Finite Group Databasebeta

← #6679712

Subgroups — #6679712

Order 512.

1737 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39737C211yesmaximal, characteristic, complemented
2#36218C211yesmaximal, characteristic
3#32958C211yesmaximal, characteristic, complemented
4#31797C211yesmaximal, characteristic, complemented
5#31777C211yesmaximal, characteristic, complemented
6#31512C211yesmaximal, characteristic, complemented
7#31500C211yesmaximal, characteristic, complemented
8#31341C211yesmaximal, characteristic, complemented
9#31321C211yesmaximal, characteristic, complemented
10#30650C211yesmaximal, characteristic, complemented
11#30644C211yesmaximal, characteristic, complemented
12#29928C211yesmaximal, characteristic, complemented
13#29854C211yesmaximal, characteristic, complemented
14#27781C211yesmaximal, characteristic, complemented
15#27541C211yesmaximal, characteristic, complemented
16#27533C211yesmaximal, characteristic, complemented
17#26059C211yesmaximal, characteristic, complemented
18#25976C211yesmaximal, characteristic, complemented
19#25956C211yesmaximal, characteristic, complemented
20#25898C211yesmaximal, characteristic, complemented
21#25892C211yesmaximal, characteristic, complemented
22#25890C211yesmaximal, characteristic, complemented
23#25352C211yesmaximal, characteristic, complemented
24#25286C211yesmaximal, characteristic, complemented
25#25025C211yesmaximal, characteristic, complemented
26#24050C211yesmaximal, characteristic, complemented
27#24043C211yesmaximal, characteristic, complemented
28#22975C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#22141C211yesmaximal, characteristic, complemented
31#20743C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×#491C2211yescharacteristic, complemented
37C2×#489C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic, complemented
41C2×#477C2211yescharacteristic, complemented
42C2×#478C2211yescharacteristic
43C2×#478C2211yescharacteristic
44C2×#476C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#432C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48C2×#416C2211yescharacteristic
49#2857C2211yescharacteristic, complemented
50#2854—21no—
51#2850C2211yescharacteristic
52#2772—21no—
53#2772—21no—
54#2741—21no—
55#2741—21no—
56#2620—21no—
57#2562C2211yescharacteristic
58#2562C2211yescharacteristic, complemented
59#2552C2211yescharacteristic, complemented
60#2547C2211yescharacteristic
61#2545C2211yescharacteristic
62#2543—21no—
63#2536C2211yescharacteristic
64#2534—21no—
65#2511—21no—
66#2497C2211yescharacteristic
67#2497C2211yescharacteristic, complemented
68#2485C2211yescharacteristic
69#2485C2211yescharacteristic, complemented
70#2448—21no—
71#2441C2211yescharacteristic
72#2441C2211yescharacteristic, complemented
73#2429C2211yescharacteristic
74#2426C2211yescharacteristic
75#2425—21no—
76#2424—21no—
77#2415C2211yescharacteristic
78#2414C2211yescharacteristic
79#2413—21no—
80#2411—21no—
81#2365C2211yescharacteristic, complemented
82#2354C2211yescharacteristic
83#2349C2211yescharacteristic
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2323—21no—
87C4×#121C2211yescharacteristic
88C2×#388—21no—
89#2285C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2043C2211yescharacteristic, complemented
109#2043C2211yescharacteristic, complemented
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1981C2211yescharacteristic, complemented
135#1959C2211yescharacteristic
136#1955C2211yescharacteristic
137#1955C2211yescharacteristic, complemented
138#1954C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1940C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1925C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1894C2211yescharacteristic
153#1894C2211yescharacteristic
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic, complemented
156#1875C2211yescharacteristic
157#1873C2211yescharacteristic
158#1870C2211yescharacteristic
159#1869C2211yescharacteristic, complemented
160#1865C2211yescharacteristic, complemented
161#1865C2211yescharacteristic, complemented
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1862C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic, complemented
170#1854C2211yescharacteristic, complemented
171#1854C2211yescharacteristic, complemented
172#1851C2211yescharacteristic
173#1850C2211yescharacteristic, complemented
174#1847C2211yescharacteristic, complemented
175#1825C2211yescharacteristic, complemented
176#1825C2211yescharacteristic, complemented
177#1809C2211yescharacteristic
178#1808C2211yescharacteristic, complemented
179#1803C2211yescharacteristic, complemented
180#1803C2211yescharacteristic, complemented
181#1803C2211yescharacteristic, complemented
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1797C2211yescharacteristic, complemented
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#547—42no—
209#547—42no—
210#546—24no—
211#546—42no—
212#546—42no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121D411yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C4×#41—24no—
239C4×#41—42no—
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C42—21no—
262C22×C42C2311yescharacteristic
263#491—42no—
264#489—42no—
265#488—42no—
266#485—42no—
267#485—42no—
268#478—42no—
269#478—42no—
270#477—42no—
271#476—24no—
272#435—42no—
273#432—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292#418—42no—
293#416—42no—
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#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×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#399—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—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#392—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390D411yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389D411yescharacteristic
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#388—21no—
416#388—21no—
417#388—21no—
418#388D411yescharacteristic
419#388D411yescharacteristic
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386D411yescharacteristic
435#386D411yescharacteristic
436#385—21no—
437#385—21no—
438#384—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#382—21no—
443#382C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380D411yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C2×#95—21no—
472C2×#95—21no—
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8—21no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
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—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#124—22no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—82no—
569#123—44no—
570#123—44no—
571#123—44no—
572#123—44no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—44no—
582#121—22no—
583#121—42no—
584#121—44no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—44no—
589#121—44no—
590#120—44no—
591#120—44no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—41no—
596C4×Q8—82no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—44no—
611C4×D4—44no—
612C4×D4#4114yes—
613#117—22no—
614#117—44no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—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—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
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—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—44no—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—22no—
738#106—41no—
739#106—41no—
740#106—41no—
741#106—41no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
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#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790#97—22no—
791#97—22no—
792#97—41no—
793C4×C8—41no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—44no—
843#41—44no—
844#41—44no—
845#41—44no—
846#41—44no—
847#41—82no—
848#41—82no—
849#41—82no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8H(5,𝔽2)12yes—
865C2×D4—24no—
866C2×D4—22no—
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—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4C2×#4112yes—
903C2×D4H(5,𝔽2)12yes—
904C2×D42−1+412yes—
905C22×C4—24no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—22no—
909C22×C4—22no—
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—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C2511yescharacteristic
973M16—82no—
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—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—82no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4C2×#4112yes—
1055C22⋊C4—24no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C42—22no—
1099C42—22no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C42—81no—
1115C42C2×#4112yes—
1116C42H(5,𝔽2)12yes—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—84no—
1153C23—84no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23C23×D411yescharacteristic
1160Q8—22no—
1161Q8—22no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—84no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—48no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—82no—
1178D4—84no—
1179D4—82no—
1180D4—82no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184D4#54214yes—
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—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—44no—
1218C2×C4—48no—
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—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—82no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—162no—
1277C2×C4#54612yes—
1278C2×C4#54612yes—
1279C2×C4#57512yes—
1280C2×C4C22×#4111yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4C2×2−1+411yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C22—24no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—168no—
1330C22C2×#54611yescharacteristic
1331C22#348411yescharacteristic
1332C22#348911yescharacteristic
1333C22C2×#57511yescharacteristic
1334C22#358411yescharacteristic
1335C22#358511yescharacteristic
1336C22#358611yescharacteristic
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4C2×#54211yescharacteristic
1363C4#349411yescharacteristic
1364C4#353611yescharacteristic
1365C4#354211yescharacteristic
1366C2—44no—
1367C2—81no—
1368C2—81no—
1369C2—81no—
1370C2—161no—
1371C2#3766411yescharacteristic
1372C2#6116411yescharacteristic
1373C2#6118811yescharacteristic
1374C2#6159911yescharacteristic
1375C2#6167711yescharacteristic
1376C2#6211611yescharacteristic
1377C2#6217111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36218C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39737C2semidirect
3. #32958C2semidirect
4. #31797C2semidirect
5. #31777C2semidirect
6. #31512C2semidirect
7. #31500C2semidirect
8. #31341C2semidirect
9. #31321C2semidirect
10. #30650C2semidirect
11. #30644C2semidirect
12. #29928C2semidirect
13. #29854C2semidirect
14. #27781C2semidirect
15. #27541C2semidirect
16. #27533C2semidirect
17. #26059C2semidirect
18. #25976C2semidirect
19. #25956C2semidirect
20. #25898C2semidirect
21. #25892C2semidirect
22. #25890C2semidirect
23. #25352C2semidirect
24. #25286C2semidirect
25. #25025C2semidirect
26. #24050C2semidirect
27. #24043C2semidirect
28. #22975C2semidirect
29. #22424C2semidirect
30. #22141C2semidirect
31. #20743C2semidirect
36. C2×#491C22semidirect
40. C2×#485C22semidirect
41. C2×#477C22semidirect
46. C2×#432C22semidirect
49. #2857C22semidirect
58. #2562C22semidirect
59. #2552C22semidirect
67. #2497C22semidirect
69. #2485C22semidirect
72. #2441C22semidirect
81. #2365C22semidirect
89. #2285C22semidirect
90. #2095C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2077C22semidirect
97. #2075C22semidirect
98. #2072C22semidirect
100. #2068C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2043C22semidirect
109. #2043C22semidirect
113. #2036C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
128. #2026C22semidirect
130. #1993C22semidirect
134. #1981C22semidirect
137. #1955C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1944C22semidirect
142. #1941C22semidirect
143. #1940C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
149. #1923C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
155. #1892C22semidirect
159. #1869C22semidirect
160. #1865C22semidirect
161. #1865C22semidirect
169. #1854C22semidirect
170. #1854C22semidirect
171. #1854C22semidirect
173. #1850C22semidirect
174. #1847C22semidirect
175. #1825C22semidirect
176. #1825C22semidirect
178. #1808C22semidirect
179. #1803C22semidirect
180. #1803C22semidirect
181. #1803C22semidirect
185. #1797C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#397372
#362182
#329582
#317972
#317772
#315122
#315002
#313412
#313212
#306502
#306442
#299282
#298542
#277812
#275412
#275332
#260592
#259762
#259562
#258982
#258922
#258902
#253522
#252862
#250252
#240502
#240432
#229752
#224242
#221412
#207432