Finite Group Databasebeta

← #6909938

Subgroups — #6909938

Order 512.

1367 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38101C211yesmaximal, characteristic
2#37757C211yesmaximal, characteristic
3#32828C211yesmaximal, characteristic, complemented
4#32791C211yesmaximal, characteristic, complemented
5#31764C211yesmaximal, characteristic, complemented
6#31748C211yesmaximal, characteristic, complemented
7#31485C211yesmaximal, characteristic, complemented
8#31465C211yesmaximal, characteristic, complemented
9#30964C211yesmaximal, characteristic, complemented
10#30948C211yesmaximal, characteristic, complemented
11#30803C211yesmaximal, characteristic, complemented
12#30779C211yesmaximal, characteristic, complemented
13#30193C211yesmaximal, characteristic, complemented
14#30100C211yesmaximal, characteristic, complemented
15#30073C211yesmaximal, characteristic, complemented
16#29973C211yesmaximal, characteristic, complemented
17#29695C211yesmaximal, characteristic, complemented
18#29341C211yesmaximal, characteristic, complemented
19#29283C211yesmaximal, characteristic, complemented
20#26433C211yesmaximal, characteristic, complemented
21#26418C211yesmaximal, characteristic, complemented
22#26362C211yesmaximal, characteristic, complemented
23#26351C211yesmaximal, characteristic, complemented
24#26220C211yesmaximal, characteristic
25#26204C211yesmaximal, characteristic
26#26145C211yesmaximal, characteristic
27#26129C211yesmaximal, characteristic
28#25821C211yesmaximal, characteristic, complemented
29#24064C211yesmaximal, characteristic, complemented
30#23557C211yesmaximal, characteristic, complemented
31#22004C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#427C2211yescharacteristic
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2805—21no—
45#2802—21no—
46#2768—21no—
47#2742—21no—
48#2729—21no—
49#2728—21no—
50#2719—21no—
51#2690—21no—
52#2647C2211yescharacteristic
53#2642C2211yescharacteristic
54#2628C2211yescharacteristic
55#2621C2211yescharacteristic
56#2583—21no—
57#2571C2211yescharacteristic
58#2550C2211yescharacteristic
59#2505—21no—
60#2492C2211yescharacteristic
61#2489C2211yescharacteristic
62#2487—21no—
63#2477—21no—
64#2475—21no—
65#2453C2211yescharacteristic
66#2451C2211yescharacteristic
67#2450—21no—
68#2446—21no—
69#2442C2211yescharacteristic
70#2442C2211yescharacteristic
71#2441C2211yescharacteristic
72#2440C2211yescharacteristic
73#2421—21no—
74#2417C2211yescharacteristic
75#2415C2211yescharacteristic
76#2362C2211yescharacteristic
77#2360C2211yescharacteristic
78#2352C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2331C2211yescharacteristic
81#2330C2211yescharacteristic
82#2316C2211yescharacteristic
83C2×#389C2211yescharacteristic
84#2290C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2100C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2096C2211yescharacteristic
96#2095C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2072C2211yescharacteristic
110#2072C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2058C2211yescharacteristic
124#2058C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2057C2211yescharacteristic
129#2043C2211yescharacteristic
130#2043C2211yescharacteristic
131#2043C2211yescharacteristic
132#2043C2211yescharacteristic
133#2036C2211yescharacteristic
134#2036C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2026C2211yescharacteristic
138#2026C2211yescharacteristic
139#2024C2211yescharacteristic
140#2024C2211yescharacteristic
141#1993C2211yescharacteristic
142#1991C2211yescharacteristic
143#1989C2211yescharacteristic
144#1989C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1894C2211yescharacteristic
168#1894C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1870C2211yescharacteristic
178#1869C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic
190#1850C2211yescharacteristic
191#1840C2211yescharacteristic
192#1832C2211yescharacteristic
193#1824C2211yescharacteristic
194#1824C2211yescharacteristic
195#1817C2211yescharacteristic
196#1805C2211yescharacteristic
197#1805C2211yescharacteristic
198#1797C2211yescharacteristic
199#1750C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#544—42no—
206#544—42no—
207#533—42no—
208#533—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4—21no—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#501—42no—
244#500—42no—
245#484—42no—
246#484—42no—
247#479—42no—
248#479—42no—
249#428—42no—
250#427—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#399—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#387—21no—
382#387—21no—
383#387—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#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386D411yescharacteristic
400#386D411yescharacteristic
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376C2311yescharacteristic
443C2×#95—21no—
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#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4C2×D411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—44no—
527#125—22no—
528#125—22no—
529#125—41no—
530#125—41no—
531#125—41no—
532#125—41no—
533#125—41no—
534#125—41no—
535#125—44no—
536#125—44no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—41no—
544C22⋊Q8—41no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—82no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—44no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—82no—
557#117—22no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—44no—
562#117—41no—
563#117—41no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—82no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—41no—
662C2×C42—41no—
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#107—22no—
671#107—22no—
672#107—22no—
673#107—22no—
674#107—22no—
675#107—22no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#106—22no—
681#106—22no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690#103—22no—
691#103—22no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—41no—
713C4×C8—41no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×Q8—24no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—42no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—41no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C42−1+412yes—
851C22×C42−1+412yes—
852C22×C4C2511yescharacteristic
853M16—44no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—44no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4H(5,𝔽2)12yes—
951C4⋊C4H(5,𝔽2)12yes—
952C4⋊C42−1+412yes—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—41no—
984C42—41no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23#53612yes—
1006C23#57812yes—
1007C23C23×D411yescharacteristic
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—84no—
1017Q8—162no—
1018Q8—162no—
1019D4—44no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—44no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—82no—
1113C2×C4—84no—
1114C2×C4—162no—
1115C2×C4—162no—
1116C2×C4—162no—
1117C2×C4#53612yes—
1118C2×C4C2×H(5,𝔽2)11yescharacteristic
1119C2×C4C2×H(5,𝔽2)11yescharacteristic
1120C2×C4C2×2−1+411yescharacteristic
1121C2×C4C2×2−1+411yescharacteristic
1122C2×C4C2×2−1+411yescharacteristic
1123C2×C4#58511yescharacteristic
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22C2×#53611yescharacteristic
1147C22#348411yescharacteristic
1148C22#348911yescharacteristic
1149C22C2×#57811yescharacteristic
1150C22#358411yescharacteristic
1151C22#358511yescharacteristic
1152C22#358611yescharacteristic
1153C4—22no—
1154C4—41no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—42no—
1165C4—42no—
1166C4—41no—
1167C4—41no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#354111yescharacteristic
1182C4#354111yescharacteristic
1183C4#355211yescharacteristic
1184C4#355211yescharacteristic
1185C2—42no—
1186C2—42no—
1187C2#4058911yescharacteristic
1188C2#6087411yescharacteristic
1189C2#6089111yescharacteristic
1190C2#6161211yescharacteristic
1191C2#6161411yescharacteristic
1192C2#6221411yescharacteristic
1193C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32828C2semidirect
4. #32791C2semidirect
5. #31764C2semidirect
6. #31748C2semidirect
7. #31485C2semidirect
8. #31465C2semidirect
9. #30964C2semidirect
10. #30948C2semidirect
11. #30803C2semidirect
12. #30779C2semidirect
13. #30193C2semidirect
14. #30100C2semidirect
15. #30073C2semidirect
16. #29973C2semidirect
17. #29695C2semidirect
18. #29341C2semidirect
19. #29283C2semidirect
20. #26433C2semidirect
21. #26418C2semidirect
22. #26362C2semidirect
23. #26351C2semidirect
28. #25821C2semidirect
29. #24064C2semidirect
30. #23557C2semidirect

Maximal subgroups

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

subgroupindex
#381012
#377572
#328282
#327912
#317642
#317482
#314852
#314652
#309642
#309482
#308032
#307792
#301932
#301002
#300732
#299732
#296952
#293412
#292832
#264332
#264182
#263622
#263512
#262202
#262042
#261452
#261292
#258212
#240642
#235572
#220042