Finite Group Databasebeta

← #7224876

Subgroups — #7224876

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 1183 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46051C211yesmaximal, characteristic, complemented
2#45993C211yesmaximal, characteristic
3#33314C211yesmaximal, characteristic, complemented
4#33268C211yesmaximal, characteristic, complemented
5#32840C211yesmaximal, characteristic, complemented
6#32838C211yesmaximal, characteristic, complemented
7#32404C211yesmaximal, characteristic, complemented
8#32396C211yesmaximal, characteristic, complemented
9#32367C211yesmaximal, characteristic, complemented
10#32364C211yesmaximal, characteristic, complemented
11#32308C211yesmaximal, characteristic
12#32301C211yesmaximal, characteristic, complemented
13#31103C211yesmaximal, characteristic, complemented
14#31100C211yesmaximal, characteristic
15#30949C211yesmaximal, characteristic, complemented
16#30946C211yesmaximal, characteristic, complemented
17#30780C211yesmaximal, characteristic
18#30779C211yesmaximal, characteristic, complemented
19#28838C211yesmaximal, characteristic, complemented
20#28813C211yesmaximal, characteristic, complemented
21#28540C211yesmaximal, characteristic, complemented
22#28019C211yesmaximal, characteristic, complemented
23#28008C211yesmaximal, characteristic, complemented
24#27944C211yesmaximal, characteristic
25#27843C211yesmaximal, characteristic, complemented
26#27802C211yesmaximal, characteristic
27#26480C211yesmaximal, characteristic, complemented
28#26074C211yesmaximal, characteristic, complemented
29#26072C211yesmaximal, characteristic, complemented
30#25036C211yesmaximal, characteristic
31#21667C211yesmaximal, characteristic, complemented
32C2×#563—21no—
33C2×#500C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#498C2211yescharacteristic
38C2×#484C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#475C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#468C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#428C2211yescharacteristic
45#2868C2211yescharacteristic
46#2863C2211yescharacteristic
47#2862C2211yescharacteristic
48#2860C2211yescharacteristic
49#2831—21no—
50#2821—21no—
51#2799—21no—
52#2775—21no—
53#2762—21no—
54#2759—21no—
55#2758—21no—
56#2721—21no—
57#2720—21no—
58#2718—21no—
59#2716—21no—
60#2680—21no—
61#2677—21no—
62#2674—21no—
63#2570C2211yescharacteristic
64#2568C2211yescharacteristic
65#2552C2211yescharacteristic
66#2551C2211yescharacteristic
67#2551C2211yescharacteristic
68#2542C2211yescharacteristic
69#2514C2211yescharacteristic
70#2512C2211yescharacteristic
71#2508C2211yescharacteristic
72#2506C2211yescharacteristic
73#2501C2211yescharacteristic
74#2499C2211yescharacteristic
75#2496C2211yescharacteristic
76#2495C2211yescharacteristic
77#2492C2211yescharacteristic
78#2491C2211yescharacteristic
79#2452C2211yescharacteristic
80#2451C2211yescharacteristic
81#2440C2211yescharacteristic
82#2440C2211yescharacteristic
83#2439C2211yescharacteristic
84#2439C2211yescharacteristic
85#2422C2211yescharacteristic
86#2421C2211yescharacteristic
87#2381—21no—
88C4×#126C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2100C2211yescharacteristic
92#2100C2211yescharacteristic
93#2096C2211yescharacteristic
94#2095C2211yescharacteristic
95#2095C2211yescharacteristic
96#2095C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2088C2211yescharacteristic
102#2086C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2083C2211yescharacteristic
111#2077C2211yescharacteristic
112#2076C2211yescharacteristic
113#2073C2211yescharacteristic
114#2073C2211yescharacteristic
115#2072C2211yescharacteristic
116#2072C2211yescharacteristic
117#2068C2211yescharacteristic
118#2066C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2057C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2057C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2034C2211yescharacteristic
132#2033C2211yescharacteristic
133#2024C2211yescharacteristic
134#2024C2211yescharacteristic
135#2023C2211yescharacteristic
136#2023C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1949C2211yescharacteristic
143#1947C2211yescharacteristic
144#1947C2211yescharacteristic
145#1947C2211yescharacteristic
146#1944C2211yescharacteristic
147#1944C2211yescharacteristic
148#1943C2211yescharacteristic
149#1942C2211yescharacteristic
150#1942C2211yescharacteristic
151#1941C2211yescharacteristic
152#1941C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic
156#1935C2211yescharacteristic
157#1934C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1918C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1847C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1847C2211yescharacteristic
189#1847C2211yescharacteristic
190#1845C2211yescharacteristic
191#1839C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205#563—48no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#126D411yescharacteristic
220C2×#125—21no—
221C2×#125—21no—
222C2×#124—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237#500—42no—
238#500—42no—
239#500—42no—
240#498—42no—
241#498—42no—
242#484—42no—
243#482—42no—
244#475—42no—
245#474—42no—
246#468—42no—
247C4×SD16—42no—
248#428—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#401—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388D411yescharacteristic
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387D411yescharacteristic
417#387D411yescharacteristic
418#387D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#384—21no—
424#384—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#383—21no—
434#383—21no—
435#383D411yescharacteristic
436#382—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C43C2311yescharacteristic
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—22no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—44no—
530C4⋊Q8—44no—
531C4⋊Q8—44no—
532C4⋊Q8—82no—
533#126—24no—
534#126—44no—
535#126—44no—
536#126—44no—
537#125—44no—
538#125—44no—
539#124—44no—
540#123—44no—
541#123—44no—
542#123—82no—
543C22⋊Q8—44no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—82no—
550#121—41no—
551#121—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×D4—41no—
555C4×D4—41no—
556#117—41no—
557#117—41no—
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—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—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—22no—
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—22no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701C22⋊C8—22no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704#97—22no—
705#97—22no—
706#97—22no—
707#97—22no—
708#97—22no—
709C4×C8—22no—
710C4×C8—22no—
711C4×C8—22no—
712C4×C8—22no—
713#95—21no—
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#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
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
767C24—21no—
768C24C22×D411yescharacteristic
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—42no—
800C2×D4—81no—
801C2×D4—81no—
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—21no—
822C22×C4—21no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C2511yescharacteristic
843SD16—44no—
844M16—44no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
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×C8H(5,𝔽2)12yes—
864C2×C8H(5,𝔽2)12yes—
865C2×C82−1+412yes—
866C2×C82−1+412yes—
867C2×C82−1+412yes—
868C2×C82−1+412yes—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
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—41no—
901C4⋊C4—41no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
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—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
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⋊C4AGL(1,ℤ/8)14yes—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C42—22no—
965C42—22no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—41no—
979C42—41no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23C23×D411yescharacteristic
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—162no—
1006Q8—162no—
1007Q8—162no—
1008Q8—162no—
1009Q8—162no—
1010Q8—162no—
1011D4—41no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—162no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
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—21no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
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—162no—
1101C2×C4—162no—
1102C2×C4C2×AGL(1,ℤ/8)12yes—
1103C2×C4C2×AGL(1,ℤ/8)12yes—
1104C2×C4C2×AGL(1,ℤ/8)12yes—
1105C2×C4#57812yes—
1106C2×C4C2×H(5,𝔽2)11yescharacteristic
1107C2×C4C2×H(5,𝔽2)11yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4C2×2−1+411yescharacteristic
1110C2×C4C2×2−1+411yescharacteristic
1111C2×C4C2×2−1+411yescharacteristic
1112C8—22no—
1113C8—22no—
1114C8—22no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8#56314yescomplemented
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22#349811yescharacteristic
1135C22#349911yescharacteristic
1136C22#349911yescharacteristic
1137C22C22×AGL(1,ℤ/8)11yescharacteristic
1138C22C2×#57811yescharacteristic
1139C22#358511yescharacteristic
1140C22#358611yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4C2×#56311yescharacteristic
1170C4#354411yescharacteristic
1171C4#355211yescharacteristic
1172C4#355211yescharacteristic
1173C2—81no—
1174C2—161no—
1175C2#4599311yescharacteristic
1176C2#6244711yescharacteristic
1177C2#6246011yescharacteristic
1178C2#6247911yescharacteristic
1179C2#6249811yescharacteristic
1180C2#6250911yescharacteristic
1181C2#6251911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46051C2semidirect
3. #33314C2semidirect
4. #33268C2semidirect
5. #32840C2semidirect
6. #32838C2semidirect
7. #32404C2semidirect
8. #32396C2semidirect
9. #32367C2semidirect
10. #32364C2semidirect
12. #32301C2semidirect
13. #31103C2semidirect
15. #30949C2semidirect
16. #30946C2semidirect
18. #30779C2semidirect
19. #28838C2semidirect
20. #28813C2semidirect
21. #28540C2semidirect
22. #28019C2semidirect
23. #28008C2semidirect
25. #27843C2semidirect
27. #26480C2semidirect
28. #26074C2semidirect
29. #26072C2semidirect
31. #21667C2semidirect
1119. C8#563semidirect

Maximal subgroups

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

subgroupindex
#460512
#459932
#333142
#332682
#328402
#328382
#324042
#323962
#323672
#323642
#323082
#323012
#311032
#311002
#309492
#309462
#307802
#307792
#288382
#288132
#285402
#280192
#280082
#279442
#278432
#278022
#264802
#260742
#260722
#250362
#216672