Finite Group Databasebeta

← #7254856

Subgroups — #7254856

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42803C211yesmaximal, characteristic, complemented
2#42674C211yesmaximal, characteristic
3#32783C211yesmaximal, characteristic, complemented
4#31539C211yesmaximal, characteristic, complemented
5#31528C211yesmaximal, characteristic, complemented
6#31200C211yesmaximal, characteristic, complemented
7#31193C211yesmaximal, characteristic, complemented
8#31117C211yesmaximal, characteristic, complemented
9#31117C211yesmaximal, characteristic, complemented
10#30644C211yesmaximal, characteristic, complemented
11#30639C211yesmaximal, characteristic, complemented
12#30588C211yesmaximal, characteristic, complemented
13#30586C211yesmaximal, characteristic, complemented
14#30570C211yesmaximal, characteristic, complemented
15#30562C211yesmaximal, characteristic, complemented
16#29307C211yesmaximal, characteristic, complemented
17#28786C211yesmaximal, characteristic, complemented
18#28778C211yesmaximal, characteristic, complemented
19#26395C211yesmaximal, characteristic, complemented
20#26379C211yesmaximal, characteristic, complemented
21#25612C211yesmaximal, characteristic, complemented
22#25562C211yesmaximal, characteristic, complemented
23#25555C211yesmaximal, characteristic, complemented
24#25546C211yesmaximal, characteristic, complemented
25#25532C211yesmaximal, characteristic, complemented
26#25420C211yesmaximal, characteristic, complemented
27#25417C211yesmaximal, characteristic, complemented
28#24139C211yesmaximal, characteristic, complemented
29#24126C211yesmaximal, characteristic, complemented
30#24072C211yesmaximal, characteristic, complemented
31#22336C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×#541C2211yescharacteristic
36C2×#497C2211yescharacteristic
37C2×#488C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#470C2211yescharacteristic
47C2×#468C2211yescharacteristic
48C2×#467C2211yescharacteristic
49C2×#465C2211yescharacteristic
50C2×#441C2211yescharacteristic
51C2×C4×SD16C2211yescharacteristic
52#2823—21no—
53#2813—21no—
54#2727—21no—
55#2726—21no—
56#2725—21no—
57#2725—21no—
58#2707—21no—
59#2707—21no—
60#2705—21no—
61#2705—21no—
62#2664—21no—
63#2630—21no—
64#2629—21no—
65#2629C2211yescharacteristic
66#2624—21no—
67#2620C2211yescharacteristic
68#2601—21no—
69#2565C2211yescharacteristic
70#2538C2211yescharacteristic
71#2538C2211yescharacteristic
72#2536C2211yescharacteristic
73#2485—21no—
74#2454C2211yescharacteristic
75#2453C2211yescharacteristic
76#2442C2211yescharacteristic
77#2441C2211yescharacteristic
78#2441C2211yescharacteristic
79#2441C2211yescharacteristic
80#2429C2211yescharacteristic
81#2429C2211yescharacteristic
82#2427C2211yescharacteristic
83#2426C2211yescharacteristic
84#2417C2211yescharacteristic
85#2415C2211yescharacteristic
86#2415C2211yescharacteristic
87#2415C2211yescharacteristic
88#2414C2211yescharacteristic
89#2414C2211yescharacteristic
90#2392C2211yescharacteristic
91Q8×C4⋊C4C2211yescharacteristic
92#2316C2211yescharacteristic
93#2097C2211yescharacteristic
94#2095C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2026C2211yescharacteristic
130#2026C2211yescharacteristic
131#2026C2211yescharacteristic
132#2025C2211yescharacteristic
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#1992C2211yescharacteristic
142#1992C2211yescharacteristic
143#1991C2211yescharacteristic
144#1973C2211yescharacteristic
145#1969C2211yescharacteristic
146#1956C2211yescharacteristic
147#1955C2211yescharacteristic
148#1954C2211yescharacteristic
149#1944C2211yescharacteristic
150#1944C2211yescharacteristic
151#1944C2211yescharacteristic
152#1942C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1917C2211yescharacteristic
158#1916C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1872C2211yescharacteristic
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1853C2211yescharacteristic
191#1853C2211yescharacteristic
192#1852C2211yescharacteristic
193#1818C2211yescharacteristic
194#1809C2211yescharacteristic
195#1808C2211yescharacteristic
196#1804C2211yescharacteristic
197#1803C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#553—42no—
210#553—42no—
211#552—42no—
212#552—42no—
213#552—42no—
214#552—42no—
215#541—42no—
216#541—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267#497—42no—
268#488—42no—
269#485—42no—
270#485—42no—
271#485—42no—
272#485—42no—
273#485—42no—
274#481—42no—
275#479—42no—
276#479—42no—
277#470—42no—
278#468—42no—
279#467—42no—
280#465—42no—
281#441—42no—
282C4×SD16—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#400—21no—
340#400—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#399—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398D411yescharacteristic
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#397D411yescharacteristic
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396D411yescharacteristic
378#396D411yescharacteristic
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394D411yescharacteristic
390#394D411yescharacteristic
391#394D411yescharacteristic
392#392—21no—
393#392—21no—
394#392D411yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#390—21no—
400#390—21no—
401#390—21no—
402#390—21no—
403#390—21no—
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#386—21no—
448#386—21no—
449#385—21no—
450#385—21no—
451#384—21no—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#382C2311yescharacteristic
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468C4×C4⋊C4—21no—
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546#126—44no—
547#126—44no—
548#126—44no—
549#126—44no—
550#126—44no—
551#125—22no—
552#125—22no—
553#125—22no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—44no—
560#125—44no—
561#125—44no—
562#125—44no—
563#124—41no—
564#124—41no—
565#123—44no—
566#123—44no—
567#123—44no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586#121—22no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—44no—
591#121—41no—
592#121—41no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—44no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—41no—
616#117—41no—
617#117—44no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—44no—
622#117—41no—
623#117—41no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#107—22no—
744#107—41no—
745#107—41no—
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107—41no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—22no—
756#106—41no—
757#106—41no—
758#106—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#102—22no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C22⋊C8—22no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795#97—41no—
796#97—41no—
797C4×C8—41no—
798C4×C8—41no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8H(5,𝔽2)12yes—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—24no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2511yescharacteristic
931Q16—44no—
932Q16—82no—
933SD16—44no—
934SD16—82no—
935M16—82no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—82no—
959C2×C82−1+412yes—
960C2×C82−1+412yes—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4H(5,𝔽2)12yes—
1032C4⋊C4H(5,𝔽2)12yes—
1033C4⋊C4H(5,𝔽2)12yes—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C42—24no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23C23×D411yescharacteristic
1121Q8—22no—
1122Q8—22no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—82no—
1138D4—82no—
1139D4—82no—
1140D4—84no—
1141D4—162no—
1142D4—162no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—162no—
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×2−1+411yescharacteristic
1241C2×C4C2×2−1+411yescharacteristic
1242C8—22no—
1243C8—22no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22#348411yescharacteristic
1279C22#348411yescharacteristic
1280C22#349911yescharacteristic
1281C22#358411yescharacteristic
1282C22#358411yescharacteristic
1283C22#358611yescharacteristic
1284C22#358611yescharacteristic
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—42no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#353611yescharacteristic
1312C4#353611yescharacteristic
1313C4#354811yescharacteristic
1314C4#354811yescharacteristic
1315C2—81no—
1316C2—81no—
1317C2—81no—
1318C2—161no—
1319C2#4642311yescharacteristic
1320C2#6162611yescharacteristic
1321C2#6163711yescharacteristic
1322C2#6164911yescharacteristic
1323C2#6168111yescharacteristic
1324C2#6251711yescharacteristic
1325C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42674C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42803C2semidirect
3. #32783C2semidirect
4. #31539C2semidirect
5. #31528C2semidirect
6. #31200C2semidirect
7. #31193C2semidirect
8. #31117C2semidirect
9. #31117C2semidirect
10. #30644C2semidirect
11. #30639C2semidirect
12. #30588C2semidirect
13. #30586C2semidirect
14. #30570C2semidirect
15. #30562C2semidirect
16. #29307C2semidirect
17. #28786C2semidirect
18. #28778C2semidirect
19. #26395C2semidirect
20. #26379C2semidirect
21. #25612C2semidirect
22. #25562C2semidirect
23. #25555C2semidirect
24. #25546C2semidirect
25. #25532C2semidirect
26. #25420C2semidirect
27. #25417C2semidirect
28. #24139C2semidirect
29. #24126C2semidirect
30. #24072C2semidirect
31. #22336C2semidirect

Maximal subgroups

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

subgroupindex
#428032
#426742
#327832
#315392
#315282
#312002
#311932
#311172
#306442
#306392
#305882
#305862
#305702
#305622
#293072
#287862
#287782
#263952
#263792
#256122
#255622
#255552
#255462
#255322
#254202
#254172
#241392
#241262
#240722
#223362