Finite Group Databasebeta

← #7615404

Subgroups — #7615404

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45425C211yesmaximal, characteristic, complemented
2#44966C211yesmaximal, characteristic, complemented
3#32657C211yesmaximal, characteristic, complemented
4#32654C211yesmaximal, characteristic, complemented
5#32651C211yesmaximal, characteristic, complemented
6#32651C211yesmaximal, characteristic, complemented
7#28836C211yesmaximal, characteristic, complemented
8#28830C211yesmaximal, characteristic, complemented
9#28546C211yesmaximal, characteristic, complemented
10#28544C211yesmaximal, characteristic
11#28293C211yesmaximal, characteristic, complemented
12#28288C211yesmaximal, characteristic, complemented
13#28278C211yesmaximal, characteristic, complemented
14#28276C211yesmaximal, characteristic
15#28271C211yesmaximal, characteristic, complemented
16#28269C211yesmaximal, characteristic
17#26545C211yesmaximal, characteristic, complemented
18#26545C211yesmaximal, characteristic, complemented
19#26543C211yesmaximal, characteristic, complemented
20#26542C211yesmaximal, characteristic, complemented
21#24822C211yesmaximal, characteristic, complemented
22#24819C211yesmaximal, characteristic, complemented
23#24816C211yesmaximal, characteristic, complemented
24#24814C211yesmaximal, characteristic, complemented
25#23189C211yesmaximal, characteristic
26#23186C211yesmaximal, characteristic
27#22679C211yesmaximal, characteristic, complemented
28#22676C211yesmaximal, characteristic
29#21730C211yesmaximal, characteristic, complemented
30#21717C211yesmaximal, characteristic, complemented
31#21694C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#495C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#446C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#441C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48#2790—21no—
49#2788—21no—
50#2768—21no—
51#2763—21no—
52#2763—21no—
53#2742—21no—
54#2742—21no—
55#2720—21no—
56#2589—21no—
57#2589—21no—
58#2587—21no—
59#2583—21no—
60#2582C2211yescharacteristic
61#2581C2211yescharacteristic
62#2581C2211yescharacteristic
63#2581C2211yescharacteristic
64#2580C2211yescharacteristic
65#2580C2211yescharacteristic
66#2580C2211yescharacteristic
67#2574—21no—
68#2571C2211yescharacteristic
69#2571C2211yescharacteristic
70#2571C2211yescharacteristic
71#2568C2211yescharacteristic
72#2566C2211yescharacteristic
73#2565C2211yescharacteristic
74#2563C2211yescharacteristic
75#2552C2211yescharacteristic
76#2538C2211yescharacteristic
77#2505—21no—
78#2505—21no—
79#2473—21no—
80#2399C2211yescharacteristic
81#2367C2211yescharacteristic
82#2367C2211yescharacteristic
83#2367C2211yescharacteristic
84#2367C2211yescharacteristic
85#2351C2211yescharacteristic
86Q8×C4⋊C4C2211yescharacteristic
87#2349C2211yescharacteristic
88D4×C4⋊C4C2211yescharacteristic
89#2331C2211yescharacteristic
90#2330C2211yescharacteristic
91#2326C2211yescharacteristic
92#2326C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2095C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2085C2211yescharacteristic
107#2084C2211yescharacteristic
108#2084C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#1991C2211yescharacteristic
126#1990C2211yescharacteristic
127#1984C2211yescharacteristic
128#1984C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1971C2211yescharacteristic
136#1971C2211yescharacteristic
137#1970C2211yescharacteristic
138#1969C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1959C2211yescharacteristic
142#1959C2211yescharacteristic
143#1948C2211yescharacteristic
144#1947C2211yescharacteristic
145#1947C2211yescharacteristic
146#1947C2211yescharacteristic
147#1944C2211yescharacteristic
148#1944C2211yescharacteristic
149#1944C2211yescharacteristic
150#1943C2211yescharacteristic
151#1942C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1940C2211yescharacteristic
156#1940C2211yescharacteristic
157#1939C2211yescharacteristic
158#1939C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1846C2211yescharacteristic
179#1846C2211yescharacteristic
180#1844C2211yescharacteristic
181#1843C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1770C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C22×C4⋊C4—21no—
228#501—24no—
229#495Q818yescomplemented
230#479—42no—
231#478—42no—
232#477—42no—
233#474—42no—
234#446—42no—
235#446—42no—
236#442—24no—
237#442—42no—
238#441—24no—
239#441—42no—
240C4×Q16—42no—
241C4×SD16—42no—
242C4×SD16—42no—
243C4×D8—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
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#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398D411yescharacteristic
329#398D411yescharacteristic
330#398D411yescharacteristic
331#398D411yescharacteristic
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395D411yescharacteristic
340#395D411yescharacteristic
341#395D411yescharacteristic
342#395D411yescharacteristic
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
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#388—21no—
389#388—21no—
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#388—21no—
399#388—21no—
400#387—21no—
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#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#382—21no—
439#382—21no—
440#382—21no—
441#382—21no—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468#376C2311yescharacteristic
469C2×#95—21no—
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16C2×Q814yes—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16C2×Q814yes—
515C2×SD16C2×Q814yes—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8C2×Q814yes—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529#125—22no—
530#125—22no—
531#125—82no—
532#124—22no—
533#124—22no—
534#124C2×Q814yes—
535#124C2×Q814yes—
536C22⋊Q8—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
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—21no—
596C2×C4⋊C4—82no—
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⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
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⋊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×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×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#107—22no—
663#107—22no—
664#107—22no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
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#102—22no—
705#102—22no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—22no—
720#97#4114yes—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—41no—
725C4×C8C2×Q814yes—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—41no—
793C2×Q8—41no—
794C2×Q8—41no—
795C2×Q8—41no—
796C2×Q8—41no—
797C2×Q8—41no—
798C2×Q8—42no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8C22×Q812yes—
802C2×Q8C22×Q812yes—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4C22×Q812yes—
814C2×D4C22×Q812yes—
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—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C2511yescharacteristic
862Q16—28no—
863SD16—44no—
864SD16—44no—
865D8—28no—
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—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8C22×Q812yes—
886C2×C8C22×Q812yes—
887C2×C8C2×#4112yes—
888C2×C8C2×#4112yes—
889C2×C8H(5,𝔽2)12yes—
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—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
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⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—42no—
992C42—42no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42C22×Q812yes—
1002C42C2×#4112yes—
1003C42H(5,𝔽2)12yes—
1004C422−1+412yes—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C23×D411yescharacteristic
1020Q8—22no—
1021Q8—22no—
1022Q8—22no—
1023Q8—22no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—82no—
1029Q8—82no—
1030Q8—162no—
1031D4—22no—
1032D4—22no—
1033D4—22no—
1034D4—22no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
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—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
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—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—84no—
1120C2×C4—162no—
1121C2×C4—162no—
1122C2×C4—162no—
1123C2×C4—162no—
1124C2×C4—162no—
1125C2×C4D4×Q812yes—
1126C2×C4D4×Q812yes—
1127C2×C4#55012yes—
1128C2×C4#55012yes—
1129C2×C4C23×Q811yescharacteristic
1130C2×C4C22×#4111yescharacteristic
1131C2×C4C2×H(5,𝔽2)11yescharacteristic
1132C2×C4C2×H(5,𝔽2)11yescharacteristic
1133C2×C4C2×2−1+411yescharacteristic
1134C2×C4#58511yescharacteristic
1135C8—22no—
1136C8—22no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8#55414yes—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22C2×D4×Q811yescharacteristic
1158C22C2×#55011yescharacteristic
1159C22#349611yescharacteristic
1160C22#358411yescharacteristic
1161C22#358411yescharacteristic
1162C22#358511yescharacteristic
1163C22#358611yescharacteristic
1164C4—22no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—42no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4C2×#55411yescharacteristic
1193C4#350111yescharacteristic
1194C4#350711yescharacteristic
1195C4#354811yescharacteristic
1196C2—82no—
1197C2—82no—
1198C2#5982311yescharacteristic
1199C2#6137511yescharacteristic
1200C2#6138011yescharacteristic
1201C2#6142311yescharacteristic
1202C2#6142411yescharacteristic
1203C2#6231611yescharacteristic
1204C2#6231811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
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. #45425C2semidirect
2. #44966C2semidirect
3. #32657C2semidirect
4. #32654C2semidirect
5. #32651C2semidirect
6. #32651C2semidirect
7. #28836C2semidirect
8. #28830C2semidirect
9. #28546C2semidirect
11. #28293C2semidirect
12. #28288C2semidirect
13. #28278C2semidirect
15. #28271C2semidirect
17. #26545C2semidirect
18. #26545C2semidirect
19. #26543C2semidirect
20. #26542C2semidirect
21. #24822C2semidirect
22. #24819C2semidirect
23. #24816C2semidirect
24. #24814C2semidirect
27. #22679C2semidirect
29. #21730C2semidirect
30. #21717C2semidirect
229. #495Q8semidirect

Maximal subgroups

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

subgroupindex
#454252
#449662
#326572
#326542
#326512
#288362
#288302
#285462
#285442
#282932
#282882
#282782
#282762
#282712
#282692
#265452
#265432
#265422
#248222
#248192
#248162
#248142
#231892
#231862
#226792
#226762
#217302
#217172
#216942