Finite Group Databasebeta

← #6801547

Subgroups — #6801547

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39730C211yesmaximal, characteristic, complemented
2#35531C211yesmaximal, characteristic, complemented
3#32919C211yesmaximal, characteristic, complemented
4#31912C211yesmaximal, characteristic, complemented
5#31898C211yesmaximal, characteristic, complemented
6#31594C211yesmaximal, characteristic, complemented
7#31580C211yesmaximal, characteristic, complemented
8#31216C211yesmaximal, characteristic, complemented
9#31212C211yesmaximal, characteristic, complemented
10#30750C211yesmaximal, characteristic, complemented
11#30735C211yesmaximal, characteristic, complemented
12#29765C211yesmaximal, characteristic, complemented
13#29718C211yesmaximal, characteristic, complemented
14#28881C211yesmaximal, characteristic, complemented
15#28880C211yesmaximal, characteristic, complemented
16#28321C211yesmaximal, characteristic, complemented
17#28309C211yesmaximal, characteristic, complemented
18#28126C211yesmaximal, characteristic, complemented
19#28119C211yesmaximal, characteristic, complemented
20#27218C211yesmaximal, characteristic, complemented
21#27204C211yesmaximal, characteristic, complemented
22#26611C211yesmaximal, characteristic, complemented
23#26593C211yesmaximal, characteristic, complemented
24#26267C211yesmaximal, characteristic, complemented
25#26254C211yesmaximal, characteristic, complemented
26#25734C211yesmaximal, characteristic
27#24220C211yesmaximal, characteristic, complemented
28#22626C211yesmaximal, characteristic, complemented
29#22094C211yesmaximal, characteristic, complemented
30#22040C211yesmaximal, characteristic, complemented
31#21460C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#493C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic, complemented
41C2×#460C2211yescharacteristic
42C2×#463C2211yescharacteristic, complemented
43C2×#452C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#447C2211yescharacteristic
49C2×#440C2211yescharacteristic, complemented
50C2×C4×D8C2211yescharacteristic, complemented
51#2850C2211yescharacteristic
52#2795—21no—
53#2778—21no—
54#2756—21no—
55#2718—21no—
56#2620C2211yescharacteristic
57#2619C2211yescharacteristic
58#2576—21no—
59#2570C2211yescharacteristic, complemented
60#2544C2211yescharacteristic, complemented
61#2518—21no—
62#2514C2211yescharacteristic, complemented
63#2512C2211yescharacteristic, complemented
64#2504—21no—
65#2501—21no—
66#2500—21no—
67#2500—21no—
68#2467—21no—
69#2457—21no—
70#2448C2211yescharacteristic
71#2448C2211yescharacteristic
72#2448C2211yescharacteristic
73#2448C2211yescharacteristic
74#2448C2211yescharacteristic, complemented
75#2445C2211yescharacteristic
76#2445C2211yescharacteristic
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic, complemented
80#2418—21no—
81#2418—21no—
82#2418—21no—
83#2418—21no—
84#2367C2211yescharacteristic, complemented
85#2357C2211yescharacteristic, complemented
86#2324C2211yescharacteristic
87#2323C2211yescharacteristic
88#2317C2211yescharacteristic
89#2309C2211yescharacteristic
90C4×#121C2211yescharacteristic
91#2297C2211yescharacteristic
92C2×#390C2211yescharacteristic
93#2285C2211yescharacteristic
94#2097C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic, complemented
118#2042C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic, complemented
121#2041C2211yescharacteristic, complemented
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic, complemented
132#2011C2211yescharacteristic
133#2011C2211yescharacteristic
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1973C2211yescharacteristic
137#1972C2211yescharacteristic
138#1970C2211yescharacteristic
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic
141#1970C2211yescharacteristic, complemented
142#1969C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic, complemented
145#1968C2211yescharacteristic, complemented
146#1961C2211yescharacteristic
147#1958C2211yescharacteristic
148#1944C2211yescharacteristic, complemented
149#1942C2211yescharacteristic, complemented
150#1939C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic, complemented
175#1879C2211yescharacteristic, complemented
176#1879C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1874C2211yescharacteristic
181#1874C2211yescharacteristic
182#1872C2211yescharacteristic
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1852C2211yescharacteristic
188#1825C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1770C2211yescharacteristic, complemented
197C8×C4⋊C4C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217#535—42no—
218#535—42no—
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239#520—42no—
240#520—42no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4—21no—
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C42C2311yescharacteristic
260#496—42no—
261#493—42no—
262#485—24no—
263#482—42no—
264#482—42no—
265#464—42no—
266#464—42no—
267#463—42no—
268#460—42no—
269#452—42no—
270#450—42no—
271#449—24no—
272#449—42no—
273#447—24no—
274#447—42no—
275#440—42no—
276C4×D8—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#401—21no—
334#400—21no—
335#400—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#392—21no—
368#392—21no—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#384—21no—
446#384D411yescharacteristic
447#384D411yescharacteristic
448#384C2311yescharacteristic
449#383—21no—
450#382—21no—
451#382D411yescharacteristic
452#382D411yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#380D411yescharacteristic
457#380D411yescharacteristic
458#380D411yescharacteristic
459#380D411yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462#379—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
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
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×Q16—22no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582#127—22no—
583#127—22no—
584#127—41no—
585#127—41no—
586#127—41no—
587#127—41no—
588#126—82no—
589#124—22no—
590#124—22no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—41no—
597#123—82no—
598#123—82no—
599#123—82no—
600#123—82no—
601#123—82no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—44no—
609#121—44no—
610#120—44no—
611#120—44no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—82no—
629#117—22no—
630#117—22no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—44no—
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—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—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—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—82no—
724C2×C22⋊C4—82no—
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—41no—
737C2×C42—41no—
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#107—22no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107—41no—
751#106—22no—
752#106—41no—
753#106—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792C22⋊C8—22no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8#4114yes—
796#97—41no—
797#97—41no—
798C4×C8—41no—
799C4×C8—41no—
800C4×C8—41no—
801C4×C8—41no—
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#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—42no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848#41—44no—
849#41—44no—
850#41—44no—
851#41—44no—
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×Q8H(5,𝔽2)12yes—
864C2×D4—24no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4H(5,𝔽2)12yes—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—24no—
933C22×C4—21no—
934C22×C4—22no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C2×#4112yes—
981C22×C4H(5,𝔽2)12yes—
982C22×C4C2511yescharacteristic
983Q16—82no—
984SD16—44no—
985SD16—82no—
986SD16—82no—
987SD16—82no—
988SD16—82no—
989D8—44no—
990D8—82no—
991D8—82no—
992D8—82no—
993D8—82no—
994D8—82no—
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—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8C2×#4112yes—
1018C2×C8C2×#4112yes—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
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—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
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—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—41no—
1129C42—41no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—81no—
1134C42—81no—
1135C42—81no—
1136C42—81no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—84no—
1179C23—84no—
1180C23—84no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23—162no—
1185C23#55012yes—
1186C23C23×D411yescharacteristic
1187Q8—22no—
1188Q8—22no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195D4—22no—
1196D4—22no—
1197D4—48no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224D4—162no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—48no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—82no—
1301C2×C4—82no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4#55012yes—
1308C2×C4#57612yes—
1309C2×C4C22×#4111yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4C2×H(5,𝔽2)11yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4#58511yescharacteristic
1314C2×C4#58511yescharacteristic
1315C8—22no—
1316C8—22no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—168no—
1366C22#344911yescharacteristic
1367C22C2×#55011yescharacteristic
1368C22#348411yescharacteristic
1369C22C2×#57611yescharacteristic
1370C22#358411yescharacteristic
1371C22#358411yescharacteristic
1372C22#358511yescharacteristic
1373C4—22no—
1374C4—22no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—42no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4#351311yescharacteristic
1398C4#351311yescharacteristic
1399C4#353411yescharacteristic
1400C4#353411yescharacteristic
1401C2—42no—
1402C2—82no—
1403C2—161no—
1404C2—161no—
1405C2—161no—
1406C2—161no—
1407C2#3912811yescharacteristic
1408C2#6098611yescharacteristic
1409C2#6100011yescharacteristic
1410C2#6140611yescharacteristic
1411C2#6142411yescharacteristic
1412C2#6166311yescharacteristic
1413C2#6168811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25734C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39730C2semidirect
2. #35531C2semidirect
3. #32919C2semidirect
4. #31912C2semidirect
5. #31898C2semidirect
6. #31594C2semidirect
7. #31580C2semidirect
8. #31216C2semidirect
9. #31212C2semidirect
10. #30750C2semidirect
11. #30735C2semidirect
12. #29765C2semidirect
13. #29718C2semidirect
14. #28881C2semidirect
15. #28880C2semidirect
16. #28321C2semidirect
17. #28309C2semidirect
18. #28126C2semidirect
19. #28119C2semidirect
20. #27218C2semidirect
21. #27204C2semidirect
22. #26611C2semidirect
23. #26593C2semidirect
24. #26267C2semidirect
25. #26254C2semidirect
27. #24220C2semidirect
28. #22626C2semidirect
29. #22094C2semidirect
30. #22040C2semidirect
31. #21460C2semidirect
40. C2×#464C22semidirect
42. C2×#463C22semidirect
49. C2×#440C22semidirect
50. C2×C4×D8C22semidirect
59. #2570C22semidirect
60. #2544C22semidirect
62. #2514C22semidirect
63. #2512C22semidirect
74. #2448C22semidirect
79. #2445C22semidirect
84. #2367C22semidirect
85. #2357C22semidirect
94. #2097C22semidirect
97. #2092C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2066C22semidirect
108. #2065C22semidirect
109. #2065C22semidirect
112. #2055C22semidirect
117. #2054C22semidirect
120. #2041C22semidirect
121. #2041C22semidirect
123. #2015C22semidirect
131. #2012C22semidirect
141. #1970C22semidirect
142. #1969C22semidirect
144. #1968C22semidirect
145. #1968C22semidirect
148. #1944C22semidirect
149. #1942C22semidirect
150. #1939C22semidirect
151. #1939C22semidirect
152. #1935C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
158. #1926C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
174. #1879C22semidirect
175. #1879C22semidirect
176. #1879C22semidirect
177. #1878C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1862C22semidirect
189. #1803C22semidirect
190. #1802C22semidirect
196. #1770C22semidirect
197. C8×C4⋊C4C22semidirect
198. #1762C22semidirect
199. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#397302
#355312
#329192
#319122
#318982
#315942
#315802
#312162
#312122
#307502
#307352
#297652
#297182
#288812
#288802
#283212
#283092
#281262
#281192
#272182
#272042
#266112
#265932
#262672
#262542
#257342
#242202
#226262
#220942
#220402
#214602