Finite Group Databasebeta

← #6843719

Subgroups — #6843719

Order 512.

1581 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40094C211yesmaximal, characteristic, complemented
2#40044C211yesmaximal, characteristic
3#33128C211yesmaximal, characteristic, complemented
4#32527C211yesmaximal, characteristic, complemented
5#32459C211yesmaximal, characteristic, complemented
6#31332C211yesmaximal, characteristic, complemented
7#31326C211yesmaximal, characteristic, complemented
8#31243C211yesmaximal, characteristic, complemented
9#31058C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#30403C211yesmaximal, characteristic, complemented
12#30019C211yesmaximal, characteristic, complemented
13#30017C211yesmaximal, characteristic, complemented
14#29078C211yesmaximal, characteristic, complemented
15#29076C211yesmaximal, characteristic, complemented
16#28095C211yesmaximal, characteristic, complemented
17#28094C211yesmaximal, characteristic, complemented
18#28067C211yesmaximal, characteristic, complemented
19#28063C211yesmaximal, characteristic, complemented
20#27227C211yesmaximal, characteristic, complemented
21#27225C211yesmaximal, characteristic, complemented
22#27037C211yesmaximal, characteristic, complemented
23#27031C211yesmaximal, characteristic, complemented
24#25343C211yesmaximal, characteristic, complemented
25#25342C211yesmaximal, characteristic, complemented
26#25114C211yesmaximal, characteristic, complemented
27#25112C211yesmaximal, characteristic, complemented
28#22875C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic, complemented
30C4×#465C211yesmaximal, characteristic, complemented
31C8×#121C211yesmaximal, characteristic, complemented
32C2×#479C2211yescharacteristic, complemented
33C2×#478C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#448C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C2×C8×D4C2211yescharacteristic, complemented
44C22×#103C2211yescharacteristic, complemented
45C22×#102C2211yescharacteristic
46C22×C4×C8C2211yescharacteristic, complemented
47#2855C2211yescharacteristic, complemented
48#2854C2211yescharacteristic
49#2788—21no—
50#2778—21no—
51#2778—21no—
52#2770—21no—
53#2745—21no—
54#2735—21no—
55#2708—21no—
56#2668—21no—
57#2666—21no—
58#2649—21no—
59#2576—21no—
60#2572—21no—
61#2562C2211yescharacteristic
62#2562C2211yescharacteristic, complemented
63#2536C2211yescharacteristic
64#2535C2211yescharacteristic
65#2514C2211yescharacteristic, complemented
66#2513C2211yescharacteristic
67#2495C2211yescharacteristic, complemented
68#2494C2211yescharacteristic
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic
71#2487C2211yescharacteristic
72#2486C2211yescharacteristic
73#2456—21no—
74#2454C2211yescharacteristic
75#2453C2211yescharacteristic, complemented
76#2418—21no—
77#2417C2211yescharacteristic
78#2416C2211yescharacteristic
79#2409C2211yescharacteristic
80#2409C2211yescharacteristic, complemented
81#2408C2211yescharacteristic
82#2408C2211yescharacteristic
83#2361C2211yescharacteristic
84#2360C2211yescharacteristic
85Q8×C22⋊C4C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2335—21no—
88#2321—21no—
89C4×C22⋊Q8C2211yescharacteristic, complemented
90C4×#121C2211yescharacteristic
91C4×#121C2211yescharacteristic
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2075C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1991C2211yescharacteristic, complemented
133#1991C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1954C2211yescharacteristic
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic, complemented
171#1892C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1824C2211yescharacteristic, complemented
187#1823C2211yescharacteristic
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic, complemented
190#1807C2211yescharacteristic, complemented
191#1807C2211yescharacteristic, complemented
192#1797C2211yescharacteristic, complemented
193#1787C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121—21no—
222C2×#121D411yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#479—42no—
243#478—42no—
244#465—24no—
245#465—42no—
246#450—24no—
247#450—42no—
248#448—24no—
249#448—42no—
250C4×SD16—42no—
251C8×D4—42no—
252C8×D4—42no—
253C8×D4—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102—42no—
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C4×C8—42no—
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#401—21no—
312#401—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—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#393—21no—
347#393—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390D411yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389D411yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
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#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386D411yescharacteristic
416#386D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#383—21no—
426#383—21no—
427#382—21no—
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380D411yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16#4114yes—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#123—44no—
566#123—82no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575#121—24no—
576#121—22no—
577#121—22no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—82no—
585#120—44no—
586#120—82no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—82no—
602C4×D4—82no—
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—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—22no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—22no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C4×C8—22no—
752C4×C8—22no—
753C4×C8—41no—
754C4×C8—41no—
755C4×C8—41no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—42no—
806C24—42no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24C22×D411yescharacteristic
813C24C22×D411yescharacteristic
814C24C22×D411yescharacteristic
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—42no—
827C2×Q8—44no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—82no—
831C2×Q8—82no—
832C2×Q8—82no—
833C2×Q8C2×#4112yes—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4#13514yes—
873C2×D4C2×#4112yes—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—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—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—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
939SD16—44no—
940SD16—82no—
941SD16—82no—
942SD16—82no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
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—44no—
965C2×C8—44no—
966C2×C8—82no—
967C2×C8—82no—
968C2×C8C2×#4112yes—
969C2×C8H(5,𝔽2)12yes—
970C2×C8H(5,𝔽2)12yes—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
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—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
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—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
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—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—41no—
1073C42—41no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23C2×#13512yes—
1120C23C2×#13512yes—
1121C23#57712yes—
1122C23C23×D411yescharacteristic
1123Q8—22no—
1124Q8—22no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—84no—
1132D4—22no—
1133D4—22no—
1134D4—44no—
1135D4—44no—
1136D4—44no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—162no—
1147D4—162no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—44no—
1181C2×C4—44no—
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—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4C2×#13512yes—
1241C2×C4#57712yes—
1242C2×C4C22×#4111yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C8—22no—
1249C8—22no—
1250C8—22no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—168no—
1292C22D4×#4111yescharacteristic
1293C22#349611yescharacteristic
1294C22#349611yescharacteristic
1295C22C22×#13511yescharacteristic
1296C22C2×#57711yescharacteristic
1297C22C2×#57711yescharacteristic
1298C22#358411yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#345911yescharacteristic
1325C4#351411yescharacteristic
1326C4#353411yescharacteristic
1327C4#356811yescharacteristic
1328C2—42no—
1329C2—42no—
1330C2—42no—
1331C2—82no—
1332C2—161no—
1333C2#3945211yescharacteristic
1334C2#6143211yescharacteristic
1335C2#6149011yescharacteristic
1336C2#6224711yescharacteristic
1337C2#6225011yescharacteristic
1338C2#6226811yescharacteristic
1339C2#6233911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#40044C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40094C2semidirect
3. #33128C2semidirect
4. #32527C2semidirect
5. #32459C2semidirect
6. #31332C2semidirect
7. #31326C2semidirect
8. #31243C2semidirect
9. #31058C2semidirect
10. #30408C2semidirect
11. #30403C2semidirect
12. #30019C2semidirect
13. #30017C2semidirect
14. #29078C2semidirect
15. #29076C2semidirect
16. #28095C2semidirect
17. #28094C2semidirect
18. #28067C2semidirect
19. #28063C2semidirect
20. #27227C2semidirect
21. #27225C2semidirect
22. #27037C2semidirect
23. #27031C2semidirect
24. #25343C2semidirect
25. #25342C2semidirect
26. #25114C2semidirect
27. #25112C2semidirect
28. #22875C2semidirect
29. #22874C2semidirect
30. C4×#465C2semidirect
31. C8×#121C2semidirect
32. C2×#479C22semidirect
43. C2×C8×D4C22semidirect
44. C22×#103C22semidirect
46. C22×C4×C8C22semidirect
47. #2855C22semidirect
62. #2562C22semidirect
65. #2514C22semidirect
67. #2495C22semidirect
75. #2453C22semidirect
80. #2409C22semidirect
85. Q8×C22⋊C4C22semidirect
89. C4×C22⋊Q8C22semidirect
92. #2097C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2076C22semidirect
101. #2075C22semidirect
102. #2074C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
108. #2066C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
118. #2036C22semidirect
121. #2035C22semidirect
128. #2026C22semidirect
132. #1991C22semidirect
133. #1991C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1941C22semidirect
143. #1941C22semidirect
144. #1941C22semidirect
145. #1939C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
155. #1927C22semidirect
159. #1923C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
170. #1892C22semidirect
171. #1892C22semidirect
179. #1869C22semidirect
180. #1865C22semidirect
184. #1853C22semidirect
185. #1853C22semidirect
186. #1824C22semidirect
189. #1808C22semidirect
190. #1807C22semidirect
191. #1807C22semidirect
192. #1797C22semidirect
193. #1787C22semidirect
195. C4×#106C22semidirect
196. C8×C4⋊C4C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
202. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#400942
#400442
#331282
#325272
#324592
#313322
#313262
#312432
#310582
#304082
#304032
#300192
#300172
#290782
#290762
#280952
#280942
#280672
#280632
#272272
#272252
#270372
#270312
#253432
#253422
#251142
#251122
#228752
#228742
C4×#4652
C8×#1212