Finite Group Databasebeta

← #7085989

Subgroups — #7085989

Order 512.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45031C211yesmaximal, characteristic, complemented
2#42899C211yesmaximal, characteristic, complemented
3#32440C211yesmaximal, characteristic, complemented
4#32309C211yesmaximal, characteristic, complemented
5#31637C211yesmaximal, characteristic, complemented
6#31594C211yesmaximal, characteristic, complemented
7#31218C211yesmaximal, characteristic, complemented
8#31004C211yesmaximal, characteristic, complemented
9#30936C211yesmaximal, characteristic, complemented
10#30788C211yesmaximal, characteristic, complemented
11#29588C211yesmaximal, characteristic, complemented
12#29204C211yesmaximal, characteristic, complemented
13#28885C211yesmaximal, characteristic, complemented
14#28868C211yesmaximal, characteristic, complemented
15#28537C211yesmaximal, characteristic, complemented
16#28353C211yesmaximal, characteristic
17#27208C211yesmaximal, characteristic, complemented
18#26888C211yesmaximal, characteristic, complemented
19#26569C211yesmaximal, characteristic, complemented
20#26492C211yesmaximal, characteristic, complemented
21#26375C211yesmaximal, characteristic, complemented
22#26098C211yesmaximal, characteristic, complemented
23#25968C211yesmaximal, characteristic, complemented
24#25152C211yesmaximal, characteristic, complemented
25#25038C211yesmaximal, characteristic, complemented
26#24909C211yesmaximal, characteristic, complemented
27#23808C211yesmaximal, characteristic, complemented
28#23285C211yesmaximal, characteristic, complemented
29#23010C211yesmaximal, characteristic, complemented
30#22884C211yesmaximal, characteristic, complemented
31#22157C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#479C2211yescharacteristic, complemented
35C2×#478C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#460C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47#2837—21no—
48#2796—21no—
49#2781—21no—
50#2778—21no—
51#2771—21no—
52#2749—21no—
53#2744—21no—
54#2697—21no—
55#2693—21no—
56#2654—21no—
57#2651—21no—
58#2647C2211yescharacteristic, complemented
59#2598—21no—
60#2594—21no—
61#2570C2211yescharacteristic, complemented
62#2566C2211yescharacteristic
63#2565C2211yescharacteristic, complemented
64#2513C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2495C2211yescharacteristic
67#2490C2211yescharacteristic
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic, complemented
70#2448C2211yescharacteristic, complemented
71#2445C2211yescharacteristic
72#2445C2211yescharacteristic
73#2441C2211yescharacteristic
74#2433C2211yescharacteristic
75#2426C2211yescharacteristic
76#2422C2211yescharacteristic
77#2421C2211yescharacteristic
78#2420C2211yescharacteristic
79#2418—21no—
80#2412—21no—
81#2411—21no—
82#2401C2211yescharacteristic
83#2366C2211yescharacteristic
84#2362C2211yescharacteristic
85#2354C2211yescharacteristic
86#2351C2211yescharacteristic, complemented
87D4×C22⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2328C2211yescharacteristic
90#2326C2211yescharacteristic, complemented
91#2319C2211yescharacteristic
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic, complemented
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2085C2211yescharacteristic, complemented
103#2077C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2071C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2067C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2059C2211yescharacteristic, complemented
115#2055C2211yescharacteristic, complemented
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic, complemented
118#2041C2211yescharacteristic
119#2036C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic, complemented
125#2025C2211yescharacteristic, complemented
126#2014C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic, complemented
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2000C2211yescharacteristic
132#1983C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic, complemented
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1961C2211yescharacteristic
140#1961C2211yescharacteristic
141#1957C2211yescharacteristic
142#1949C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1947C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1894C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1877C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1847C2211yescharacteristic, complemented
190#1835C2211yescharacteristic, complemented
191#1809C2211yescharacteristic
192#1804C2211yescharacteristic
193#1802C2211yescharacteristic
194#1786C2211yescharacteristic
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1768C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238#499—42no—
239#482—42no—
240#479—42no—
241#478—42no—
242#469—42no—
243#463—24no—
244#460—24no—
245#450—24no—
246#447—42no—
247#442—42no—
248#440—42no—
249C4×SD16—42no—
250C4×SD16—42no—
251C4×D8—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
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×C4⋊C8C2311yescharacteristic
271#418—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#401D411yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400D411yescharacteristic
317#400D411yescharacteristic
318#400D411yescharacteristic
319#399—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397D411yescharacteristic
337#397D411yescharacteristic
338#397D411yescharacteristic
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396D411yescharacteristic
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#392—21no—
357#392—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#389—21no—
377#389—21no—
378#389—21no—
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#383—21no—
437#382—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
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#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16#4114yes—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548#127—22no—
549#127—22no—
550#127—41no—
551#127—41no—
552#125—41no—
553#125—41no—
554#125—41no—
555#125—41no—
556#124—22no—
557#124—41no—
558#123—82no—
559#123—82no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#120—82no—
568#120—82no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—82no—
588#117—41no—
589#117—41no—
590#117—82no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
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—82no—
673C2×C22⋊C4—82no—
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—22no—
702#106—22no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—41no—
716#103—41no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—41no—
743#97—22no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8C2×#4112yes—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—44no—
841C2×D4—42no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4C2×#4112yes—
859C2×D42−1+412yes—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C2511yescharacteristic
910SD16—44no—
911SD16—44no—
912SD16—44no—
913D8—44no—
914D8—44no—
915D8—82no—
916M16—82no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8C2×#4112yes—
939C2×C8H(5,𝔽2)12yes—
940C2×C8H(5,𝔽2)12yes—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—42no—
1052C42—42no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—21no—
1066C23—21no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23C23×D411yescharacteristic
1101Q8—22no—
1102Q8—22no—
1103Q8—41no—
1104Q8—41no—
1105D4—22no—
1106D4—22no—
1107D4—22no—
1108D4—22no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—84no—
1122D4—84no—
1123D4—162no—
1124D4—162no—
1125D4—162no—
1126D4—162no—
1127D4—162no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
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—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—84no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4C22×#4111yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C8—22no—
1220C8—22no—
1221C8—22no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C22—42no—
1228C22—41no—
1229C22—42no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—41no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—168no—
1263C22D4×#4111yescharacteristic
1264C22#348911yescharacteristic
1265C22#349811yescharacteristic
1266C22#358411yescharacteristic
1267C22#358511yescharacteristic
1268C22#358511yescharacteristic
1269C22#358511yescharacteristic
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—42no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4#350511yescharacteristic
1296C4#352011yescharacteristic
1297C4#353311yescharacteristic
1298C4#353511yescharacteristic
1299C2—81no—
1300C2—82no—
1301C2—82no—
1302C2—161no—
1303C2—161no—
1304C2#4416211yescharacteristic
1305C2#6150411yescharacteristic
1306C2#6153511yescharacteristic
1307C2#6217511yescharacteristic
1308C2#6222311yescharacteristic
1309C2#6244111yescharacteristic
1310C2#6246111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28353C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45031C2semidirect
2. #42899C2semidirect
3. #32440C2semidirect
4. #32309C2semidirect
5. #31637C2semidirect
6. #31594C2semidirect
7. #31218C2semidirect
8. #31004C2semidirect
9. #30936C2semidirect
10. #30788C2semidirect
11. #29588C2semidirect
12. #29204C2semidirect
13. #28885C2semidirect
14. #28868C2semidirect
15. #28537C2semidirect
17. #27208C2semidirect
18. #26888C2semidirect
19. #26569C2semidirect
20. #26492C2semidirect
21. #26375C2semidirect
22. #26098C2semidirect
23. #25968C2semidirect
24. #25152C2semidirect
25. #25038C2semidirect
26. #24909C2semidirect
27. #23808C2semidirect
28. #23285C2semidirect
29. #23010C2semidirect
30. #22884C2semidirect
31. #22157C2semidirect
32. C2×#499C22semidirect
34. C2×#479C22semidirect
42. C2×#440C22semidirect
45. C2×C4×D8C22semidirect
58. #2647C22semidirect
61. #2570C22semidirect
63. #2565C22semidirect
64. #2513C22semidirect
69. #2454C22semidirect
70. #2448C22semidirect
86. #2351C22semidirect
90. #2326C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
94. #2096C22semidirect
96. #2094C22semidirect
100. #2092C22semidirect
101. #2085C22semidirect
102. #2085C22semidirect
105. #2073C22semidirect
106. #2071C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
110. #2067C22semidirect
114. #2059C22semidirect
115. #2055C22semidirect
117. #2054C22semidirect
124. #2025C22semidirect
125. #2025C22semidirect
128. #2012C22semidirect
132. #1983C22semidirect
136. #1972C22semidirect
142. #1949C22semidirect
143. #1947C22semidirect
144. #1947C22semidirect
145. #1944C22semidirect
146. #1943C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
150. #1936C22semidirect
152. #1934C22semidirect
153. #1933C22semidirect
155. #1926C22semidirect
156. #1925C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1919C22semidirect
163. #1917C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
170. #1880C22semidirect
175. #1865C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
184. #1862C22semidirect
188. #1847C22semidirect
189. #1847C22semidirect
190. #1835C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1768C22semidirect
198. #1763C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#450312
#428992
#324402
#323092
#316372
#315942
#312182
#310042
#309362
#307882
#295882
#292042
#288852
#288682
#285372
#283532
#272082
#268882
#265692
#264922
#263752
#260982
#259682
#251522
#250382
#249092
#238082
#232852
#230102
#228842
#221572