Finite Group Databasebeta

← #7197474

Subgroups — #7197474

Order 512.

1619 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59250C211yesmaximal, characteristic, complemented
2#59147C211yesmaximal, characteristic, complemented
3#32193C211yesmaximal, characteristic, complemented
4#32179C211yesmaximal, characteristic, complemented
5#31910C211yesmaximal, characteristic, complemented
6#31899C211yesmaximal, characteristic, complemented
7#31310C211yesmaximal, characteristic, complemented
8#31308C211yesmaximal, characteristic, complemented
9#30526C211yesmaximal, characteristic, complemented
10#30519C211yesmaximal, characteristic
11#27771C211yesmaximal, characteristic, complemented
12#27633C211yesmaximal, characteristic, complemented
13#27521C211yesmaximal, characteristic, complemented
14#27518C211yesmaximal, characteristic, complemented
15#27240C211yesmaximal, characteristic, complemented
16#27239C211yesmaximal, characteristic, complemented
17#26719C211yesmaximal, characteristic, complemented
18#26708C211yesmaximal, characteristic, complemented
19#26468C211yesmaximal, characteristic, complemented
20#26325C211yesmaximal, characteristic, complemented
21#25298C211yesmaximal, characteristic, complemented
22#25280C211yesmaximal, characteristic, complemented
23#25277C211yesmaximal, characteristic, complemented
24#24634C211yesmaximal, characteristic, complemented
25#24215C211yesmaximal, characteristic, complemented
26#24192C211yesmaximal, characteristic, complemented
27#23696C211yesmaximal, characteristic, complemented
28#23098C211yesmaximal, characteristic, complemented
29#22549C211yesmaximal, characteristic, complemented
30#22102C211yesmaximal, characteristic, complemented
31#21806C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#488C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic
36C2×#477C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#448C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#446C2211yescharacteristic, complemented
43C2×C4×D8C2211yescharacteristic, complemented
44C2×#431C2211yescharacteristic
45#2777—21no—
46#2759—21no—
47#2712—21no—
48#2710—21no—
49#2592C2211yescharacteristic
50#2580C2211yescharacteristic, complemented
51#2560—21no—
52#2557—21no—
53#2550C2211yescharacteristic, complemented
54#2548C2211yescharacteristic
55#2544C2211yescharacteristic
56#2544C2211yescharacteristic
57#2527—21no—
58#2521—21no—
59#2513C2211yescharacteristic, complemented
60#2512C2211yescharacteristic, complemented
61#2496C2211yescharacteristic
62#2494C2211yescharacteristic
63#2491C2211yescharacteristic
64#2490C2211yescharacteristic
65#2472—21no—
66#2466—21no—
67#2459—21no—
68#2448C2211yescharacteristic
69#2447—21no—
70#2447C2211yescharacteristic
71#2436C2211yescharacteristic
72#2433C2211yescharacteristic
73#2418—21no—
74#2412—21no—
75#2373—21no—
76#2370C2211yescharacteristic, complemented
77#2369C2211yescharacteristic, complemented
78#2367C2211yescharacteristic
79#2358—21no—
80#2357C2211yescharacteristic, complemented
81#2355C2211yescharacteristic, complemented
82Q8×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86C4×#121C2211yescharacteristic
87#2283C2211yescharacteristic
88#2095C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2086C2211yescharacteristic, complemented
91#2077C2211yescharacteristic
92#2075C2211yescharacteristic
93#2075C2211yescharacteristic
94#2074C2211yescharacteristic, complemented
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2067C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2055C2211yescharacteristic, complemented
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic, complemented
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic, complemented
124#2012C2211yescharacteristic, complemented
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#1999C2211yescharacteristic
128#1984C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic, complemented
136#1983C2211yescharacteristic, complemented
137#1982C2211yescharacteristic
138#1982C2211yescharacteristic
139#1973C2211yescharacteristic, complemented
140#1972C2211yescharacteristic
141#1970C2211yescharacteristic
142#1968C2211yescharacteristic, complemented
143#1961C2211yescharacteristic
144#1959C2211yescharacteristic, complemented
145#1958C2211yescharacteristic
146#1958C2211yescharacteristic
147#1958C2211yescharacteristic
148#1958C2211yescharacteristic
149#1949C2211yescharacteristic, complemented
150#1949C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1939C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1935C2211yescharacteristic, complemented
156#1934C2211yescharacteristic
157#1933C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic, complemented
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic, complemented
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic
170#1923C2211yescharacteristic
171#1923C2211yescharacteristic
172#1921C2211yescharacteristic, complemented
173#1920C2211yescharacteristic, complemented
174#1917C2211yescharacteristic, complemented
175#1917C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1880C2211yescharacteristic, complemented
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1805C2211yescharacteristic, complemented
185#1804C2211yescharacteristic, complemented
186#1804C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1797C2211yescharacteristic
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195C4×#107C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic, complemented
202C4×#102C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#559—24no—
211#559—42no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124—24no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—42no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8D411yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#488—42no—
252#486—42no—
253#478—42no—
254#477—42no—
255#463—24no—
256#463—42no—
257#448—42no—
258#447—42no—
259#446—42no—
260C4×D8—42no—
261#431—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
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
324C2×C4×C8C2311yescharacteristic
325#401—21no—
326#400—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#395—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#392—21no—
356#392—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391D411yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389—21no—
384#389D411yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
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#388—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387D411yescharacteristic
414#387D411yescharacteristic
415#386—21no—
416#386—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#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#381—21no—
438#381—21no—
439#380—21no—
440#380D411yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376—21no—
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—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8C2×D411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555#127—22no—
556#127—41no—
557#127—41no—
558#127—41no—
559#126—44no—
560#126—82no—
561#125—22no—
562#125—41no—
563#124—22no—
564#124—22no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—22no—
569#124—44no—
570#124—44no—
571#124—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—44no—
577#124—82no—
578#124#4114yes—
579#123—44no—
580#123—44no—
581C22⋊Q8—42no—
582#121—22no—
583#121—41no—
584#121—41no—
585#121—41no—
586#120—44no—
587#120—82no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—44no—
603C4×D4—82no—
604C4×D4—82no—
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⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
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—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—44no—
680C2×C22⋊C4—44no—
681C2×C22⋊C4—82no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—22no—
687C2×C42—22no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—41no—
712#106—41no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—22no—
723#103—22no—
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#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
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—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—41no—
764#97—41no—
765C4×C8—22no—
766C4×C8—22no—
767C4×C8—41no—
768C4×C8—41no—
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#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24C22×D411yescharacteristic
823C2×Q8—22no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—41no—
836C2×Q8—41no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—82no—
844C2×Q8—82no—
845C2×Q8—82no—
846C2×Q8—82no—
847C2×Q8C2×#4112yes—
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—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—81no—
896C2×D4C2×#4112yes—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C2511yescharacteristic
950SD16—82no—
951SD16—82no—
952D8—44no—
953D8—82no—
954D8—82no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4H(5,𝔽2)12yes—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—22no—
1026C22⋊C4—41no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—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—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C42—22no—
1068C42—22no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42C2×#4112yes—
1090C42H(5,𝔽2)12yes—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—22no—
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—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23#57612yes—
1133C23C23×D411yescharacteristic
1134Q8—22no—
1135Q8—22no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—82no—
1143Q8—84no—
1144Q8—162no—
1145D4—22no—
1146D4—22no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
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—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—44no—
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—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—82no—
1246C2×C4—84no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4#54612yes—
1252C2×C4#54612yes—
1253C2×C4#57512yes—
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4#58511yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—168no—
1304C22C2×#54611yescharacteristic
1305C22#348711yescharacteristic
1306C22#348811yescharacteristic
1307C22C2×#57511yescharacteristic
1308C22C2×#57611yescharacteristic
1309C22#358411yescharacteristic
1310C22#358411yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#351411yescharacteristic
1337C4#352111yescharacteristic
1338C4#354011yescharacteristic
1339C4#354611yescharacteristic
1340C2—42no—
1341C2—82no—
1342C2—161no—
1343C2—161no—
1344C2—161no—
1345C2#4540411yescharacteristic
1346C2#6115411yescharacteristic
1347C2#6117111yescharacteristic
1348C2#6189811yescharacteristic
1349C2#6193011yescharacteristic
1350C2#6199211yescharacteristic
1351C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30519C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59250C2semidirect
2. #59147C2semidirect
3. #32193C2semidirect
4. #32179C2semidirect
5. #31910C2semidirect
6. #31899C2semidirect
7. #31310C2semidirect
8. #31308C2semidirect
9. #30526C2semidirect
11. #27771C2semidirect
12. #27633C2semidirect
13. #27521C2semidirect
14. #27518C2semidirect
15. #27240C2semidirect
16. #27239C2semidirect
17. #26719C2semidirect
18. #26708C2semidirect
19. #26468C2semidirect
20. #26325C2semidirect
21. #25298C2semidirect
22. #25280C2semidirect
23. #25277C2semidirect
24. #24634C2semidirect
25. #24215C2semidirect
26. #24192C2semidirect
27. #23696C2semidirect
28. #23098C2semidirect
29. #22549C2semidirect
30. #22102C2semidirect
31. #21806C2semidirect
34. C2×#488C22semidirect
36. C2×#477C22semidirect
42. C2×#446C22semidirect
43. C2×C4×D8C22semidirect
50. #2580C22semidirect
53. #2550C22semidirect
59. #2513C22semidirect
60. #2512C22semidirect
76. #2370C22semidirect
77. #2369C22semidirect
80. #2357C22semidirect
81. #2355C22semidirect
88. #2095C22semidirect
90. #2086C22semidirect
94. #2074C22semidirect
96. #2068C22semidirect
99. #2067C22semidirect
100. #2067C22semidirect
101. #2066C22semidirect
102. #2055C22semidirect
103. #2055C22semidirect
106. #2054C22semidirect
109. #2042C22semidirect
110. #2042C22semidirect
117. #2026C22semidirect
119. #2024C22semidirect
123. #2012C22semidirect
124. #2012C22semidirect
128. #1984C22semidirect
135. #1983C22semidirect
136. #1983C22semidirect
139. #1973C22semidirect
142. #1968C22semidirect
144. #1959C22semidirect
149. #1949C22semidirect
150. #1949C22semidirect
151. #1939C22semidirect
152. #1939C22semidirect
153. #1939C22semidirect
155. #1935C22semidirect
157. #1933C22semidirect
158. #1928C22semidirect
159. #1928C22semidirect
160. #1928C22semidirect
161. #1927C22semidirect
163. #1926C22semidirect
167. #1925C22semidirect
172. #1921C22semidirect
173. #1920C22semidirect
174. #1917C22semidirect
175. #1917C22semidirect
176. #1880C22semidirect
177. #1880C22semidirect
180. #1865C22semidirect
181. #1863C22semidirect
184. #1805C22semidirect
185. #1804C22semidirect
186. #1804C22semidirect
195. C4×#107C22semidirect
196. C8×C4⋊C4C22semidirect
197. #1763C22semidirect
199. C4×#103C22semidirect
201. C4×#102C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#592502
#591472
#321932
#321792
#319102
#318992
#313102
#313082
#305262
#305192
#277712
#276332
#275212
#275182
#272402
#272392
#267192
#267082
#264682
#263252
#252982
#252802
#252772
#246342
#242152
#241922
#236962
#230982
#225492
#221022
#218062