Finite Group Databasebeta

← #6594162

Subgroups — #6594162

Order 512.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37875C211yesmaximal, characteristic, complemented
2#37869C211yesmaximal, characteristic
3#33292C211yesmaximal, characteristic, complemented
4#33048C211yesmaximal, characteristic, complemented
5#33045C211yesmaximal, characteristic, complemented
6#29229C211yesmaximal, characteristic, complemented
7#29152C211yesmaximal, characteristic, complemented
8#27986C211yesmaximal, characteristic, complemented
9#27982C211yesmaximal, characteristic, complemented
10#27971C211yesmaximal, characteristic, complemented
11#27968C211yesmaximal, characteristic, complemented
12#27744C211yesmaximal, characteristic, complemented
13#27743C211yesmaximal, characteristic, complemented
14#27736C211yesmaximal, characteristic, complemented
15#27733C211yesmaximal, characteristic, complemented
16#27726C211yesmaximal, characteristic, complemented
17#27726C211yesmaximal, characteristic, complemented
18#27720C211yesmaximal, characteristic, complemented
19#27719C211yesmaximal, characteristic, complemented
20#27717C211yesmaximal, characteristic, complemented
21#27712C211yesmaximal, characteristic, complemented
22#27710C211yesmaximal, characteristic, complemented
23#27704C211yesmaximal, characteristic, complemented
24#22503C211yesmaximal, characteristic, complemented
25#22501C211yesmaximal, characteristic, complemented
26#22493C211yesmaximal, characteristic, complemented
27#22492C211yesmaximal, characteristic, complemented
28#21644C211yesmaximal, characteristic, complemented
29#20765C211yesmaximal, characteristic, complemented
30#20763C211yesmaximal, characteristic, complemented
31#20487C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#436C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#405C2211yescharacteristic
38C2×C4×M16C2211yescharacteristic
39#2857C2211yescharacteristic
40#2856C2211yescharacteristic
41#2774—21no—
42#2768—21no—
43#2763—21no—
44#2755—21no—
45#2672—21no—
46#2672—21no—
47#2671—21no—
48#2671—21no—
49#2660C2211yescharacteristic
50#2660C2211yescharacteristic
51#2628C2211yescharacteristic
52#2619C2211yescharacteristic
53#2571C2211yescharacteristic
54#2570C2211yescharacteristic
55#2566C2211yescharacteristic
56#2564—21no—
57#2549—21no—
58#2542C2211yescharacteristic
59#2505—21no—
60#2501C2211yescharacteristic
61#2500C2211yescharacteristic
62#2500C2211yescharacteristic
63#2500C2211yescharacteristic
64#2479—21no—
65#2479—21no—
66#2461—21no—
67#2461—21no—
68#2450—21no—
69#2442C2211yescharacteristic
70#2442C2211yescharacteristic
71#2440C2211yescharacteristic
72#2439C2211yescharacteristic
73#2352C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75#2331C2211yescharacteristic
76#2328C2211yescharacteristic
77#2317C2211yescharacteristic
78#2317C2211yescharacteristic
79#2290C2211yescharacteristic
80#2285C2211yescharacteristic
81C2×#382C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2025C2211yescharacteristic
103#2025C2211yescharacteristic
104#2023C2211yescharacteristic
105#2023C2211yescharacteristic
106#1993C2211yescharacteristic
107#1993C2211yescharacteristic
108#1993C2211yescharacteristic
109#1993C2211yescharacteristic
110#1992C2211yescharacteristic
111#1992C2211yescharacteristic
112#1991C2211yescharacteristic
113#1991C2211yescharacteristic
114#1990C2211yescharacteristic
115#1990C2211yescharacteristic
116#1990C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1988C2211yescharacteristic
120#1987C2211yescharacteristic
121#1961C2211yescharacteristic
122#1961C2211yescharacteristic
123#1957C2211yescharacteristic
124#1936C2211yescharacteristic
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1895C2211yescharacteristic
137#1895C2211yescharacteristic
138#1895C2211yescharacteristic
139#1895C2211yescharacteristic
140#1895C2211yescharacteristic
141#1895C2211yescharacteristic
142#1893C2211yescharacteristic
143#1893C2211yescharacteristic
144#1875C2211yescharacteristic
145#1875C2211yescharacteristic
146#1874C2211yescharacteristic
147#1874C2211yescharacteristic
148#1874C2211yescharacteristic
149#1874C2211yescharacteristic
150#1874C2211yescharacteristic
151#1874C2211yescharacteristic
152#1836C2211yescharacteristic
153#1836C2211yescharacteristic
154#1836C2211yescharacteristic
155#1836C2211yescharacteristic
156#1836C2211yescharacteristic
157#1836C2211yescharacteristic
158#1836C2211yescharacteristic
159#1836C2211yescharacteristic
160#1836C2211yescharacteristic
161#1836C2211yescharacteristic
162#1835C2211yescharacteristic
163#1835C2211yescharacteristic
164#1835C2211yescharacteristic
165#1835C2211yescharacteristic
166#1835C2211yescharacteristic
167#1834C2211yescharacteristic
168#1834C2211yescharacteristic
169#1825C2211yescharacteristic
170#1825C2211yescharacteristic
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1824C2211yescharacteristic
176#1823C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1802C2211yescharacteristic
180#1802C2211yescharacteristic
181#1771C2211yescharacteristic
182#1770C2211yescharacteristic
183#1768C2211yescharacteristic
184#1762C2211yescharacteristic
185#1762C2211yescharacteristic
186C4×#102C2211yescharacteristic
187C4×#102C2211yescharacteristic
188#1753C2211yescharacteristic
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1752C2211yescharacteristic
192#1750C2211yescharacteristic
193#1749C2211yescharacteristic
194#1736C2211yescharacteristic
195#1736C2211yescharacteristic
196#1736C2211yescharacteristic
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#555—24no—
208#555—24no—
209#553—24no—
210#553—24no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#486—24no—
252#436—24no—
253#435—24no—
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276#405—24no—
277C4×M16—24no—
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#393—21no—
328#392—21no—
329#392—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#390—21no—
335#390—21no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388D411yescharacteristic
363#388D411yescharacteristic
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387D411yescharacteristic
371#387D411yescharacteristic
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386D411yescharacteristic
378#386D411yescharacteristic
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385D411yescharacteristic
391#385D411yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#382—21no—
401#382—21no—
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2311yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430#376C2311yescharacteristic
431C2×#95—21no—
432C2×#95—21no—
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#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
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535#127—22no—
536#127—22no—
537#126—44no—
538#125—22no—
539#125—22no—
540#125—41no—
541#125—41no—
542#124—44no—
543#124—44no—
544#123—44no—
545#123—82no—
546#123—82no—
547C22⋊Q8—82no—
548C22⋊Q8—82no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551#121—22no—
552#121—22no—
553#121—22no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—22no—
559#121—44no—
560#121—44no—
561#121—82no—
562#121—82no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—44no—
568C4×D4—82no—
569C4×D4#4114yes—
570C4×D4#4114yes—
571#117—22no—
572#117—22no—
573#117—22no—
574#117—22no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—44no—
580#117—41no—
581#117—41no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
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⋊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⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×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⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C4⋊C8—22no—
692C4⋊C8—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—41no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—41no—
724C4×C8#4114yes—
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#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C24—21no—
769C24C22×D411yescharacteristic
770C24C22×D411yescharacteristic
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
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—41no—
793C2×D4—41no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4#12414yes—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
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×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4C2511yescharacteristic
876M16—44no—
877M16—44no—
878M16—44no—
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×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—44no—
902C2×C8C2×#4112yes—
903C2×C8C2×#4112yes—
904C4⋊C4—22no—
905C4⋊C4—22no—
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—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4#12414yes—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4#12414yes—
1003C22⋊C4#12414yes—
1004C42—22no—
1005C42—22no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42C2×#4112yes—
1019C42C2×#4112yes—
1020C42C2×#4112yes—
1021C422−1+412yes—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23C2×#12412yes—
1049C23C2×#12412yes—
1050C23C23×D411yescharacteristic
1051Q8—162no—
1052Q8—162no—
1053Q8—162no—
1054D4—44no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—84no—
1064D4—162no—
1065D4—162no—
1066D4—162no—
1067D4—162no—
1068D4—162no—
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—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
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—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
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—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—82no—
1150C2×C4—82no—
1151C2×C4—84no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4—162no—
1155C2×C4—162no—
1156C2×C4—162no—
1157C2×C4C2×#12412yes—
1158C2×C4C2×#12412yes—
1159C2×C4C2×#12412yes—
1160C2×C4C2×#12412yes—
1161C2×C4#54712yes—
1162C2×C4#54712yes—
1163C2×C4C22×#4111yescharacteristic
1164C2×C4C22×#4111yescharacteristic
1165C2×C4C22×#4111yescharacteristic
1166C2×C4C2×2−1+411yescharacteristic
1167C2×C4#58511yescharacteristic
1168C2×C4#58511yescharacteristic
1169C8—22no—
1170C8—22no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22C22×#12411yescharacteristic
1206C22C2×#54711yescharacteristic
1207C22#350011yescharacteristic
1208C22#358511yescharacteristic
1209C22#358511yescharacteristic
1210C22#358511yescharacteristic
1211C22#358611yescharacteristic
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4#347511yescharacteristic
1239C4#347511yescharacteristic
1240C4#351511yescharacteristic
1241C4#351511yescharacteristic
1242C2—42no—
1243C2—42no—
1244C2—161no—
1245C2—161no—
1246C2#3616411yescharacteristic
1247C2#6062111yescharacteristic
1248C2#6062611yescharacteristic
1249C2#6126711yescharacteristic
1250C2#6126811yescharacteristic
1251C2#6256911yescharacteristic
1252C2#6257011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37869C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37875C2semidirect
3. #33292C2semidirect
4. #33048C2semidirect
5. #33045C2semidirect
6. #29229C2semidirect
7. #29152C2semidirect
8. #27986C2semidirect
9. #27982C2semidirect
10. #27971C2semidirect
11. #27968C2semidirect
12. #27744C2semidirect
13. #27743C2semidirect
14. #27736C2semidirect
15. #27733C2semidirect
16. #27726C2semidirect
17. #27726C2semidirect
18. #27720C2semidirect
19. #27719C2semidirect
20. #27717C2semidirect
21. #27712C2semidirect
22. #27710C2semidirect
23. #27704C2semidirect
24. #22503C2semidirect
25. #22501C2semidirect
26. #22493C2semidirect
27. #22492C2semidirect
28. #21644C2semidirect
29. #20765C2semidirect
30. #20763C2semidirect
31. #20487C2semidirect

Maximal subgroups

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

subgroupindex
#378752
#378692
#332922
#330482
#330452
#292292
#291522
#279862
#279822
#279712
#279682
#277442
#277432
#277362
#277332
#277262
#277202
#277192
#277172
#277122
#277102
#277042
#225032
#225012
#224932
#224922
#216442
#207652
#207632
#204872