Finite Group Databasebeta

← #6841652

Subgroups — #6841652

Order 512.

1217 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40189C211yesmaximal, characteristic, complemented
2#39780C211yesmaximal, characteristic
3#33268C211yesmaximal, characteristic
4#32538C211yesmaximal, characteristic
5#32523C211yesmaximal, characteristic, complemented
6#32521C211yesmaximal, characteristic, complemented
7#32381C211yesmaximal, characteristic, complemented
8#32378C211yesmaximal, characteristic
9#31251C211yesmaximal, characteristic
10#30955C211yesmaximal, characteristic
11#30948C211yesmaximal, characteristic, complemented
12#30147C211yesmaximal, characteristic, complemented
13#30146C211yesmaximal, characteristic
14#29101C211yesmaximal, characteristic
15#29075C211yesmaximal, characteristic
16#28971C211yesmaximal, characteristic, complemented
17#28966C211yesmaximal, characteristic
18#28804C211yesmaximal, characteristic, complemented
19#28794C211yesmaximal, characteristic, complemented
20#28060C211yesmaximal, characteristic, complemented
21#28053C211yesmaximal, characteristic, complemented
22#28049C211yesmaximal, characteristic
23#28043C211yesmaximal, characteristic
24#27516C211yesmaximal, characteristic
25#27508C211yesmaximal, characteristic
26#26887C211yesmaximal, characteristic, complemented
27#26887C211yesmaximal, characteristic, complemented
28#23078C211yesmaximal, characteristic, complemented
29#23071C211yesmaximal, characteristic
30#21726C211yesmaximal, characteristic, complemented
31#21674C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#478C2211yescharacteristic
35#2863C2211yescharacteristic
36#2860C2211yescharacteristic
37#2798—21no—
38#2772—21no—
39#2762—21no—
40#2758—21no—
41#2739—21no—
42#2719—21no—
43#2719—21no—
44#2689—21no—
45#2664—21no—
46#2655—21no—
47#2570C2211yescharacteristic
48#2552C2211yescharacteristic
49#2550C2211yescharacteristic
50#2550C2211yescharacteristic
51#2514C2211yescharacteristic
52#2513C2211yescharacteristic
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2511C2211yescharacteristic
56#2511C2211yescharacteristic
57#2509C2211yescharacteristic
58#2509C2211yescharacteristic
59#2509C2211yescharacteristic
60#2508C2211yescharacteristic
61#2506C2211yescharacteristic
62#2506C2211yescharacteristic
63#2469—21no—
64#2462—21no—
65#2454C2211yescharacteristic
66#2453—21no—
67#2453C2211yescharacteristic
68#2452C2211yescharacteristic
69#2451C2211yescharacteristic
70#2421—21no—
71#2370C2211yescharacteristic
72#2370C2211yescharacteristic
73#2357C2211yescharacteristic
74#2355C2211yescharacteristic
75#2336—21no—
76#2334—21no—
77C4×C4⋊Q8C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×#125C2211yescharacteristic
80#2097C2211yescharacteristic
81#2097C2211yescharacteristic
82#2097C2211yescharacteristic
83#2094C2211yescharacteristic
84#2094C2211yescharacteristic
85#2092C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2072C2211yescharacteristic
103#2071C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2024C2211yescharacteristic
119#2023C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1990C2211yescharacteristic
123#1990C2211yescharacteristic
124#1973C2211yescharacteristic
125#1973C2211yescharacteristic
126#1968C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1940C2211yescharacteristic
143#1940C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1921C2211yescharacteristic
165#1920C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1919C2211yescharacteristic
174#1919C2211yescharacteristic
175#1918C2211yescharacteristic
176#1917C2211yescharacteristic
177#1917C2211yescharacteristic
178#1916C2211yescharacteristic
179#1916C2211yescharacteristic
180#1880C2211yescharacteristic
181#1877C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1844C2211yescharacteristic
185#1836C2211yescharacteristic
186#1835C2211yescharacteristic
187#1831C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1770C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125D411yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219#500—24no—
220#479—24no—
221#478—24no—
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271#401—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#399—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#396—21no—
305#396—21no—
306#396—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#393—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389D411yescharacteristic
340#389D411yescharacteristic
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#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—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#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#387D411yescharacteristic
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383—21no—
406#383—21no—
407#382—21no—
408#382—21no—
409#382D411yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
438C43C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×D4C2411yescharacteristic
485C23×C4—21no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501#126—44no—
502#126—82no—
503#125—22no—
504#125—22no—
505#125—42no—
506#125—41no—
507#125—41no—
508#125—44no—
509#125—82no—
510#125—82no—
511C22⋊Q8—82no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×Q8—82no—
515C4×Q8—82no—
516C4×D4—22no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2×D411yescharacteristic
556C2×C4⋊C4C2×D411yescharacteristic
557C2×C4⋊C4C2×D411yescharacteristic
558C2×C4⋊C4C2×D411yescharacteristic
559C2×C4⋊C4C2×D411yescharacteristic
560C2×C4⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614#107—22no—
615#107—22no—
616#107—22no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#107#4114yes—
622#106—22no—
623#106—22no—
624#106—22no—
625#106—22no—
626#106—22no—
627#106—41no—
628#106—41no—
629#106—41no—
630#106—41no—
631#106—41no—
632#106—41no—
633C4⋊C8—22no—
634C4⋊C8—22no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—41no—
638C4⋊C8—41no—
639#103—22no—
640#103—22no—
641#103—22no—
642#103—22no—
643#103—41no—
644#103—41no—
645#103—41no—
646#102—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—41no—
651#102—41no—
652#102—41no—
653#97—22no—
654#97—22no—
655#97—22no—
656#97—22no—
657#97—41no—
658#97—41no—
659C4×C8—22no—
660C4×C8—22no—
661C4×C8—41no—
662C4×C8—41no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725C24—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—42no—
735C2×Q8—42no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—42no—
760C22×C4—81no—
761C22×C4—81no—
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C2511yescharacteristic
777SD16—82no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8C2×#4112yes—
799C2×C82−1+412yes—
800C2×C82−1+412yes—
801C2×C82−1+412yes—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—41no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4C2×#4112yes—
876C4⋊C4C2×#4112yes—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—81no—
883C22⋊C4—81no—
884C22⋊C4—81no—
885C22⋊C4—81no—
886C22⋊C4—81no—
887C22⋊C4—81no—
888C22⋊C4—81no—
889C22⋊C4—81no—
890C42—22no—
891C42—22no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—41no—
907C42—41no—
908C42—42no—
909C42—42no—
910C42—81no—
911C42—81no—
912C42—81no—
913C42—81no—
914C42—81no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23C23×D411yescharacteristic
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8—41no—
931Q8—84no—
932Q8—84no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—162no—
1023C2×C4#57512yes—
1024C2×C4#57712yes—
1025C2×C4C22×#4111yescharacteristic
1026C2×C4C2×2−1+411yescharacteristic
1027C2×C4C2×2−1+411yescharacteristic
1028C2×C4C2×2−1+411yescharacteristic
1029C2×C4#58511yescharacteristic
1030C2×C4#58511yescharacteristic
1031C8—22no—
1032C8—22no—
1033C8—22no—
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C8—41no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22D4×#4111yescharacteristic
1047C22#349711yescharacteristic
1048C22#349911yescharacteristic
1049C22C2×#57511yescharacteristic
1050C22C2×#57711yescharacteristic
1051C22#358511yescharacteristic
1052C22#358611yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—41no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—41no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4#346111yescharacteristic
1083C4#352311yescharacteristic
1084C4#356311yescharacteristic
1085C4#356411yescharacteristic
1086C2—161no—
1087C2#3944711yescharacteristic
1088C2#6145811yescharacteristic
1089C2#6152211yescharacteristic
1090C2#6239511yescharacteristic
1091C2#6240211yescharacteristic
1092C2#6248311yescharacteristic
1093C2#6249811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40189C2semidirect
5. #32523C2semidirect
6. #32521C2semidirect
7. #32381C2semidirect
11. #30948C2semidirect
12. #30147C2semidirect
16. #28971C2semidirect
18. #28804C2semidirect
19. #28794C2semidirect
20. #28060C2semidirect
21. #28053C2semidirect
26. #26887C2semidirect
27. #26887C2semidirect
28. #23078C2semidirect
30. #21726C2semidirect
31. #21674C2semidirect

Maximal subgroups

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

subgroupindex
#401892
#397802
#332682
#325382
#325232
#325212
#323812
#323782
#312512
#309552
#309482
#301472
#301462
#291012
#290752
#289712
#289662
#288042
#287942
#280602
#280532
#280492
#280432
#275162
#275082
#268872
#230782
#230712
#217262
#216742