Finite Group Databasebeta

← #7093704

Subgroups — #7093704

Order 512.

1544 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44985C211yesmaximal, characteristic, complemented
2#42535C211yesmaximal, characteristic, complemented
3#32672C211yesmaximal, characteristic, complemented
4#32612C211yesmaximal, characteristic, complemented
5#32284C211yesmaximal, characteristic, complemented
6#32076C211yesmaximal, characteristic, complemented
7#31862C211yesmaximal, characteristic, complemented
8#30709C211yesmaximal, characteristic, complemented
9#30523C211yesmaximal, characteristic, complemented
10#30501C211yesmaximal, characteristic
11#29530C211yesmaximal, characteristic, complemented
12#29507C211yesmaximal, characteristic, complemented
13#28908C211yesmaximal, characteristic, complemented
14#28342C211yesmaximal, characteristic, complemented
15#28085C211yesmaximal, characteristic, complemented
16#27929C211yesmaximal, characteristic, complemented
17#26975C211yesmaximal, characteristic, complemented
18#26620C211yesmaximal, characteristic, complemented
19#26571C211yesmaximal, characteristic, complemented
20#26546C211yesmaximal, characteristic, complemented
21#26330C211yesmaximal, characteristic, complemented
22#26132C211yesmaximal, characteristic, complemented
23#25056C211yesmaximal, characteristic, complemented
24#25035C211yesmaximal, characteristic, complemented
25#24921C211yesmaximal, characteristic, complemented
26#24861C211yesmaximal, characteristic, complemented
27#23812C211yesmaximal, characteristic, complemented
28#23274C211yesmaximal, characteristic, complemented
29#23032C211yesmaximal, characteristic, complemented
30#22870C211yesmaximal, characteristic, complemented
31#22228C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#480C2211yescharacteristic, complemented
36C2×#467C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic
45C22×#107C2211yescharacteristic, complemented
46C22×#102C2211yescharacteristic
47#2827—21no—
48#2807—21no—
49#2796—21no—
50#2773—21no—
51#2741—21no—
52#2735—21no—
53#2724—21no—
54#2697—21no—
55#2696—21no—
56#2644C2211yescharacteristic
57#2630—21no—
58#2626—21no—
59#2602—21no—
60#2592C2211yescharacteristic
61#2592C2211yescharacteristic, complemented
62#2580—21no—
63#2540C2211yescharacteristic
64#2538C2211yescharacteristic
65#2502C2211yescharacteristic
66#2501C2211yescharacteristic
67#2501C2211yescharacteristic, complemented
68#2497C2211yescharacteristic
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic, complemented
71#2458—21no—
72#2455—21no—
73#2435C2211yescharacteristic
74#2427C2211yescharacteristic
75#2426C2211yescharacteristic
76#2423C2211yescharacteristic
77#2423C2211yescharacteristic
78#2422C2211yescharacteristic, complemented
79#2418—21no—
80#2417C2211yescharacteristic
81#2408C2211yescharacteristic
82#2398C2211yescharacteristic
83#2361C2211yescharacteristic
84#2361C2211yescharacteristic
85#2360C2211yescharacteristic, complemented
86Q8×C4⋊C4C2211yescharacteristic, complemented
87D4×C4⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2330C2211yescharacteristic, complemented
90#2326C2211yescharacteristic
91#2326C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2093C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2093C2211yescharacteristic, complemented
100#2093C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2083C2211yescharacteristic, complemented
103#2076C2211yescharacteristic
104#2072C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2068C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2025C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2001C2211yescharacteristic, complemented
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic, complemented
131#1999C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1984C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1970C2211yescharacteristic
139#1970C2211yescharacteristic
140#1969C2211yescharacteristic, complemented
141#1959C2211yescharacteristic
142#1959C2211yescharacteristic
143#1947C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic, complemented
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic, complemented
167#1921C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1893C2211yescharacteristic
171#1892C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1872C2211yescharacteristic, complemented
178#1872C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1852C2211yescharacteristic
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic, complemented
190#1845C2211yescharacteristic, complemented
191#1845C2211yescharacteristic, complemented
192#1808C2211yescharacteristic
193#1802C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×C4×Q8—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246#488—24no—
247#484—42no—
248#480—42no—
249#480—42no—
250#467—42no—
251#466—42no—
252#465—24no—
253#450—42no—
254#447—24no—
255#440—42no—
256#440—42no—
257C4×Q16—42no—
258C4×D8—42no—
259C2×#107—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102—42no—
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400D411yescharacteristic
320#400D411yescharacteristic
321#399—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397D411yescharacteristic
343#397D411yescharacteristic
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#393—21no—
360#393—21no—
361#393D411yescharacteristic
362#393D411yescharacteristic
363#392—21no—
364#392—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—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#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#382—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552#125—22no—
553#125—41no—
554#124—22no—
555#124—41no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—41no—
560#123—82no—
561#123—82no—
562#123—82no—
563#123—82no—
564#123—82no—
565C22⋊Q8—22no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—82no—
574#121—22no—
575#121—22no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#120—82no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—82no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—82no—
599C4×D4—82no—
600C4×D4—82no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—22no—
715#107—22no—
716#107—22no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102#4114yes—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—22no—
764#97—41no—
765#97—41no—
766C4×C8—22no—
767C4×C8—22no—
768C4×C8—41no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806C24—21no—
807C24—21no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C2×Q8—22no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—41no—
832C2×Q8—41no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—44no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4C2×#4112yes—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
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—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
929Q16—44no—
930SD16—44no—
931SD16—44no—
932SD16—82no—
933D8—44no—
934D8—82no—
935C2×C8—21no—
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—44no—
957C2×C8—82no—
958C2×C8C2×#4112yes—
959C2×C8H(5,𝔽2)12yes—
960C2×C8H(5,𝔽2)12yes—
961C4⋊C4—21no—
962C4⋊C4—21no—
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—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4C2×#4112yes—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—42no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—84no—
1116C23—84no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23#57612yes—
1123C23#57812yes—
1124C23C23×D411yescharacteristic
1125Q8—44no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134D4—22no—
1135D4—22no—
1136D4—44no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
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—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
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—41no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4#57612yes—
1241C2×C4C22×#4111yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4#58511yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C8—22no—
1248C8—22no—
1249C8—22no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—168no—
1291C22D4×#4111yescharacteristic
1292C22#348511yescharacteristic
1293C22#349811yescharacteristic
1294C22C2×#57611yescharacteristic
1295C22C2×#57611yescharacteristic
1296C22C2×#57811yescharacteristic
1297C22#358611yescharacteristic
1298C4—22no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4#350611yescharacteristic
1324C4#351311yescharacteristic
1325C4#353311yescharacteristic
1326C4#354011yescharacteristic
1327C2—42no—
1328C2—42no—
1329C2—82no—
1330C2—161no—
1331C2—161no—
1332C2#4427211yescharacteristic
1333C2#6148211yescharacteristic
1334C2#6152311yescharacteristic
1335C2#6174411yescharacteristic
1336C2#6176411yescharacteristic
1337C2#6243111yescharacteristic
1338C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30501C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44985C2semidirect
2. #42535C2semidirect
3. #32672C2semidirect
4. #32612C2semidirect
5. #32284C2semidirect
6. #32076C2semidirect
7. #31862C2semidirect
8. #30709C2semidirect
9. #30523C2semidirect
11. #29530C2semidirect
12. #29507C2semidirect
13. #28908C2semidirect
14. #28342C2semidirect
15. #28085C2semidirect
16. #27929C2semidirect
17. #26975C2semidirect
18. #26620C2semidirect
19. #26571C2semidirect
20. #26546C2semidirect
21. #26330C2semidirect
22. #26132C2semidirect
23. #25056C2semidirect
24. #25035C2semidirect
25. #24921C2semidirect
26. #24861C2semidirect
27. #23812C2semidirect
28. #23274C2semidirect
29. #23032C2semidirect
30. #22870C2semidirect
31. #22228C2semidirect
35. C2×#480C22semidirect
42. C2×#440C22semidirect
43. C2×C4×Q16C22semidirect
45. C22×#107C22semidirect
61. #2592C22semidirect
67. #2501C22semidirect
70. #2489C22semidirect
78. #2422C22semidirect
85. #2360C22semidirect
86. Q8×C4⋊C4C22semidirect
89. #2330C22semidirect
91. #2326C22semidirect
92. #2100C22semidirect
93. #2095C22semidirect
94. #2095C22semidirect
99. #2093C22semidirect
100. #2093C22semidirect
101. #2083C22semidirect
102. #2083C22semidirect
104. #2072C22semidirect
105. #2072C22semidirect
107. #2068C22semidirect
108. #2059C22semidirect
110. #2055C22semidirect
112. #2042C22semidirect
122. #2015C22semidirect
127. #2001C22semidirect
130. #2000C22semidirect
132. #1992C22semidirect
133. #1985C22semidirect
134. #1984C22semidirect
140. #1969C22semidirect
143. #1947C22semidirect
144. #1947C22semidirect
145. #1944C22semidirect
146. #1942C22semidirect
148. #1936C22semidirect
149. #1936C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1928C22semidirect
155. #1927C22semidirect
162. #1925C22semidirect
164. #1924C22semidirect
166. #1923C22semidirect
167. #1921C22semidirect
168. #1918C22semidirect
169. #1918C22semidirect
171. #1892C22semidirect
177. #1872C22semidirect
178. #1872C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
186. #1862C22semidirect
189. #1852C22semidirect
190. #1845C22semidirect
191. #1845C22semidirect
195. #1776C22semidirect
198. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#449852
#425352
#326722
#326122
#322842
#320762
#318622
#307092
#305232
#305012
#295302
#295072
#289082
#283422
#280852
#279292
#269752
#266202
#265712
#265462
#263302
#261322
#250562
#250352
#249212
#248612
#238122
#232742
#230322
#228702
#222282