Finite Group Databasebeta

← #6846803

Subgroups — #6846803

Order 512.

1181 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42902C211yesmaximal, characteristic
2#42765C211yesmaximal, characteristic, complemented
3#33271C211yesmaximal, characteristic
4#32481C211yesmaximal, characteristic, complemented
5#32435C211yesmaximal, characteristic
6#32320C211yesmaximal, characteristic, complemented
7#31905C211yesmaximal, characteristic
8#31877C211yesmaximal, characteristic, complemented
9#31161C211yesmaximal, characteristic
10#30881C211yesmaximal, characteristic
11#30806C211yesmaximal, characteristic, complemented
12#30158C211yesmaximal, characteristic
13#30140C211yesmaximal, characteristic, complemented
14#29098C211yesmaximal, characteristic, complemented
15#29089C211yesmaximal, characteristic, complemented
16#29031C211yesmaximal, characteristic
17#29029C211yesmaximal, characteristic
18#28963C211yesmaximal, characteristic, complemented
19#28954C211yesmaximal, characteristic, complemented
20#28892C211yesmaximal, characteristic, complemented
21#28880C211yesmaximal, characteristic
22#27826C211yesmaximal, characteristic
23#27754C211yesmaximal, characteristic
24#27575C211yesmaximal, characteristic, complemented
25#27441C211yesmaximal, characteristic, complemented
26#26783C211yesmaximal, characteristic
27#26715C211yesmaximal, characteristic
28#23107C211yesmaximal, characteristic
29#22967C211yesmaximal, characteristic, complemented
30#21678C211yesmaximal, characteristic, complemented
31#21645C211yesmaximal, characteristic, complemented
32C2×#487C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#464C2211yescharacteristic
35#2838—21no—
36#2833—21no—
37#2798—21no—
38#2787—21no—
39#2775—21no—
40#2766—21no—
41#2766—21no—
42#2758—21no—
43#2755—21no—
44#2744—21no—
45#2667—21no—
46#2655—21no—
47#2655—21no—
48#2650—21no—
49#2645C2211yescharacteristic
50#2644C2211yescharacteristic
51#2577—21no—
52#2570C2211yescharacteristic
53#2563C2211yescharacteristic
54#2550C2211yescharacteristic
55#2545C2211yescharacteristic
56#2514—21no—
57#2514C2211yescharacteristic
58#2514C2211yescharacteristic
59#2514C2211yescharacteristic
60#2514C2211yescharacteristic
61#2509C2211yescharacteristic
62#2509C2211yescharacteristic
63#2508C2211yescharacteristic
64#2507C2211yescharacteristic
65#2453C2211yescharacteristic
66#2451C2211yescharacteristic
67#2451C2211yescharacteristic
68#2451C2211yescharacteristic
69#2448C2211yescharacteristic
70#2448C2211yescharacteristic
71#2447C2211yescharacteristic
72#2446C2211yescharacteristic
73#2402C2211yescharacteristic
74#2370C2211yescharacteristic
75#2367C2211yescharacteristic
76#2355C2211yescharacteristic
77#2351C2211yescharacteristic
78#2331C2211yescharacteristic
79#2327C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2099C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2074C2211yescharacteristic
93#2074C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2058C2211yescharacteristic
105#2057C2211yescharacteristic
106#2056C2211yescharacteristic
107#2056C2211yescharacteristic
108#2056C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2026C2211yescharacteristic
115#2025C2211yescharacteristic
116#2024C2211yescharacteristic
117#2023C2211yescharacteristic
118#2016C2211yescharacteristic
119#2015C2211yescharacteristic
120#1993C2211yescharacteristic
121#1993C2211yescharacteristic
122#1991C2211yescharacteristic
123#1988C2211yescharacteristic
124#1983C2211yescharacteristic
125#1971C2211yescharacteristic
126#1969C2211yescharacteristic
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic
129#1968C2211yescharacteristic
130#1960C2211yescharacteristic
131#1959C2211yescharacteristic
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1944C2211yescharacteristic
136#1942C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1939C2211yescharacteristic
141#1939C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1935C2211yescharacteristic
151#1935C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1877C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1835C2211yescharacteristic
185#1832C2211yescharacteristic
186#1805C2211yescharacteristic
187#1804C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218#487—24no—
219#479—24no—
220#464—24no—
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×C4⋊C8C2311yescharacteristic
231C2×C4⋊C8C2311yescharacteristic
232C2×C4⋊C8C2311yescharacteristic
233C2×C4⋊C8C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×#103C2311yescharacteristic
237C2×#103C2311yescharacteristic
238C2×#103C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#401—21no—
273#401—21no—
274#401—21no—
275#401—21no—
276#401—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#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400D411yescharacteristic
293#400D411yescharacteristic
294#400D411yescharacteristic
295#400D411yescharacteristic
296#399—21no—
297#399—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398D411yescharacteristic
309#398D411yescharacteristic
310#398D411yescharacteristic
311#398D411yescharacteristic
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#393—21no—
327#393—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
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#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#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#383—21no—
414#383—21no—
415#382—21no—
416#382—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#380—21no—
425#380—21no—
426C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442#376C2311yescharacteristic
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×Q8C2411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C2×Q16—22no—
489C2×Q16—41no—
490C2×Q16—41no—
491C2×Q16—41no—
492C2×Q16—41no—
493C2×Q16—41no—
494C2×SD16—22no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511#125—22no—
512#125—41no—
513#124—22no—
514#124—41no—
515#124—41no—
516#124—41no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×D4—41no—
528C4×D4—41no—
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⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—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×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613#107—22no—
614#107—41no—
615#107—41no—
616#107—41no—
617#106—22no—
618#106—41no—
619#106—41no—
620#106—41no—
621#106—41no—
622C4⋊C8—22no—
623C4⋊C8—22no—
624C4⋊C8—41no—
625C4⋊C8—41no—
626C4⋊C8—41no—
627C4⋊C8—41no—
628#103—22no—
629#103—22no—
630#103—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103—41no—
639#103—41no—
640#103—41no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103—41no—
646#103#4114yes—
647#102—22no—
648#102—22no—
649#102—41no—
650#102—41no—
651#102—41no—
652#102—41no—
653#102—41no—
654#97—22no—
655#97—41no—
656#97—41no—
657#97—41no—
658#97—41no—
659C4×C8—22no—
660C4×C8—41no—
661C4×C8—41no—
662C4×C8—41no—
663C4×C8—41no—
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#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736C24—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—42no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8C2×#4112yes—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C2511yescharacteristic
800Q16—82no—
801Q16—82no—
802SD16—82no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8C2×#4112yes—
826C2×C82−1+412yes—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4C2×#4112yes—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C22⋊C4—81no—
895C22⋊C4—81no—
896C22⋊C4—81no—
897C22⋊C4—81no—
898C22⋊C4—81no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42—42no—
921C42—81no—
922C42—81no—
923C42—81no—
924C42—81no—
925C42—81no—
926C42—81no—
927C42—81no—
928C42—81no—
929C42—81no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23C23×D411yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942Q8—41no—
943Q8—41no—
944Q8—41no—
945Q8—41no—
946Q8—41no—
947Q8—41no—
948Q8—41no—
949Q8—41no—
950Q8—162no—
951Q8—162no—
952D4—41no—
953D4—41no—
954D4—41no—
955D4—41no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
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—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
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—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—162no—
1044C2×C4C22×#4111yescharacteristic
1045C2×C4C2×2−1+411yescharacteristic
1046C2×C4#58511yescharacteristic
1047C2×C4#58511yescharacteristic
1048C2×C4#58511yescharacteristic
1049C2×C4#58511yescharacteristic
1050C8—22no—
1051C8—22no—
1052C8—41no—
1053C8—41no—
1054C8—41no—
1055C8—41no—
1056C8—41no—
1057C8—41no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22D4×#4111yescharacteristic
1066C22#349711yescharacteristic
1067C22#350011yescharacteristic
1068C22#358411yescharacteristic
1069C22#358411yescharacteristic
1070C22#358611yescharacteristic
1071C22#358611yescharacteristic
1072C4—42no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4#346111yescharacteristic
1102C4#352111yescharacteristic
1103C4#355311yescharacteristic
1104C4#356611yescharacteristic
1105C2—161no—
1106C2#3945911yescharacteristic
1107C2#6148611yescharacteristic
1108C2#6151111yescharacteristic
1109C2#6240911yescharacteristic
1110C2#6241211yescharacteristic
1111C2#6260011yescharacteristic
1112C2#6261511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42765C2semidirect
4. #32481C2semidirect
6. #32320C2semidirect
8. #31877C2semidirect
11. #30806C2semidirect
13. #30140C2semidirect
14. #29098C2semidirect
15. #29089C2semidirect
18. #28963C2semidirect
19. #28954C2semidirect
20. #28892C2semidirect
24. #27575C2semidirect
25. #27441C2semidirect
29. #22967C2semidirect
30. #21678C2semidirect
31. #21645C2semidirect

Maximal subgroups

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

subgroupindex
#429022
#427652
#332712
#324812
#324352
#323202
#319052
#318772
#311612
#308812
#308062
#301582
#301402
#290982
#290892
#290312
#290292
#289632
#289542
#288922
#288802
#278262
#277542
#275752
#274412
#267832
#267152
#231072
#229672
#216782
#216452