Finite Group Databasebeta

← #6480139

Subgroups — #6480139

Order 512.

1407 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35271C211yesmaximal, characteristic, complemented
2#35270C211yesmaximal, characteristic, complemented
3#33145C211yesmaximal, characteristic, complemented
4#33145C211yesmaximal, characteristic, complemented
5#33143C211yesmaximal, characteristic, complemented
6#33143C211yesmaximal, characteristic, complemented
7#30295C211yesmaximal, characteristic, complemented
8#30245C211yesmaximal, characteristic
9#30198C211yesmaximal, characteristic, complemented
10#30197C211yesmaximal, characteristic, complemented
11#29590C211yesmaximal, characteristic, complemented
12#29589C211yesmaximal, characteristic, complemented
13#29586C211yesmaximal, characteristic, complemented
14#29584C211yesmaximal, characteristic, complemented
15#29570C211yesmaximal, characteristic, complemented
16#29569C211yesmaximal, characteristic, complemented
17#29566C211yesmaximal, characteristic, complemented
18#29564C211yesmaximal, characteristic, complemented
19#29530C211yesmaximal, characteristic, complemented
20#29528C211yesmaximal, characteristic, complemented
21#29527C211yesmaximal, characteristic, complemented
22#29524C211yesmaximal, characteristic, complemented
23#29510C211yesmaximal, characteristic, complemented
24#29507C211yesmaximal, characteristic, complemented
25#29505C211yesmaximal, characteristic, complemented
26#29504C211yesmaximal, characteristic, complemented
27#22191C211yesmaximal, characteristic, complemented
28#22190C211yesmaximal, characteristic, complemented
29#22187C211yesmaximal, characteristic, complemented
30#22186C211yesmaximal, characteristic, complemented
31#20365C211yesmaximal, characteristic, complemented
32C2×#469C2211yescharacteristic
33C2×#469C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37C2×C4×M16C2211yescharacteristic
38#2857C2211yescharacteristic
39#2856C2211yescharacteristic
40#2855C2211yescharacteristic
41#2854C2211yescharacteristic
42#2854C2211yescharacteristic
43#2854C2211yescharacteristic
44#2851C2211yescharacteristic
45#2850C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2645C2211yescharacteristic
49#2644C2211yescharacteristic
50#2644C2211yescharacteristic
51#2644C2211yescharacteristic
52#2641C2211yescharacteristic
53#2640C2211yescharacteristic
54#2532—21no—
55#2531—21no—
56#2531—21no—
57#2530—21no—
58#2529—21no—
59#2527—21no—
60#2526—21no—
61#2526—21no—
62#2510—21no—
63#2488—21no—
64#2450—21no—
65#2444—21no—
66#2444—21no—
67#2425—21no—
68#2425—21no—
69#2419—21no—
70#2331C2211yescharacteristic
71#2330C2211yescharacteristic
72#2328C2211yescharacteristic
73#2326C2211yescharacteristic
74#2320C2211yescharacteristic
75#2319C2211yescharacteristic
76#2319C2211yescharacteristic
77#2319C2211yescharacteristic
78C4×C22⋊Q8C2211yescharacteristic
79C4×#121C2211yescharacteristic
80C4×#121C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C2×#376C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2096C2211yescharacteristic
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2074C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2058C2211yescharacteristic
102#2057C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2026C2211yescharacteristic
108#2025C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2014C2211yescharacteristic
112#2012C2211yescharacteristic
113#2012C2211yescharacteristic
114#2011C2211yescharacteristic
115#1973C2211yescharacteristic
116#1973C2211yescharacteristic
117#1972C2211yescharacteristic
118#1972C2211yescharacteristic
119#1970C2211yescharacteristic
120#1970C2211yescharacteristic
121#1968C2211yescharacteristic
122#1968C2211yescharacteristic
123#1944C2211yescharacteristic
124#1944C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1942C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1941C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1928C2211yescharacteristic
148#1927C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1746C2211yescharacteristic
192#1746C2211yescharacteristic
193#1746C2211yescharacteristic
194#1746C2211yescharacteristic
195#1746C2211yescharacteristic
196#1746C2211yescharacteristic
197#1746C2211yescharacteristic
198#1746C2211yescharacteristic
199#1728C2211yescharacteristic
200#1728C2211yescharacteristic
201#1728C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#469—24no—
236#469—24no—
237#468—24no—
238#468—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C4×M16—24no—
276C4×M16—24no—
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#393—21no—
316#393—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#390—21no—
325#390—21no—
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389—21no—
339#389—21no—
340#389—21no—
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#383—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#381—21no—
414#381—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432#376D411yescharacteristic
433#376D411yescharacteristic
434#376D411yescharacteristic
435#376D411yescharacteristic
436#376C2311yescharacteristic
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439#376C2311yescharacteristic
440C2×#95D411yescharacteristic
441C2×#95D411yescharacteristic
442C2×#95D411yescharacteristic
443C2×#95D411yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2411yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8—41no—
515C2×D8—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16#4114yes—
527C2×M16#4114yes—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538#127—41no—
539#127—41no—
540#125—41no—
541#125—41no—
542#124—41no—
543#124—41no—
544#123—82no—
545#123—82no—
546#123—82no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—82no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—22no—
554#121—22no—
555#121—22no—
556#121—82no—
557#121—82no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—82no—
567C4×D4—82no—
568C4×D4—82no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
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×C42—22no—
644C2×C42—22no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42—41no—
653C2×C42—41no—
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666#107—22no—
667#107—22no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#103—22no—
679#103—22no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#97—22no—
703#97—22no—
704#97—22no—
705#97—22no—
706C4×C8—22no—
707C4×C8—22no—
708C4×C8—22no—
709C4×C8—22no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762C24—21no—
763C24—21no—
764C24—21no—
765C24C22×D411yescharacteristic
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—42no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2511yescharacteristic
868SD16—82no—
869SD16—82no—
870D8—82no—
871D8—82no—
872M16—44no—
873M16—44no—
874M16—44no—
875M16—44no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8C2×#4112yes—
897C2×C8C2×#4112yes—
898C2×C8C2×#4112yes—
899C2×C8C2×#4112yes—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C42—22no—
987C42—22no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—42no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23#53212yes—
1037C23C23×D411yescharacteristic
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—162no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—84no—
1056D4—84no—
1057D4—84no—
1058D4—162no—
1059D4—162no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—82no—
1142C2×C4—82no—
1143C2×C4—82no—
1144C2×C4—82no—
1145C2×C4—82no—
1146C2×C4—82no—
1147C2×C4—162no—
1148C2×C4—162no—
1149C2×C4—162no—
1150C2×C4#53212yes—
1151C2×C4C22×#4111yescharacteristic
1152C2×C4C22×#4111yescharacteristic
1153C2×C4#58511yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—22no—
1158C8—22no—
1159C8—22no—
1160C8—22no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22C2×#53211yescharacteristic
1194C22#344911yescharacteristic
1195C22#344911yescharacteristic
1196C22#358511yescharacteristic
1197C22#358511yescharacteristic
1198C22#358511yescharacteristic
1199C22#358611yescharacteristic
1200C4—22no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4#349111yescharacteristic
1227C4#349111yescharacteristic
1228C4#349311yescharacteristic
1229C4#349311yescharacteristic
1230C2—42no—
1231C2—161no—
1232C2—161no—
1233C2—161no—
1234C2#3511911yescharacteristic
1235C2#6070311yescharacteristic
1236C2#6070411yescharacteristic
1237C2#6100311yescharacteristic
1238C2#6100311yescharacteristic
1239C2#6100411yescharacteristic
1240C2#6100411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30245C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35271C2semidirect
2. #35270C2semidirect
3. #33145C2semidirect
4. #33145C2semidirect
5. #33143C2semidirect
6. #33143C2semidirect
7. #30295C2semidirect
9. #30198C2semidirect
10. #30197C2semidirect
11. #29590C2semidirect
12. #29589C2semidirect
13. #29586C2semidirect
14. #29584C2semidirect
15. #29570C2semidirect
16. #29569C2semidirect
17. #29566C2semidirect
18. #29564C2semidirect
19. #29530C2semidirect
20. #29528C2semidirect
21. #29527C2semidirect
22. #29524C2semidirect
23. #29510C2semidirect
24. #29507C2semidirect
25. #29505C2semidirect
26. #29504C2semidirect
27. #22191C2semidirect
28. #22190C2semidirect
29. #22187C2semidirect
30. #22186C2semidirect
31. #20365C2semidirect

Maximal subgroups

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

subgroupindex
#352712
#352702
#331452
#331432
#302952
#302452
#301982
#301972
#295902
#295892
#295862
#295842
#295702
#295692
#295662
#295642
#295302
#295282
#295272
#295242
#295102
#295072
#295052
#295042
#221912
#221902
#221872
#221862
#203652