Finite Group Databasebeta

← #7607954

Subgroups — #7607954

Order 512.

1538 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59711C211yesmaximal, characteristic, complemented
2#59698C211yesmaximal, characteristic, complemented
3#32163C211yesmaximal, characteristic, complemented
4#32136C211yesmaximal, characteristic, complemented
5#32048C211yesmaximal, characteristic, complemented
6#31116C211yesmaximal, characteristic, complemented
7#29394C211yesmaximal, characteristic, complemented
8#29365C211yesmaximal, characteristic, complemented
9#29095C211yesmaximal, characteristic, complemented
10#29054C211yesmaximal, characteristic, complemented
11#28931C211yesmaximal, characteristic, complemented
12#28907C211yesmaximal, characteristic
13#28882C211yesmaximal, characteristic, complemented
14#28046C211yesmaximal, characteristic, complemented
15#27783C211yesmaximal, characteristic, complemented
16#27697C211yesmaximal, characteristic, complemented
17#27571C211yesmaximal, characteristic, complemented
18#27406C211yesmaximal, characteristic, complemented
19#27143C211yesmaximal, characteristic, complemented
20#27111C211yesmaximal, characteristic, complemented
21#26916C211yesmaximal, characteristic, complemented
22#26737C211yesmaximal, characteristic, complemented
23#26704C211yesmaximal, characteristic, complemented
24#26640C211yesmaximal, characteristic, complemented
25#23226C211yesmaximal, characteristic, complemented
26#23132C211yesmaximal, characteristic, complemented
27#22968C211yesmaximal, characteristic, complemented
28#22938C211yesmaximal, characteristic, complemented
29#21665C211yesmaximal, characteristic, complemented
30#21646C211yesmaximal, characteristic, complemented
31#21288C211yesmaximal, characteristic, complemented
32C2×#556—21no—
33C2×#489C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#440C2211yescharacteristic
39#2757—21no—
40#2716—21no—
41#2700—21no—
42#2691—21no—
43#2603—21no—
44#2600—21no—
45#2599—21no—
46#2579—21no—
47#2551C2211yescharacteristic
48#2544C2211yescharacteristic
49#2531—21no—
50#2512C2211yescharacteristic
51#2512C2211yescharacteristic
52#2512C2211yescharacteristic
53#2507C2211yescharacteristic
54#2502C2211yescharacteristic
55#2496C2211yescharacteristic
56#2491C2211yescharacteristic
57#2491C2211yescharacteristic
58#2474—21no—
59#2469—21no—
60#2468—21no—
61#2466—21no—
62#2465—21no—
63#2452C2211yescharacteristic
64#2447C2211yescharacteristic
65#2440C2211yescharacteristic
66#2428C2211yescharacteristic
67#2427C2211yescharacteristic
68#2426C2211yescharacteristic
69#2367C2211yescharacteristic
70#2365C2211yescharacteristic
71#2365C2211yescharacteristic
72#2361—21no—
73#2361C2211yescharacteristic
74#2361C2211yescharacteristic
75#2361C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2344C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×#127C2211yescharacteristic
80C4×#126C2211yescharacteristic
81#2295C2211yescharacteristic
82#2293C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2094C2211yescharacteristic
87#2088C2211yescharacteristic
88#2087C2211yescharacteristic
89#2083C2211yescharacteristic
90#2083C2211yescharacteristic
91#2072C2211yescharacteristic
92#2071C2211yescharacteristic
93#2067C2211yescharacteristic
94#2067C2211yescharacteristic
95#2057C2211yescharacteristic
96#2057C2211yescharacteristic
97#2055C2211yescharacteristic
98#2054C2211yescharacteristic
99#2042C2211yescharacteristic
100#2042C2211yescharacteristic
101#2041C2211yescharacteristic
102#2035C2211yescharacteristic
103#2033C2211yescharacteristic
104#2033C2211yescharacteristic
105#2033C2211yescharacteristic
106#2024C2211yescharacteristic
107#2024C2211yescharacteristic
108#2023C2211yescharacteristic
109#2023C2211yescharacteristic
110#2012C2211yescharacteristic
111#2012C2211yescharacteristic
112#2011C2211yescharacteristic
113#2000C2211yescharacteristic
114#1999C2211yescharacteristic
115#1990C2211yescharacteristic
116#1990C2211yescharacteristic
117#1987C2211yescharacteristic
118#1983C2211yescharacteristic
119#1983C2211yescharacteristic
120#1973C2211yescharacteristic
121#1970C2211yescharacteristic
122#1968C2211yescharacteristic
123#1959C2211yescharacteristic
124#1957C2211yescharacteristic
125#1948C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic
138#1934C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1919C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1916C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1872C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1862C2211yescharacteristic
180#1853C2211yescharacteristic
181#1839C2211yescharacteristic
182#1834C2211yescharacteristic
183#1824C2211yescharacteristic
184#1802C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1771C2211yescharacteristic
188#1771C2211yescharacteristic
189#1770C2211yescharacteristic
190#1763C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#556—48no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126D411yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117—21no—
245C22×C4⋊C4—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248#489—24no—
249#486—24no—
250#480—24no—
251#474—24no—
252#466—24no—
253#440—24no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#392—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390—21no—
344#390—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#388D411yescharacteristic
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#387D411yescharacteristic
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383D411yescharacteristic
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376—21no—
446C43C2311yescharacteristic
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#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2411yescharacteristic
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8—41no—
514C22×C8—22no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—44no—
532#127—22no—
533#127—41no—
534#126—24no—
535#126—44no—
536#126—44no—
537#126—44no—
538#126—82no—
539#124—22no—
540#124—41no—
541#124—41no—
542#124—41no—
543#124—44no—
544#124—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—44no—
556C4×Q8—22no—
557C4×Q8—41no—
558C4×Q8—44no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—44no—
572C4×D4—82no—
573C4×D4—82no—
574C4×D4—82no—
575C4×D4—82no—
576#117—44no—
577#117—44no—
578C2×C4⋊C4—22no—
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⋊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—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—82no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
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×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×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⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#107—22no—
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107#4114yes—
692#106—41no—
693#106—41no—
694#106—41no—
695C4⋊C8—22no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102#4114yes—
724C22⋊C8—22no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727#97—22no—
728#97—22no—
729#97—41no—
730#97—41no—
731#97—41no—
732#97—41no—
733C4×C8—22no—
734C4×C8—41no—
735C4×C8—41no—
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#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C24C22×D411yescharacteristic
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—42no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4C2×#4112yes—
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—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C2511yescharacteristic
882SD16—44no—
883D8—82no—
884D8—82no—
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—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—82no—
908C2×C8C2×#4112yes—
909C2×C8C2×#4112yes—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
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—21no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
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⋊C4C2×#4112yes—
965C4⋊C4C2×#4112yes—
966C4⋊C4C2×#4112yes—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
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—81no—
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—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4AGL(1,ℤ/8)14yes—
1006C42—22no—
1007C42—22no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—41no—
1021C42—41no—
1022C42—42no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23C2×AGL(1,ℤ/8)12yes—
1059C23C23×D411yescharacteristic
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—84no—
1065Q8—84no—
1066Q8—84no—
1067D4—22no—
1068D4—22no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—84no—
1080D4—84no—
1081D4—84no—
1082D4—84no—
1083D4—84no—
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—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
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—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—84no—
1164C2×C4—84no—
1165C2×C4—84no—
1166C2×C4—162no—
1167C2×C4—162no—
1168C2×C4—162no—
1169C2×C4—162no—
1170C2×C4C2×AGL(1,ℤ/8)12yes—
1171C2×C4C2×AGL(1,ℤ/8)12yes—
1172C2×C4#57812yes—
1173C2×C4C22×#4111yescharacteristic
1174C2×C4C22×#4111yescharacteristic
1175C2×C4#58511yescharacteristic
1176C2×C4#58511yescharacteristic
1177C2×C4#58511yescharacteristic
1178C2×C4#58511yescharacteristic
1179C8—22no—
1180C8—22no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C8—41no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22D4×#4111yescharacteristic
1216C22D4×#4111yescharacteristic
1217C22#350011yescharacteristic
1218C22C22×AGL(1,ℤ/8)11yescharacteristic
1219C22C2×#57811yescharacteristic
1220C22#358511yescharacteristic
1221C22#358511yescharacteristic
1222C4—22no—
1223C4—22no—
1224C4—22no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—42no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4#348011yescharacteristic
1249C4#349311yescharacteristic
1250C4#352111yescharacteristic
1251C4#356611yescharacteristic
1252C2—42no—
1253C2—82no—
1254C2—161no—
1255C2—161no—
1256C2#5979211yescharacteristic
1257C2#6145111yescharacteristic
1258C2#6145111yescharacteristic
1259C2#6152411yescharacteristic
1260C2#6155811yescharacteristic
1261C2#6253811yescharacteristic
1262C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28907C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59711C2semidirect
2. #59698C2semidirect
3. #32163C2semidirect
4. #32136C2semidirect
5. #32048C2semidirect
6. #31116C2semidirect
7. #29394C2semidirect
8. #29365C2semidirect
9. #29095C2semidirect
10. #29054C2semidirect
11. #28931C2semidirect
13. #28882C2semidirect
14. #28046C2semidirect
15. #27783C2semidirect
16. #27697C2semidirect
17. #27571C2semidirect
18. #27406C2semidirect
19. #27143C2semidirect
20. #27111C2semidirect
21. #26916C2semidirect
22. #26737C2semidirect
23. #26704C2semidirect
24. #26640C2semidirect
25. #23226C2semidirect
26. #23132C2semidirect
27. #22968C2semidirect
28. #22938C2semidirect
29. #21665C2semidirect
30. #21646C2semidirect
31. #21288C2semidirect

Maximal subgroups

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

subgroupindex
#597112
#596982
#321632
#321362
#320482
#311162
#293942
#293652
#290952
#290542
#289312
#289072
#288822
#280462
#277832
#276972
#275712
#274062
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