Finite Group Databasebeta

← #6916307

Subgroups — #6916307

Order 512.

1479 conjugacy classes of subgroups.

The subgroup lattice has 1311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37894C211yesmaximal, characteristic, complemented
2#37492C211yesmaximal, characteristic
3#32833C211yesmaximal, characteristic, complemented
4#32732C211yesmaximal, characteristic, complemented
5#32543C211yesmaximal, characteristic, complemented
6#32531C211yesmaximal, characteristic, complemented
7#31919C211yesmaximal, characteristic, complemented
8#31903C211yesmaximal, characteristic, complemented
9#30680C211yesmaximal, characteristic, complemented
10#30676C211yesmaximal, characteristic, complemented
11#30618C211yesmaximal, characteristic, complemented
12#30598C211yesmaximal, characteristic, complemented
13#30390C211yesmaximal, characteristic, complemented
14#30252C211yesmaximal, characteristic, complemented
15#30139C211yesmaximal, characteristic, complemented
16#29935C211yesmaximal, characteristic, complemented
17#29714C211yesmaximal, characteristic, complemented
18#28575C211yesmaximal, characteristic, complemented
19#28396C211yesmaximal, characteristic, complemented
20#27874C211yesmaximal, characteristic, complemented
21#27686C211yesmaximal, characteristic, complemented
22#26342C211yesmaximal, characteristic, complemented
23#26340C211yesmaximal, characteristic, complemented
24#25128C211yesmaximal, characteristic
25#25112C211yesmaximal, characteristic
26#25084C211yesmaximal, characteristic, complemented
27#25084C211yesmaximal, characteristic, complemented
28#24783C211yesmaximal, characteristic, complemented
29#24781C211yesmaximal, characteristic, complemented
30C2×#2092C211yesmaximal, characteristic, complemented
31#22697C211yesmaximal, characteristic, complemented
32C2×#477C2211yescharacteristic, complemented
33C2×#475C2211yescharacteristic, complemented
34C2×#470C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#467C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic, complemented
39C2×#465C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C22×#107C2211yescharacteristic
47C22×#106C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50#2857C2211yescharacteristic
51#2830—21no—
52#2829—21no—
53#2772—21no—
54#2772—21no—
55#2766—21no—
56#2766—21no—
57#2662—21no—
58#2651—21no—
59#2647C2211yescharacteristic, complemented
60#2644C2211yescharacteristic
61#2640C2211yescharacteristic
62#2626—21no—
63#2624C2211yescharacteristic
64#2622—21no—
65#2621C2211yescharacteristic, complemented
66#2620C2211yescharacteristic
67#2569—21no—
68#2569—21no—
69#2514C2211yescharacteristic, complemented
70#2514C2211yescharacteristic, complemented
71#2512C2211yescharacteristic
72#2510—21no—
73#2510—21no—
74#2491C2211yescharacteristic
75#2480—21no—
76#2472—21no—
77#2448C2211yescharacteristic
78#2440C2211yescharacteristic
79#2435C2211yescharacteristic
80#2426C2211yescharacteristic
81#2421C2211yescharacteristic, complemented
82#2421C2211yescharacteristic, complemented
83#2417C2211yescharacteristic
84#2417C2211yescharacteristic
85#2417C2211yescharacteristic
86#2408C2211yescharacteristic
87#2360C2211yescharacteristic
88#2360C2211yescharacteristic
89#2327C2211yescharacteristic, complemented
90#2314C2211yescharacteristic, complemented
91C4×C22⋊Q8C2211yescharacteristic
92C2×#390C2211yescharacteristic
93#2290C2211yescharacteristic
94C2×#382C2211yescharacteristic
95#2101C2211yescharacteristic, complemented
96#2101C2211yescharacteristic, complemented
97#2097C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2096C2211yescharacteristic, complemented
100#2095C2211yescharacteristic, complemented
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic
104#2092C2211yescharacteristic
105#2092C2211yescharacteristic
106#2092C2211yescharacteristic
107#2092C2211yescharacteristic
108#2092C2211yescharacteristic
109#2088C2211yescharacteristic, complemented
110#2087C2211yescharacteristic, complemented
111#2083C2211yescharacteristic, complemented
112#2072C2211yescharacteristic, complemented
113#2071C2211yescharacteristic
114#2071C2211yescharacteristic
115#2068C2211yescharacteristic, complemented
116#2068C2211yescharacteristic, complemented
117#2068C2211yescharacteristic, complemented
118#2067C2211yescharacteristic
119#2067C2211yescharacteristic
120#2067C2211yescharacteristic
121#2066C2211yescharacteristic, complemented
122#2066C2211yescharacteristic, complemented
123#2066C2211yescharacteristic, complemented
124#2065C2211yescharacteristic
125#2058C2211yescharacteristic, complemented
126#2057C2211yescharacteristic, complemented
127#2055C2211yescharacteristic
128#2055C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2055C2211yescharacteristic
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2043C2211yescharacteristic, complemented
136#2042C2211yescharacteristic
137#2042C2211yescharacteristic
138#2036C2211yescharacteristic, complemented
139#2036C2211yescharacteristic, complemented
140#2035C2211yescharacteristic, complemented
141#2035C2211yescharacteristic, complemented
142#2034C2211yescharacteristic
143#2033C2211yescharacteristic
144#2016C2211yescharacteristic, complemented
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2000C2211yescharacteristic
150#2000C2211yescharacteristic
151#1983C2211yescharacteristic
152#1983C2211yescharacteristic
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic, complemented
155#1969C2211yescharacteristic, complemented
156#1968C2211yescharacteristic
157#1949C2211yescharacteristic, complemented
158#1949C2211yescharacteristic, complemented
159#1948C2211yescharacteristic, complemented
160#1947C2211yescharacteristic, complemented
161#1944C2211yescharacteristic, complemented
162#1942C2211yescharacteristic, complemented
163#1940C2211yescharacteristic, complemented
164#1939C2211yescharacteristic, complemented
165#1936C2211yescharacteristic
166#1934C2211yescharacteristic
167#1928C2211yescharacteristic, complemented
168#1928C2211yescharacteristic, complemented
169#1925C2211yescharacteristic
170#1925C2211yescharacteristic
171#1921C2211yescharacteristic, complemented
172#1919C2211yescharacteristic, complemented
173#1895C2211yescharacteristic
174#1893C2211yescharacteristic
175#1892C2211yescharacteristic
176#1892C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1878C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1872C2211yescharacteristic
184#1872C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1853C2211yescharacteristic
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic, complemented
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1850C2211yescharacteristic, complemented
193#1832C2211yescharacteristic, complemented
194#1809C2211yescharacteristic, complemented
195#1808C2211yescharacteristic, complemented
196#1805C2211yescharacteristic, complemented
197#1805C2211yescharacteristic, complemented
198#1798C2211yescharacteristic, complemented
199#1797C2211yescharacteristic
200#1768C2211yescharacteristic, complemented
201#1729C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#477—42no—
242#475—42no—
243#470—42no—
244#468—42no—
245#467—42no—
246#467—42no—
247#467—42no—
248#465—42no—
249#464—42no—
250#464—42no—
251#450—42no—
252#450—42no—
253#435—42no—
254C8×D4—42no—
255C2×#107—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106—42no—
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102—42no—
296C2×#102—42no—
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#401—21no—
316#401—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
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#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#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#392—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
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#389C2311yescharacteristic
397#389C2311yescharacteristic
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#388D411yescharacteristic
408#388D411yescharacteristic
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#387D411yescharacteristic
423#387D411yescharacteristic
424#386—21no—
425#386—21no—
426#386—21no—
427#386D411yescharacteristic
428#386D411yescharacteristic
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385D411yescharacteristic
434#385D411yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#383—21no—
438#383—21no—
439#382—21no—
440#382—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
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#376C2311yescharacteristic
468C2×#95—21no—
469C2×#95—21no—
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#126—82no—
563#124—41no—
564#124—41no—
565#124—41no—
566#124—41no—
567#124—82no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#120—82no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—22no—
593C4×D4—22no—
594#117—41no—
595#117—41no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
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—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
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—82no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#103—22no—
725#103—22no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
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—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756#97—41no—
757C4×C8—41no—
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#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#95—21no—
795#95—21no—
796#95—21no—
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
806#95C2×D411yescharacteristic
807C24—21no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C2×Q8—21no—
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—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
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—21no—
853C2×D4—21no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—42no—
857C2×D4—82no—
858C2×D4—82no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
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—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4H(5,𝔽2)12yes—
919C22×C42−1+412yes—
920C22×C4C2511yescharacteristic
921Q16—82no—
922Q16—82no—
923SD16—82no—
924SD16—82no—
925SD16—82no—
926SD16—82no—
927M16—82no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
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—44no—
951C2×C8—44no—
952C2×C8—82no—
953C2×C8H(5,𝔽2)12yes—
954C2×C8H(5,𝔽2)12yes—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
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—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
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—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
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—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—41no—
1060C42—41no—
1061C42—42no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—162no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23#53712yes—
1100C23#57712yes—
1101C23#57812yes—
1102C23C23×D411yescharacteristic
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—162no—
1116D4—44no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126D4—162no—
1127D4—162no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
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—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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—82no—
1214C2×C4—82no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4#53712yes—
1219C2×C4C2×H(5,𝔽2)11yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C2×C4#58511yescharacteristic
1224C2×C4#58511yescharacteristic
1225C8—22no—
1226C8—22no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—168no—
1261C22#325814yes—
1262C22C2×#53711yescharacteristic
1263C22#348511yescharacteristic
1264C22#349811yescharacteristic
1265C22C2×#57711yescharacteristic
1266C22C2×#57811yescharacteristic
1267C22#358411yescharacteristic
1268C22#358511yescharacteristic
1269C4—22no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4#353411yescharacteristic
1296C4#353411yescharacteristic
1297C4#354111yescharacteristic
1298C4#354111yescharacteristic
1299C2—24no—
1300C2—81no—
1301C2—161no—
1302C2—161no—
1303C2#4136811yescharacteristic
1304C2C2×#325811yescharacteristic
1305C2#6093311yescharacteristic
1306C2#6175411yescharacteristic
1307C2#6177011yescharacteristic
1308C2#6243711yescharacteristic
1309C2#6245711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
1. #37894C2semidirect
3. #32833C2semidirect
4. #32732C2semidirect
5. #32543C2semidirect
6. #32531C2semidirect
7. #31919C2semidirect
8. #31903C2semidirect
9. #30680C2semidirect
10. #30676C2semidirect
11. #30618C2semidirect
12. #30598C2semidirect
13. #30390C2semidirect
14. #30252C2semidirect
15. #30139C2semidirect
16. #29935C2semidirect
17. #29714C2semidirect
18. #28575C2semidirect
19. #28396C2semidirect
20. #27874C2semidirect
21. #27686C2semidirect
22. #26342C2semidirect
23. #26340C2semidirect
26. #25084C2semidirect
27. #25084C2semidirect
28. #24783C2semidirect
29. #24781C2semidirect
30. C2×#2092C2semidirect
31. #22697C2semidirect
32. C2×#477C22semidirect
33. C2×#475C22semidirect
34. C2×#470C22semidirect
38. C2×#467C22semidirect
59. #2647C22semidirect
65. #2621C22semidirect
69. #2514C22semidirect
70. #2514C22semidirect
81. #2421C22semidirect
82. #2421C22semidirect
89. #2327C22semidirect
90. #2314C22semidirect
95. #2101C22semidirect
96. #2101C22semidirect
97. #2097C22semidirect
98. #2097C22semidirect
99. #2096C22semidirect
100. #2095C22semidirect
109. #2088C22semidirect
110. #2087C22semidirect
111. #2083C22semidirect
112. #2072C22semidirect
115. #2068C22semidirect
116. #2068C22semidirect
117. #2068C22semidirect
121. #2066C22semidirect
122. #2066C22semidirect
123. #2066C22semidirect
125. #2058C22semidirect
126. #2057C22semidirect
135. #2043C22semidirect
138. #2036C22semidirect
139. #2036C22semidirect
140. #2035C22semidirect
141. #2035C22semidirect
144. #2016C22semidirect
154. #1971C22semidirect
155. #1969C22semidirect
157. #1949C22semidirect
158. #1949C22semidirect
159. #1948C22semidirect
160. #1947C22semidirect
161. #1944C22semidirect
162. #1942C22semidirect
163. #1940C22semidirect
164. #1939C22semidirect
167. #1928C22semidirect
168. #1928C22semidirect
171. #1921C22semidirect
172. #1919C22semidirect
179. #1878C22semidirect
180. #1878C22semidirect
185. #1865C22semidirect
186. #1863C22semidirect
189. #1851C22semidirect
192. #1850C22semidirect
193. #1832C22semidirect
194. #1809C22semidirect
195. #1808C22semidirect
196. #1805C22semidirect
197. #1805C22semidirect
198. #1798C22semidirect
200. #1768C22semidirect
201. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#378942
#374922
#328332
#327322
#325432
#325312
#319192
#319032
#306802
#306762
#306182
#305982
#303902
#302522
#301392
#299352
#297142
#285752
#283962
#278742
#276862
#263422
#263402
#251282
#251122
#250842
#247832
#247812
C2×#20922
#226972