Finite Group Databasebeta

← #7338928

Subgroups — #7338928

Order 512.

1545 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59100C211yesmaximal, characteristic
2#45488C211yesmaximal, characteristic, complemented
3#32085C211yesmaximal, characteristic, complemented
4#31972C211yesmaximal, characteristic, complemented
5#31793C211yesmaximal, characteristic, complemented
6#31496C211yesmaximal, characteristic, complemented
7#31333C211yesmaximal, characteristic, complemented
8#31309C211yesmaximal, characteristic, complemented
9#31288C211yesmaximal, characteristic, complemented
10#31287C211yesmaximal, characteristic, complemented
11#31132C211yesmaximal, characteristic, complemented
12#30957C211yesmaximal, characteristic, complemented
13#30832C211yesmaximal, characteristic, complemented
14#30773C211yesmaximal, characteristic, complemented
15#29955C211yesmaximal, characteristic, complemented
16#29691C211yesmaximal, characteristic, complemented
17#29107C211yesmaximal, characteristic, complemented
18#28970C211yesmaximal, characteristic, complemented
19#28065C211yesmaximal, characteristic, complemented
20#27785C211yesmaximal, characteristic, complemented
21#27535C211yesmaximal, characteristic, complemented
22#27258C211yesmaximal, characteristic, complemented
23#27103C211yesmaximal, characteristic, complemented
24#27058C211yesmaximal, characteristic, complemented
25#26773C211yesmaximal, characteristic, complemented
26#26466C211yesmaximal, characteristic, complemented
27#25963C211yesmaximal, characteristic, complemented
28#25896C211yesmaximal, characteristic
29#25674C211yesmaximal, characteristic, complemented
30#24035C211yesmaximal, characteristic
31#22361C211yesmaximal, characteristic, complemented
32C2×#563—21no—
33C2×#548C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#477C2211yescharacteristic
40C2×#477C2211yescharacteristic
41C2×#477C2211yescharacteristic
42C22×#103C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2817—21no—
46#2722—21no—
47#2717—21no—
48#2713—21no—
49#2713—21no—
50#2700—21no—
51#2689—21no—
52#2689—21no—
53#2672—21no—
54#2556—21no—
55#2551C2211yescharacteristic
56#2551C2211yescharacteristic
57#2547C2211yescharacteristic
58#2545C2211yescharacteristic
59#2506C2211yescharacteristic
60#2506C2211yescharacteristic
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2496C2211yescharacteristic
64#2496C2211yescharacteristic
65#2491C2211yescharacteristic
66#2486C2211yescharacteristic
67#2476—21no—
68#2474—21no—
69#2465—21no—
70#2460—21no—
71#2451C2211yescharacteristic
72#2448C2211yescharacteristic
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic
75#2434C2211yescharacteristic
76#2432C2211yescharacteristic
77#2426C2211yescharacteristic
78#2415C2211yescharacteristic
79#2367—21no—
80#2365C2211yescharacteristic
81#2362C2211yescharacteristic
82Q8×C22⋊C4C2211yescharacteristic
83C4×#123C2211yescharacteristic
84#2297C2211yescharacteristic
85#2096C2211yescharacteristic
86#2095C2211yescharacteristic
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2083C2211yescharacteristic
92#2075C2211yescharacteristic
93#2075C2211yescharacteristic
94#2072C2211yescharacteristic
95#2072C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2057C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2043C2211yescharacteristic
109#2043C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2024C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic
133#1990C2211yescharacteristic
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1981C2211yescharacteristic
137#1959C2211yescharacteristic
138#1956C2211yescharacteristic
139#1956C2211yescharacteristic
140#1955C2211yescharacteristic
141#1947C2211yescharacteristic
142#1944C2211yescharacteristic
143#1943C2211yescharacteristic
144#1939C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1921C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1872C2211yescharacteristic
170#1869C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1852C2211yescharacteristic
182#1850C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1808C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1797C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1771C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#563—48no—
207#548—42no—
208#548—42no—
209#533—42no—
210#533—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123D411yescharacteristic
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×C4×Q8—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C42C2311yescharacteristic
255#500—42no—
256#489—42no—
257#487—42no—
258#480—42no—
259#477—42no—
260#477—42no—
261#477—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—21no—
351#395—21no—
352#395—21no—
353#395—21no—
354#395—21no—
355#395—21no—
356#395—21no—
357#395—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#393—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
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#388D411yescharacteristic
407#388D411yescharacteristic
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
420#386—21no—
421#386—21no—
422#386D411yescharacteristic
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#381—21no—
435#381D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
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#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547#126—44no—
548#126—44no—
549#126—44no—
550#126—44no—
551#125—44no—
552#125—44no—
553#125—44no—
554#124—22no—
555#124—41no—
556#124—41no—
557#124—41no—
558#124—44no—
559#124—44no—
560#124—44no—
561#123—24no—
562#123—44no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575#121—22no—
576#121—44no—
577#121—41no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—44no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590#117—44no—
591#117—41no—
592#117—41no—
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—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—22no—
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—41no—
708#106—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754#97—41no—
755C4×C8—41no—
756C4×C8—41no—
757C4×C8—41no—
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#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—21no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805#41—82no—
806#41—82no—
807#41—82no—
808#41—82no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—82no—
842C2×Q8—82no—
843C2×Q8—82no—
844C2×Q8H(5,𝔽2)12yes—
845C2×Q82−1+412yes—
846C2×D4—22no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—81no—
860C2×D4—81no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
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—22no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
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×C4C2511yescharacteristic
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
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—82no—
941C4⋊C4—24no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
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—41no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4H(5,𝔽2)12yes—
1006C22⋊C4—24no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4AGL(1,ℤ/8)14yes—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—41no—
1048C42—41no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23C2×AGL(1,ℤ/8)12yes—
1079C23C23×D411yescharacteristic
1080Q8—22no—
1081Q8—22no—
1082Q8—22no—
1083Q8—22no—
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—84no—
1093Q8—84no—
1094Q8—162no—
1095Q8—162no—
1096Q8—162no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—82no—
1102D4—84no—
1103D4—84no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—44no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—82no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—162no—
1194C2×C4C2×AGL(1,ℤ/8)12yes—
1195C2×C4C2×AGL(1,ℤ/8)12yes—
1196C2×C4#57812yes—
1197C2×C4#57812yes—
1198C2×C4C2×H(5,𝔽2)11yescharacteristic
1199C2×C4C2×H(5,𝔽2)11yescharacteristic
1200C2×C4C2×2−1+411yescharacteristic
1201C2×C4#58511yescharacteristic
1202C2×C4#58511yescharacteristic
1203C2×C4#58511yescharacteristic
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22#348411yescharacteristic
1234C22#348911yescharacteristic
1235C22#350011yescharacteristic
1236C22C22×AGL(1,ℤ/8)11yescharacteristic
1237C22C2×#57811yescharacteristic
1238C22C2×#57811yescharacteristic
1239C22#358411yescharacteristic
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—42no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—42no—
1254C4—41no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4#353511yescharacteristic
1268C4#355111yescharacteristic
1269C4#356011yescharacteristic
1270C4#356111yescharacteristic
1271C2—42no—
1272C2—81no—
1273C2—161no—
1274C2#4795611yescharacteristic
1275C2#6159811yescharacteristic
1276C2#6163411yescharacteristic
1277C2#6213211yescharacteristic
1278C2#6222011yescharacteristic
1279C2#6253811yescharacteristic
1280C2#6256011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45488C2semidirect
3. #32085C2semidirect
4. #31972C2semidirect
5. #31793C2semidirect
6. #31496C2semidirect
7. #31333C2semidirect
8. #31309C2semidirect
9. #31288C2semidirect
10. #31287C2semidirect
11. #31132C2semidirect
12. #30957C2semidirect
13. #30832C2semidirect
14. #30773C2semidirect
15. #29955C2semidirect
16. #29691C2semidirect
17. #29107C2semidirect
18. #28970C2semidirect
19. #28065C2semidirect
20. #27785C2semidirect
21. #27535C2semidirect
22. #27258C2semidirect
23. #27103C2semidirect
24. #27058C2semidirect
25. #26773C2semidirect
26. #26466C2semidirect
27. #25963C2semidirect
29. #25674C2semidirect
31. #22361C2semidirect

Maximal subgroups

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

subgroupindex
#591002
#454882
#320852
#319722
#317932
#314962
#313332
#313092
#312882
#312872
#311322
#309572
#308322
#307732
#299552
#296912
#291072
#289702
#280652
#277852
#275352
#272582
#271032
#270582
#267732
#264662
#259632
#258962
#256742
#240352
#223612