Finite Group Databasebeta

← #6585845

Subgroups — #6585845

Order 512.

1509 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35958C211yesmaximal, characteristic, complemented
2#35928C211yesmaximal, characteristic
3#33292C211yesmaximal, characteristic, complemented
4#33205C211yesmaximal, characteristic
5#33204C211yesmaximal, characteristic, complemented
6#28808C211yesmaximal, characteristic, complemented
7#28803C211yesmaximal, characteristic, complemented
8#27823C211yesmaximal, characteristic, complemented
9#27818C211yesmaximal, characteristic, complemented
10#26458C211yesmaximal, characteristic, complemented
11#26454C211yesmaximal, characteristic, complemented
12#26284C211yesmaximal, characteristic, complemented
13#26277C211yesmaximal, characteristic, complemented
14#26115C211yesmaximal, characteristic
15#26107C211yesmaximal, characteristic
16#26031C211yesmaximal, characteristic, complemented
17#26022C211yesmaximal, characteristic, complemented
18#25488C211yesmaximal, characteristic, complemented
19#25487C211yesmaximal, characteristic, complemented
20#24834C211yesmaximal, characteristic
21#24825C211yesmaximal, characteristic
22#24337C211yesmaximal, characteristic
23#24330C211yesmaximal, characteristic
24#22972C211yesmaximal, characteristic
25#22963C211yesmaximal, characteristic
26#22778C211yesmaximal, characteristic
27#22776C211yesmaximal, characteristic
28#22526C211yesmaximal, characteristic
29#22523C211yesmaximal, characteristic
30#21717C211yesmaximal, characteristic, complemented
31#20504C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#446C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2666—21no—
44#2660C2211yescharacteristic
45#2660C2211yescharacteristic
46#2659—21no—
47#2612—21no—
48#2605—21no—
49#2586—21no—
50#2585—21no—
51#2584C2211yescharacteristic
52#2583—21no—
53#2582C2211yescharacteristic
54#2581C2211yescharacteristic
55#2571C2211yescharacteristic
56#2570C2211yescharacteristic
57#2568C2211yescharacteristic
58#2567C2211yescharacteristic
59#2565C2211yescharacteristic
60#2551C2211yescharacteristic
61#2551C2211yescharacteristic
62#2550C2211yescharacteristic
63#2550C2211yescharacteristic
64#2549—21no—
65#2549—21no—
66#2520—21no—
67#2520—21no—
68#2440—21no—
69#2440—21no—
70#2434—21no—
71#2402—21no—
72#2399C2211yescharacteristic
73C2×#395—21no—
74#2370C2211yescharacteristic
75#2369C2211yescharacteristic
76#2356C2211yescharacteristic
77#2355C2211yescharacteristic
78#2355C2211yescharacteristic
79#2355C2211yescharacteristic
80#2349C2211yescharacteristic
81#2349C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84#2276C2211yescharacteristic
85#2275C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2099C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2083C2211yescharacteristic
98#2068C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2059C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2026C2211yescharacteristic
107#2024C2211yescharacteristic
108#2024C2211yescharacteristic
109#2024C2211yescharacteristic
110#1993C2211yescharacteristic
111#1993C2211yescharacteristic
112#1993C2211yescharacteristic
113#1993C2211yescharacteristic
114#1992C2211yescharacteristic
115#1992C2211yescharacteristic
116#1991C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1990C2211yescharacteristic
120#1990C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1987C2211yescharacteristic
129#1987C2211yescharacteristic
130#1984C2211yescharacteristic
131#1984C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1944C2211yescharacteristic
141#1943C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1940C2211yescharacteristic
145#1940C2211yescharacteristic
146#1939C2211yescharacteristic
147#1939C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1843C2211yescharacteristic
169#1836C2211yescharacteristic
170#1836C2211yescharacteristic
171#1835C2211yescharacteristic
172#1834C2211yescharacteristic
173#1805C2211yescharacteristic
174#1805C2211yescharacteristic
175#1804C2211yescharacteristic
176#1804C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1804C2211yescharacteristic
180#1803C2211yescharacteristic
181#1803C2211yescharacteristic
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191C8×C4⋊C4C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C23×Q8—21no—
204C22×SD16C2311yescharacteristic
205#554—24no—
206#554—42no—
207D4×Q8—24no—
208D4×Q8—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C22×C4⋊C4—21no—
238C22×C4⋊C4—21no—
239C22×C4⋊C4—21no—
240#479—42no—
241#478—24no—
242#476—24no—
243#475—42no—
244#446—42no—
245#446—42no—
246#440—24no—
247#440Q818yescomplemented
248C4×SD16—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398D411yescharacteristic
313#398D411yescharacteristic
314#398D411yescharacteristic
315#398D411yescharacteristic
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395D411yescharacteristic
331#395D411yescharacteristic
332#395D411yescharacteristic
333#395D411yescharacteristic
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
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#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
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#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#384—21no—
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#382—21no—
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439#376—21no—
440#376—21no—
441#376C2311yescharacteristic
442C2×#95—21no—
443C2×#95—21no—
444C2×#95—21no—
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
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—44no—
497C22×Q8—82no—
498C22×Q8—82no—
499C22×Q8C2×D411yescharacteristic
500C22×Q8C2×D411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16C2×Q814yes—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—82no—
532C4⋊Q8—82no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—41no—
539C22⋊Q8—44no—
540C22⋊Q8—44no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544C22⋊Q8—44no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8C2×Q814yescomplemented
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4C2×Q814yes—
567C4×D4#4114yes—
568C4×D4#4114yes—
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—44no—
606C2×C4⋊C4—82no—
607C2×C4⋊C4—82no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
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×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663#107—22no—
664#107—22no—
665#107—41no—
666#107C2×Q814yescomplemented
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103C2×Q814yescomplemented
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102C2×Q814yes—
698#97—22no—
699#97—22no—
700#97—41no—
701#97—41no—
702#97C2×Q814yescomplemented
703C4×C8—22no—
704C4×C8—22no—
705C4×C8—22no—
706C4×C8—41no—
707C4×C8—41no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
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#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
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
764C24—21no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—41no—
774C2×Q8—41no—
775C2×Q8—41no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
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—816no—
792C2×Q8C22×Q812yes—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4C22×Q812yes—
797C2×D4C2×#4112yes—
798C2×D4C2×#4112yes—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
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—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
850SD16—28no—
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×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×C8C22×Q812yes—
874C2×C8C22×Q812yes—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
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—21no—
907C4⋊C4—21no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
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—42no—
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⋊C4C22×Q812yes—
950C4⋊C4C22×Q812yes—
951C4⋊C4C2×#4112yes—
952C4⋊C4C2×#4112yes—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C42—24no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—42no—
970C42—42no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42C22×Q812yes—
982C42C2×#4112yes—
983C42C2×#4112yes—
984C42H(5,𝔽2)12yes—
985C422−1+412yes—
986C422−1+412yes—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C23×D411yescharacteristic
995Q8—22no—
996Q8—22no—
997Q8—44no—
998Q8—41no—
999Q8—41no—
1000Q8—82no—
1001Q8—84no—
1002Q8—84no—
1003Q8—84no—
1004Q8—162no—
1005Q8—162no—
1006D4—22no—
1007D4—22no—
1008D4—22no—
1009D4#53314yes—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
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—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—41no—
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—84no—
1091C2×C4—84no—
1092C2×C4—84no—
1093C2×C4—84no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4—162no—
1097C2×C4#54612yes—
1098C2×C4#54612yes—
1099C2×C4#54812yes—
1100C2×C4#54812yes—
1101C2×C4D4×Q812yes—
1102C2×C4D4×Q812yes—
1103C2×C4#57712yes—
1104C2×C4C23×Q811yescharacteristic
1105C2×C4C22×#4111yescharacteristic
1106C2×C4C22×#4111yescharacteristic
1107C2×C4C2×H(5,𝔽2)11yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4C2×2−1+411yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C22—24no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22C2×#54611yescharacteristic
1126C22C2×#54811yescharacteristic
1127C22C2×D4×Q811yescharacteristic
1128C22C2×#57711yescharacteristic
1129C22#358411yescharacteristic
1130C22#358511yescharacteristic
1131C22#358611yescharacteristic
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4C2×#53311yescharacteristic
1162C4#350311yescharacteristic
1163C4#350911yescharacteristic
1164C4#351111yescharacteristic
1165C2—44no—
1166C2#3612911yescharacteristic
1167C2#6118411yescharacteristic
1168C2#6119811yescharacteristic
1169C2#6132611yescharacteristic
1170C2#6133611yescharacteristic
1171C2#6138311yescharacteristic
1172C2#6138511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35958C2semidirect
3. #33292C2semidirect
5. #33204C2semidirect
6. #28808C2semidirect
7. #28803C2semidirect
8. #27823C2semidirect
9. #27818C2semidirect
10. #26458C2semidirect
11. #26454C2semidirect
12. #26284C2semidirect
13. #26277C2semidirect
16. #26031C2semidirect
17. #26022C2semidirect
18. #25488C2semidirect
19. #25487C2semidirect
30. #21717C2semidirect
247. #440Q8semidirect
554. C4×Q8C2×Q8semidirect
666. #107C2×Q8semidirect
690. #103C2×Q8semidirect
702. #97C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#359582
#359282
#332922
#332052
#332042
#288082
#288032
#278232
#278182
#264582
#264542
#262842
#262772
#261152
#261072
#260312
#260222
#254882
#254872
#248342
#248252
#243372
#243302
#229722
#229632
#227782
#227762
#225262
#225232
#217172
#205042