Finite Group Databasebeta

← #6929932

Subgroups — #6929932

Order 512.

1233 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39260C211yesmaximal, characteristic
2#37887C211yesmaximal, characteristic, complemented
3#32854C211yesmaximal, characteristic, complemented
4#32745C211yesmaximal, characteristic, complemented
5#32424C211yesmaximal, characteristic, complemented
6#32408C211yesmaximal, characteristic, complemented
7#32023C211yesmaximal, characteristic, complemented
8#32011C211yesmaximal, characteristic
9#32007C211yesmaximal, characteristic, complemented
10#31995C211yesmaximal, characteristic
11#31502C211yesmaximal, characteristic, complemented
12#31494C211yesmaximal, characteristic, complemented
13#30374C211yesmaximal, characteristic, complemented
14#30166C211yesmaximal, characteristic, complemented
15#30102C211yesmaximal, characteristic, complemented
16#30088C211yesmaximal, characteristic, complemented
17#29911C211yesmaximal, characteristic, complemented
18#29267C211yesmaximal, characteristic, complemented
19#29174C211yesmaximal, characteristic, complemented
20#27873C211yesmaximal, characteristic, complemented
21#27679C211yesmaximal, characteristic, complemented
22#27480C211yesmaximal, characteristic, complemented
23#27465C211yesmaximal, characteristic, complemented
24#27415C211yesmaximal, characteristic, complemented
25#27398C211yesmaximal, characteristic, complemented
26#27384C211yesmaximal, characteristic, complemented
27#27371C211yesmaximal, characteristic, complemented
28#27315C211yesmaximal, characteristic, complemented
29#27296C211yesmaximal, characteristic, complemented
30#23767C211yesmaximal, characteristic, complemented
31#22006C211yesmaximal, characteristic, complemented
32#2857C2211yescharacteristic
33#2855C2211yescharacteristic
34#2786—21no—
35#2770—21no—
36#2750—21no—
37#2749—21no—
38#2747—21no—
39#2741—21no—
40#2702—21no—
41#2690—21no—
42#2647C2211yescharacteristic
43#2647C2211yescharacteristic
44#2628C2211yescharacteristic
45#2625C2211yescharacteristic
46#2603—21no—
47#2579—21no—
48#2538C2211yescharacteristic
49#2535C2211yescharacteristic
50#2533—21no—
51#2532—21no—
52#2530—21no—
53#2520—21no—
54#2519—21no—
55#2507C2211yescharacteristic
56#2506C2211yescharacteristic
57#2497C2211yescharacteristic
58#2497C2211yescharacteristic
59#2496C2211yescharacteristic
60#2496C2211yescharacteristic
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic
63#2481—21no—
64#2427C2211yescharacteristic
65#2427C2211yescharacteristic
66#2356C2211yescharacteristic
67D4×C4⋊C4C2211yescharacteristic
68#2347C2211yescharacteristic
69#2346C2211yescharacteristic
70#2331C2211yescharacteristic
71#2326C2211yescharacteristic
72#2324C2211yescharacteristic
73#2314C2211yescharacteristic
74C4×#121C2211yescharacteristic
75#2290C2211yescharacteristic
76#2285C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2077C2211yescharacteristic
106#2077C2211yescharacteristic
107#2077C2211yescharacteristic
108#2077C2211yescharacteristic
109#2076C2211yescharacteristic
110#2076C2211yescharacteristic
111#2075C2211yescharacteristic
112#2075C2211yescharacteristic
113#2072C2211yescharacteristic
114#2072C2211yescharacteristic
115#2072C2211yescharacteristic
116#2071C2211yescharacteristic
117#2068C2211yescharacteristic
118#2068C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2024C2211yescharacteristic
132#2023C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1948C2211yescharacteristic
136#1948C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1943C2211yescharacteristic
140#1941C2211yescharacteristic
141#1935C2211yescharacteristic
142#1933C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1924C2211yescharacteristic
146#1923C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1917C2211yescharacteristic
158#1916C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1870C2211yescharacteristic
168#1869C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1840C2211yescharacteristic
188#1832C2211yescharacteristic
189#1817C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#107C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1750C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125—21no—
209C2×#124C2311yescharacteristic
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4—21no—
225C22×C42C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270#400—21no—
271#400—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#399—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#397—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#395—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#393—21no—
309#392—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#390—21no—
317#390—21no—
318#390C2311yescharacteristic
319#389—21no—
320#389—21no—
321#389—21no—
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388D411yescharacteristic
353#388D411yescharacteristic
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387D411yescharacteristic
371#387D411yescharacteristic
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386D411yescharacteristic
379#386D411yescharacteristic
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385D411yescharacteristic
387#385D411yescharacteristic
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#383—21no—
394#383—21no—
395#382—21no—
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#381—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2311yescharacteristic
428C4×C22⋊C4C2311yescharacteristic
429#376—21no—
430#376—21no—
431#376C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8—21no—
479C22×Q8C2411yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C2×D411yescharacteristic
483C22×D4C2411yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4C2×D411yescharacteristic
488C23×C4C2×D411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—41no—
494C22×C8—41no—
495C22×C8—41no—
496C22×C8—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507#126—82no—
508#126—82no—
509#125—82no—
510#124—22no—
511#124—41no—
512C22⋊Q8—41no—
513C22⋊Q8—41no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516C22⋊Q8—82no—
517#121—22no—
518#121—22no—
519#121—41no—
520#121—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C4×D4—41no—
528C4×D4—41no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—82no—
532#117—41no—
533#117—41no—
534#117—41no—
535#117—41no—
536#117—41no—
537#117—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
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—82no—
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#102—22no—
666#102—22no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673C22⋊C8—41no—
674C22⋊C8—41no—
675C22⋊C8—41no—
676C22⋊C8—41no—
677C22⋊C8—41no—
678C22⋊C8—41no—
679#97—41no—
680C4×C8—41no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
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#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735C24—21no—
736C24C22×D411yescharacteristic
737C24C22×D411yescharacteristic
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—42no—
745C2×Q8—81no—
746C2×Q8—81no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D42−1+412yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C2511yescharacteristic
817M16—82no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—82no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C22⋊C4—22no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—41no—
948C42—41no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C23×D411yescharacteristic
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—162no—
985D4—22no—
986D4—22no—
987D4—41no—
988D4—41no—
989D4—82no—
990D4—84no—
991D4—162no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
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—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
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—82no—
1081C2×C4—82no—
1082C2×C4—84no—
1083C2×C4—162no—
1084C2×C4—162no—
1085C2×C4#57712yes—
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4#58511yescharacteristic
1088C2×C4#58511yescharacteristic
1089C2×C4#58511yescharacteristic
1090C2×C4#58511yescharacteristic
1091C2×C4#58511yescharacteristic
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—42no—
1111C22—41no—
1112C22—42no—
1113C22—41no—
1114C22—41no—
1115C22—42no—
1116C22—41no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22#344911yescharacteristic
1122C22#348511yescharacteristic
1123C22#348911yescharacteristic
1124C22C2×#57711yescharacteristic
1125C22#358411yescharacteristic
1126C22#358511yescharacteristic
1127C22#358611yescharacteristic
1128C4—22no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4#355311yescharacteristic
1156C4#355311yescharacteristic
1157C4#356611yescharacteristic
1158C4#356611yescharacteristic
1159C2—81no—
1160C2—81no—
1161C2—82no—
1162C2#4142511yescharacteristic
1163C2#6098411yescharacteristic
1164C2#6098911yescharacteristic
1165C2#6177011yescharacteristic
1166C2#6178211yescharacteristic
1167C2#6217111yescharacteristic
1168C2#6218911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37887C2semidirect
3. #32854C2semidirect
4. #32745C2semidirect
5. #32424C2semidirect
6. #32408C2semidirect
7. #32023C2semidirect
9. #32007C2semidirect
11. #31502C2semidirect
12. #31494C2semidirect
13. #30374C2semidirect
14. #30166C2semidirect
15. #30102C2semidirect
16. #30088C2semidirect
17. #29911C2semidirect
18. #29267C2semidirect
19. #29174C2semidirect
20. #27873C2semidirect
21. #27679C2semidirect
22. #27480C2semidirect
23. #27465C2semidirect
24. #27415C2semidirect
25. #27398C2semidirect
26. #27384C2semidirect
27. #27371C2semidirect
28. #27315C2semidirect
29. #27296C2semidirect
30. #23767C2semidirect
31. #22006C2semidirect

Maximal subgroups

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

subgroupindex
#392602
#378872
#328542
#327452
#324242
#324082
#320232
#320112
#320072
#319952
#315022
#314942
#303742
#301662
#301022
#300882
#299112
#292672
#291742
#278732
#276792
#274802
#274652
#274152
#273982
#273842
#273712
#273152
#272962
#237672
#220062