Finite Group Databasebeta

← #6796354

Subgroups — #6796354

Order 512.

1632 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37859C211yesmaximal, characteristic, complemented
2#37664C211yesmaximal, characteristic
3#33054C211yesmaximal, characteristic, complemented
4#31950C211yesmaximal, characteristic, complemented
5#31844C211yesmaximal, characteristic, complemented
6#31744C211yesmaximal, characteristic, complemented
7#31708C211yesmaximal, characteristic, complemented
8#31357C211yesmaximal, characteristic, complemented
9#31298C211yesmaximal, characteristic, complemented
10#30660C211yesmaximal, characteristic, complemented
11#30543C211yesmaximal, characteristic, complemented
12#29787C211yesmaximal, characteristic, complemented
13#29731C211yesmaximal, characteristic, complemented
14#29175C211yesmaximal, characteristic, complemented
15#28590C211yesmaximal, characteristic, complemented
16#27874C211yesmaximal, characteristic, complemented
17#27541C211yesmaximal, characteristic, complemented
18#27419C211yesmaximal, characteristic, complemented
19#27339C211yesmaximal, characteristic, complemented
20#27100C211yesmaximal, characteristic, complemented
21#26748C211yesmaximal, characteristic, complemented
22#26678C211yesmaximal, characteristic, complemented
23#26631C211yesmaximal, characteristic, complemented
24#25514C211yesmaximal, characteristic, complemented
25#24905C211yesmaximal, characteristic, complemented
26#24561C211yesmaximal, characteristic, complemented
27#24385C211yesmaximal, characteristic
28#21896C211yesmaximal, characteristic, complemented
29#21761C211yesmaximal, characteristic
30#21535C211yesmaximal, characteristic, complemented
31#21053C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C2×#489C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#467C2211yescharacteristic, complemented
39C2×#450C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic, complemented
41C2×#424C2211yescharacteristic, complemented
42C2×#407C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C2×#405C2211yescharacteristic, complemented
45#2848C2211yescharacteristic
46#2848C2211yescharacteristic
47#2745—21no—
48#2739—21no—
49#2736—21no—
50#2735—21no—
51#2701—21no—
52#2691—21no—
53#2686—21no—
54#2672—21no—
55#2628C2211yescharacteristic, complemented
56#2625C2211yescharacteristic, complemented
57#2624C2211yescharacteristic
58#2620C2211yescharacteristic
59#2575—21no—
60#2574—21no—
61#2530—21no—
62#2527—21no—
63#2499C2211yescharacteristic, complemented
64#2497C2211yescharacteristic
65#2494C2211yescharacteristic
66#2492C2211yescharacteristic
67#2491C2211yescharacteristic
68#2480—21no—
69#2440C2211yescharacteristic
70#2439C2211yescharacteristic, complemented
71#2437—21no—
72#2435—21no—
73#2435C2211yescharacteristic
74#2427C2211yescharacteristic
75#2426C2211yescharacteristic
76#2422C2211yescharacteristic
77#2421C2211yescharacteristic
78#2405—21no—
79#2362C2211yescharacteristic, complemented
80#2360C2211yescharacteristic
81#2346C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic, complemented
85#2314C2211yescharacteristic, complemented
86#2280C2211yescharacteristic
87#2280C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2092C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic, complemented
116#2036C2211yescharacteristic, complemented
117#2035C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#2015C2211yescharacteristic, complemented
123#2015C2211yescharacteristic, complemented
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic, complemented
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1990C2211yescharacteristic, complemented
129#1988C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1983C2211yescharacteristic, complemented
132#1983C2211yescharacteristic, complemented
133#1973C2211yescharacteristic, complemented
134#1958C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1925C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1925C2211yescharacteristic, complemented
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1924C2211yescharacteristic, complemented
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic, complemented
153#1923C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic, complemented
167#1892C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1873C2211yescharacteristic, complemented
177#1872C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1809C2211yescharacteristic, complemented
190#1808C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198C4×#107C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic, complemented
201#1729C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#542—24no—
214#542—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#124—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—24no—
235C2×#121—42no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251#489—42no—
252#485—42no—
253#468—24no—
254#468—42no—
255#467—42no—
256#450—42no—
257C4×SD16—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267#424—42no—
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298#407—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
308#405—42no—
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#401—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#391—21no—
354#391—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—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#385—21no—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381D411yescharacteristic
422#381D411yescharacteristic
423#380—21no—
424#380D411yescharacteristic
425#380D411yescharacteristic
426#380D411yescharacteristic
427#380D411yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443#379—21no—
444#379D411yescharacteristic
445#379D411yescharacteristic
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
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#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25C2×D411yescharacteristic
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—44no—
511C22×D4—82no—
512C22×D4—82no—
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
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#126—44no—
564#124—22no—
565#124—41no—
566#124—41no—
567#124—41no—
568#124—44no—
569#124—82no—
570#123—44no—
571#123—82no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—44no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—44no—
592#121—41no—
593#121—41no—
594#121—44no—
595#121#4114yes—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604#117—22no—
605#117—22no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612C2×C4⋊C4—22no—
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—41no—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
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—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—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—22no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728#103—22no—
729#103—22no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762#97—22no—
763#97—41no—
764C4×C8—22no—
765C4×C8—41no—
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#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—22no—
810C24—22no—
811C24—21no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24—41no—
816C24—41no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
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—21no—
838C2×Q8—21no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×D4—24no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—81no—
865C2×D4—82no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—816no—
876C2×D4C2×#4112yes—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
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—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
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×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2×#4112yes—
941C22×C4H(5,𝔽2)12yes—
942C22×C4C2511yescharacteristic
943Q16—82no—
944SD16—44no—
945SD16—82no—
946M16—44no—
947M16—82no—
948C2×C8—21no—
949C2×C8—21no—
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—44no—
972C2×C8—82no—
973C2×C8H(5,𝔽2)12yes—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
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—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4C2×#4112yes—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—24no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—42no—
1082C42—42no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
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—22no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—44no—
1110C23—44no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—82no—
1125C23—82no—
1126C23—82no—
1127C23—84no—
1128C23—84no—
1129C23—82no—
1130C23—82no—
1131C23—84no—
1132C23—84no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23#54612yes—
1137C23#57812yes—
1138C23C23×D411yescharacteristic
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—162no—
1148Q8—162no—
1149D4—22no—
1150D4—22no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—84no—
1158D4—84no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
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—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—82no—
1249C2×C4—82no—
1250C2×C4—82no—
1251C2×C4—84no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4#54612yes—
1255C2×C4C22×#4111yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
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—42no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—41no—
1293C22—88no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22#344911yescharacteristic
1307C22C2×#54611yescharacteristic
1308C22#349611yescharacteristic
1309C22C2×#57811yescharacteristic
1310C22#358411yescharacteristic
1311C22#358511yescharacteristic
1312C22#358511yescharacteristic
1313C4—22no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4#351311yescharacteristic
1339C4#352111yescharacteristic
1340C4#354211yescharacteristic
1341C4#354511yescharacteristic
1342C2—42no—
1343C2—42no—
1344C2—81no—
1345C2—82no—
1346C2—161no—
1347C2#3894411yescharacteristic
1348C2#6098111yescharacteristic
1349C2#6098511yescharacteristic
1350C2#6117311yescharacteristic
1351C2#6117511yescharacteristic
1352C2#6231011yescharacteristic
1353C2#6231211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37859C2semidirect
3. #33054C2semidirect
4. #31950C2semidirect
5. #31844C2semidirect
6. #31744C2semidirect
7. #31708C2semidirect
8. #31357C2semidirect
9. #31298C2semidirect
10. #30660C2semidirect
11. #30543C2semidirect
12. #29787C2semidirect
13. #29731C2semidirect
14. #29175C2semidirect
15. #28590C2semidirect
16. #27874C2semidirect
17. #27541C2semidirect
18. #27419C2semidirect
19. #27339C2semidirect
20. #27100C2semidirect
21. #26748C2semidirect
22. #26678C2semidirect
23. #26631C2semidirect
24. #25514C2semidirect
25. #24905C2semidirect
26. #24561C2semidirect
28. #21896C2semidirect
30. #21535C2semidirect
31. #21053C2semidirect
34. C2×#489C22semidirect
35. C2×#485C22semidirect
38. C2×#467C22semidirect
40. C2×C4×SD16C22semidirect
41. C2×#424C22semidirect
44. C2×#405C22semidirect
55. #2628C22semidirect
56. #2625C22semidirect
63. #2499C22semidirect
70. #2439C22semidirect
79. #2362C22semidirect
81. #2346C22semidirect
84. #2323C22semidirect
85. #2314C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2092C22semidirect
91. #2092C22semidirect
92. #2087C22semidirect
93. #2086C22semidirect
94. #2083C22semidirect
95. #2083C22semidirect
99. #2076C22semidirect
100. #2072C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
103. #2067C22semidirect
104. #2066C22semidirect
105. #2065C22semidirect
106. #2057C22semidirect
107. #2057C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2042C22semidirect
111. #2042C22semidirect
115. #2036C22semidirect
116. #2036C22semidirect
120. #2024C22semidirect
121. #2023C22semidirect
122. #2015C22semidirect
123. #2015C22semidirect
125. #2001C22semidirect
128. #1990C22semidirect
129. #1988C22semidirect
130. #1987C22semidirect
131. #1983C22semidirect
132. #1983C22semidirect
133. #1973C22semidirect
134. #1958C22semidirect
135. #1943C22semidirect
136. #1936C22semidirect
137. #1935C22semidirect
138. #1934C22semidirect
139. #1934C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1928C22semidirect
143. #1925C22semidirect
144. #1925C22semidirect
145. #1925C22semidirect
148. #1924C22semidirect
149. #1924C22semidirect
152. #1923C22semidirect
153. #1923C22semidirect
154. #1921C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
160. #1894C22semidirect
161. #1894C22semidirect
166. #1892C22semidirect
167. #1892C22semidirect
168. #1880C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1877C22semidirect
176. #1873C22semidirect
178. #1863C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
182. #1854C22semidirect
184. #1836C22semidirect
185. #1825C22semidirect
188. #1809C22semidirect
189. #1809C22semidirect
190. #1808C22semidirect
191. #1805C22semidirect
192. #1804C22semidirect
193. #1803C22semidirect
194. #1802C22semidirect
198. C4×#107C22semidirect
199. #1763C22semidirect
200. #1762C22semidirect
201. #1729C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#378592
#376642
#330542
#319502
#318442
#317442
#317082
#313572
#312982
#306602
#305432
#297872
#297312
#291752
#285902
#278742
#275412
#274192
#273392
#271002
#267482
#266782
#266312
#255142
#249052
#245612
#243852
#218962
#217612
#215352
#210532