Finite Group Databasebeta

← #7288301

Subgroups — #7288301

Order 512.

1540 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42783C211yesmaximal, characteristic, complemented
2#42680C211yesmaximal, characteristic, complemented
3#32804C211yesmaximal, characteristic, complemented
4#32643C211yesmaximal, characteristic, complemented
5#32605C211yesmaximal, characteristic, complemented
6#32044C211yesmaximal, characteristic, complemented
7#31496C211yesmaximal, characteristic, complemented
8#31309C211yesmaximal, characteristic, complemented
9#31139C211yesmaximal, characteristic, complemented
10#31008C211yesmaximal, characteristic, complemented
11#30924C211yesmaximal, characteristic, complemented
12#30710C211yesmaximal, characteristic, complemented
13#30650C211yesmaximal, characteristic, complemented
14#30548C211yesmaximal, characteristic, complemented
15#30523C211yesmaximal, characteristic, complemented
16#29453C211yesmaximal, characteristic, complemented
17#29404C211yesmaximal, characteristic, complemented
18#28912C211yesmaximal, characteristic, complemented
19#28760C211yesmaximal, characteristic, complemented
20#27405C211yesmaximal, characteristic, complemented
21#27271C211yesmaximal, characteristic, complemented
22#27255C211yesmaximal, characteristic, complemented
23#26983C211yesmaximal, characteristic, complemented
24#26643C211yesmaximal, characteristic, complemented
25#25654C211yesmaximal, characteristic, complemented
26#25085C211yesmaximal, characteristic, complemented
27#24495C211yesmaximal, characteristic, complemented
28#24450C211yesmaximal, characteristic
29#24205C211yesmaximal, characteristic, complemented
30#24037C211yesmaximal, characteristic, complemented
31#22390C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#488C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#479C2211yescharacteristic, complemented
40C2×#468C2211yescharacteristic
41C2×#465C2211yescharacteristic, complemented
42C2×#463C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#440C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47C2×#416C2211yescharacteristic
48#2829—21no—
49#2816—21no—
50#2800—21no—
51#2772—21no—
52#2723—21no—
53#2718—21no—
54#2718—21no—
55#2705—21no—
56#2685—21no—
57#2685—21no—
58#2663—21no—
59#2658C2211yescharacteristic
60#2644—21no—
61#2644C2211yescharacteristic, complemented
62#2626—21no—
63#2624—21no—
64#2592C2211yescharacteristic
65#2584C2211yescharacteristic, complemented
66#2542C2211yescharacteristic
67#2538C2211yescharacteristic, complemented
68#2530—21no—
69#2496C2211yescharacteristic, complemented
70#2490C2211yescharacteristic
71#2490C2211yescharacteristic, complemented
72#2485C2211yescharacteristic
73#2482—21no—
74#2441C2211yescharacteristic
75#2441C2211yescharacteristic, complemented
76#2435C2211yescharacteristic
77#2435C2211yescharacteristic
78#2432C2211yescharacteristic
79#2432C2211yescharacteristic
80#2429C2211yescharacteristic
81#2429C2211yescharacteristic
82#2426C2211yescharacteristic
83#2426C2211yescharacteristic
84#2422C2211yescharacteristic
85#2414C2211yescharacteristic
86#2398C2211yescharacteristic
87#2363C2211yescharacteristic, complemented
88#2346C2211yescharacteristic
89#2330C2211yescharacteristic, complemented
90#2319C2211yescharacteristic
91#2095C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic, complemented
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2054C2211yescharacteristic
104#2043C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2043C2211yescharacteristic, complemented
108#2043C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2033C2211yescharacteristic
125#2026C2211yescharacteristic, complemented
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2013C2211yescharacteristic, complemented
129#2013C2211yescharacteristic, complemented
130#2013C2211yescharacteristic, complemented
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#1999C2211yescharacteristic
139#1985C2211yescharacteristic, complemented
140#1984C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1983C2211yescharacteristic
144#1981C2211yescharacteristic, complemented
145#1981C2211yescharacteristic, complemented
146#1972C2211yescharacteristic
147#1970C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic
150#1956C2211yescharacteristic, complemented
151#1944C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1924C2211yescharacteristic, complemented
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1921C2211yescharacteristic, complemented
168#1920C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1918C2211yescharacteristic, complemented
171#1894C2211yescharacteristic
172#1894C2211yescharacteristic
173#1893C2211yescharacteristic
174#1892C2211yescharacteristic, complemented
175#1880C2211yescharacteristic, complemented
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic, complemented
182#1873C2211yescharacteristic, complemented
183#1870C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1863C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1851C2211yescharacteristic
192#1850C2211yescharacteristic, complemented
193#1840C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1768C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—42no—
213#556—42no—
214#546—42no—
215#546—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C22⋊C4—21no—
253#491—42no—
254#488—42no—
255#488—42no—
256#485—42no—
257#482—42no—
258#479—42no—
259#468—42no—
260#465—42no—
261#463—42no—
262#449—42no—
263#447—42no—
264#440—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277#416—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400D411yescharacteristic
328#400D411yescharacteristic
329#399—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397D411yescharacteristic
350#397D411yescharacteristic
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#395—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394D411yescharacteristic
377#394D411yescharacteristic
378#393—21no—
379#393D411yescharacteristic
380#393D411yescharacteristic
381#392—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#386—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#384—21no—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382—21no—
448#381—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457#379—21no—
458#379—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376—21no—
469#376C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#126—44no—
563#126—44no—
564#126—82no—
565#125—22no—
566#125—41no—
567#125—41no—
568#125—41no—
569#124—22no—
570#124—22no—
571#124—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#123—44no—
580#123—82no—
581C22⋊Q8—22no—
582C22⋊Q8—41no—
583C22⋊Q8—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—82no—
593#121—22no—
594#121—22no—
595#121—41no—
596#121—41no—
597#121—44no—
598#121—41no—
599#121—41no—
600#120—44no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613#117—22no—
614#117—41no—
615#117—44no—
616#117—41no—
617#117—41no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
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—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⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—44no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—22no—
731#107—41no—
732#107—41no—
733#106—22no—
734#106—22no—
735#106—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
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—22no—
766#102—22no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—41no—
785#97—41no—
786C4×C8—41no—
787C4×C8—41no—
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#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—44no—
835#41—82no—
836#41—82no—
837#41—82no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
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—41no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4H(5,𝔽2)12yes—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—24no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
946SD16—44no—
947SD16—82no—
948SD16—82no—
949D8—82no—
950D8—82no—
951M16—82no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
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—82no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4H(5,𝔽2)12yes—
1031C4⋊C4H(5,𝔽2)12yes—
1032C22⋊C4—24no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
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—
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—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
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—42no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
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—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—84no—
1138C23—84no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23C23×D411yescharacteristic
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—82no—
1158D4—22no—
1159D4—22no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—82no—
1171D4—84no—
1172D4—84no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
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—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—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
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—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—162no—
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4#58511yescharacteristic
1266C2×C4#58511yescharacteristic
1267C2×C4#58511yescharacteristic
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—42no—
1285C22—41no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
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—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—168no—
1312C22#348411yescharacteristic
1313C22#348811yescharacteristic
1314C22#350011yescharacteristic
1315C22#358411yescharacteristic
1316C22#358411yescharacteristic
1317C22#358511yescharacteristic
1318C22#358611yescharacteristic
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4#353311yescharacteristic
1345C4#354011yescharacteristic
1346C4#354211yescharacteristic
1347C4#354611yescharacteristic
1348C2—81no—
1349C2—81no—
1350C2—82no—
1351C2—161no—
1352C2—161no—
1353C2#4771911yescharacteristic
1354C2#6161411yescharacteristic
1355C2#6162611yescharacteristic
1356C2#6201411yescharacteristic
1357C2#6204811yescharacteristic
1358C2#6255511yescharacteristic
1359C2#6256911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24450C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42783C2semidirect
2. #42680C2semidirect
3. #32804C2semidirect
4. #32643C2semidirect
5. #32605C2semidirect
6. #32044C2semidirect
7. #31496C2semidirect
8. #31309C2semidirect
9. #31139C2semidirect
10. #31008C2semidirect
11. #30924C2semidirect
12. #30710C2semidirect
13. #30650C2semidirect
14. #30548C2semidirect
15. #30523C2semidirect
16. #29453C2semidirect
17. #29404C2semidirect
18. #28912C2semidirect
19. #28760C2semidirect
20. #27405C2semidirect
21. #27271C2semidirect
22. #27255C2semidirect
23. #26983C2semidirect
24. #26643C2semidirect
25. #25654C2semidirect
26. #25085C2semidirect
27. #24495C2semidirect
29. #24205C2semidirect
30. #24037C2semidirect
31. #22390C2semidirect
34. C2×#491C22semidirect
39. C2×#479C22semidirect
41. C2×#465C22semidirect
45. C2×#440C22semidirect
61. #2644C22semidirect
65. #2584C22semidirect
67. #2538C22semidirect
69. #2496C22semidirect
71. #2490C22semidirect
75. #2441C22semidirect
87. #2363C22semidirect
89. #2330C22semidirect
91. #2095C22semidirect
92. #2088C22semidirect
93. #2083C22semidirect
98. #2066C22semidirect
100. #2065C22semidirect
101. #2059C22semidirect
102. #2055C22semidirect
104. #2043C22semidirect
105. #2043C22semidirect
106. #2043C22semidirect
107. #2043C22semidirect
108. #2043C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
123. #2035C22semidirect
125. #2026C22semidirect
128. #2013C22semidirect
129. #2013C22semidirect
130. #2013C22semidirect
137. #2000C22semidirect
139. #1985C22semidirect
140. #1984C22semidirect
144. #1981C22semidirect
145. #1981C22semidirect
150. #1956C22semidirect
151. #1944C22semidirect
153. #1935C22semidirect
155. #1934C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
161. #1925C22semidirect
163. #1924C22semidirect
164. #1924C22semidirect
166. #1921C22semidirect
167. #1921C22semidirect
168. #1920C22semidirect
169. #1919C22semidirect
170. #1918C22semidirect
174. #1892C22semidirect
175. #1880C22semidirect
178. #1877C22semidirect
181. #1873C22semidirect
182. #1873C22semidirect
185. #1865C22semidirect
187. #1863C22semidirect
188. #1863C22semidirect
192. #1850C22semidirect
193. #1840C22semidirect
194. #1803C22semidirect
199. #1768C22semidirect
200. C4×#103C22semidirect
202. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#427832
#426802
#328042
#326432
#326052
#320442
#314962
#313092
#311392
#310082
#309242
#307102
#306502
#305482
#305232
#294532
#294042
#289122
#287602
#274052
#272712
#272552
#269832
#266432
#256542
#250852
#244952
#244502
#242052
#240372
#223902