Finite Group Databasebeta

← #7005147

Subgroups — #7005147

Order 512.

1639 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59016C211yesmaximal, characteristic
2#39605C211yesmaximal, characteristic
3#32114C211yesmaximal, characteristic, complemented
4#32000C211yesmaximal, characteristic, complemented
5#31692C211yesmaximal, characteristic, complemented
6#31608C211yesmaximal, characteristic, complemented
7#31388C211yesmaximal, characteristic, complemented
8#31356C211yesmaximal, characteristic, complemented
9#31263C211yesmaximal, characteristic, complemented
10#31019C211yesmaximal, characteristic, complemented
11#28977C211yesmaximal, characteristic, complemented
12#28553C211yesmaximal, characteristic, complemented
13#28142C211yesmaximal, characteristic, complemented
14#28069C211yesmaximal, characteristic, complemented
15#27697C211yesmaximal, characteristic, complemented
16#27524C211yesmaximal, characteristic, complemented
17#26414C211yesmaximal, characteristic, complemented
18#26302C211yesmaximal, characteristic, complemented
19#26204C211yesmaximal, characteristic, complemented
20#26132C211yesmaximal, characteristic, complemented
21#25545C211yesmaximal, characteristic, complemented
22#25234C211yesmaximal, characteristic, complemented
23#25206C211yesmaximal, characteristic, complemented
24#24906C211yesmaximal, characteristic, complemented
25#24552C211yesmaximal, characteristic, complemented
26#24380C211yesmaximal, characteristic, complemented
27C2×#2076C211yesmaximal, characteristic, complemented
28#23024C211yesmaximal, characteristic, complemented
29#22842C211yesmaximal, characteristic
30#22487C211yesmaximal, characteristic, complemented
31#21759C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#467C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#451C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic, complemented
40C2×C8×D4C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C22×#107C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45#2848C2211yescharacteristic
46#2788—21no—
47#2784—21no—
48#2780—21no—
49#2768—21no—
50#2704—21no—
51#2692—21no—
52#2626—21no—
53#2563C2211yescharacteristic
54#2549—21no—
55#2538C2211yescharacteristic
56#2538C2211yescharacteristic
57#2505—21no—
58#2502C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2492C2211yescharacteristic
62#2492C2211yescharacteristic
63#2487C2211yescharacteristic
64#2473—21no—
65#2450—21no—
66#2450—21no—
67#2440C2211yescharacteristic
68#2440C2211yescharacteristic
69#2437—21no—
70#2423C2211yescharacteristic
71#2423C2211yescharacteristic
72#2417—21no—
73#2417C2211yescharacteristic
74#2417C2211yescharacteristic
75#2417C2211yescharacteristic
76#2417C2211yescharacteristic
77#2409C2211yescharacteristic
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80#2358—21no—
81D4×C4⋊C4C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83Q8×C22⋊C4C2211yescharacteristic
84#2321—21no—
85C4×#120C2211yescharacteristic
86C2×#380C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2095C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic, complemented
107#2076C2211yescharacteristic, complemented
108#2072C2211yescharacteristic, complemented
109#2072C2211yescharacteristic, complemented
110#2068C2211yescharacteristic, complemented
111#2068C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2056C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2024C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic, complemented
127#2001C2211yescharacteristic, complemented
128#1990C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1987C2211yescharacteristic, complemented
132#1969C2211yescharacteristic, complemented
133#1954C2211yescharacteristic
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1933C2211yescharacteristic, complemented
137#1933C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1923C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic
150#1892C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1892C2211yescharacteristic, complemented
158#1892C2211yescharacteristic, complemented
159#1878C2211yescharacteristic, complemented
160#1878C2211yescharacteristic, complemented
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1872C2211yescharacteristic
165#1872C2211yescharacteristic
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1869C2211yescharacteristic
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic
172#1863C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic, complemented
179#1852C2211yescharacteristic, complemented
180#1850C2211yescharacteristic
181#1850C2211yescharacteristic
182#1834C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic
186#1824C2211yescharacteristic, complemented
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1787C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195C4×#107C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C8×C22⋊C4C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#554—24no—
213#554—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—24no—
224C2×C22⋊Q8—42no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#120D411yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C22×C4⋊C4—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#484—42no—
257#484—42no—
258#467—24no—
259#467—42no—
260#451—42no—
261C4×Q16—42no—
262C8×D4—42no—
263C8×D4—42no—
264C2×#107—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×C22⋊C8—42no—
299C2×C22⋊C8—42no—
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386D411yescharacteristic
394#386D411yescharacteristic
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385D411yescharacteristic
412#385D411yescharacteristic
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#382—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379D411yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C2×#95—21no—
454C2×#95—21no—
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
493C25C2×D411yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#125—44no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—44no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—82no—
588C22⋊Q8—82no—
589C22⋊Q8#4114yes—
590#120Q1618yescomplemented
591C4×Q8—22no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—44no—
604C4×D4—82no—
605C4×D4—82no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
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—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—22no—
723#107—22no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C4×C8—22no—
766C4×C8—41no—
767C4×C8—41no—
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#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809C24—22no—
810C24—22no—
811C24—41no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24C2×Q1614yes—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—82no—
847C2×Q8—82no—
848C2×Q8—82no—
849C2×Q8—82no—
850C2×Q8C2×#4112yes—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4C2×Q1614yes—
858C2×D4C2×Q1614yes—
859C2×D4C2×Q1614yes—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—82no—
917C22×C4—82no—
918C22×C4—82no—
919C22×C4—82no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
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×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
946C22×C4H(5,𝔽2)12yes—
947C22×C4C2511yescharacteristic
948Q16—44no—
949Q16—82no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
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—44no—
974C2×C8—82no—
975C2×C8—82no—
976C2×C8—82no—
977C2×C8—82no—
978C2×C8H(5,𝔽2)12yes—
979C4⋊C4—24no—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
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—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4C2×#4112yes—
1044C22⋊C4—24no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4C2×Q1614yes—
1078C22⋊C4C2×Q1614yes—
1079C22⋊C4C2×Q1614yes—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—28no—
1115C23—44no—
1116C23—44no—
1117C23—82no—
1118C23—82no—
1119C23—82no—
1120C23—82no—
1121C23#54612yes—
1122C23C22×Q1612yes—
1123C23C22×Q1612yes—
1124C23C22×Q1612yes—
1125C23C22×Q1612yes—
1126C23#57712yes—
1127C23C23×D411yescharacteristic
1128Q8—22no—
1129Q8—22no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—84no—
1141Q8—162no—
1142Q8—162no—
1143D4—28no—
1144D4—44no—
1145D4—44no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—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—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—82no—
1237C2×C4—82no—
1238C2×C4—82no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4#54612yes—
1248C2×C4C22×Q1612yes—
1249C2×C4C22×Q1612yes—
1250C2×C4C22×Q1612yes—
1251C2×C4C22×#4111yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4C2×H(5,𝔽2)11yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C2×C4#58511yescharacteristic
1257C8—22no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—88no—
1293C22#329914yes—
1294C22C2×#54611yescharacteristic
1295C22#348511yescharacteristic
1296C22#349611yescharacteristic
1297C22C23×Q1611yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358411yescharacteristic
1300C22#358511yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4#351311yescharacteristic
1328C4#352111yescharacteristic
1329C4#355811yescharacteristic
1330C4#356011yescharacteristic
1331C2—24no—
1332C2—42no—
1333C2—42no—
1334C2—42no—
1335C2#4302111yescharacteristic
1336C2C2×#329911yescharacteristic
1337C2#6119511yescharacteristic
1338C2#6169811yescharacteristic
1339C2#6177011yescharacteristic
1340C2#6224611yescharacteristic
1341C2#6231911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32114C2semidirect
4. #32000C2semidirect
5. #31692C2semidirect
6. #31608C2semidirect
7. #31388C2semidirect
8. #31356C2semidirect
9. #31263C2semidirect
10. #31019C2semidirect
11. #28977C2semidirect
12. #28553C2semidirect
13. #28142C2semidirect
14. #28069C2semidirect
15. #27697C2semidirect
16. #27524C2semidirect
17. #26414C2semidirect
18. #26302C2semidirect
19. #26204C2semidirect
20. #26132C2semidirect
21. #25545C2semidirect
22. #25234C2semidirect
23. #25206C2semidirect
24. #24906C2semidirect
25. #24552C2semidirect
26. #24380C2semidirect
27. C2×#2076C2semidirect
28. #23024C2semidirect
30. #22487C2semidirect
31. #21759C2semidirect
35. C2×#484C22semidirect
39. C2×C4×Q16C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
91. #2095C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2083C22semidirect
95. #2083C22semidirect
106. #2076C22semidirect
107. #2076C22semidirect
108. #2072C22semidirect
109. #2072C22semidirect
110. #2068C22semidirect
111. #2068C22semidirect
112. #2057C22semidirect
113. #2056C22semidirect
114. #2056C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
121. #2024C22semidirect
122. #2024C22semidirect
123. #2024C22semidirect
126. #2001C22semidirect
127. #2001C22semidirect
128. #1990C22semidirect
129. #1990C22semidirect
130. #1987C22semidirect
131. #1987C22semidirect
132. #1969C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
136. #1933C22semidirect
137. #1933C22semidirect
138. #1933C22semidirect
139. #1933C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1928C22semidirect
143. #1928C22semidirect
146. #1921C22semidirect
147. #1921C22semidirect
156. #1892C22semidirect
157. #1892C22semidirect
158. #1892C22semidirect
159. #1878C22semidirect
160. #1878C22semidirect
167. #1872C22semidirect
168. #1872C22semidirect
172. #1863C22semidirect
173. #1863C22semidirect
174. #1863C22semidirect
175. #1863C22semidirect
178. #1852C22semidirect
179. #1852C22semidirect
182. #1834C22semidirect
186. #1824C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
191. #1803C22semidirect
195. C4×#107C22semidirect
196. C4×#103C22semidirect
202. C2×#340C22semidirect
590. #120Q16semidirect

Maximal subgroups

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

subgroupindex
#590162
#396052
#321142
#320002
#316922
#316082
#313882
#313562
#312632
#310192
#289772
#285532
#281422
#280692
#276972
#275242
#264142
#263022
#262042
#261322
#255452
#252342
#252062
#249062
#245522
#243802
C2×#20762
#230242
#228422
#224872
#217592