteristic
1086C2—82no—
1087C2#3972411yescharacteristic
1088C2#6086711yescharacteristic
1089C2#6089211yescharacteristic
1090C2#6133711yescharacteristic
1091C2#6134011yescharacteristic
1092C2#6215611yescharacteristic
1093C2#6223011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39753C2semidirect
4. #32336C2semidirect
5. #32328C2semidirect
6. #32322C2semidirect
7. #32314C2semidirect
14. #29291C2semidirect
15. #29282C2semidirect
16. #29281C2semidirect
17. #29229C2semidirect
18. #29228C2semidirect
19. #29225C2semidirect
20. #28808C2semidirect
21. #28802C2semidirect
24. #26290C2semidirect
25. #26289C2semidirect
28. #22824C2semidirect

Maximal subgroups

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

subgroupindex
#397532
#351752
#331972
#323362
#323282
#323222
#323142
#314782
#314702
#314662
#314582
#298742
#292912
#292822
#292812
#292292
#292282
#292252
#288082
#288022
#277432
#277392
#262902
#262892
#250032
#250022
#228242
#221232
#216172