Finite Group Databasebeta

← #7078327

Subgroups — #7078327

Order 512.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45019C211yesmaximal, characteristic, complemented
2#45003C211yesmaximal, characteristic, complemented
3#32538C211yesmaximal, characteristic, complemented
4#32532C211yesmaximal, characteristic, complemented
5#32438C211yesmaximal, characteristic, complemented
6#32437C211yesmaximal, characteristic, complemented
7#32075C211yesmaximal, characteristic, complemented
8#32050C211yesmaximal, characteristic, complemented
9#30685C211yesmaximal, characteristic, complemented
10#30679C211yesmaximal, characteristic, complemented
11#28781C211yesmaximal, characteristic, complemented
12#27594C211yesmaximal, characteristic, complemented
13#27593C211yesmaximal, characteristic, complemented
14#27493C211yesmaximal, characteristic, complemented
15#27488C211yesmaximal, characteristic, complemented
16#26563C211yesmaximal, characteristic, complemented
17#26548C211yesmaximal, characteristic, complemented
18#25964C211yesmaximal, characteristic, complemented
19#25958C211yesmaximal, characteristic, complemented
20#25221C211yesmaximal, characteristic, complemented
21#25216C211yesmaximal, characteristic, complemented
22#24873C211yesmaximal, characteristic, complemented
23#24862C211yesmaximal, characteristic, complemented
24#24688C211yesmaximal, characteristic, complemented
25#24677C211yesmaximal, characteristic, complemented
26#24277C211yesmaximal, characteristic
27#23544C211yesmaximal, characteristic, complemented
28#22714C211yesmaximal, characteristic, complemented
29#22442C211yesmaximal, characteristic, complemented
30#22074C211yesmaximal, characteristic, complemented
31#21967C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#481C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#424C2211yescharacteristic
43C2×#416C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2796—21no—
46#2778—21no—
47#2745—21no—
48#2740—21no—
49#2737—21no—
50#2735—21no—
51#2697—21no—
52#2696—21no—
53#2602—21no—
54#2578—21no—
55#2569—21no—
56#2566C2211yescharacteristic
57#2563C2211yescharacteristic, complemented
58#2514C2211yescharacteristic, complemented
59#2513C2211yescharacteristic
60#2513C2211yescharacteristic
61#2511C2211yescharacteristic, complemented
62#2501C2211yescharacteristic
63#2499C2211yescharacteristic, complemented
64#2498—21no—
65#2492C2211yescharacteristic, complemented
66#2490C2211yescharacteristic
67#2482—21no—
68#2477—21no—
69#2471—21no—
70#2441C2211yescharacteristic
71#2440C2211yescharacteristic
72#2422C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2418—21no—
75#2408C2211yescharacteristic
76#2407C2211yescharacteristic
77#2395C2211yescharacteristic
78#2363C2211yescharacteristic, complemented
79#2361C2211yescharacteristic
80#2354C2211yescharacteristic
81#2354C2211yescharacteristic, complemented
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2314C2211yescharacteristic
87#2314C2211yescharacteristic
88#2311C2211yescharacteristic
89#2309C2211yescharacteristic
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2093C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2023C2211yescharacteristic
128#2000C2211yescharacteristic
129#1999C2211yescharacteristic
130#1992C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1970C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1948C2211yescharacteristic, complemented
145#1948C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic, complemented
163#1923C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1875C2211yescharacteristic
171#1872C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1851C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1835C2211yescharacteristic, complemented
187#1818C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic, complemented
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#106C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240#482—42no—
241#481—42no—
242#478—42no—
243#476—42no—
244#469—42no—
245#468—42no—
246#442—42no—
247C4×D8—42no—
248#436—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265#424—24no—
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#416—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102—42no—
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#401—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400D411yescharacteristic
313#399—21no—
314#399—21no—
315#399—21no—
316#399D411yescharacteristic
317#398—21no—
318#398D411yescharacteristic
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397D411yescharacteristic
329#397D411yescharacteristic
330#397D411yescharacteristic
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394D411yescharacteristic
341#394D411yescharacteristic
342#393—21no—
343#393—21no—
344#393—21no—
345#392—21no—
346#392—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#383—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C2×#95—21no—
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526AGL(1,ℤ/8)—416no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16#4114yes—
545C22×C8—22no—
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—
558#125—41no—
559#125—41no—
560#123—82no—
561#123—82no—
562#123—82no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—82no—
566#121—22no—
567#121—22no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#120—82no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—82no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—82no—
591#117—82no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
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—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—22no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747#97—41no—
748C4×C8—22no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806#41—44no—
807#41—44no—
808#41—82no—
809#41—82no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4H(5,𝔽2)12yes—
858C2×D4H(5,𝔽2)12yes—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C2×#4112yes—
916C22×C42−1+412yes—
917C22×C4C2511yescharacteristic
918SD16—44no—
919SD16—44no—
920D8—28no—
921D8—44no—
922M16—44no—
923M16—82no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—82no—
947C2×C8C2×#4112yes—
948C2×C8C2×#4112yes—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—22no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—84no—
1099C23—84no—
1100C23—162no—
1101C23—162no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23#54712yes—
1106C23C23×D411yescharacteristic
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—162no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—22no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—84no—
1125D4—82no—
1126D4—84no—
1127D4—84no—
1128D4—162no—
1129D4—162no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4#54712yes—
1219C2×C4#57712yes—
1220C2×C4C22×#4111yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×H(5,𝔽2)11yescharacteristic
1223C2×C4C2×2−1+411yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C8—22no—
1227C8—22no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—42no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—168no—
1270C22C2×#54711yescharacteristic
1271C22#348811yescharacteristic
1272C22#348811yescharacteristic
1273C22C2×#57711yescharacteristic
1274C22#358411yescharacteristic
1275C22#358511yescharacteristic
1276C22#358511yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4#349011yescharacteristic
1303C4#351011yescharacteristic
1304C4#353511yescharacteristic
1305C4#353511yescharacteristic
1306C2—42no—
1307C2—81no—
1308C2—82no—
1309C2—82no—
1310C2—161no—
1311C2#4395911yescharacteristic
1312C2#6127411yescharacteristic
1313C2#6127911yescharacteristic
1314C2#6202711yescharacteristic
1315C2#6203311yescharacteristic
1316C2#6206311yescharacteristic
1317C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24277C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45019C2semidirect
2. #45003C2semidirect
3. #32538C2semidirect
4. #32532C2semidirect
5. #32438C2semidirect
6. #32437C2semidirect
7. #32075C2semidirect
8. #32050C2semidirect
9. #30685C2semidirect
10. #30679C2semidirect
11. #28781C2semidirect
12. #27594C2semidirect
13. #27593C2semidirect
14. #27493C2semidirect
15. #27488C2semidirect
16. #26563C2semidirect
17. #26548C2semidirect
18. #25964C2semidirect
19. #25958C2semidirect
20. #25221C2semidirect
21. #25216C2semidirect
22. #24873C2semidirect
23. #24862C2semidirect
24. #24688C2semidirect
25. #24677C2semidirect
27. #23544C2semidirect
28. #22714C2semidirect
29. #22442C2semidirect
30. #22074C2semidirect
31. #21967C2semidirect
33. C2×#481C22semidirect
35. C2×#478C22semidirect
57. #2563C22semidirect
58. #2514C22semidirect
61. #2511C22semidirect
63. #2499C22semidirect
65. #2492C22semidirect
72. #2422C22semidirect
78. #2363C22semidirect
81. #2354C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2096C22semidirect
97. #2092C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
103. #2073C22semidirect
104. #2072C22semidirect
105. #2071C22semidirect
106. #2068C22semidirect
107. #2066C22semidirect
110. #2059C22semidirect
111. #2057C22semidirect
122. #2035C22semidirect
125. #2033C22semidirect
126. #2026C22semidirect
130. #1992C22semidirect
131. #1990C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1948C22semidirect
143. #1948C22semidirect
144. #1948C22semidirect
145. #1948C22semidirect
146. #1943C22semidirect
147. #1942C22semidirect
148. #1940C22semidirect
149. #1939C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
161. #1925C22semidirect
162. #1924C22semidirect
163. #1923C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
171. #1872C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
179. #1854C22semidirect
181. #1853C22semidirect
183. #1851C22semidirect
184. #1851C22semidirect
186. #1835C22semidirect
190. #1809C22semidirect
194. #1802C22semidirect
199. C4×#106C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#450192
#450032
#325382
#325322
#324382
#324372
#320752
#320502
#306852
#306792
#287812
#275942
#275932
#274932
#274882
#265632
#265482
#259642
#259582
#252212
#252162
#248732
#248622
#246882
#246772
#242772
#235442
#227142
#224422
#220742
#219672