Finite Group Databasebeta

← #6800398

Subgroups — #6800398

Order 512.

1229 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39603C211yesmaximal, characteristic
2#35286C211yesmaximal, characteristic
3#33152C211yesmaximal, characteristic
4#32337C211yesmaximal, characteristic, complemented
5#32332C211yesmaximal, characteristic, complemented
6#32321C211yesmaximal, characteristic, complemented
7#32316C211yesmaximal, characteristic, complemented
8#31481C211yesmaximal, characteristic, complemented
9#31476C211yesmaximal, characteristic, complemented
10#31465C211yesmaximal, characteristic, complemented
11#31460C211yesmaximal, characteristic, complemented
12#29978C211yesmaximal, characteristic
13#29975C211yesmaximal, characteristic
14#28806C211yesmaximal, characteristic, complemented
15#28804C211yesmaximal, characteristic, complemented
16#27971C211yesmaximal, characteristic
17#27970C211yesmaximal, characteristic
18#27966C211yesmaximal, characteristic
19#27745C211yesmaximal, characteristic, complemented
20#27741C211yesmaximal, characteristic, complemented
21#27656C211yesmaximal, characteristic
22#27656C211yesmaximal, characteristic
23#27648C211yesmaximal, characteristic
24#26524C211yesmaximal, characteristic, complemented
25#26523C211yesmaximal, characteristic, complemented
26#26123C211yesmaximal, characteristic, complemented
27#26122C211yesmaximal, characteristic, complemented
28#22628C211yesmaximal, characteristic
29#22087C211yesmaximal, characteristic
30#22087C211yesmaximal, characteristic
31#21583C211yesmaximal, characteristic
32C2×#484C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#485C2211yescharacteristic
35#2859—21no—
36#2859—21no—
37#2851C2211yescharacteristic
38#2792—21no—
39#2791—21no—
40#2788—21no—
41#2768—21no—
42#2647—21no—
43#2647—21no—
44#2629C2211yescharacteristic
45#2628C2211yescharacteristic
46#2574—21no—
47#2571C2211yescharacteristic
48#2571C2211yescharacteristic
49#2571C2211yescharacteristic
50#2571C2211yescharacteristic
51#2565C2211yescharacteristic
52#2552C2211yescharacteristic
53#2552C2211yescharacteristic
54#2552C2211yescharacteristic
55#2552C2211yescharacteristic
56#2550C2211yescharacteristic
57#2522—21no—
58#2520—21no—
59#2508—21no—
60#2508C2211yescharacteristic
61#2507C2211yescharacteristic
62#2453C2211yescharacteristic
63#2451C2211yescharacteristic
64#2442—21no—
65#2442—21no—
66#2442—21no—
67#2442—21no—
68#2370C2211yescharacteristic
69#2351C2211yescharacteristic
70#2323C2211yescharacteristic
71#2323C2211yescharacteristic
72#2317C2211yescharacteristic
73#2317C2211yescharacteristic
74#2316C2211yescharacteristic
75#2316C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77#2285C2211yescharacteristic
78C2×#384C2211yescharacteristic
79C4×#117C2211yescharacteristic
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#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2087C2211yescharacteristic
101#2087C2211yescharacteristic
102#2086C2211yescharacteristic
103#2086C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2083C2211yescharacteristic
107#2083C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2074C2211yescharacteristic
111#2074C2211yescharacteristic
112#2072C2211yescharacteristic
113#2072C2211yescharacteristic
114#2072C2211yescharacteristic
115#2072C2211yescharacteristic
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#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1947C2211yescharacteristic
133#1947C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1942C2211yescharacteristic
139#1942C2211yescharacteristic
140#1940C2211yescharacteristic
141#1940C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1873C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1863C2211yescharacteristic
166#1863C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1836C2211yescharacteristic
171#1836C2211yescharacteristic
172#1836C2211yescharacteristic
173#1836C2211yescharacteristic
174#1835C2211yescharacteristic
175#1834C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1803C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—21no—
205C2×#125—21no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C4⋊C4—21no—
219C22×C4⋊C4—21no—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#485—24no—
224#484—24no—
225#484—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×C22⋊C8C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#399—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#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#396—21no—
293#396—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#393—21no—
298#391—21no—
299#391—21no—
300#391C2311yescharacteristic
301#391C2311yescharacteristic
302#391C2311yescharacteristic
303#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
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#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
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#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#388—21no—
345#388—21no—
346#388—21no—
347#388—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#385—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#384—21no—
369#384—21no—
370#384D411yescharacteristic
371#384D411yescharacteristic
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#384C2311yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#382—21no—
382#382—21no—
383#382—21no—
384#382—21no—
385#382—21no—
386#382—21no—
387#382D411yescharacteristic
388#382D411yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380D411yescharacteristic
400#380D411yescharacteristic
401#380D411yescharacteristic
402#380D411yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423#376—21no—
424C43—21no—
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#340C2311yescharacteristic
468#340C2311yescharacteristic
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×Q8C2411yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C4⋊Q8—41no—
497C4⋊Q8—41no—
498#125—22no—
499#125—22no—
500#125—41no—
501#125—41no—
502#125—82no—
503#125—82no—
504#125—82no—
505#125—82no—
506C22⋊Q8—22no—
507C22⋊Q8#4114yes—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—41no—
511C4×Q8—41no—
512C4×Q8—41no—
513C4×Q8—41no—
514#117—22no—
515#117—22no—
516#117—41no—
517#117—41no—
518#117—41no—
519#117—41no—
520#117—41no—
521#117—41no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
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⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—82no—
573C2×C4⋊C4—82no—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—22no—
634#107—22no—
635#107—22no—
636#107—22no—
637#107—22no—
638#107—41no—
639#107—41no—
640#107—41no—
641#106—22no—
642#106—41no—
643#106—41no—
644#106—41no—
645C4⋊C8—22no—
646C4⋊C8—22no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649C4⋊C8—41no—
650C4⋊C8—41no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—41no—
658#103—41no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663#97—22no—
664#97—22no—
665#97—41no—
666#97—41no—
667C4×C8—41no—
668C4×C8—41no—
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#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24C22×D411yescharacteristic
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—81no—
729C2×Q8—81no—
730C2×Q8—81no—
731C2×Q8C2×#4112yes—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
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—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—81no—
761C22×C4—81no—
762C22×C4—81no—
763C22×C4—81no—
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×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C2×#4112yes—
778C22×C42−1+412yes—
779C22×C4C2511yescharacteristic
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—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C4⋊C4—24no—
805C4⋊C4—22no—
806C4⋊C4—22no—
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—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
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⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4C2×#4112yes—
892C22⋊C4—24no—
893C22⋊C4—41no—
894C22⋊C4—41no—
895C22⋊C4—41no—
896C22⋊C4—41no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C42—22no—
903C42—22no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—42no—
915C42—42no—
916C42—42no—
917C42—42no—
918C42—42no—
919C42—42no—
920C42—42no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C422−1+412yes—
927C422−1+412yes—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23#54812yes—
935C23C23×D411yescharacteristic
936Q8—22no—
937Q8—22no—
938Q8—41no—
939Q8—41no—
940Q8—162no—
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—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
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—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—44no—
983C2×C4—44no—
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—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—162no—
1031C2×C4—162no—
1032C2×C4#53612yes—
1033C2×C4#53612yes—
1034C2×C4#54812yes—
1035C2×C4#57812yes—
1036C2×C4C22×#4111yescharacteristic
1037C2×C4C2×2−1+411yescharacteristic
1038C2×C4C2×2−1+411yescharacteristic
1039C2×C4C2×2−1+411yescharacteristic
1040C2×C4#58511yescharacteristic
1041C2×C4#58511yescharacteristic
1042C8—41no—
1043C8—41no—
1044C8—41no—
1045C8—41no—
1046C8—41no—
1047C8—41no—
1048C8—41no—
1049C8—41no—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22C2×#53611yescharacteristic
1058C22C2×#54811yescharacteristic
1059C22#348511yescharacteristic
1060C22C2×#57811yescharacteristic
1061C22#358511yescharacteristic
1062C22#358511yescharacteristic
1063C22#358611yescharacteristic
1064C4—22no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—42no—
1077C4—41no—
1078C4—42no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4#351511yescharacteristic
1094C4#351511yescharacteristic
1095C4#356311yescharacteristic
1096C4#356311yescharacteristic
1097C2—42no—
1098C2#3912211yescharacteristic
1099C2#6086711yescharacteristic
1100C2#6087411yescharacteristic
1101C2#6133711yescharacteristic
1102C2#6134211yescharacteristic
1103C2#6179911yescharacteristic
1104C2#6181611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #32337C2semidirect
5. #32332C2semidirect
6. #32321C2semidirect
7. #32316C2semidirect
8. #31481C2semidirect
9. #31476C2semidirect
10. #31465C2semidirect
11. #31460C2semidirect
14. #28806C2semidirect
15. #28804C2semidirect
19. #27745C2semidirect
20. #27741C2semidirect
24. #26524C2semidirect
25. #26523C2semidirect
26. #26123C2semidirect
27. #26122C2semidirect

Maximal subgroups

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

subgroupindex
#396032
#352862
#331522
#323372
#323322
#323212
#323162
#314812
#314762
#314652
#314602
#299782
#299752
#288062
#288042
#279712
#279702
#279662
#277452
#277412
#276562
#276482
#265242
#265232
#261232
#261222
#226282
#220872
#215832