Finite Group Databasebeta

← #6820815

Subgroups — #6820815

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42939C211yesmaximal, characteristic
2#42697C211yesmaximal, characteristic, complemented
3#33188C211yesmaximal, characteristic
4#32661C211yesmaximal, characteristic, complemented
5#32660C211yesmaximal, characteristic, complemented
6#32535C211yesmaximal, characteristic, complemented
7#32534C211yesmaximal, characteristic, complemented
8#31585C211yesmaximal, characteristic, complemented
9#31583C211yesmaximal, characteristic, complemented
10#31576C211yesmaximal, characteristic, complemented
11#31572C211yesmaximal, characteristic, complemented
12#29769C211yesmaximal, characteristic
13#29764C211yesmaximal, characteristic, complemented
14#28836C211yesmaximal, characteristic, complemented
15#28835C211yesmaximal, characteristic, complemented
16#28278C211yesmaximal, characteristic, complemented
17#28275C211yesmaximal, characteristic, complemented
18#28015C211yesmaximal, characteristic, complemented
19#28010C211yesmaximal, characteristic, complemented
20#27944C211yesmaximal, characteristic
21#27940C211yesmaximal, characteristic, complemented
22#26269C211yesmaximal, characteristic, complemented
23#26266C211yesmaximal, characteristic, complemented
24#25215C211yesmaximal, characteristic, complemented
25#25211C211yesmaximal, characteristic
26#25206C211yesmaximal, characteristic, complemented
27#25204C211yesmaximal, characteristic
28#23041C211yesmaximal, characteristic
29#23038C211yesmaximal, characteristic, complemented
30#21604C211yesmaximal, characteristic, complemented
31#21160C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#441C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#428C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2836—21no—
48#2835—21no—
49#2794—21no—
50#2792—21no—
51#2767—21no—
52#2767—21no—
53#2707—21no—
54#2695—21no—
55#2694—21no—
56#2687—21no—
57#2667—21no—
58#2664—21no—
59#2652—21no—
60#2652—21no—
61#2621C2211yescharacteristic
62#2620C2211yescharacteristic
63#2582C2211yescharacteristic
64#2581C2211yescharacteristic
65#2581C2211yescharacteristic
66#2571C2211yescharacteristic
67#2571C2211yescharacteristic
68#2556—21no—
69#2552C2211yescharacteristic
70#2552C2211yescharacteristic
71#2538C2211yescharacteristic
72#2517—21no—
73#2512C2211yescharacteristic
74#2511C2211yescharacteristic
75#2511C2211yescharacteristic
76#2511C2211yescharacteristic
77#2502C2211yescharacteristic
78#2501C2211yescharacteristic
79#2499C2211yescharacteristic
80#2499C2211yescharacteristic
81#2448C2211yescharacteristic
82#2447C2211yescharacteristic
83#2446C2211yescharacteristic
84#2446C2211yescharacteristic
85#2396C2211yescharacteristic
86#2363C2211yescharacteristic
87#2362C2211yescharacteristic
88#2360C2211yescharacteristic
89#2360C2211yescharacteristic
90#2317C2211yescharacteristic
91#2316C2211yescharacteristic
92#2097C2211yescharacteristic
93#2096C2211yescharacteristic
94#2096C2211yescharacteristic
95#2096C2211yescharacteristic
96#2095C2211yescharacteristic
97#2095C2211yescharacteristic
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2083C2211yescharacteristic
107#2083C2211yescharacteristic
108#2072C2211yescharacteristic
109#2072C2211yescharacteristic
110#2072C2211yescharacteristic
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2056C2211yescharacteristic
125#2056C2211yescharacteristic
126#2055C2211yescharacteristic
127#2055C2211yescharacteristic
128#2043C2211yescharacteristic
129#2043C2211yescharacteristic
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#1985C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1971C2211yescharacteristic
136#1971C2211yescharacteristic
137#1969C2211yescharacteristic
138#1969C2211yescharacteristic
139#1969C2211yescharacteristic
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1958C2211yescharacteristic
144#1956C2211yescharacteristic
145#1948C2211yescharacteristic
146#1948C2211yescharacteristic
147#1947C2211yescharacteristic
148#1947C2211yescharacteristic
149#1944C2211yescharacteristic
150#1944C2211yescharacteristic
151#1944C2211yescharacteristic
152#1943C2211yescharacteristic
153#1943C2211yescharacteristic
154#1943C2211yescharacteristic
155#1942C2211yescharacteristic
156#1942C2211yescharacteristic
157#1941C2211yescharacteristic
158#1941C2211yescharacteristic
159#1940C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1880C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1877C2211yescharacteristic
174#1874C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1872C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1863C2211yescharacteristic
181#1862C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1847C2211yescharacteristic
185#1847C2211yescharacteristic
186#1847C2211yescharacteristic
187#1845C2211yescharacteristic
188#1844C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1798C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231#497—42no—
232#485—42no—
233#484—42no—
234#483—42no—
235#482—42no—
236#470—24no—
237#468—24no—
238#467—42no—
239#465—42no—
240#446—42no—
241#441—42no—
242#440—42no—
243#428—24no—
244#428—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297#405—42no—
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
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#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400D411yescharacteristic
321#399—21no—
322#399—21no—
323#399—21no—
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#398D411yescharacteristic
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396D411yescharacteristic
355#396D411yescharacteristic
356#395—21no—
357#395—21no—
358#395D411yescharacteristic
359#394—21no—
360#394—21no—
361#393D411yescharacteristic
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—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#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#382—21no—
445#382—21no—
446#382—21no—
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#381—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
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
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16#4114yes—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531#126—82no—
532#125—82no—
533#125—82no—
534#124—41no—
535#124—41no—
536#123—82no—
537#123—82no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—82no—
545#121—22no—
546#121—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×D4—41no—
556C4×D4—41no—
557#117—22no—
558#117—22no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
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—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#107—22no—
665#107—22no—
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#107—41no—
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—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690#103—22no—
691#103—22no—
692#103—22no—
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—
706#103—41no—
707#103—41no—
708#102—22no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714C22⋊C8—22no—
715C22⋊C8—22no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—41no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—41no—
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#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#95—21no—
769#95—21no—
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—
781C24C22×D411yescharacteristic
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—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—42no—
810C2×D4—81no—
811C2×D4—81no—
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—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
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×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C2×#4112yes—
854C22×C4H(5,𝔽2)12yes—
855C22×C4C2511yescharacteristic
856Q16—44no—
857Q16—82no—
858SD16—44no—
859SD16—82no—
860M16—28no—
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—21no—
879C2×C8—21no—
880C2×C8—44no—
881C2×C8C2×#4112yes—
882C2×C8C2×#4112yes—
883C2×C8H(5,𝔽2)12yes—
884C2×C82−1+412yes—
885C2×C82−1+412yes—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
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—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⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
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—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—42no—
993C42—42no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23#55012yes—
1015C23C23×D411yescharacteristic
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—82no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—162no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
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—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
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—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—162no—
1120C2×C4—162no—
1121C2×C4—162no—
1122C2×C4#55012yes—
1123C2×C4#57712yes—
1124C2×C4#57812yes—
1125C2×C4C22×#4111yescharacteristic
1126C2×C4C2×H(5,𝔽2)11yescharacteristic
1127C2×C4C2×H(5,𝔽2)11yescharacteristic
1128C2×C4C2×2−1+411yescharacteristic
1129C2×C4C2×2−1+411yescharacteristic
1130C2×C4#58511yescharacteristic
1131C8—22no—
1132C8—22no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8#53914yes—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22C2×#55011yescharacteristic
1154C22#349611yescharacteristic
1155C22#349911yescharacteristic
1156C22C2×#57711yescharacteristic
1157C22C2×#57811yescharacteristic
1158C22#358511yescharacteristic
1159C22#358611yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4C2×#53911yescharacteristic
1189C4#350711yescharacteristic
1190C4#353611yescharacteristic
1191C4#355911yescharacteristic
1192C2—42no—
1193C2—161no—
1194C2#3938411yescharacteristic
1195C2#6142111yescharacteristic
1196C2#6142211yescharacteristic
1197C2#6229411yescharacteristic
1198C2#6234311yescharacteristic
1199C2#6251311yescharacteristic
1200C2#6251611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42697C2semidirect
4. #32661C2semidirect
5. #32660C2semidirect
6. #32535C2semidirect
7. #32534C2semidirect
8. #31585C2semidirect
9. #31583C2semidirect
10. #31576C2semidirect
11. #31572C2semidirect
13. #29764C2semidirect
14. #28836C2semidirect
15. #28835C2semidirect
16. #28278C2semidirect
17. #28275C2semidirect
18. #28015C2semidirect
19. #28010C2semidirect
21. #27940C2semidirect
22. #26269C2semidirect
23. #26266C2semidirect
24. #25215C2semidirect
26. #25206C2semidirect
29. #23038C2semidirect
30. #21604C2semidirect
31. #21160C2semidirect

Maximal subgroups

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

subgroupindex
#429392
#426972
#331882
#326612
#326602
#325352
#325342
#315852
#315832
#315762
#315722
#297692
#297642
#288362
#288352
#282782
#282752
#280152
#280102
#279442
#279402
#262692
#262662
#252152
#252112
#252062
#252042
#230412
#230382
#216042
#211602