Finite Group Databasebeta

← #6560435

Subgroups — #6560435

Order 512.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39426C211yesmaximal, characteristic, complemented
2#38206C211yesmaximal, characteristic, complemented
3#30368C211yesmaximal, characteristic, complemented
4#30336C211yesmaximal, characteristic, complemented
5#30192C211yesmaximal, characteristic, complemented
6#29552C211yesmaximal, characteristic, complemented
7#29516C211yesmaximal, characteristic, complemented
8#29175C211yesmaximal, characteristic, complemented
9#29079C211yesmaximal, characteristic, complemented
10#29072C211yesmaximal, characteristic, complemented
11#28992C211yesmaximal, characteristic, complemented
12#28976C211yesmaximal, characteristic, complemented
13#28319C211yesmaximal, characteristic, complemented
14#27794C211yesmaximal, characteristic, complemented
15#27791C211yesmaximal, characteristic, complemented
16#26496C211yesmaximal, characteristic, complemented
17#26484C211yesmaximal, characteristic, complemented
18#25821C211yesmaximal, characteristic, complemented
19#25508C211yesmaximal, characteristic, complemented
20#25263C211yesmaximal, characteristic, complemented
21#25235C211yesmaximal, characteristic, complemented
22#25132C211yesmaximal, characteristic, complemented
23#25108C211yesmaximal, characteristic, complemented
24#23778C211yesmaximal, characteristic, complemented
25#23580C211yesmaximal, characteristic, complemented
26#23456C211yesmaximal, characteristic, complemented
27#22946C211yesmaximal, characteristic, complemented
28#22921C211yesmaximal, characteristic, complemented
29#22870C211yesmaximal, characteristic, complemented
30#22868C211yesmaximal, characteristic, complemented
31#20562C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#540C2211yescharacteristic, complemented
34C2×#501C2211yescharacteristic, complemented
35C2×#500C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2860C2211yescharacteristic
49#2858C2211yescharacteristic, complemented
50#2753—21no—
51#2736—21no—
52#2723—21no—
53#2711—21no—
54#2696—21no—
55#2685—21no—
56#2676—21no—
57#2674—21no—
58#2628C2211yescharacteristic
59#2628C2211yescharacteristic, complemented
60#2624C2211yescharacteristic
61#2619C2211yescharacteristic
62#2610—21no—
63#2558—21no—
64#2540—21no—
65#2526—21no—
66#2513C2211yescharacteristic
67#2491—21no—
68#2491C2211yescharacteristic
69#2491C2211yescharacteristic, complemented
70#2490C2211yescharacteristic, complemented
71#2485C2211yescharacteristic
72#2482—21no—
73#2472—21no—
74#2461—21no—
75#2454C2211yescharacteristic, complemented
76#2452C2211yescharacteristic
77#2452C2211yescharacteristic, complemented
78#2420C2211yescharacteristic
79#2416C2211yescharacteristic
80#2414C2211yescharacteristic
81#2408C2211yescharacteristic
82#2363C2211yescharacteristic
83#2361C2211yescharacteristic
84#2346C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2324C2211yescharacteristic
87#2309C2211yescharacteristic
88C4×#125C2211yescharacteristic, complemented
89#2293C2211yescharacteristic
90#2293C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2073C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2059C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2041C2211yescharacteristic, complemented
112#2041C2211yescharacteristic, complemented
113#2034C2211yescharacteristic, complemented
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic, complemented
126#2023C2211yescharacteristic, complemented
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#1999C2211yescharacteristic
130#1999C2211yescharacteristic
131#1993C2211yescharacteristic, complemented
132#1991C2211yescharacteristic, complemented
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1970C2211yescharacteristic
136#1970C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic
141#1944C2211yescharacteristic, complemented
142#1942C2211yescharacteristic, complemented
143#1942C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1934C2211yescharacteristic, complemented
152#1934C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic, complemented
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1864C2211yescharacteristic, complemented
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1809C2211yescharacteristic, complemented
182#1808C2211yescharacteristic, complemented
183C4×#107C2211yescharacteristic, complemented
184C4×#106C2211yescharacteristic, complemented
185#1770C2211yescharacteristic, complemented
186C8×C4⋊C4C2211yescharacteristic, complemented
187C4×C4⋊C8C2211yescharacteristic, complemented
188#1762C2211yescharacteristic, complemented
189C4×#102C2211yescharacteristic
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic, complemented
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic
197#1750C2211yescharacteristic, complemented
198#1744C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#544—42no—
213#544—42no—
214#540—42no—
215#540—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#501—42no—
259#500—42no—
260#482—24no—
261#482—24no—
262#469—42no—
263#466—42no—
264#447—24no—
265#447—24no—
266#442—42no—
267C4×D8—42no—
268#436—24no—
269C8×D4—24no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#418—42no—
285C2×#102—42no—
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390D411yescharacteristic
371#390D411yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389D411yescharacteristic
387#389D411yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388D411yescharacteristic
416#388D411yescharacteristic
417#388D411yescharacteristic
418#388D411yescharacteristic
419#387—21no—
420#387—21no—
421#387—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#382—21no—
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#376—21no—
461C43C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—44no—
566#127—41no—
567#127—41no—
568#126—82no—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—44no—
574#124—82no—
575#124—82no—
576#124—82no—
577#124—82no—
578#123—44no—
579#123—44no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—82no—
583C22⋊Q8—82no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—44no—
595#121—44no—
596#121—41no—
597#121—41no—
598#121—82no—
599#120—82no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—82no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—82no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—22no—
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—41no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
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—82no—
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×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#107—41no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
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—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8#4114yes—
772C22⋊C8#4114yes—
773#97—41no—
774#97—41no—
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#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C2×Q8—42no—
825C2×Q8—42no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D42−1+412yes—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
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—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2×#4112yes—
941C22×C4C2×#4112yes—
942C22×C4C2511yescharacteristic
943D8—44no—
944D8—44no—
945D8—82no—
946D8—82no—
947M16—82no—
948M16—82no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
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—82no—
970C2×C8—82no—
971C2×C8C2×#4112yes—
972C2×C8C2×#4112yes—
973C2×C8C2×#4112yes—
974C2×C8C2×#4112yes—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—22no—
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—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1023C4⋊C4H(5,𝔽2)12yes—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
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—81no—
1052C22⋊C4—81no—
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—
1080C42—22no—
1081C42—22no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—41no—
1093C42—41no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C23—21no—
1101C23—21no—
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—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—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—84no—
1142C23—84no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23#53212yes—
1149C23C23×D411yescharacteristic
1150Q8—162no—
1151Q8—162no—
1152Q8—162no—
1153D4—22no—
1154D4—22no—
1155D4—44no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—84no—
1171D4—84no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
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—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
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—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4#53212yes—
1262C2×C4#57612yes—
1263C2×C4#57612yes—
1264C2×C4C22×#4111yescharacteristic
1265C2×C4C22×#4111yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×2−1+411yescharacteristic
1269C2×C4#58511yescharacteristic
1270C8—22no—
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—41no—
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—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—168no—
1321C22C2×#53211yescharacteristic
1322C22#348411yescharacteristic
1323C22#348911yescharacteristic
1324C22C2×#57611yescharacteristic
1325C22C2×#57611yescharacteristic
1326C22#358411yescharacteristic
1327C22#358411yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#351411yescharacteristic
1353C4#351411yescharacteristic
1354C4#352011yescharacteristic
1355C4#352011yescharacteristic
1356C2—42no—
1357C2—81no—
1358C2—82no—
1359C2—161no—
1360C2—161no—
1361C2—161no—
1362C2#3594011yescharacteristic
1363C2#6069511yescharacteristic
1364C2#6070711yescharacteristic
1365C2#6166111yescharacteristic
1366C2#6166611yescharacteristic
1367C2#6221111yescharacteristic
1368C2#6221511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39426C2semidirect
2. #38206C2semidirect
3. #30368C2semidirect
4. #30336C2semidirect
5. #30192C2semidirect
6. #29552C2semidirect
7. #29516C2semidirect
8. #29175C2semidirect
9. #29079C2semidirect
10. #29072C2semidirect
11. #28992C2semidirect
12. #28976C2semidirect
13. #28319C2semidirect
14. #27794C2semidirect
15. #27791C2semidirect
16. #26496C2semidirect
17. #26484C2semidirect
18. #25821C2semidirect
19. #25508C2semidirect
20. #25263C2semidirect
21. #25235C2semidirect
22. #25132C2semidirect
23. #25108C2semidirect
24. #23778C2semidirect
25. #23580C2semidirect
26. #23456C2semidirect
27. #22946C2semidirect
28. #22921C2semidirect
29. #22870C2semidirect
30. #22868C2semidirect
31. #20562C2semidirect
33. C2×#540C22semidirect
34. C2×#501C22semidirect
35. C2×#500C22semidirect
49. #2858C22semidirect
59. #2628C22semidirect
69. #2491C22semidirect
70. #2490C22semidirect
75. #2454C22semidirect
77. #2452C22semidirect
88. C4×#125C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2077C22semidirect
98. #2076C22semidirect
99. #2073C22semidirect
100. #2073C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
105. #2059C22semidirect
106. #2059C22semidirect
107. #2057C22semidirect
108. #2057C22semidirect
111. #2041C22semidirect
112. #2041C22semidirect
113. #2034C22semidirect
116. #2033C22semidirect
125. #2023C22semidirect
126. #2023C22semidirect
131. #1993C22semidirect
132. #1991C22semidirect
141. #1944C22semidirect
142. #1942C22semidirect
143. #1942C22semidirect
144. #1941C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
151. #1934C22semidirect
152. #1934C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1921C22semidirect
158. #1921C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
164. #1895C22semidirect
168. #1893C22semidirect
173. #1864C22semidirect
176. #1862C22semidirect
181. #1809C22semidirect
182. #1808C22semidirect
183. C4×#107C22semidirect
184. C4×#106C22semidirect
185. #1770C22semidirect
186. C8×C4⋊C4C22semidirect
187. C4×C4⋊C8C22semidirect
188. #1762C22semidirect
191. C4×#102C22semidirect
193. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
197. #1750C22semidirect
198. #1744C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#394262
#382062
#303682
#303362
#301922
#295522
#295162
#291752
#290792
#290722
#289922
#289762
#283192
#277942
#277912
#264962
#264842
#258212
#255082
#252632
#252352
#251322
#251082
#237782
#235802
#234562
#229462
#229212
#228702
#228682
#205622