Finite Group Databasebeta

← #7603229

Subgroups — #7603229

Order 512.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59325C211yesmaximal, characteristic, complemented
2#59147C211yesmaximal, characteristic
3#32093C211yesmaximal, characteristic, complemented
4#32088C211yesmaximal, characteristic, complemented
5#31649C211yesmaximal, characteristic, complemented
6#31644C211yesmaximal, characteristic, complemented
7#29014C211yesmaximal, characteristic, complemented
8#29012C211yesmaximal, characteristic, complemented
9#28408C211yesmaximal, characteristic, complemented
10#28402C211yesmaximal, characteristic, complemented
11#27771C211yesmaximal, characteristic, complemented
12#27684C211yesmaximal, characteristic, complemented
13#27260C211yesmaximal, characteristic, complemented
14#27254C211yesmaximal, characteristic
15#26470C211yesmaximal, characteristic, complemented
16#26324C211yesmaximal, characteristic, complemented
17#25960C211yesmaximal, characteristic, complemented
18#25955C211yesmaximal, characteristic, complemented
19#25297C211yesmaximal, characteristic, complemented
20#25086C211yesmaximal, characteristic, complemented
21#25080C211yesmaximal, characteristic
22#24734C211yesmaximal, characteristic, complemented
23#24217C211yesmaximal, characteristic, complemented
24#24194C211yesmaximal, characteristic, complemented
25#23000C211yesmaximal, characteristic, complemented
26#22874C211yesmaximal, characteristic, complemented
27#22871C211yesmaximal, characteristic, complemented
28#22543C211yesmaximal, characteristic, complemented
29C8×C22⋊Q8C211yesmaximal, characteristic, complemented
30C4×#465C211yesmaximal, characteristic, complemented
31C2×#1958C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#488C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic, complemented
42C2×#460C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×C8×Q8C2211yescharacteristic, complemented
46C2×C4×Q16C2211yescharacteristic, complemented
47C2×C4×SD16C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic, complemented
49C22×#103C2211yescharacteristic
50C22×#103C2211yescharacteristic
51C22×#102C2211yescharacteristic
52C22×#102C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2774—21no—
55#2755—21no—
56#2712—21no—
57#2710—21no—
58#2592C2211yescharacteristic
59#2581C2211yescharacteristic, complemented
60#2568C2211yescharacteristic, complemented
61#2565C2211yescharacteristic, complemented
62#2557—21no—
63#2550C2211yescharacteristic, complemented
64#2549—21no—
65#2548C2211yescharacteristic
66#2544C2211yescharacteristic
67#2544C2211yescharacteristic
68#2520—21no—
69#2509C2211yescharacteristic, complemented
70#2508—21no—
71#2508C2211yescharacteristic, complemented
72#2505—21no—
73#2505—21no—
74#2472—21no—
75#2459—21no—
76#2448C2211yescharacteristic
77#2447C2211yescharacteristic
78#2442C2211yescharacteristic
79#2440C2211yescharacteristic
80#2436C2211yescharacteristic
81#2433C2211yescharacteristic
82#2418—21no—
83#2412—21no—
84#2368—21no—
85#2367C2211yescharacteristic
86#2360C2211yescharacteristic
87#2360C2211yescharacteristic
88#2358—21no—
89#2355C2211yescharacteristic, complemented
90#2351C2211yescharacteristic, complemented
91Q8×C22⋊C4C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93C4×C22⋊Q8C2211yescharacteristic
94C4×C22⋊Q8C2211yescharacteristic
95C4×#121C2211yescharacteristic
96C2×#382C2211yescharacteristic
97#2101C2211yescharacteristic, complemented
98#2101C2211yescharacteristic, complemented
99#2096C2211yescharacteristic, complemented
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic, complemented
102#2092C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2056C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic, complemented
128#2014C2211yescharacteristic
129#1984C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1969C2211yescharacteristic, complemented
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic, complemented
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1958C2211yescharacteristic
142#1958C2211yescharacteristic
143#1958C2211yescharacteristic
144#1958C2211yescharacteristic
145#1958C2211yescharacteristic, complemented
146#1957C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1949C2211yescharacteristic, complemented
149#1941C2211yescharacteristic, complemented
150#1939C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1933C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1807C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1797C2211yescharacteristic
191#1787C2211yescharacteristic
192#1786C2211yescharacteristic
193C4×#106C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195C8×C4⋊C4C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#559—24no—
213#559—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—24no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—42no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8D411yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C42C2311yescharacteristic
254#488—42no—
255#486—42no—
256#478—42no—
257#475—42no—
258#465—24no—
259#464—24no—
260#464—42no—
261#464—42no—
262#460—42no—
263#451—24no—
264#450—24no—
265C8×Q8—42no—
266C4×Q16—42no—
267C4×SD16—42no—
268C4×SD16—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103—42no—
283C2×#103—42no—
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
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×#102—42no—
302C2×#102—42no—
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C4×C8—42no—
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
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#400—21no—
342#399—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#395—21no—
354#395—21no—
355#395—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391D411yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#390—21no—
382#390—21no—
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389D411yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387D411yescharacteristic
422#387D411yescharacteristic
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385D411yescharacteristic
440#385D411yescharacteristic
441#384C2311yescharacteristic
442#382—21no—
443#382—21no—
444#382—21no—
445#382—21no—
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#380—21no—
453#380—21no—
454#380D411yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C2×#95—21no—
477C2×#95—21no—
478#340C2311yescharacteristic
479#340C2311yescharacteristic
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—21no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2×D411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
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—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570#127—22no—
571#127—41no—
572#127—41no—
573#127—41no—
574#125—41no—
575#125—41no—
576#124—22no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—22no—
581#124—22no—
582#124—44no—
583#124—44no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—44no—
590#124#4114yes—
591#123—44no—
592#123—44no—
593C22⋊Q8—22no—
594C22⋊Q8—24no—
595C22⋊Q8—44no—
596C22⋊Q8#4114yes—
597#121—22no—
598#121—22no—
599#120—44no—
600#120—82no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—44no—
620C4×D4—82no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—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—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—82no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—41no—
721#107—41no—
722#106—22no—
723#106—22no—
724#106—41no—
725#106—41no—
726#106—41no—
727C4⋊C8—22no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C4×C8—22no—
774C4×C8—22no—
775C4×C8—22no—
776C4×C8—22no—
777C4×C8—41no—
778C4×C8—41no—
779C4×C8—41no—
780C4×C8—41no—
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#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C2×Q8—22no—
841C2×Q8—22no—
842C2×Q8—21no—
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—41no—
859C2×Q8—42no—
860C2×Q8—44no—
861C2×Q8—44no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—82no—
868C2×Q8—82no—
869C2×Q8C2×#4112yes—
870C2×Q8C2×#4112yes—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
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—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4C2×#4112yes—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—22no—
921C22×C4—22no—
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—21no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
966C22×C42−1+412yes—
967C22×C4C2511yescharacteristic
968Q16—44no—
969Q16—82no—
970SD16—44no—
971SD16—44no—
972SD16—82no—
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—21no—
995C2×C8—44no—
996C2×C8—44no—
997C2×C8H(5,𝔽2)12yes—
998C2×C8H(5,𝔽2)12yes—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—24no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
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—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
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⋊C4C2×#4112yes—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—24no—
1054C22⋊C4—24no—
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—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4#13514yes—
1082C42—22no—
1083C42—22no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—42no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42C2×#4112yes—
1104C42H(5,𝔽2)12yes—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—22no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
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—41no—
1129C23—41no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23—84no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23#54812yes—
1138C23C2×#13512yes—
1139C23#57712yes—
1140C23C23×D411yescharacteristic
1141Q8—22no—
1142Q8—22no—
1143Q8—22no—
1144Q8—22no—
1145Q8—44no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—84no—
1155Q8—162no—
1156D4—22no—
1157D4—22no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
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—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
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—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
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—21no—
1214C2×C4—21no—
1215C2×C4—44no—
1216C2×C4—44no—
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—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4#54612yes—
1260C2×C4#54612yes—
1261C2×C4#54812yes—
1262C2×C4C2×#13512yes—
1263C2×C4C2×#13512yes—
1264C2×C4C22×#4111yescharacteristic
1265C2×C4C22×#4111yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4C2×2−1+411yescharacteristic
1270C8—22no—
1271C8—22no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22#336514yes—
1307C22C2×#54611yescharacteristic
1308C22C2×#54811yescharacteristic
1309C22#349811yescharacteristic
1310C22C22×#13511yescharacteristic
1311C22C2×#57711yescharacteristic
1312C22#358411yescharacteristic
1313C22#358411yescharacteristic
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4#348111yescharacteristic
1341C4#351911yescharacteristic
1342C4#352011yescharacteristic
1343C4#353611yescharacteristic
1344C2—24no—
1345C2—82no—
1346C2—161no—
1347C2—161no—
1348C2#5965011yescharacteristic
1349C2#6112411yescharacteristic
1350C2#6117211yescharacteristic
1351C2C2×#336511yescharacteristic
1352C2#6133111yescharacteristic
1353C2#6241911yescharacteristic
1354C2#6243511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
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
1. #59325C2semidirect
3. #32093C2semidirect
4. #32088C2semidirect
5. #31649C2semidirect
6. #31644C2semidirect
7. #29014C2semidirect
8. #29012C2semidirect
9. #28408C2semidirect
10. #28402C2semidirect
11. #27771C2semidirect
12. #27684C2semidirect
13. #27260C2semidirect
15. #26470C2semidirect
16. #26324C2semidirect
17. #25960C2semidirect
18. #25955C2semidirect
19. #25297C2semidirect
20. #25086C2semidirect
22. #24734C2semidirect
23. #24217C2semidirect
24. #24194C2semidirect
25. #23000C2semidirect
26. #22874C2semidirect
27. #22871C2semidirect
28. #22543C2semidirect
29. C8×C22⋊Q8C2semidirect
30. C4×#465C2semidirect
31. C2×#1958C2semidirect
34. C2×#488C22semidirect
36. C2×#475C22semidirect
41. C2×#464C22semidirect
45. C2×C8×Q8C22semidirect
46. C2×C4×Q16C22semidirect
48. C2×C4×SD16C22semidirect
59. #2581C22semidirect
60. #2568C22semidirect
61. #2565C22semidirect
63. #2550C22semidirect
69. #2509C22semidirect
71. #2508C22semidirect
89. #2355C22semidirect
90. #2351C22semidirect
97. #2101C22semidirect
98. #2101C22semidirect
99. #2096C22semidirect
101. #2092C22semidirect
102. #2092C22semidirect
103. #2074C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
111. #2056C22semidirect
115. #2042C22semidirect
116. #2042C22semidirect
117. #2042C22semidirect
121. #2026C22semidirect
123. #2024C22semidirect
127. #2015C22semidirect
129. #1984C22semidirect
132. #1983C22semidirect
134. #1969C22semidirect
136. #1968C22semidirect
145. #1958C22semidirect
147. #1949C22semidirect
148. #1949C22semidirect
149. #1941C22semidirect
150. #1939C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1933C22semidirect
158. #1933C22semidirect
159. #1928C22semidirect
160. #1927C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
179. #1863C22semidirect
187. #1804C22semidirect
188. #1804C22semidirect
189. #1803C22semidirect
193. C4×#106C22semidirect
194. C8×C4⋊C4C22semidirect
195. C8×C4⋊C4C22semidirect
196. C8×C4⋊C4C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#593252
#591472
#320932
#320882
#316492
#316442
#290142
#290122
#284082
#284022
#277712
#276842
#272602
#272542
#264702
#263242
#259602
#259552
#252972
#250862
#250802
#247342
#242172
#241942
#230002
#228742
#228712
#225432
C8×C22⋊Q82
C4×#4652
C2×#19582