Finite Group Databasebeta

← #6605803

Subgroups — #6605803

Order 512.

1687 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36386C211yesmaximal, characteristic
2#36363C211yesmaximal, characteristic, complemented
3#33288C211yesmaximal, characteristic, complemented
4#33053C211yesmaximal, characteristic, complemented
5#33051C211yesmaximal, characteristic, complemented
6#29352C211yesmaximal, characteristic, complemented
7#29339C211yesmaximal, characteristic, complemented
8#29335C211yesmaximal, characteristic, complemented
9#29128C211yesmaximal, characteristic, complemented
10#29113C211yesmaximal, characteristic, complemented
11#29110C211yesmaximal, characteristic, complemented
12#27819C211yesmaximal, characteristic, complemented
13#27774C211yesmaximal, characteristic, complemented
14#27754C211yesmaximal, characteristic, complemented
15#27733C211yesmaximal, characteristic, complemented
16#27718C211yesmaximal, characteristic, complemented
17#27713C211yesmaximal, characteristic, complemented
18#27713C211yesmaximal, characteristic, complemented
19#27712C211yesmaximal, characteristic, complemented
20#27267C211yesmaximal, characteristic, complemented
21#27265C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27262C211yesmaximal, characteristic, complemented
24#22486C211yesmaximal, characteristic, complemented
25#22486C211yesmaximal, characteristic, complemented
26#22414C211yesmaximal, characteristic
27#22414C211yesmaximal, characteristic
28C4×#489C211yesmaximal, characteristic, complemented
29#21086C211yesmaximal, characteristic, complemented
30C2×#1936C211yesmaximal, characteristic, complemented
31D4×#97C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C2×#416C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#97C2211yescharacteristic
44C22×#97C2211yescharacteristic, complemented
45#2864C2211yescharacteristic, complemented
46#2861C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic, complemented
49#2851C2211yescharacteristic
50#2850C2211yescharacteristic
51#2586—21no—
52#2585—21no—
53#2570C2211yescharacteristic, complemented
54#2566C2211yescharacteristic
55#2559—21no—
56#2559—21no—
57#2558—21no—
58#2558—21no—
59#2550C2211yescharacteristic, complemented
60#2545C2211yescharacteristic
61#2534—21no—
62#2534—21no—
63#2522—21no—
64#2503C2211yescharacteristic
65#2500C2211yescharacteristic
66#2465—21no—
67#2450—21no—
68#2449—21no—
69#2441C2211yescharacteristic, complemented
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2439C2211yescharacteristic, complemented
73#2435C2211yescharacteristic
74#2432C2211yescharacteristic
75#2368—21no—
76#2360—21no—
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2342—21no—
80#2342—21no—
81C4×C4⋊Q8C2211yescharacteristic, complemented
82C4×#124C2211yescharacteristic
83#2297C2211yescharacteristic
84#2296C2211yescharacteristic, complemented
85C2×#390C2211yescharacteristic
86C2×#389C2211yescharacteristic
87C42×D4C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2043C2211yescharacteristic, complemented
101#2043C2211yescharacteristic, complemented
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2025C2211yescharacteristic
107#2025C2211yescharacteristic
108#2024C2211yescharacteristic, complemented
109#2024C2211yescharacteristic, complemented
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#1993C2211yescharacteristic, complemented
113#1993C2211yescharacteristic, complemented
114#1992C2211yescharacteristic, complemented
115#1991C2211yescharacteristic, complemented
116#1991C2211yescharacteristic, complemented
117#1989C2211yescharacteristic, complemented
118#1989C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1960C2211yescharacteristic, complemented
122#1959C2211yescharacteristic
123#1959C2211yescharacteristic
124#1958C2211yescharacteristic
125#1958C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic, complemented
161#1892C2211yescharacteristic, complemented
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1873C2211yescharacteristic, complemented
165#1873C2211yescharacteristic, complemented
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1836C2211yescharacteristic, complemented
171#1836C2211yescharacteristic, complemented
172#1836C2211yescharacteristic, complemented
173#1825C2211yescharacteristic, complemented
174#1825C2211yescharacteristic, complemented
175#1823C2211yescharacteristic
176#1823C2211yescharacteristic
177#1805C2211yescharacteristic, complemented
178#1805C2211yescharacteristic, complemented
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1770C2211yescharacteristic, complemented
186#1770C2211yescharacteristic, complemented
187#1767C2211yescharacteristic, complemented
188C4×#103C2211yescharacteristic, complemented
189C4×#103C2211yescharacteristic, complemented
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195#1752C2211yescharacteristic, complemented
196#1749C2211yescharacteristic
197#1749C2211yescharacteristic, complemented
198#1735C2211yescharacteristic, complemented
199#1735C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#552—24no—
210#552—24no—
211#546—24no—
212#546—24no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4D411yescharacteristic
237C2×C4×D4D411yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C4⋊C4—21no—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253#491—42no—
254#489—24no—
255#489—42no—
256C8×D4—24no—
257C8×D4—24no—
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#416—24no—
261#416—42no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102—24no—
279C2×#102—42no—
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×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97—42no—
301C2×#97—42no—
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#393—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#381—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4D411yescharacteristic
437C4×C4⋊C4D411yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C2×#95—21no—
454C43C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—22no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#126—44no—
554#125—22no—
555#125—22no—
556#125—41no—
557#125—41no—
558#125—44no—
559#124—22no—
560#124—22no—
561#124—22no—
562#124—41no—
563#124—41no—
564#124—41no—
565#123—44no—
566#123—44no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—82no—
576#121—22no—
577#121—22no—
578#121—44no—
579#120—44no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—82no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—42no—
586C4×D4—42no—
587C4×D4#4114yes—
588C4×D4#4114yes—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—41no—
593#117—44no—
594#117—41no—
595#117—41no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—82no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
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—44no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C4⋊C8—22no—
712C4⋊C8—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
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#4114yes—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749#97—22no—
750#97—22no—
751#97—22no—
752#97—22no—
753#97—41no—
754#97—41no—
755#97—41no—
756#97—41no—
757#97—41no—
758#97—41no—
759C4×C8—22no—
760C4×C8—22no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812#41—44no—
813#41—44no—
814#41—82no—
815#41—82no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—42no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—21no—
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—44no—
848C2×D4—44no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4#12414yes—
861C2×D4C2×#4112yes—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2511yescharacteristic
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—44no—
951C2×C8—44no—
952C2×C8—44no—
953C2×C8—44no—
954C2×C8C2×#4112yes—
955C2×C8H(5,𝔽2)12yes—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
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#12414yes—
1013C4⋊C4C2×#4112yes—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—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—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#12414yes—
1049C22⋊C4#12414yes—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—41no—
1059C42—41no—
1060C42—41no—
1061C42—41no—
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42C2×#4112yes—
1073C42C2×#4112yes—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—84no—
1099C23—84no—
1100C23—84no—
1101C23—84no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23C2×#12412yes—
1106C23C2×#12412yes—
1107C23#57512yes—
1108C23#57512yes—
1109C23C23×D411yescharacteristic
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—84no—
1119Q8—162no—
1120D4—28no—
1121D4—22no—
1122D4—22no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—84no—
1130D4—84no—
1131D4—162no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
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—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—84no—
1215C2×C4—82no—
1216C2×C4—82no—
1217C2×C4—82no—
1218C2×C4—82no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4C2×#12412yes—
1224C2×C4C2×#12412yes—
1225C2×C4C2×#12412yes—
1226C2×C4C2×#12412yes—
1227C2×C4C22×#4111yescharacteristic
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C8—22no—
1234C8—22no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—168no—
1269C22#313514yes—
1270C22C22×#12411yescharacteristic
1271C22D4×#4111yescharacteristic
1272C22#349611yescharacteristic
1273C22C2×#57511yescharacteristic
1274C22C2×#57511yescharacteristic
1275C22#358511yescharacteristic
1276C22#358611yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4#347511yescharacteristic
1304C4#348111yescharacteristic
1305C4#351311yescharacteristic
1306C4#352111yescharacteristic
1307C2—24no—
1308C2—42no—
1309C2—82no—
1310C2—161no—
1311C2#3623811yescharacteristic
1312C2C2×#313511yescharacteristic
1313C2#6062511yescharacteristic
1314C2#6145411yescharacteristic
1315C2#6145511yescharacteristic
1316C2#6229711yescharacteristic
1317C2#6230111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36363C2semidirect
3. #33288C2semidirect
4. #33053C2semidirect
5. #33051C2semidirect
6. #29352C2semidirect
7. #29339C2semidirect
8. #29335C2semidirect
9. #29128C2semidirect
10. #29113C2semidirect
11. #29110C2semidirect
12. #27819C2semidirect
13. #27774C2semidirect
14. #27754C2semidirect
15. #27733C2semidirect
16. #27718C2semidirect
17. #27713C2semidirect
18. #27713C2semidirect
19. #27712C2semidirect
20. #27267C2semidirect
21. #27265C2semidirect
22. #27262C2semidirect
23. #27262C2semidirect
24. #22486C2semidirect
25. #22486C2semidirect
28. C4×#489C2semidirect
29. #21086C2semidirect
30. C2×#1936C2semidirect
31. D4×#97C2semidirect
34. C2×#491C22semidirect
44. C22×#97C22semidirect
45. #2864C22semidirect
48. #2857C22semidirect
53. #2570C22semidirect
59. #2550C22semidirect
69. #2441C22semidirect
72. #2439C22semidirect
81. C4×C4⋊Q8C22semidirect
84. #2296C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
93. #2099C22semidirect
96. #2072C22semidirect
97. #2072C22semidirect
100. #2043C22semidirect
101. #2043C22semidirect
108. #2024C22semidirect
109. #2024C22semidirect
112. #1993C22semidirect
113. #1993C22semidirect
114. #1992C22semidirect
115. #1991C22semidirect
116. #1991C22semidirect
117. #1989C22semidirect
118. #1989C22semidirect
121. #1960C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
160. #1892C22semidirect
161. #1892C22semidirect
164. #1873C22semidirect
165. #1873C22semidirect
170. #1836C22semidirect
171. #1836C22semidirect
172. #1836C22semidirect
173. #1825C22semidirect
174. #1825C22semidirect
177. #1805C22semidirect
178. #1805C22semidirect
185. #1770C22semidirect
186. #1770C22semidirect
187. #1767C22semidirect
188. C4×#103C22semidirect
189. C4×#103C22semidirect
194. #1752C22semidirect
195. #1752C22semidirect
197. #1749C22semidirect
198. #1735C22semidirect
199. #1735C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#363862
#363632
#332882
#330532
#330512
#293522
#293392
#293352
#291282
#291132
#291102
#278192
#277742
#277542
#277332
#277182
#277132
#277122
#272672
#272652
#272622
#224862
#224142
C4×#4892
#210862
C2×#19362
D4×#972