Finite Group Databasebeta

← #7335170

Subgroups — #7335170

Order 512.

1509 conjugacy classes of subgroups.

The subgroup lattice has 1337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53104C211yesmaximal, characteristic, complemented
2#45097C211yesmaximal, characteristic, complemented
3#32637C211yesmaximal, characteristic, complemented
4#32622C211yesmaximal, characteristic, complemented
5#32183C211yesmaximal, characteristic, complemented
6#32163C211yesmaximal, characteristic, complemented
7#32092C211yesmaximal, characteristic, complemented
8#31577C211yesmaximal, characteristic, complemented
9#31315C211yesmaximal, characteristic, complemented
10#31294C211yesmaximal, characteristic, complemented
11#30992C211yesmaximal, characteristic, complemented
12#30883C211yesmaximal, characteristic, complemented
13#30817C211yesmaximal, characteristic, complemented
14#30545C211yesmaximal, characteristic, complemented
15#30184C211yesmaximal, characteristic, complemented
16#29630C211yesmaximal, characteristic
17#29474C211yesmaximal, characteristic, complemented
18#28882C211yesmaximal, characteristic, complemented
19#27773C211yesmaximal, characteristic, complemented
20#27764C211yesmaximal, characteristic, complemented
21#27534C211yesmaximal, characteristic, complemented
22#27526C211yesmaximal, characteristic, complemented
23#27243C211yesmaximal, characteristic, complemented
24#27065C211yesmaximal, characteristic, complemented
25#26827C211yesmaximal, characteristic, complemented
26#26770C211yesmaximal, characteristic, complemented
27#25867C211yesmaximal, characteristic, complemented
28#25659C211yesmaximal, characteristic, complemented
29#24895C211yesmaximal, characteristic, complemented
30#24192C211yesmaximal, characteristic, complemented
31#22324C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#489C2211yescharacteristic, complemented
36C2×#488C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic, complemented
42#2837—21no—
43#2836—21no—
44#2827—21no—
45#2821—21no—
46#2764—21no—
47#2738—21no—
48#2731—21no—
49#2715—21no—
50#2701—21no—
51#2697—21no—
52#2686—21no—
53#2684—21no—
54#2629C2211yescharacteristic
55#2624C2211yescharacteristic
56#2592C2211yescharacteristic
57#2580C2211yescharacteristic, complemented
58#2570C2211yescharacteristic, complemented
59#2550C2211yescharacteristic, complemented
60#2547C2211yescharacteristic
61#2546C2211yescharacteristic, complemented
62#2545C2211yescharacteristic
63#2544C2211yescharacteristic
64#2534—21no—
65#2513C2211yescharacteristic, complemented
66#2512C2211yescharacteristic, complemented
67#2509C2211yescharacteristic, complemented
68#2495C2211yescharacteristic
69#2495C2211yescharacteristic
70#2491C2211yescharacteristic
71#2454C2211yescharacteristic, complemented
72#2447C2211yescharacteristic
73#2445C2211yescharacteristic
74#2444—21no—
75#2435C2211yescharacteristic
76#2432C2211yescharacteristic
77#2425—21no—
78#2420C2211yescharacteristic
79#2418—21no—
80#2396C2211yescharacteristic
81#2366C2211yescharacteristic
82#2339C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2323C2211yescharacteristic
85#2097C2211yescharacteristic, complemented
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic, complemented
88#2083C2211yescharacteristic, complemented
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic
91#2075C2211yescharacteristic
92#2074C2211yescharacteristic, complemented
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic, complemented
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2054C2211yescharacteristic
104#2054C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2034C2211yescharacteristic
122#2026C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2013C2211yescharacteristic, complemented
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic, complemented
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#2000C2211yescharacteristic
133#1985C2211yescharacteristic, complemented
134#1984C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic, complemented
137#1981C2211yescharacteristic, complemented
138#1973C2211yescharacteristic, complemented
139#1972C2211yescharacteristic
140#1970C2211yescharacteristic
141#1968C2211yescharacteristic, complemented
142#1960C2211yescharacteristic, complemented
143#1959C2211yescharacteristic
144#1958C2211yescharacteristic
145#1958C2211yescharacteristic
146#1957C2211yescharacteristic
147#1941C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic, complemented
183#1864C2211yescharacteristic, complemented
184#1864C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1818C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1771C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#559—42no—
211#559—42no—
212#535—42no—
213#535—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C22⋊C4—21no—
248#490—42no—
249#489—42no—
250#488—42no—
251#476—42no—
252#463—42no—
253#449—42no—
254#447—42no—
255C4×D8—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400D411yescharacteristic
321#399—21no—
322#399—21no—
323#399—21no—
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398D411yescharacteristic
332#398D411yescharacteristic
333#397—21no—
334#397—21no—
335#397—21no—
336#397—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#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396D411yescharacteristic
352#396D411yescharacteristic
353#395—21no—
354#395D411yescharacteristic
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393D411yescharacteristic
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
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#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384C2311yescharacteristic
434#383—21no—
435#383—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#381—21no—
441#381—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379—21no—
450#379—21no—
451#379—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C2×#95—21no—
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—82no—
553#127—22no—
554#127—22no—
555#127—22no—
556#127—41no—
557#126—82no—
558#125—41no—
559#125—41no—
560#124—22no—
561#124—22no—
562#124—22no—
563#124—41no—
564#124—41no—
565#124—41no—
566#124—41no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—44no—
571#124—82no—
572#123—44no—
573#123—44no—
574#123—82no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577#121—44no—
578#121—44no—
579#121—41no—
580#121—41no—
581#120—44no—
582#120—44no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—44no—
598C4×D4—82no—
599#117—41no—
600#117—41no—
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⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
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—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—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—41no—
701#107—41no—
702#107—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
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—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
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#95C2×D411yescharacteristic
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
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—42no—
806C24—42no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24C22×D411yescharacteristic
813#41—82no—
814#41—82no—
815#41—82no—
816#41—82no—
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—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—41no—
830C2×Q8—41no—
831C2×Q8—41no—
832C2×Q8—42no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4H(5,𝔽2)12yes—
883C2×D4H(5,𝔽2)12yes—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2511yescharacteristic
934SD16—82no—
935SD16—82no—
936D8—44no—
937D8—82no—
938D8—82no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
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—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—42no—
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⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
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—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
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—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—22no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
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—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23C23×D411yescharacteristic
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—82no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
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—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—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—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4C2×H(5,𝔽2)11yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4#58511yescharacteristic
1241C2×C4#58511yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—41no—
1253C22—42no—
1254C22—42no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—42no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—42no—
1263C22—41no—
1264C22—41no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—168no—
1288C22#348411yescharacteristic
1289C22#348711yescharacteristic
1290C22#350011yescharacteristic
1291C22#358411yescharacteristic
1292C22#358411yescharacteristic
1293C22#358511yescharacteristic
1294C22#358511yescharacteristic
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4#353311yescharacteristic
1321C4#354511yescharacteristic
1322C4#356011yescharacteristic
1323C4#356011yescharacteristic
1324C2—81no—
1325C2—82no—
1326C2—82no—
1327C2—161no—
1328C2—161no—
1329C2#4794811yescharacteristic
1330C2#6161411yescharacteristic
1331C2#6167811yescharacteristic
1332C2#6193111yescharacteristic
1333C2#6193811yescharacteristic
1334C2#6260111yescharacteristic
1335C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#29630C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53104C2semidirect
2. #45097C2semidirect
3. #32637C2semidirect
4. #32622C2semidirect
5. #32183C2semidirect
6. #32163C2semidirect
7. #32092C2semidirect
8. #31577C2semidirect
9. #31315C2semidirect
10. #31294C2semidirect
11. #30992C2semidirect
12. #30883C2semidirect
13. #30817C2semidirect
14. #30545C2semidirect
15. #30184C2semidirect
17. #29474C2semidirect
18. #28882C2semidirect
19. #27773C2semidirect
20. #27764C2semidirect
21. #27534C2semidirect
22. #27526C2semidirect
23. #27243C2semidirect
24. #27065C2semidirect
25. #26827C2semidirect
26. #26770C2semidirect
27. #25867C2semidirect
28. #25659C2semidirect
29. #24895C2semidirect
30. #24192C2semidirect
31. #22324C2semidirect
35. C2×#489C22semidirect
41. C2×C4×D8C22semidirect
57. #2580C22semidirect
58. #2570C22semidirect
59. #2550C22semidirect
61. #2546C22semidirect
65. #2513C22semidirect
66. #2512C22semidirect
67. #2509C22semidirect
71. #2454C22semidirect
85. #2097C22semidirect
87. #2092C22semidirect
88. #2083C22semidirect
92. #2074C22semidirect
95. #2072C22semidirect
99. #2066C22semidirect
100. #2066C22semidirect
101. #2059C22semidirect
102. #2055C22semidirect
104. #2054C22semidirect
105. #2043C22semidirect
113. #2042C22semidirect
122. #2026C22semidirect
123. #2024C22semidirect
125. #2013C22semidirect
129. #2012C22semidirect
133. #1985C22semidirect
134. #1984C22semidirect
136. #1983C22semidirect
137. #1981C22semidirect
138. #1973C22semidirect
141. #1968C22semidirect
142. #1960C22semidirect
147. #1941C22semidirect
149. #1936C22semidirect
150. #1936C22semidirect
151. #1935C22semidirect
153. #1933C22semidirect
154. #1933C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
160. #1926C22semidirect
161. #1925C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1918C22semidirect
169. #1917C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
172. #1916C22semidirect
173. #1880C22semidirect
177. #1879C22semidirect
178. #1877C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
182. #1864C22semidirect
183. #1864C22semidirect
184. #1864C22semidirect
185. #1863C22semidirect
189. #1804C22semidirect
190. #1804C22semidirect
197. #1771C22semidirect
198. #1770C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#531042
#450972
#326372
#326222
#321832
#321632
#320922
#315772
#313152
#312942
#309922
#308832
#308172
#305452
#301842
#296302
#294742
#288822
#277732
#277642
#275342
#275262
#272432
#270652
#268272
#267702
#258672
#256592
#248952
#241922
#223242