Finite Group Databasebeta

← #6742157

Subgroups — #6742157

Order 512.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40100C211yesmaximal, characteristic, complemented
2#36162C211yesmaximal, characteristic
3#32905C211yesmaximal, characteristic, complemented
4#31526C211yesmaximal, characteristic, complemented
5#31506C211yesmaximal, characteristic, complemented
6#31157C211yesmaximal, characteristic, complemented
7#31058C211yesmaximal, characteristic
8#30531C211yesmaximal, characteristic, complemented
9#30469C211yesmaximal, characteristic, complemented
10#30464C211yesmaximal, characteristic, complemented
11#30424C211yesmaximal, characteristic
12#30326C211yesmaximal, characteristic, complemented
13#30013C211yesmaximal, characteristic, complemented
14#29100C211yesmaximal, characteristic, complemented
15#28922C211yesmaximal, characteristic, complemented
16#27392C211yesmaximal, characteristic, complemented
17#27342C211yesmaximal, characteristic, complemented
18#27122C211yesmaximal, characteristic, complemented
19#27087C211yesmaximal, characteristic, complemented
20#26918C211yesmaximal, characteristic, complemented
21#26745C211yesmaximal, characteristic, complemented
22#26599C211yesmaximal, characteristic, complemented
23#25329C211yesmaximal, characteristic, complemented
24#25177C211yesmaximal, characteristic, complemented
25#25099C211yesmaximal, characteristic, complemented
26#24127C211yesmaximal, characteristic, complemented
27#23983C211yesmaximal, characteristic, complemented
28#23194C211yesmaximal, characteristic, complemented
29#22865C211yesmaximal, characteristic, complemented
30#22359C211yesmaximal, characteristic, complemented
31#21453C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#451C2211yescharacteristic, complemented
42C2×#448C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic
49C2×C4×Q16C2211yescharacteristic, complemented
50C2×#419C2211yescharacteristic, complemented
51#2857C2211yescharacteristic
52#2855C2211yescharacteristic
53#2849—21no—
54#2787—21no—
55#2774—21no—
56#2745—21no—
57#2695—21no—
58#2666—21no—
59#2578—21no—
60#2574—21no—
61#2565C2211yescharacteristic, complemented
62#2536C2211yescharacteristic
63#2514C2211yescharacteristic, complemented
64#2496C2211yescharacteristic, complemented
65#2489C2211yescharacteristic
66#2489C2211yescharacteristic, complemented
67#2482—21no—
68#2467—21no—
69#2467—21no—
70#2460—21no—
71#2460—21no—
72#2454C2211yescharacteristic
73#2454C2211yescharacteristic
74#2446C2211yescharacteristic, complemented
75#2435C2211yescharacteristic
76#2434C2211yescharacteristic, complemented
77#2429C2211yescharacteristic
78#2427C2211yescharacteristic
79#2427C2211yescharacteristic
80#2411—21no—
81#2409C2211yescharacteristic
82#2408C2211yescharacteristic
83#2367C2211yescharacteristic
84#2367C2211yescharacteristic
85#2365C2211yescharacteristic, complemented
86#2363C2211yescharacteristic
87#2363C2211yescharacteristic
88#2344C2211yescharacteristic
89Q8×C22⋊C4C2211yescharacteristic, complemented
90#2334—21no—
91C4×C22⋊Q8C2211yescharacteristic
92C4×#123C2211yescharacteristic
93#2280—21no—
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2016C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2013C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic
131#2001C2211yescharacteristic
132#2001C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#1991C2211yescharacteristic, complemented
135#1989C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1981C2211yescharacteristic, complemented
138#1971C2211yescharacteristic, complemented
139#1971C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1954C2211yescharacteristic
144#1939C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic, complemented
157#1924C2211yescharacteristic, complemented
158#1923C2211yescharacteristic
159#1921C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1872C2211yescharacteristic
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1870C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1854C2211yescharacteristic, complemented
188#1852C2211yescharacteristic
189#1851C2211yescharacteristic, complemented
190#1825C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1797C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216#552—42no—
217#552—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123D411yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—42no—
245C2×C4×D4—42no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257#497—24no—
258#488—42no—
259#479—42no—
260#468—42no—
261#464—42no—
262#461—42no—
263#461—42no—
264#451—42no—
265#450—24no—
266#450—42no—
267#450—42no—
268#448—24no—
269#448—42no—
270#440—42no—
271#440—42no—
272C4×Q16—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#419—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#401—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#393—21no—
359#392—21no—
360#391—21no—
361#391—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387D411yescharacteristic
415#387D411yescharacteristic
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386D411yescharacteristic
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385D411yescharacteristic
432#384C2311yescharacteristic
433#383—21no—
434#382—21no—
435#382—21no—
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381D411yescharacteristic
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—44no—
530C23×C4—44no—
531C23×C4—82no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16#4114yes—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578#126—44no—
579#126—44no—
580#125—22no—
581#125—41no—
582#125—41no—
583#125—41no—
584#125—44no—
585#124—22no—
586#124—22no—
587#124—41no—
588#124—41no—
589#123—42no—
590#123—44no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603#121—22no—
604#121—22no—
605#121—41no—
606#121—41no—
607#120—82no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—44no—
628#117—22no—
629#117—41no—
630#117—44no—
631#117—82no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
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—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—44no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—41no—
724C2×C42—41no—
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—22no—
733#107—22no—
734#107—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781#97—22no—
782#97—41no—
783#97—41no—
784C4×C8—41no—
785C4×C8—41no—
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#95—21no—
798#95—21no—
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#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832C24—21no—
833C24—21no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
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×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—42no—
867C2×Q8—44no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—82no—
871C2×Q8—82no—
872C2×Q8—82no—
873C2×Q8C2×#4112yes—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4C2×#4112yes—
901C2×D4H(5,𝔽2)12yes—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—816no—
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C2511yescharacteristic
966Q16—44no—
967Q16—82no—
968Q16—82no—
969SD16—44no—
970SD16—44no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
974SD16—82no—
975M16—82no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8C2×#4112yes—
1000C4⋊C4—24no—
1001C4⋊C4—22no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4H(5,𝔽2)12yes—
1051C4⋊C4H(5,𝔽2)12yes—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—41no—
1100C42—41no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—48no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—84no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—84no—
1144C23#57712yes—
1145C23C23×D411yescharacteristic
1146Q8—22no—
1147Q8—22no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—84no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—48no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—82no—
1173D4—162no—
1174D4—162no—
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—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—44no—
1214C2×C4—48no—
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—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4#57512yes—
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—22no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—42no—
1294C22—41no—
1295C22—42no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—41no—
1303C22—816no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22D4×#4111yescharacteristic
1313C22#348411yescharacteristic
1314C22#348811yescharacteristic
1315C22C2×#57511yescharacteristic
1316C22C2×#57711yescharacteristic
1317C22#358611yescharacteristic
1318C22#358611yescharacteristic
1319C4—22no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—42no—
1327C4—42no—
1328C4—41no—
1329C4—41no—
1330C4—42no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4#345911yescharacteristic
1346C4#351911yescharacteristic
1347C4#354011yescharacteristic
1348C4#354211yescharacteristic
1349C2—42no—
1350C2—81no—
1351C2—82no—
1352C2—82no—
1353C2#3782511yescharacteristic
1354C2#6146311yescharacteristic
1355C2#6152011yescharacteristic
1356C2#6160111yescharacteristic
1357C2#6165211yescharacteristic
1358C2#6196711yescharacteristic
1359C2#6200811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40100C2semidirect
3. #32905C2semidirect
4. #31526C2semidirect
5. #31506C2semidirect
6. #31157C2semidirect
8. #30531C2semidirect
9. #30469C2semidirect
10. #30464C2semidirect
12. #30326C2semidirect
13. #30013C2semidirect
14. #29100C2semidirect
15. #28922C2semidirect
16. #27392C2semidirect
17. #27342C2semidirect
18. #27122C2semidirect
19. #27087C2semidirect
20. #26918C2semidirect
21. #26745C2semidirect
22. #26599C2semidirect
23. #25329C2semidirect
24. #25177C2semidirect
25. #25099C2semidirect
26. #24127C2semidirect
27. #23983C2semidirect
28. #23194C2semidirect
29. #22865C2semidirect
30. #22359C2semidirect
31. #21453C2semidirect
36. C2×#479C22semidirect
41. C2×#451C22semidirect
49. C2×C4×Q16C22semidirect
50. C2×#419C22semidirect
61. #2565C22semidirect
63. #2514C22semidirect
64. #2496C22semidirect
66. #2489C22semidirect
74. #2446C22semidirect
76. #2434C22semidirect
85. #2365C22semidirect
89. Q8×C22⋊C4C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2084C22semidirect
100. #2072C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2066C22semidirect
104. #2059C22semidirect
105. #2056C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
113. #2036C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
124. #2016C22semidirect
132. #2001C22semidirect
134. #1991C22semidirect
135. #1989C22semidirect
137. #1981C22semidirect
138. #1971C22semidirect
139. #1971C22semidirect
144. #1939C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1933C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
156. #1924C22semidirect
157. #1924C22semidirect
159. #1921C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
165. #1894C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
178. #1873C22semidirect
183. #1865C22semidirect
184. #1865C22semidirect
187. #1854C22semidirect
189. #1851C22semidirect
190. #1825C22semidirect
191. #1805C22semidirect
196. #1776C22semidirect
197. #1771C22semidirect
200. C4×#103C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#401002
#361622
#329052
#315262
#315062
#311572
#310582
#305312
#304692
#304642
#304242
#303262
#300132
#291002
#289222
#273922
#273422
#271222
#270872
#269182
#267452
#265992
#253292
#251772
#250992
#241272
#239832
#231942
#228652
#223592
#214532