Finite Group Databasebeta

← #7018543

Subgroups — #7018543

Order 512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59198C211yesmaximal, characteristic
2#59016C211yesmaximal, characteristic
3#32280C211yesmaximal, characteristic, complemented
4#32280C211yesmaximal, characteristic, complemented
5#31998C211yesmaximal, characteristic, complemented
6#31772C211yesmaximal, characteristic, complemented
7#31772C211yesmaximal, characteristic, complemented
8#31320C211yesmaximal, characteristic, complemented
9#31089C211yesmaximal, characteristic, complemented
10#30777C211yesmaximal, characteristic, complemented
11#28098C211yesmaximal, characteristic, complemented
12#27601C211yesmaximal, characteristic, complemented
13#27328C211yesmaximal, characteristic, complemented
14#27160C211yesmaximal, characteristic, complemented
15#27098C211yesmaximal, characteristic, complemented
16#27034C211yesmaximal, characteristic, complemented
17#26128C211yesmaximal, characteristic, complemented
18#26060C211yesmaximal, characteristic, complemented
19#25990C211yesmaximal, characteristic, complemented
20#25955C211yesmaximal, characteristic, complemented
21#25702C211yesmaximal, characteristic, complemented
22#25014C211yesmaximal, characteristic, complemented
23#24937C211yesmaximal, characteristic, complemented
24#24863C211yesmaximal, characteristic, complemented
25#24097C211yesmaximal, characteristic, complemented
26#24003C211yesmaximal, characteristic, complemented
27C2×#2035C211yesmaximal, characteristic, complemented
28D4×#106C211yesmaximal, characteristic, complemented
29#22571C211yesmaximal, characteristic, complemented
30#22028C211yesmaximal, characteristic
31#21938C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#551—21no—
34C22×C22⋊Q8C2211yescharacteristic
35C2×#498C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#483C2211yescharacteristic, complemented
39C2×#475C2211yescharacteristic, complemented
40C2×C8×D4C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#106C2211yescharacteristic, complemented
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46#2722—21no—
47#2717—21no—
48#2704—21no—
49#2692—21no—
50#2549—21no—
51#2547C2211yescharacteristic
52#2538C2211yescharacteristic
53#2502C2211yescharacteristic
54#2496C2211yescharacteristic
55#2496C2211yescharacteristic
56#2492C2211yescharacteristic
57#2486C2211yescharacteristic
58#2486C2211yescharacteristic
59#2486C2211yescharacteristic
60#2483—21no—
61#2473—21no—
62#2450—21no—
63#2440C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2438—21no—
67#2438—21no—
68#2437—21no—
69#2423C2211yescharacteristic
70#2419—21no—
71#2419—21no—
72#2417—21no—
73#2417C2211yescharacteristic
74#2417C2211yescharacteristic
75#2409C2211yescharacteristic
76#2360C2211yescharacteristic
77#2358—21no—
78D4×C4⋊C4C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2344C2211yescharacteristic
82#2344C2211yescharacteristic
83Q8×C22⋊C4C2211yescharacteristic
84C4×#120C2211yescharacteristic
85C2×#380C2211yescharacteristic
86C2×#380C2211yescharacteristic
87C2×#380C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2058C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2035C2211yescharacteristic, complemented
126#2035C2211yescharacteristic, complemented
127#2024C2211yescharacteristic, complemented
128#1987C2211yescharacteristic, complemented
129#1954C2211yescharacteristic
130#1954C2211yescharacteristic
131#1948C2211yescharacteristic, complemented
132#1948C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1933C2211yescharacteristic, complemented
137#1933C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1923C2211yescharacteristic
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic
147#1923C2211yescharacteristic
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1892C2211yescharacteristic, complemented
153#1892C2211yescharacteristic, complemented
154#1872C2211yescharacteristic
155#1872C2211yescharacteristic
156#1872C2211yescharacteristic, complemented
157#1869C2211yescharacteristic
158#1869C2211yescharacteristic
159#1869C2211yescharacteristic
160#1865C2211yescharacteristic, complemented
161#1865C2211yescharacteristic, complemented
162#1865C2211yescharacteristic, complemented
163#1865C2211yescharacteristic, complemented
164#1853C2211yescharacteristic
165#1853C2211yescharacteristic
166#1853C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1853C2211yescharacteristic
174#1853C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1850C2211yescharacteristic
182#1844C2211yescharacteristic, complemented
183#1844C2211yescharacteristic, complemented
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic
186#1824C2211yescharacteristic, complemented
187#1823C2211yescharacteristic
188#1823C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1779C2211yescharacteristic
198C4×#106C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#554—42no—
209#554—42no—
210#551—48no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#124—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—42no—
228C2×C22⋊Q8—42no—
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×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261#498—42no—
262#483—42no—
263#483—42no—
264#483—42no—
265#475—42no—
266C8×D4—24no—
267C2×#106—42no—
268C2×#106—42no—
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×#103—24no—
293C2×#103—42no—
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×C22⋊C8—24no—
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#395—21no—
355#395—21no—
356#395—21no—
357#393—21no—
358#393—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386D411yescharacteristic
395#386D411yescharacteristic
396#386D411yescharacteristic
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#385D411yescharacteristic
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379D411yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C2×#95—21no—
458C2×#95—21no—
459C2×#95—21no—
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#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25C2×D411yescharacteristic
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
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—21no—
520C23×C4—21no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4—41no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8#4114yes—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C4⋊Q8—22no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#126—44no—
554#126—44no—
555#125—44no—
556#124—44no—
557#123—44no—
558#123—44no—
559#123—44no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—82no—
579#120SD1618yes—
580C4×Q8—22no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—82no—
594#117—44no—
595#117—44no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
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—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—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—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4—44no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#106—22no—
715#106—22no—
716#106—22no—
717#106—22no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106—41no—
733#106—41no—
734C4⋊C8—22no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C4×C8—22no—
767C4×C8—41no—
768C4×C8—41no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—22no—
812C24—22no—
813C24—41no—
814C24—41no—
815C24—41no—
816C24—41no—
817C24C2×SD1614yes—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
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—42no—
834C2×Q8—42no—
835C2×Q8—44no—
836C2×Q8—44no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—82no—
845C2×Q8—82no—
846C2×Q8H(5,𝔽2)12yes—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4C2×SD1614yes—
854C2×D4C2×SD1614yes—
855C2×D4C2×SD1614yes—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
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—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—22no—
882C22×C4—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
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—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—82no—
920C22×C4—82no—
921C22×C4—82no—
922C22×C4—82no—
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×C4—81no—
936C22×C4—81no—
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C2×#4112yes—
948C22×C42−1+412yes—
949C22×C4C2511yescharacteristic
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—44no—
973C2×C8—44no—
974C2×C8—82no—
975C2×C8C2×#4112yes—
976C2×C8C2×#4112yes—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—21no—
980C4⋊C4—21no—
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—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1043C22⋊C4—24no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
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—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4C2×SD1614yes—
1075C22⋊C4C2×SD1614yes—
1076C22⋊C4C2×SD1614yes—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
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—28no—
1112C23—44no—
1113C23—44no—
1114C23—82no—
1115C23—82no—
1116C23—82no—
1117C23—82no—
1118C23#54712yes—
1119C23C22×SD1612yes—
1120C23C22×SD1612yes—
1121C23C22×SD1612yes—
1122C23C22×SD1612yes—
1123C23#57712yes—
1124C23C23×D411yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—84no—
1134Q8—162no—
1135Q8—162no—
1136D4—28no—
1137D4—44no—
1138D4—44no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
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—41no—
1172C2×C4—41no—
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—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—82no—
1230C2×C4—82no—
1231C2×C4—82no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4#54712yes—
1243C2×C4C22×SD1612yes—
1244C2×C4C22×SD1612yes—
1245C2×C4C22×SD1612yes—
1246C2×C4C22×#4111yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×2−1+411yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C8—22no—
1253C8—22no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—88no—
1288C22#333514yes—
1289C22C2×#54711yescharacteristic
1290C22#348411yescharacteristic
1291C22#348511yescharacteristic
1292C22C23×SD1611yescharacteristic
1293C22C2×#57711yescharacteristic
1294C22#358611yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#349411yescharacteristic
1323C4#350511yescharacteristic
1324C4#353511yescharacteristic
1325C4#356111yescharacteristic
1326C2—24no—
1327C2—42no—
1328C2—42no—
1329C2—42no—
1330C2#4305311yescharacteristic
1331C2C2×#333511yescharacteristic
1332C2#6126911yescharacteristic
1333C2#6156211yescharacteristic
1334C2#6161811yescharacteristic
1335C2#6169511yescharacteristic
1336C2#6175511yescharacteristic
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. #32280C2semidirect
4. #32280C2semidirect
5. #31998C2semidirect
6. #31772C2semidirect
7. #31772C2semidirect
8. #31320C2semidirect
9. #31089C2semidirect
10. #30777C2semidirect
11. #28098C2semidirect
12. #27601C2semidirect
13. #27328C2semidirect
14. #27160C2semidirect
15. #27098C2semidirect
16. #27034C2semidirect
17. #26128C2semidirect
18. #26060C2semidirect
19. #25990C2semidirect
20. #25955C2semidirect
21. #25702C2semidirect
22. #25014C2semidirect
23. #24937C2semidirect
24. #24863C2semidirect
25. #24097C2semidirect
26. #24003C2semidirect
27. C2×#2035C2semidirect
28. D4×#106C2semidirect
29. #22571C2semidirect
31. #21938C2semidirect
35. C2×#498C22semidirect
38. C2×#483C22semidirect
39. C2×#475C22semidirect
42. C22×#106C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2096C22semidirect
91. #2096C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
96. #2084C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2072C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2058C22semidirect
109. #2058C22semidirect
110. #2058C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
125. #2035C22semidirect
126. #2035C22semidirect
127. #2024C22semidirect
128. #1987C22semidirect
131. #1948C22semidirect
132. #1948C22semidirect
133. #1948C22semidirect
134. #1941C22semidirect
135. #1941C22semidirect
136. #1933C22semidirect
137. #1933C22semidirect
138. #1933C22semidirect
139. #1933C22semidirect
140. #1927C22semidirect
141. #1927C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1892C22semidirect
153. #1892C22semidirect
156. #1872C22semidirect
160. #1865C22semidirect
161. #1865C22semidirect
162. #1865C22semidirect
163. #1865C22semidirect
178. #1853C22semidirect
179. #1853C22semidirect
180. #1853C22semidirect
182. #1844C22semidirect
183. #1844C22semidirect
186. #1824C22semidirect
193. #1807C22semidirect
194. #1803C22semidirect
198. C4×#106C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#591982
#590162
#322802
#319982
#317722
#313202
#310892
#307772
#280982
#276012
#273282
#271602
#270982
#270342
#261282
#260602
#259902
#259552
#257022
#250142
#249372
#248632
#240972
#240032
C2×#20352
D4×#1062
#225712
#220282
#219382