Finite Group Databasebeta

← #7500035

Subgroups — #7500035

Order 512.

1222 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53113C211yesmaximal, characteristic
2#45435C211yesmaximal, characteristic, complemented
3#32683C211yesmaximal, characteristic, complemented
4#32637C211yesmaximal, characteristic
5#32575C211yesmaximal, characteristic, complemented
6#32568C211yesmaximal, characteristic
7#32242C211yesmaximal, characteristic
8#32228C211yesmaximal, characteristic, complemented
9#32150C211yesmaximal, characteristic, complemented
10#32134C211yesmaximal, characteristic, complemented
11#30954C211yesmaximal, characteristic
12#30949C211yesmaximal, characteristic, complemented
13#30829C211yesmaximal, characteristic
14#30824C211yesmaximal, characteristic
15#30163C211yesmaximal, characteristic
16#30162C211yesmaximal, characteristic, complemented
17#29529C211yesmaximal, characteristic
18#29528C211yesmaximal, characteristic, complemented
19#28684C211yesmaximal, characteristic, complemented
20#28649C211yesmaximal, characteristic
21#27141C211yesmaximal, characteristic, complemented
22#27140C211yesmaximal, characteristic
23#27024C211yesmaximal, characteristic, complemented
24#27007C211yesmaximal, characteristic
25#26887C211yesmaximal, characteristic, complemented
26#26884C211yesmaximal, characteristic, complemented
27#26715C211yesmaximal, characteristic
28#26696C211yesmaximal, characteristic
29#25487C211yesmaximal, characteristic, complemented
30#25477C211yesmaximal, characteristic
31#22245C211yesmaximal, characteristic, complemented
32C2×#498C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#446C2211yescharacteristic
38#2838—21no—
39#2831—21no—
40#2831—21no—
41#2817—21no—
42#2793—21no—
43#2792—21no—
44#2792—21no—
45#2745—21no—
46#2734—21no—
47#2734—21no—
48#2720—21no—
49#2690—21no—
50#2645C2211yescharacteristic
51#2644C2211yescharacteristic
52#2592C2211yescharacteristic
53#2586—21no—
54#2586—21no—
55#2581C2211yescharacteristic
56#2567C2211yescharacteristic
57#2567C2211yescharacteristic
58#2567C2211yescharacteristic
59#2551—21no—
60#2551—21no—
61#2551C2211yescharacteristic
62#2551C2211yescharacteristic
63#2551C2211yescharacteristic
64#2551C2211yescharacteristic
65#2546C2211yescharacteristic
66#2546C2211yescharacteristic
67#2538C2211yescharacteristic
68#2513C2211yescharacteristic
69#2511C2211yescharacteristic
70#2509C2211yescharacteristic
71#2506C2211yescharacteristic
72#2452C2211yescharacteristic
73#2451C2211yescharacteristic
74#2448C2211yescharacteristic
75#2447C2211yescharacteristic
76#2399C2211yescharacteristic
77#2370C2211yescharacteristic
78#2370C2211yescharacteristic
79#2370C2211yescharacteristic
80#2370C2211yescharacteristic
81#2330C2211yescharacteristic
82#2330C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2096C2211yescharacteristic
88#2094C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2026C2211yescharacteristic
124#2026C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2024C2211yescharacteristic
128#2024C2211yescharacteristic
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#1993C2211yescharacteristic
132#1990C2211yescharacteristic
133#1988C2211yescharacteristic
134#1987C2211yescharacteristic
135#1987C2211yescharacteristic
136#1984C2211yescharacteristic
137#1984C2211yescharacteristic
138#1983C2211yescharacteristic
139#1949C2211yescharacteristic
140#1947C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1943C2211yescharacteristic
144#1943C2211yescharacteristic
145#1943C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1921C2211yescharacteristic
171#1920C2211yescharacteristic
172#1920C2211yescharacteristic
173#1920C2211yescharacteristic
174#1920C2211yescharacteristic
175#1920C2211yescharacteristic
176#1920C2211yescharacteristic
177#1919C2211yescharacteristic
178#1919C2211yescharacteristic
179#1919C2211yescharacteristic
180#1919C2211yescharacteristic
181#1919C2211yescharacteristic
182#1919C2211yescharacteristic
183#1918C2211yescharacteristic
184#1918C2211yescharacteristic
185#1917C2211yescharacteristic
186#1917C2211yescharacteristic
187#1917C2211yescharacteristic
188#1917C2211yescharacteristic
189#1916C2211yescharacteristic
190#1916C2211yescharacteristic
191#1916C2211yescharacteristic
192#1916C2211yescharacteristic
193#1865C2211yescharacteristic
194#1865C2211yescharacteristic
195#1864C2211yescharacteristic
196#1864C2211yescharacteristic
197#1832C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#107C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1746C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224#498—42no—
225#489—42no—
226#476—42no—
227#475—42no—
228#446—42no—
229#446—42no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274#401—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#399—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398D411yescharacteristic
292#398D411yescharacteristic
293#398D411yescharacteristic
294#398D411yescharacteristic
295#397—21no—
296#397—21no—
297#397—21no—
298#397—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#396—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395D411yescharacteristic
325#395D411yescharacteristic
326#395D411yescharacteristic
327#395D411yescharacteristic
328#393—21no—
329#393—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
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#389—21no—
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#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—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#385—21no—
407#385—21no—
408#384—21no—
409#384—21no—
410#384—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#380—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
435#376C2311yescharacteristic
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#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2×D411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506C4⋊Q8—41no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509C4⋊Q8—41no—
510C4⋊Q8—41no—
511C4⋊Q8—41no—
512C4⋊Q8—82no—
513C4⋊Q8—82no—
514C4⋊Q8—82no—
515C4⋊Q8—82no—
516C4⋊Q8—82no—
517C4⋊Q8—82no—
518#125—22no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—82no—
523#124—41no—
524#124—41no—
525C22⋊Q8—82no—
526C22⋊Q8—82no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×D4—41no—
534C4×D4—41no—
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⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632#107—22no—
633#107—22no—
634#107—22no—
635#107—22no—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—22no—
640#106—22no—
641#106—22no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648C4⋊C8—22no—
649C4⋊C8—22no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—22no—
659#103—41no—
660#103—41no—
661#103—41no—
662#102—22no—
663#102—22no—
664#102—22no—
665#102—22no—
666#102—22no—
667#102—41no—
668#102—41no—
669#102—41no—
670#97—22no—
671#97—22no—
672#97—41no—
673C4×C8—22no—
674C4×C8—41no—
675C4×C8—41no—
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
732C24—21no—
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—41no—
742C2×Q8—41no—
743C2×Q8—41no—
744C2×Q8—41no—
745C2×Q8—42no—
746C2×Q8—42no—
747C2×Q8—81no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C22×C4—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—42no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
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×C8H(5,𝔽2)12yes—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
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—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
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⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C42−1+412yes—
900C4⋊C42−1+412yes—
901C4⋊C42−1+412yes—
902C4⋊C42−1+412yes—
903C22⋊C4—42no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—42no—
931C42—42no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23C23×D411yescharacteristic
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—82no—
954Q8—82no—
955Q8—162no—
956Q8—162no—
957Q8—162no—
958Q8—162no—
959Q8—162no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
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—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
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—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
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—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—162no—
1050C2×C4#57712yes—
1051C2×C4#57712yes—
1052C2×C4C2×H(5,𝔽2)11yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4C2×2−1+411yescharacteristic
1055C2×C4C2×2−1+411yescharacteristic
1056C2×C4C2×2−1+411yescharacteristic
1057C2×C4#58511yescharacteristic
1058C8—22no—
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22#348611yescharacteristic
1074C22#348611yescharacteristic
1075C22#349611yescharacteristic
1076C22C2×#57711yescharacteristic
1077C22C2×#57711yescharacteristic
1078C22#358511yescharacteristic
1079C22#358611yescharacteristic
1080C4—22no—
1081C4—22no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—42no—
1092C4—41no—
1093C4—42no—
1094C4—41no—
1095C4—42no—
1096C4—41no—
1097C4—42no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4#354411yescharacteristic
1110C4#355011yescharacteristic
1111C4#355511yescharacteristic
1112C4#355511yescharacteristic
1113C2—161no—
1114C2#5207911yescharacteristic
1115C2#6185811yescharacteristic
1116C2#6186011yescharacteristic
1117C2#6187111yescharacteristic
1118C2#6187911yescharacteristic
1119C2#6230711yescharacteristic
1120C2#6230811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45435C2semidirect
3. #32683C2semidirect
5. #32575C2semidirect
8. #32228C2semidirect
9. #32150C2semidirect
10. #32134C2semidirect
12. #30949C2semidirect
16. #30162C2semidirect
18. #29528C2semidirect
19. #28684C2semidirect
21. #27141C2semidirect
23. #27024C2semidirect
25. #26887C2semidirect
26. #26884C2semidirect
29. #25487C2semidirect
31. #22245C2semidirect

Maximal subgroups

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

subgroupindex
#531132
#454352
#326832
#326372
#325752
#325682
#322422
#322282
#321502
#321342
#309542
#309492
#308292
#308242
#301632
#301622
#295292
#295282
#286842
#286492
#271412
#271402
#270242
#270072
#268872
#268842
#267152
#266962
#254872
#254772
#222452