Finite Group Databasebeta

← #6867335

Subgroups — #6867335

Order 512.

1217 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39296C211yesmaximal, characteristic
2#35578C211yesmaximal, characteristic
3#33155C211yesmaximal, characteristic
4#31763C211yesmaximal, characteristic
5#31761C211yesmaximal, characteristic
6#31703C211yesmaximal, characteristic
7#31697C211yesmaximal, characteristic
8#31450C211yesmaximal, characteristic
9#31446C211yesmaximal, characteristic
10#30803C211yesmaximal, characteristic
11#30779C211yesmaximal, characteristic
12#30160C211yesmaximal, characteristic, complemented
13#30151C211yesmaximal, characteristic, complemented
14#29528C211yesmaximal, characteristic, complemented
15#29519C211yesmaximal, characteristic, complemented
16#29283C211yesmaximal, characteristic, complemented
17#29274C211yesmaximal, characteristic, complemented
18#28821C211yesmaximal, characteristic, complemented
19#28795C211yesmaximal, characteristic, complemented
20#27887C211yesmaximal, characteristic
21#27823C211yesmaximal, characteristic, complemented
22#27742C211yesmaximal, characteristic, complemented
23#27639C211yesmaximal, characteristic
24#26512C211yesmaximal, characteristic, complemented
25#26454C211yesmaximal, characteristic, complemented
26#26104C211yesmaximal, characteristic, complemented
27#26029C211yesmaximal, characteristic, complemented
28#22638C211yesmaximal, characteristic
29#22254C211yesmaximal, characteristic, complemented
30#22251C211yesmaximal, characteristic, complemented
31#21585C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#500C2211yescharacteristic
34C2×#484C2211yescharacteristic
35#2863C2211yescharacteristic
36#2810—21no—
37#2798—21no—
38#2762—21no—
39#2759—21no—
40#2645C2211yescharacteristic
41#2628C2211yescharacteristic
42#2605—21no—
43#2596—21no—
44#2590—21no—
45#2589—21no—
46#2586—21no—
47#2570C2211yescharacteristic
48#2568C2211yescharacteristic
49#2556—21no—
50#2552C2211yescharacteristic
51#2551C2211yescharacteristic
52#2550C2211yescharacteristic
53#2550C2211yescharacteristic
54#2532—21no—
55#2514—21no—
56#2495C2211yescharacteristic
57#2494C2211yescharacteristic
58#2492C2211yescharacteristic
59#2489C2211yescharacteristic
60#2465—21no—
61#2462—21no—
62#2451—21no—
63#2441C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2439C2211yescharacteristic
67#2429—21no—
68#2369C2211yescharacteristic
69#2356C2211yescharacteristic
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2330C2211yescharacteristic
73#2323C2211yescharacteristic
74#2314C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77C4×#125C2211yescharacteristic
78#2298C2211yescharacteristic
79#2274C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2096C2211yescharacteristic
87#2095C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2083C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2074C2211yescharacteristic
101#2072C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2026C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#1993C2211yescharacteristic
121#1993C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1992C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1988C2211yescharacteristic
130#1988C2211yescharacteristic
131#1987C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1947C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1941C2211yescharacteristic
144#1940C2211yescharacteristic
145#1939C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1923C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1918C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1918C2211yescharacteristic
177#1918C2211yescharacteristic
178#1873C2211yescharacteristic
179#1854C2211yescharacteristic
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1847C2211yescharacteristic
183#1836C2211yescharacteristic
184#1835C2211yescharacteristic
185#1835C2211yescharacteristic
186#1832C2211yescharacteristic
187#1831C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1823C2211yescharacteristic
191#1805C2211yescharacteristic
192#1803C2211yescharacteristic
193#1798C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic
202#1745C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221#501—24no—
222#500—24no—
223#484—24no—
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
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×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264#401—21no—
265#401—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#399—21no—
277#399—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#397—21no—
286#397—21no—
287#397—21no—
288#396—21no—
289#396—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#395—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#393—21no—
298#393—21no—
299#393—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
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#389—21no—
328#389—21no—
329#389—21no—
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#389C2311yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388D411yescharacteristic
354#388D411yescharacteristic
355#388D411yescharacteristic
356#388D411yescharacteristic
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387D411yescharacteristic
379#387D411yescharacteristic
380#387D411yescharacteristic
381#387D411yescharacteristic
382#385—21no—
383#385—21no—
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#383—21no—
389#383—21no—
390#383—21no—
391#382—21no—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#380C2311yescharacteristic
398#380C2311yescharacteristic
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2311yescharacteristic
426#376—21no—
427#376C2311yescharacteristic
428C43C2311yescharacteristic
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×Q8—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C23×C4—21no—
488C23×C4C2411yescharacteristic
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—22no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—82no—
508#125—22no—
509#125—22no—
510#125—41no—
511#125—41no—
512#125—82no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—82no—
516C22⋊Q8—82no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—82no—
520C4×Q8—82no—
521#117—22no—
522#117—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—22no—
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—41no—
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4C2×D411yescharacteristic
591C2×C22⋊C4C2×D411yescharacteristic
592C2×C22⋊C4C2×D411yescharacteristic
593C2×C22⋊C4C2×D411yescharacteristic
594C2×C22⋊C4C2×D411yescharacteristic
595C2×C22⋊C4C2×D411yescharacteristic
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42C2×D411yescharacteristic
610C2×C42C2×D411yescharacteristic
611C2×C42C2×D411yescharacteristic
612C2×C42C2×D411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619#107—22no—
620#107—22no—
621#107—22no—
622#107—22no—
623#107—22no—
624#107—41no—
625#107—41no—
626#107—41no—
627#107—41no—
628#107#4114yes—
629#106—22no—
630#106—22no—
631#106—22no—
632#106—41no—
633#106—41no—
634#106—41no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—41no—
638C4⋊C8—41no—
639C4⋊C8—41no—
640C4⋊C8—41no—
641#103—22no—
642#103—22no—
643#103—22no—
644#103—41no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649C22⋊C8—22no—
650C22⋊C8—41no—
651C22⋊C8—41no—
652C22⋊C8—41no—
653#97—22no—
654#97—22no—
655#97—41no—
656#97—41no—
657C4×C8—22no—
658C4×C8—22no—
659#95—21no—
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#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#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
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—21no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—42no—
735C2×Q8—42no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×Q8—81no—
740C2×Q8—81no—
741C2×Q8—81no—
742C2×Q8—81no—
743C2×Q8—81no—
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—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—42no—
767C22×C4—81no—
768C22×C4—81no—
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×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C2511yescharacteristic
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—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×#4112yes—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—22no—
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—21no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
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—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
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⋊C4C2×#4112yes—
876C4⋊C4C2×#4112yes—
877C4⋊C42−1+412yes—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—41no—
882C22⋊C4—41no—
883C22⋊C4—41no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C22⋊C4—81no—
891C42—22no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—41no—
903C42—41no—
904C42—41no—
905C42—42no—
906C42—42no—
907C42—42no—
908C42—81no—
909C42—81no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C422−1+412yes—
919C422−1+412yes—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23C23×D411yescharacteristic
928Q8—41no—
929Q8—41no—
930Q8—41no—
931Q8—41no—
932Q8—84no—
933Q8—84no—
934Q8—162no—
935Q8—162no—
936Q8—162no—
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—21no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
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—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—162no—
1026C2×C4#53612yes—
1027C2×C4#53612yes—
1028C2×C4#57812yes—
1029C2×C4C22×#4111yescharacteristic
1030C2×C4C2×2−1+411yescharacteristic
1031C2×C4C2×2−1+411yescharacteristic
1032C2×C4C2×2−1+411yescharacteristic
1033C2×C4#58511yescharacteristic
1034C2×C4#58511yescharacteristic
1035C8—22no—
1036C8—41no—
1037C8—41no—
1038C8—41no—
1039C8—41no—
1040C8—41no—
1041C8—41no—
1042C8—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22C2×#53611yescharacteristic
1051C22D4×#4111yescharacteristic
1052C22#348911yescharacteristic
1053C22C2×#57811yescharacteristic
1054C22#358511yescharacteristic
1055C22#358511yescharacteristic
1056C22#358611yescharacteristic
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—42no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4#350911yescharacteristic
1087C4#351811yescharacteristic
1088C4#355511yescharacteristic
1089C4#356511yescharacteristic
1090C2—81no—
1091C2#3986711yescharacteristic
1092C2#6088511yescharacteristic
1093C2#6089311yescharacteristic
1094C2#6150611yescharacteristic
1095C2#6154411yescharacteristic
1096C2#6216511yescharacteristic
1097C2#6222611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #30160C2semidirect
13. #30151C2semidirect
14. #29528C2semidirect
15. #29519C2semidirect
16. #29283C2semidirect
17. #29274C2semidirect
18. #28821C2semidirect
19. #28795C2semidirect
21. #27823C2semidirect
22. #27742C2semidirect
24. #26512C2semidirect
25. #26454C2semidirect
26. #26104C2semidirect
27. #26029C2semidirect
29. #22254C2semidirect
30. #22251C2semidirect

Maximal subgroups

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

subgroupindex
#392962
#355782
#331552
#317632
#317612
#317032
#316972
#314502
#314462
#308032
#307792
#301602
#301512
#295282
#295192
#292832
#292742
#288212
#287952
#278872
#278232
#277422
#276392
#265122
#264542
#261042
#260292
#226382
#222542
#222512
#215852