Finite Group Databasebeta

← #6753487

Subgroups — #6753487

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37668C211yesmaximal, characteristic
2#35311C211yesmaximal, characteristic, complemented
3#32985C211yesmaximal, characteristic, complemented
4#32068C211yesmaximal, characteristic, complemented
5#32052C211yesmaximal, characteristic, complemented
6#31954C211yesmaximal, characteristic, complemented
7#31941C211yesmaximal, characteristic, complemented
8#31858C211yesmaximal, characteristic, complemented
9#31857C211yesmaximal, characteristic, complemented
10#31843C211yesmaximal, characteristic, complemented
11#31840C211yesmaximal, characteristic, complemented
12#29918C211yesmaximal, characteristic, complemented
13#29724C211yesmaximal, characteristic, complemented
14#28350C211yesmaximal, characteristic, complemented
15#28338C211yesmaximal, characteristic, complemented
16#27985C211yesmaximal, characteristic, complemented
17#27714C211yesmaximal, characteristic, complemented
18#27698C211yesmaximal, characteristic, complemented
19#27687C211yesmaximal, characteristic, complemented
20#25215C211yesmaximal, characteristic, complemented
21#25201C211yesmaximal, characteristic, complemented
22#24536C211yesmaximal, characteristic, complemented
23#24536C211yesmaximal, characteristic, complemented
24#24514C211yesmaximal, characteristic, complemented
25#24380C211yesmaximal, characteristic, complemented
26#23946C211yesmaximal, characteristic, complemented
27#23922C211yesmaximal, characteristic
28#22558C211yesmaximal, characteristic, complemented
29#22058C211yesmaximal, characteristic, complemented
30#21871C211yesmaximal, characteristic, complemented
31#20908C211yesmaximal, characteristic
32C2×#542C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#451C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#448C2211yescharacteristic
45C2×#433C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49#2855—21no—
50#2855—21no—
51#2848C2211yescharacteristic
52#2697—21no—
53#2695—21no—
54#2687—21no—
55#2684—21no—
56#2625—21no—
57#2625—21no—
58#2625C2211yescharacteristic
59#2621C2211yescharacteristic
60#2503C2211yescharacteristic
61#2503C2211yescharacteristic
62#2502C2211yescharacteristic
63#2502C2211yescharacteristic
64#2499C2211yescharacteristic
65#2499C2211yescharacteristic
66#2499C2211yescharacteristic
67#2499C2211yescharacteristic
68#2492C2211yescharacteristic
69#2484—21no—
70#2484—21no—
71#2483—21no—
72#2483—21no—
73#2468—21no—
74#2450—21no—
75#2447—21no—
76#2439C2211yescharacteristic
77#2432C2211yescharacteristic
78#2429C2211yescharacteristic
79#2427C2211yescharacteristic
80#2420C2211yescharacteristic
81#2419—21no—
82#2362C2211yescharacteristic
83#2339C2211yescharacteristic
84#2324C2211yescharacteristic
85#2317C2211yescharacteristic
86#2317C2211yescharacteristic
87#2310C2211yescharacteristic
88#2310C2211yescharacteristic
89#2280C2211yescharacteristic
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic, complemented
97#2092C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2072C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2056C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2056C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2024C2211yescharacteristic, complemented
120#2016C2211yescharacteristic, complemented
121#2016C2211yescharacteristic, complemented
122#2015C2211yescharacteristic, complemented
123#2015C2211yescharacteristic, complemented
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1973C2211yescharacteristic, complemented
133#1971C2211yescharacteristic, complemented
134#1969C2211yescharacteristic, complemented
135#1968C2211yescharacteristic, complemented
136#1960C2211yescharacteristic, complemented
137#1959C2211yescharacteristic, complemented
138#1958C2211yescharacteristic, complemented
139#1956C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1947C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1924C2211yescharacteristic
149#1924C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1878C2211yescharacteristic, complemented
155#1878C2211yescharacteristic, complemented
156#1877C2211yescharacteristic, complemented
157#1877C2211yescharacteristic, complemented
158#1877C2211yescharacteristic, complemented
159#1877C2211yescharacteristic, complemented
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1835C2211yescharacteristic, complemented
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1818C2211yescharacteristic
189#1805C2211yescharacteristic, complemented
190#1804C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1798C2211yescharacteristic
196#1787C2211yescharacteristic
197#1779C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1750C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#542—24no—
215#542—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221#525—24no—
222#525—42no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—42no—
229C2×C22⋊Q8—42no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117—21no—
249C2×#117—42no—
250C2×#117—42no—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C42—21no—
265#485—42no—
266#485—42no—
267#467—42no—
268#467—42no—
269#452—42no—
270#452—42no—
271#451—42no—
272#451—42no—
273#448—24no—
274#433—42no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#416—42no—
286#416—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×C22⋊C8—42no—
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×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#393—21no—
365#393—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390C2311yescharacteristic
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
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#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381—21no—
440#381—21no—
441#381—21no—
442#381—21no—
443#381—21no—
444#381—21no—
445#381—21no—
446#381—21no—
447#381D411yescharacteristic
448#381D411yescharacteristic
449#380—21no—
450#380D411yescharacteristic
451#380D411yescharacteristic
452#380D411yescharacteristic
453#380D411yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458#379D411yescharacteristic
459#379D411yescharacteristic
460C4×C4⋊C4—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C2×#95—21no—
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#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25C2×D411yescharacteristic
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4C2411yescharacteristic
522C23×C4—22no—
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#126—44no—
578#124—22no—
579#124—41no—
580#124—44no—
581#123—44no—
582#123—44no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—44no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604#121—22no—
605#121—22no—
606#121—41no—
607#121#4114yes—
608#120—44no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616C4×D4—44no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—44no—
632#117—44no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—44no—
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—44no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—44no—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#107—41no—
734#107—41no—
735#107—41no—
736#107—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
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—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781#97—41no—
782#97—41no—
783C4×C8—41no—
784C4×C8—41no—
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#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—41no—
839C24—41no—
840C24—41no—
841C24—41no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—44no—
846#41—44no—
847#41—82no—
848#41—82no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×Q8—82no—
880C2×Q8—82no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×D4—24no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4C2×#4112yes—
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—22no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C2×#4112yes—
973C22×C4H(5,𝔽2)12yes—
974C22×C4H(5,𝔽2)12yes—
975C22×C4H(5,𝔽2)12yes—
976C22×C4C2511yescharacteristic
977Q16—82no—
978Q16—82no—
979Q16—82no—
980Q16—82no—
981SD16—82no—
982SD16—82no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—82no—
1008C2×C8—82no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4C2×#4112yes—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—24no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—81no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—44no—
1134C23—44no—
1135C23—44no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—82no—
1143C23—82no—
1144C23—82no—
1145C23—82no—
1146C23#53512yes—
1147C23#54612yes—
1148C23#57812yes—
1149C23C23×D411yescharacteristic
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—84no—
1167Q8—162no—
1168D4—22no—
1169D4—22no—
1170D4—41no—
1171D4—41no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
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—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—44no—
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—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4#53512yes—
1274C2×C4#54612yes—
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—88no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22C2×#53511yescharacteristic
1319C22C2×#54611yescharacteristic
1320C22#348511yescharacteristic
1321C22C2×#57811yescharacteristic
1322C22#358411yescharacteristic
1323C22#358411yescharacteristic
1324C22#358611yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4#351311yescharacteristic
1352C4#351311yescharacteristic
1353C4#353411yescharacteristic
1354C4#353411yescharacteristic
1355C2—42no—
1356C2—42no—
1357C2—42no—
1358C2—82no—
1359C2#3802311yescharacteristic
1360C2#6079711yescharacteristic
1361C2#6081411yescharacteristic
1362C2#6117311yescharacteristic
1363C2#6118811yescharacteristic
1364C2#6176011yescharacteristic
1365C2#6177111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
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
2. #35311C2semidirect
3. #32985C2semidirect
4. #32068C2semidirect
5. #32052C2semidirect
6. #31954C2semidirect
7. #31941C2semidirect
8. #31858C2semidirect
9. #31857C2semidirect
10. #31843C2semidirect
11. #31840C2semidirect
12. #29918C2semidirect
13. #29724C2semidirect
14. #28350C2semidirect
15. #28338C2semidirect
16. #27985C2semidirect
17. #27714C2semidirect
18. #27698C2semidirect
19. #27687C2semidirect
20. #25215C2semidirect
21. #25201C2semidirect
22. #24536C2semidirect
23. #24536C2semidirect
24. #24514C2semidirect
25. #24380C2semidirect
26. #23946C2semidirect
28. #22558C2semidirect
29. #22058C2semidirect
30. #21871C2semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2097C22semidirect
95. #2095C22semidirect
96. #2093C22semidirect
97. #2092C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
100. #2074C22semidirect
101. #2074C22semidirect
102. #2074C22semidirect
103. #2074C22semidirect
104. #2074C22semidirect
105. #2072C22semidirect
106. #2072C22semidirect
107. #2072C22semidirect
108. #2068C22semidirect
109. #2066C22semidirect
110. #2056C22semidirect
111. #2056C22semidirect
112. #2056C22semidirect
113. #2056C22semidirect
114. #2056C22semidirect
115. #2056C22semidirect
118. #2024C22semidirect
119. #2024C22semidirect
120. #2016C22semidirect
121. #2016C22semidirect
122. #2015C22semidirect
123. #2015C22semidirect
130. #1993C22semidirect
131. #1990C22semidirect
132. #1973C22semidirect
133. #1971C22semidirect
134. #1969C22semidirect
135. #1968C22semidirect
136. #1960C22semidirect
137. #1959C22semidirect
138. #1958C22semidirect
139. #1956C22semidirect
140. #1949C22semidirect
141. #1947C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1933C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
154. #1878C22semidirect
155. #1878C22semidirect
156. #1877C22semidirect
157. #1877C22semidirect
158. #1877C22semidirect
159. #1877C22semidirect
184. #1836C22semidirect
185. #1835C22semidirect
189. #1805C22semidirect
190. #1804C22semidirect
191. #1804C22semidirect
192. #1803C22semidirect
193. #1802C22semidirect
194. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#376682
#353112
#329852
#320682
#320522
#319542
#319412
#318582
#318572
#318432
#318402
#299182
#297242
#283502
#283382
#279852
#277142
#276982
#276872
#252152
#252012
#245362
#245142
#243802
#239462
#239222
#225582
#220582
#218712
#209082