Finite Group Databasebeta

← #7536499

Subgroups — #7536499

Order 512.

1697 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59148C211yesmaximal, characteristic
2#36552C211yesmaximal, characteristic, complemented
3#32187C211yesmaximal, characteristic, complemented
4#32169C211yesmaximal, characteristic, complemented
5#31922C211yesmaximal, characteristic, complemented
6#31908C211yesmaximal, characteristic, complemented
7#28747C211yesmaximal, characteristic, complemented
8#28342C211yesmaximal, characteristic
9#28333C211yesmaximal, characteristic, complemented
10#27765C211yesmaximal, characteristic, complemented
11#27212C211yesmaximal, characteristic, complemented
12#27191C211yesmaximal, characteristic, complemented
13#26542C211yesmaximal, characteristic, complemented
14#26330C211yesmaximal, characteristic, complemented
15#25730C211yesmaximal, characteristic
16#25643C211yesmaximal, characteristic, complemented
17#25379C211yesmaximal, characteristic, complemented
18#25084C211yesmaximal, characteristic
19#25082C211yesmaximal, characteristic, complemented
20#24752C211yesmaximal, characteristic, complemented
21#24641C211yesmaximal, characteristic, complemented
22#24629C211yesmaximal, characteristic, complemented
23#24532C211yesmaximal, characteristic, complemented
24#24530C211yesmaximal, characteristic
25#23192C211yesmaximal, characteristic, complemented
26#22954C211yesmaximal, characteristic, complemented
27#22874C211yesmaximal, characteristic
28#22859C211yesmaximal, characteristic, complemented
29#22544C211yesmaximal, characteristic, complemented
30#21581C211yesmaximal, characteristic, complemented
31C2×#1983C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#462C2211yescharacteristic, complemented
41C2×#462C2211yescharacteristic, complemented
42C2×#451C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#446C2211yescharacteristic, complemented
47C2×#441C2211yescharacteristic, complemented
48C2×C4×SD16C2211yescharacteristic
49C22×C4⋊C8C2211yescharacteristic
50C22×#103C2211yescharacteristic
51C22×#103C2211yescharacteristic
52C22×#102C2211yescharacteristic
53C22×#102C2211yescharacteristic
54#2857C2211yescharacteristic
55#2851—21no—
56#2715—21no—
57#2700—21no—
58#2592C2211yescharacteristic
59#2590—21no—
60#2590—21no—
61#2568C2211yescharacteristic, complemented
62#2552C2211yescharacteristic, complemented
63#2547C2211yescharacteristic
64#2545C2211yescharacteristic
65#2545C2211yescharacteristic
66#2521—21no—
67#2511C2211yescharacteristic, complemented
68#2511C2211yescharacteristic, complemented
69#2508—21no—
70#2505—21no—
71#2505—21no—
72#2502C2211yescharacteristic
73#2502C2211yescharacteristic
74#2480—21no—
75#2480—21no—
76#2474—21no—
77#2453—21no—
78#2448C2211yescharacteristic
79#2447C2211yescharacteristic
80#2437—21no—
81#2435C2211yescharacteristic
82#2434C2211yescharacteristic
83#2367C2211yescharacteristic
84#2365C2211yescharacteristic, complemented
85#2360C2211yescharacteristic
86#2360C2211yescharacteristic
87#2355C2211yescharacteristic, complemented
88#2355C2211yescharacteristic, complemented
89Q8×C4⋊C4C2211yescharacteristic, complemented
90#2342—21no—
91Q8×C22⋊C4C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93C4×C22⋊Q8—21no—
94C4×C22⋊Q8C2211yescharacteristic
95C4×C22⋊Q8C2211yescharacteristic
96C2×C4×C4⋊C4C2211yescharacteristic
97#2095C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2093C2211yescharacteristic
100#2093C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2056C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2056C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2043C2211yescharacteristic, complemented
118#2042C2211yescharacteristic
119#2016C2211yescharacteristic, complemented
120#2016C2211yescharacteristic, complemented
121#2016C2211yescharacteristic, complemented
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#1985C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic
139#1981C2211yescharacteristic, complemented
140#1981C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1971C2211yescharacteristic, complemented
144#1969C2211yescharacteristic, complemented
145#1969C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1959C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic
150#1959C2211yescharacteristic
151#1956C2211yescharacteristic, complemented
152#1956C2211yescharacteristic, complemented
153#1947C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1940C2211yescharacteristic, complemented
156#1939C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1934C2211yescharacteristic
159#1928C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1927C2211yescharacteristic, complemented
163#1926C2211yescharacteristic
164#1925C2211yescharacteristic
165#1918C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1872C2211yescharacteristic
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1853C2211yescharacteristic
185#1850C2211yescharacteristic
186#1850C2211yescharacteristic
187#1824C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1749C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#556—24no—
218#556—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#124—24no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—42no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8D411yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42—21no—
256C22×C42C2311yescharacteristic
257#497—24no—
258#497—42no—
259#484—24no—
260#467—42no—
261#467—42no—
262#464—42no—
263#462—42no—
264#462—42no—
265#451—24no—
266#451—42no—
267#450—24no—
268#450—42no—
269#446—42no—
270#441—42no—
271C4×SD16—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8—42no—
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×#103—42no—
288C2×#103—42no—
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×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#102—42no—
314C2×#102—42no—
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#395—21no—
359#395—21no—
360#394—21no—
361#394—21no—
362#393—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391D411yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389D411yescharacteristic
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#387—21no—
408#387—21no—
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#387D411yescharacteristic
421#387D411yescharacteristic
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385D411yescharacteristic
436#385D411yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#382—21no—
443#382—21no—
444#382—21no—
445#381—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380D411yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—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×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479C2×#95—21no—
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
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—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
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×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
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×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583#126—44no—
584#126—44no—
585#125—82no—
586#124—22no—
587#124—22no—
588#124—22no—
589#124—22no—
590#124—22no—
591#124—22no—
592#124—44no—
593#124—44no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—41no—
599#124#4114yes—
600C22⋊Q8—24no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—44no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—82no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625#117—44no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—44no—
704C2×C22⋊C4—44no—
705C2×C22⋊C4—44no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—22no—
711C2×C42—22no—
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×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—82no—
725C2×C42C2×D411yescharacteristic
726C2×C42C2×D411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#106—22no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
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#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783C22⋊C8—22no—
784C22⋊C8#4114yes—
785#97—22no—
786#97—22no—
787#97—41no—
788#97—41no—
789C4×C8—41no—
790C4×C8—41no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C2×Q8—22no—
849C2×Q8—22no—
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—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—41no—
880C2×Q8—42no—
881C2×Q8—44no—
882C2×Q8—44no—
883C2×Q8—42no—
884C2×Q8—81no—
885C2×Q8—82no—
886C2×Q8—82no—
887C2×Q8C2×#4112yes—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—81no—
906C2×D4C2×#4112yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—22no—
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—41no—
930C22×C4—41no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C2×#4112yes—
960C22×C4H(5,𝔽2)12yes—
961C22×C4C2511yescharacteristic
962Q16—44no—
963Q16—82no—
964Q16—82no—
965Q16—82no—
966Q16—82no—
967Q16—82no—
968SD16—44no—
969SD16—82no—
970SD16—82no—
971SD16—82no—
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—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—82no—
995C2×C8—82no—
996C2×C8C2×#4112yes—
997C2×C8C2×#4112yes—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
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—21no—
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—42no—
1037C4⋊C4—42no—
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⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4H(5,𝔽2)12yes—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—42no—
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—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4#13714yes—
1084C42—22no—
1085C42—22no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42C2×#4112yes—
1109C42H(5,𝔽2)12yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23#55012yes—
1136C23C2×#13712yes—
1137C23#57812yes—
1138C23C23×D411yescharacteristic
1139Q8—22no—
1140Q8—22no—
1141Q8—44no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
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—84no—
1161D4—22no—
1162D4—22no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—84no—
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—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
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—21no—
1201C2×C4—22no—
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—44no—
1211C2×C4—44no—
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—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—84no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—162no—
1257C2×C4#54612yes—
1258C2×C4#54612yes—
1259C2×C4#55012yes—
1260C2×C4C2×#13712yes—
1261C2×C4C2×#13712yes—
1262C2×C4C22×#4111yescharacteristic
1263C2×C4C22×#4111yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4#58511yescharacteristic
1268C8—22no—
1269C8—22no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22#339814yes—
1298C22C2×#54611yescharacteristic
1299C22C2×#55011yescharacteristic
1300C22#348811yescharacteristic
1301C22C22×#13711yescharacteristic
1302C22C2×#57811yescharacteristic
1303C22#358411yescharacteristic
1304C22#358511yescharacteristic
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#348111yescharacteristic
1333C4#351311yescharacteristic
1334C4#351411yescharacteristic
1335C4#354311yescharacteristic
1336C2—24no—
1337C2—82no—
1338C2—161no—
1339C2#5904611yescharacteristic
1340C2#6116211yescharacteristic
1341C2#6117311yescharacteristic
1342C2C2×#339811yescharacteristic
1343C2#6142411yescharacteristic
1344C2#6199111yescharacteristic
1345C2#6201711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36552C2semidirect
3. #32187C2semidirect
4. #32169C2semidirect
5. #31922C2semidirect
6. #31908C2semidirect
7. #28747C2semidirect
9. #28333C2semidirect
10. #27765C2semidirect
11. #27212C2semidirect
12. #27191C2semidirect
13. #26542C2semidirect
14. #26330C2semidirect
16. #25643C2semidirect
17. #25379C2semidirect
19. #25082C2semidirect
20. #24752C2semidirect
21. #24641C2semidirect
22. #24629C2semidirect
23. #24532C2semidirect
25. #23192C2semidirect
26. #22954C2semidirect
28. #22859C2semidirect
29. #22544C2semidirect
30. #21581C2semidirect
40. C2×#462C22semidirect
41. C2×#462C22semidirect
46. C2×#446C22semidirect
47. C2×#441C22semidirect
61. #2568C22semidirect
62. #2552C22semidirect
67. #2511C22semidirect
68. #2511C22semidirect
84. #2365C22semidirect
87. #2355C22semidirect
88. #2355C22semidirect
89. Q8×C4⋊C4C22semidirect
97. #2095C22semidirect
98. #2095C22semidirect
101. #2072C22semidirect
102. #2072C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
109. #2056C22semidirect
110. #2056C22semidirect
111. #2056C22semidirect
112. #2056C22semidirect
113. #2056C22semidirect
117. #2043C22semidirect
119. #2016C22semidirect
120. #2016C22semidirect
121. #2016C22semidirect
129. #1985C22semidirect
139. #1981C22semidirect
140. #1981C22semidirect
143. #1971C22semidirect
144. #1969C22semidirect
145. #1969C22semidirect
151. #1956C22semidirect
152. #1956C22semidirect
153. #1947C22semidirect
154. #1940C22semidirect
155. #1940C22semidirect
156. #1939C22semidirect
157. #1935C22semidirect
159. #1928C22semidirect
160. #1927C22semidirect
161. #1927C22semidirect
162. #1927C22semidirect
165. #1918C22semidirect
166. #1918C22semidirect
167. #1917C22semidirect
168. #1916C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
182. #1865C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1771C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#591482
#365522
#321872
#321692
#319222
#319082
#287472
#283422
#283332
#277652
#272122
#271912
#265422
#263302
#257302
#256432
#253792
#250842
#250822
#247522
#246412
#246292
#245322
#245302
#231922
#229542
#228742
#228592
#225442
#215812
C2×#19832