Finite Group Databasebeta

← #7536297

Subgroups — #7536297

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45149C211yesmaximal, characteristic, complemented
2#36033C211yesmaximal, characteristic
3#32663C211yesmaximal, characteristic, complemented
4#32604C211yesmaximal, characteristic, complemented
5#32187C211yesmaximal, characteristic, complemented
6#30754C211yesmaximal, characteristic, complemented
7#28901C211yesmaximal, characteristic, complemented
8#28588C211yesmaximal, characteristic, complemented
9#28361C211yesmaximal, characteristic
10#28322C211yesmaximal, characteristic, complemented
11#27516C211yesmaximal, characteristic, complemented
12#27220C211yesmaximal, characteristic, complemented
13#27210C211yesmaximal, characteristic, complemented
14#27070C211yesmaximal, characteristic, complemented
15#26610C211yesmaximal, characteristic, complemented
16#26589C211yesmaximal, characteristic, complemented
17#26256C211yesmaximal, characteristic, complemented
18#25784C211yesmaximal, characteristic
19#25643C211yesmaximal, characteristic, complemented
20#25215C211yesmaximal, characteristic, complemented
21#25095C211yesmaximal, characteristic, complemented
22#24493C211yesmaximal, characteristic
23#24357C211yesmaximal, characteristic
24#24195C211yesmaximal, characteristic, complemented
25#23246C211yesmaximal, characteristic, complemented
26#23194C211yesmaximal, characteristic, complemented
27#23111C211yesmaximal, characteristic, complemented
28#22937C211yesmaximal, characteristic, complemented
29#22881C211yesmaximal, characteristic, complemented
30#21459C211yesmaximal, characteristic
31#20933C211yesmaximal, characteristic
32C23×SD16C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#497C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#462C2211yescharacteristic, complemented
44C2×#451C2211yescharacteristic
45C2×#451C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic
50C2×#419C2211yescharacteristic
51C2×#418C2211yescharacteristic
52#2762—21no—
53#2758—21no—
54#2745—21no—
55#2739—21no—
56#2638—21no—
57#2621C2211yescharacteristic
58#2586—21no—
59#2581C2211yescharacteristic, complemented
60#2580C2211yescharacteristic
61#2575—21no—
62#2568C2211yescharacteristic, complemented
63#2561—21no—
64#2547C2211yescharacteristic
65#2520—21no—
66#2515—21no—
67#2514C2211yescharacteristic, complemented
68#2511C2211yescharacteristic, complemented
69#2499C2211yescharacteristic
70#2482—21no—
71#2480—21no—
72#2480—21no—
73#2468—21no—
74#2468—21no—
75#2447C2211yescharacteristic
76#2447C2211yescharacteristic
77#2446C2211yescharacteristic, complemented
78#2446C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2435C2211yescharacteristic
81#2434C2211yescharacteristic
82#2396C2211yescharacteristic
83#2395—21no—
84#2367C2211yescharacteristic
85#2367C2211yescharacteristic
86#2365C2211yescharacteristic, complemented
87#2362C2211yescharacteristic
88#2362C2211yescharacteristic
89#2357C2211yescharacteristic
90#2355C2211yescharacteristic, complemented
91#2347C2211yescharacteristic
92Q8×C22⋊C4C2211yescharacteristic
93#2323C2211yescharacteristic
94#2310C2211yescharacteristic
95#2097C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2094C2211yescharacteristic
98#2092C2211yescharacteristic
99#2085C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2056C2211yescharacteristic, complemented
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2016C2211yescharacteristic, complemented
116#2016C2211yescharacteristic, complemented
117#2016C2211yescharacteristic, complemented
118#2016C2211yescharacteristic, complemented
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2013C2211yescharacteristic
126#2013C2211yescharacteristic
127#1985C2211yescharacteristic, complemented
128#1984C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1981C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1971C2211yescharacteristic, complemented
136#1971C2211yescharacteristic, complemented
137#1971C2211yescharacteristic, complemented
138#1969C2211yescharacteristic, complemented
139#1969C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1959C2211yescharacteristic
142#1958C2211yescharacteristic
143#1947C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1892C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1873C2211yescharacteristic
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1850C2211yescharacteristic
189#1805C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16—24no—
212C22×SD16—42no—
213C22×SD16—42no—
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×M16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#556—42no—
223#556—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#126—21no—
228C2×#126—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237#518—42no—
238#518—42no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257#497—24no—
258#497—42no—
259#485—24no—
260#485—42no—
261#470—42no—
262#467—42no—
263#464—24no—
264#464—42no—
265#462—42no—
266#451—24no—
267#451—42no—
268#450—24no—
269#440—42no—
270C4×Q16—42no—
271C4×SD16—42no—
272C2×#107C2311yescharacteristic
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
284#419—42no—
285#418—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×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#401—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400D411yescharacteristic
336#399—21no—
337#399D411yescharacteristic
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#398D411yescharacteristic
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#396D411yescharacteristic
355#396D411yescharacteristic
356#395—21no—
357#395—21no—
358#395—21no—
359#395D411yescharacteristic
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#393—21no—
365#393D411yescharacteristic
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
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#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#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384C2311yescharacteristic
438#383—21no—
439#383—21no—
440#382—21no—
441#382—21no—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#381—21no—
446#381—21no—
447#381—21no—
448#381—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C22×Q8—21no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8C2×D411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—416no—
567C2×SD16#4114yes—
568C2×M16—22no—
569C2×M16—41no—
570C2×M16—41no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—41no—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588#126—44no—
589#126—44no—
590#124—22no—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—44no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—44no—
626C4×D4—44no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—44no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
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×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—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—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—22no—
729#107—41no—
730#107—41no—
731#106—22no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—22no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
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#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—22no—
772C22⋊C8#4114yes—
773#97—22no—
774#97—41no—
775#97—41no—
776#97—41no—
777C4×C8—41no—
778C4×C8—41no—
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#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#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
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—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—41no—
874C2×Q8—41no—
875C2×Q8—41no—
876C2×Q8—42no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—42no—
880C2×Q8—81no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×Q8C2×#4112yes—
884C2×D4—28no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—44no—
900C2×D4—42no—
901C2×D4C2×#4112yes—
902C2×D4H(5,𝔽2)12yes—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—24no—
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—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C2×#4112yes—
950C22×C4H(5,𝔽2)12yes—
951C22×C4C2511yescharacteristic
952Q16—44no—
953Q16—82no—
954Q16—82no—
955Q16—82no—
956Q16—82no—
957Q16—82no—
958SD16—44no—
959SD16—44no—
960SD16—44no—
961SD16—44no—
962SD16—44no—
963SD16—44no—
964M16—82no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
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—44no—
987C2×C8C2×#4112yes—
988C2×C8C2×#4112yes—
989C2×C8C2×#4112yes—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4H(5,𝔽2)12yes—
1040C22⋊C4—24no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—48no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23#55012yes—
1124C23C23×D411yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—84no—
1146Q8—82no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—22no—
1151D4—48no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
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—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—21no—
1198C2×C4—21no—
1199C2×C4—22no—
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—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4#55012yes—
1246C2×C4C22×#4111yescharacteristic
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4#58511yescharacteristic
1252C8—22no—
1253C8—22no—
1254C8—22no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—168no—
1282C22C2×#55011yescharacteristic
1283C22D4×#4111yescharacteristic
1284C22#348411yescharacteristic
1285C22#358411yescharacteristic
1286C22#358611yescharacteristic
1287C22#358611yescharacteristic
1288C22#358611yescharacteristic
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4#348111yescharacteristic
1317C4#349011yescharacteristic
1318C4#351311yescharacteristic
1319C4#354211yescharacteristic
1320C2—42no—
1321C2—82no—
1322C2—82no—
1323C2#5904511yescharacteristic
1324C2#6141811yescharacteristic
1325C2#6142311yescharacteristic
1326C2#6151411yescharacteristic
1327C2#6153811yescharacteristic
1328C2#6161311yescharacteristic
1329C2#6167411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45149C2semidirect
3. #32663C2semidirect
4. #32604C2semidirect
5. #32187C2semidirect
6. #30754C2semidirect
7. #28901C2semidirect
8. #28588C2semidirect
10. #28322C2semidirect
11. #27516C2semidirect
12. #27220C2semidirect
13. #27210C2semidirect
14. #27070C2semidirect
15. #26610C2semidirect
16. #26589C2semidirect
17. #26256C2semidirect
19. #25643C2semidirect
20. #25215C2semidirect
21. #25095C2semidirect
24. #24195C2semidirect
25. #23246C2semidirect
26. #23194C2semidirect
27. #23111C2semidirect
28. #22937C2semidirect
29. #22881C2semidirect
43. C2×#462C22semidirect
48. C2×C4×Q16C22semidirect
59. #2581C22semidirect
62. #2568C22semidirect
67. #2514C22semidirect
68. #2511C22semidirect
77. #2446C22semidirect
78. #2446C22semidirect
86. #2365C22semidirect
90. #2355C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
99. #2085C22semidirect
100. #2085C22semidirect
101. #2074C22semidirect
102. #2072C22semidirect
103. #2068C22semidirect
104. #2066C22semidirect
107. #2056C22semidirect
108. #2056C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
115. #2016C22semidirect
116. #2016C22semidirect
117. #2016C22semidirect
118. #2016C22semidirect
127. #1985C22semidirect
128. #1984C22semidirect
131. #1981C22semidirect
135. #1971C22semidirect
136. #1971C22semidirect
137. #1971C22semidirect
138. #1969C22semidirect
139. #1969C22semidirect
143. #1947C22semidirect
144. #1943C22semidirect
145. #1935C22semidirect
146. #1933C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1927C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1917C22semidirect
158. #1917C22semidirect
159. #1917C22semidirect
160. #1916C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
182. #1865C22semidirect
184. #1863C22semidirect
189. #1805C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1763C22semidirect
195. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#451492
#360332
#326632
#326042
#321872
#307542
#289012
#285882
#283612
#283222
#275162
#272202
#272102
#270702
#266102
#265892
#262562
#257842
#256432
#252152
#250952
#244932
#243572
#241952
#232462
#231942
#231112
#229372
#228812
#214592
#209332