Finite Group Databasebeta

← #7615191

Subgroups — #7615191

Order 512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1211 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C211yesmaximal, characteristic, complemented
2#59639C211yesmaximal, characteristic, complemented
3#32533C211yesmaximal, characteristic, complemented
4#32532C211yesmaximal, characteristic, complemented
5#32529C211yesmaximal, characteristic, complemented
6#32525C211yesmaximal, characteristic, complemented
7#28746C211yesmaximal, characteristic
8#28746C211yesmaximal, characteristic
9#28548C211yesmaximal, characteristic, complemented
10#28547C211yesmaximal, characteristic, complemented
11#28285C211yesmaximal, characteristic, complemented
12#28280C211yesmaximal, characteristic, complemented
13#28029C211yesmaximal, characteristic, complemented
14#28027C211yesmaximal, characteristic, complemented
15#28013C211yesmaximal, characteristic, complemented
16#28010C211yesmaximal, characteristic, complemented
17#26334C211yesmaximal, characteristic, complemented
18#26332C211yesmaximal, characteristic, complemented
19#26331C211yesmaximal, characteristic, complemented
20#26328C211yesmaximal, characteristic, complemented
21#24697C211yesmaximal, characteristic, complemented
22#24692C211yesmaximal, characteristic, complemented
23#24689C211yesmaximal, characteristic, complemented
24#24688C211yesmaximal, characteristic, complemented
25#22819C211yesmaximal, characteristic, complemented
26#22817C211yesmaximal, characteristic, complemented
27#22730C211yesmaximal, characteristic, complemented
28#22729C211yesmaximal, characteristic, complemented
29#21731C211yesmaximal, characteristic, complemented
30#21713C211yesmaximal, characteristic, complemented
31#21701C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#496C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#446C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic
44#2800—21no—
45#2800—21no—
46#2798—21no—
47#2798—21no—
48#2596—21no—
49#2596—21no—
50#2592C2211yescharacteristic
51#2592C2211yescharacteristic
52#2568C2211yescharacteristic
53#2566C2211yescharacteristic
54#2566C2211yescharacteristic
55#2548C2211yescharacteristic
56#2548C2211yescharacteristic
57#2545—21no—
58#2542C2211yescharacteristic
59#2513C2211yescharacteristic
60#2513C2211yescharacteristic
61#2513C2211yescharacteristic
62#2513C2211yescharacteristic
63#2512—21no—
64#2512C2211yescharacteristic
65#2512C2211yescharacteristic
66#2511C2211yescharacteristic
67#2511C2211yescharacteristic
68#2499—21no—
69#2492—21no—
70#2466—21no—
71#2466—21no—
72#2447—21no—
73#2421—21no—
74#2367—21no—
75#2362—21no—
76#2357C2211yescharacteristic
77#2357C2211yescharacteristic
78#2355C2211yescharacteristic
79#2355C2211yescharacteristic
80#2355C2211yescharacteristic
81#2355C2211yescharacteristic
82#2354C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84C4×C4⋊Q8C2211yescharacteristic
85C4×C4⋊Q8C2211yescharacteristic
86C4×#127C2211yescharacteristic
87C4×#125C2211yescharacteristic
88C4×#124C2211yescharacteristic
89#2097C2211yescharacteristic
90#2096C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2074C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2068C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#1993C2211yescharacteristic
122#1992C2211yescharacteristic
123#1985C2211yescharacteristic
124#1985C2211yescharacteristic
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic
136#1970C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1961C2211yescharacteristic
142#1959C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1948C2211yescharacteristic
150#1948C2211yescharacteristic
151#1948C2211yescharacteristic
152#1948C2211yescharacteristic
153#1948C2211yescharacteristic
154#1947C2211yescharacteristic
155#1942C2211yescharacteristic
156#1942C2211yescharacteristic
157#1941C2211yescharacteristic
158#1941C2211yescharacteristic
159#1940C2211yescharacteristic
160#1940C2211yescharacteristic
161#1939C2211yescharacteristic
162#1939C2211yescharacteristic
163#1928C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1926C2211yescharacteristic
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic
170#1926C2211yescharacteristic
171#1926C2211yescharacteristic
172#1926C2211yescharacteristic
173#1926C2211yescharacteristic
174#1925C2211yescharacteristic
175#1925C2211yescharacteristic
176#1925C2211yescharacteristic
177#1925C2211yescharacteristic
178#1925C2211yescharacteristic
179#1847C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1846C2211yescharacteristic
184#1844C2211yescharacteristic
185#1842C2211yescharacteristic
186#1805C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#107C2211yescharacteristic
197C4×#106C2211yescharacteristic
198#1771C2211yescharacteristic
199#1771C2211yescharacteristic
200#1770C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8D411yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229#501—24no—
230#496—24no—
231#479—42no—
232#478—42no—
233#476—42no—
234#476—42no—
235#446—24no—
236#446—24no—
237#442—24no—
238#442—42no—
239#440—24no—
240#440—42no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#399—21no—
312#399—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#393—21no—
336#393—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391D411yescharacteristic
344#391D411yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389D411yescharacteristic
374#389D411yescharacteristic
375#389D411yescharacteristic
376#389D411yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#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#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
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#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384D411yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#380—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C43C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2×D411yescharacteristic
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×D8—22no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—41no—
513C2×D8—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—42no—
525#127—22no—
526#127—22no—
527#126—82no—
528#126—82no—
529#125—22no—
530#125—22no—
531#124—22no—
532#124—22no—
533#124—44no—
534#124—82no—
535C22⋊Q8—44no—
536C22⋊Q8—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—82no—
544C4×Q8—82no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—82no—
552C4×D4—82no—
553#117—82no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#106—22no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—22no—
717#97#4114yes—
718#97#4114yes—
719C4×C8—22no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—41no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—21no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—41no—
782C2×Q8—41no—
783C2×Q8—41no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—81no—
810C2×D4—81no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C2511yescharacteristic
848SD16—44no—
849SD16—44no—
850D8—44no—
851D8—44no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8C2×#4112yes—
872C2×C8C2×#4112yes—
873C2×C8C2×#4112yes—
874C2×C8C2×#4112yes—
875C2×C82−1+412yes—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C42—22no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42C2×#4112yes—
997C42C2×#4112yes—
998C42H(5,𝔽2)12yes—
999C422−1+412yes—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23C23×D411yescharacteristic
1022Q8—44no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—82no—
1028Q8—84no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—84no—
1042D4—84no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—84no—
1119C2×C4—162no—
1120C2×C4—162no—
1121C2×C4#54712yes—
1122C2×C4#54712yes—
1123C2×C4#55012yes—
1124C2×C4#55012yes—
1125C2×C4#57512yes—
1126C2×C4#57712yes—
1127C2×C4C22×#4111yescharacteristic
1128C2×C4C22×#4111yescharacteristic
1129C2×C4C2×H(5,𝔽2)11yescharacteristic
1130C2×C4C2×2−1+411yescharacteristic
1131C2×C4C2×2−1+411yescharacteristic
1132C2×C4#58511yescharacteristic
1133C8—22no—
1134C8—22no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8#55614yes—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22C2×#54711yescharacteristic
1163C22C2×#55011yescharacteristic
1164C22#349711yescharacteristic
1165C22C2×#57511yescharacteristic
1166C22C2×#57711yescharacteristic
1167C22#358511yescharacteristic
1168C22#358511yescharacteristic
1169C4—22no—
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—22no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4C2×#55611yescharacteristic
1197C4#350611yescharacteristic
1198C4#350711yescharacteristic
1199C4#355011yescharacteristic
1200C2—161no—
1201C2—161no—
1202C2—161no—
1203C2#5982111yescharacteristic
1204C2#6125511yescharacteristic
1205C2#6127911yescharacteristic
1206C2#6140511yescharacteristic
1207C2#6142111yescharacteristic
1208C2#6237011yescharacteristic
1209C2#6239211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#496C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59679C2semidirect
2. #59639C2semidirect
3. #32533C2semidirect
4. #32532C2semidirect
5. #32529C2semidirect
6. #32525C2semidirect
9. #28548C2semidirect
10. #28547C2semidirect
11. #28285C2semidirect
12. #28280C2semidirect
13. #28029C2semidirect
14. #28027C2semidirect
15. #28013C2semidirect
16. #28010C2semidirect
17. #26334C2semidirect
18. #26332C2semidirect
19. #26331C2semidirect
20. #26328C2semidirect
21. #24697C2semidirect
22. #24692C2semidirect
23. #24689C2semidirect
24. #24688C2semidirect
25. #22819C2semidirect
26. #22817C2semidirect
27. #22730C2semidirect
28. #22729C2semidirect
29. #21731C2semidirect
30. #21713C2semidirect

Maximal subgroups

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

subgroupindex
#596792
#596392
#325332
#325322
#325292
#325252
#287462
#285482
#285472
#282852
#282802
#280292
#280272
#280132
#280102
#263342
#263322
#263312
#263282
#246972
#246922
#246892
#246882
#228192
#228172
#227302
#227292
#217312
#217132
#217012