Finite Group Databasebeta

← #7188969

Subgroups — #7188969

Order 512.

1365 conjugacy classes of subgroups.

The subgroup lattice has 1173 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45274C211yesmaximal, characteristic, complemented
2#45037C211yesmaximal, characteristic
3#32240C211yesmaximal, characteristic, complemented
4#32227C211yesmaximal, characteristic, complemented
5#31821C211yesmaximal, characteristic, complemented
6#31820C211yesmaximal, characteristic, complemented
7#31767C211yesmaximal, characteristic
8#31766C211yesmaximal, characteristic
9#31436C211yesmaximal, characteristic, complemented
10#31429C211yesmaximal, characteristic, complemented
11#27823C211yesmaximal, characteristic, complemented
12#27642C211yesmaximal, characteristic, complemented
13#27121C211yesmaximal, characteristic, complemented
14#27117C211yesmaximal, characteristic, complemented
15#27005C211yesmaximal, characteristic, complemented
16#27000C211yesmaximal, characteristic, complemented
17#26733C211yesmaximal, characteristic
18#26724C211yesmaximal, characteristic
19#26458C211yesmaximal, characteristic, complemented
20#26454C211yesmaximal, characteristic, complemented
21#26452C211yesmaximal, characteristic, complemented
22#26293C211yesmaximal, characteristic, complemented
23#25470C211yesmaximal, characteristic, complemented
24#24697C211yesmaximal, characteristic, complemented
25#24346C211yesmaximal, characteristic, complemented
26#24309C211yesmaximal, characteristic
27#23714C211yesmaximal, characteristic
28#23071C211yesmaximal, characteristic, complemented
29#22521C211yesmaximal, characteristic, complemented
30#22101C211yesmaximal, characteristic, complemented
31#21843C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×C8×Q8C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#433C2211yescharacteristic
39#2800—21no—
40#2745—21no—
41#2720—21no—
42#2716—21no—
43#2713—21no—
44#2713—21no—
45#2704—21no—
46#2700—21no—
47#2594—21no—
48#2568C2211yescharacteristic
49#2567C2211yescharacteristic
50#2551C2211yescharacteristic
51#2550C2211yescharacteristic
52#2550C2211yescharacteristic
53#2545—21no—
54#2538C2211yescharacteristic
55#2521—21no—
56#2513C2211yescharacteristic
57#2512C2211yescharacteristic
58#2506—21no—
59#2497C2211yescharacteristic
60#2494C2211yescharacteristic
61#2492—21no—
62#2491C2211yescharacteristic
63#2491C2211yescharacteristic
64#2465—21no—
65#2465—21no—
66#2453C2211yescharacteristic
67#2451—21no—
68#2451C2211yescharacteristic
69#2442C2211yescharacteristic
70#2439C2211yescharacteristic
71#2396C2211yescharacteristic
72#2370C2211yescharacteristic
73#2369C2211yescharacteristic
74#2365C2211yescharacteristic
75#2362C2211yescharacteristic
76#2360C2211yescharacteristic
77#2357C2211yescharacteristic
78#2355C2211yescharacteristic
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic
81#2314C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2058C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2000C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1993C2211yescharacteristic
125#1992C2211yescharacteristic
126#1991C2211yescharacteristic
127#1991C2211yescharacteristic
128#1990C2211yescharacteristic
129#1990C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1988C2211yescharacteristic
135#1988C2211yescharacteristic
136#1988C2211yescharacteristic
137#1988C2211yescharacteristic
138#1987C2211yescharacteristic
139#1987C2211yescharacteristic
140#1985C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1948C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1940C2211yescharacteristic
148#1940C2211yescharacteristic
149#1940C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic
153#1935C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1921C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1920C2211yescharacteristic
171#1919C2211yescharacteristic
172#1919C2211yescharacteristic
173#1918C2211yescharacteristic
174#1918C2211yescharacteristic
175#1918C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1875C2211yescharacteristic
181#1874C2211yescharacteristic
182#1865C2211yescharacteristic
183#1863C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1824C2211yescharacteristic
189#1823C2211yescharacteristic
190#1805C2211yescharacteristic
191#1805C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1798C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1770C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204#557—24no—
205#557—42no—
206#544—24no—
207#544—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×C4×Q8—21no—
231C2×C4×Q8—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240#478—24no—
241#476—42no—
242C8×Q8—42no—
243#440—42no—
244#433—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#401—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400D411yescharacteristic
295#399D411yescharacteristic
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398D411yescharacteristic
302#398D411yescharacteristic
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396D411yescharacteristic
313#396D411yescharacteristic
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395D411yescharacteristic
322#394—21no—
323#394—21no—
324#393—21no—
325#393—21no—
326#393—21no—
327#393D411yescharacteristic
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390—21no—
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
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#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
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#388—21no—
383#388—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#386—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#384—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#381—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
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×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2411yescharacteristic
499C2×SD16—22no—
500C2×SD16—41no—
501C2×SD16—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—44no—
521C4⋊Q8—44no—
522C4⋊Q8—82no—
523#126—82no—
524#125—22no—
525#125—22no—
526#125—22no—
527#125—41no—
528#125—41no—
529#125—44no—
530#125—44no—
531#125—44no—
532#125#4114yes—
533#124—82no—
534#124—82no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—44no—
538C22⋊Q8—44no—
539C22⋊Q8—82no—
540#121—22no—
541#121—41no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—44no—
551C4×Q8—82no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
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⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
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—41no—
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—22no—
662#107—22no—
663#107—22no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—41no—
685#103—41no—
686#103—41no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698#97—22no—
699#97—41no—
700#97—41no—
701C4×C8—22no—
702C4×C8—41no—
703C4×C8—41no—
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#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754C24—21no—
755C24C22×D411yescharacteristic
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q82−1+412yes—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C2511yescharacteristic
830SD16—44no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4C2×#4112yes—
923C4⋊C4C2×#4112yes—
924C4⋊C42−1+412yes—
925C4⋊C42−1+412yes—
926C22⋊C4—24no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—42no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42C2×#4112yes—
975C42H(5,𝔽2)12yes—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23C23×D411yescharacteristic
991Q8—22no—
992Q8—22no—
993Q8—44no—
994Q8—41no—
995Q8—41no—
996Q8—84no—
997Q8—84no—
998Q8—162no—
999Q8—162no—
1000Q8—162no—
1001D4—41no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—162no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—162no—
1092C2×C4—162no—
1093C2×C4#54612yes—
1094C2×C4#54612yes—
1095C2×C4#57712yes—
1096C2×C4C22×#4111yescharacteristic
1097C2×C4C2×H(5,𝔽2)11yescharacteristic
1098C2×C4C2×2−1+411yescharacteristic
1099C2×C4C2×2−1+411yescharacteristic
1100C2×C4C2×2−1+411yescharacteristic
1101C2×C4#58511yescharacteristic
1102C8—41no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22C2×#54611yescharacteristic
1125C22#348611yescharacteristic
1126C22#348911yescharacteristic
1127C22C2×#57711yescharacteristic
1128C22#358411yescharacteristic
1129C22#358511yescharacteristic
1130C22#358611yescharacteristic
1131C4—22no—
1132C4—22no—
1133C4—22no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—42no—
1138C4—42no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—41no—
1145C4—42no—
1146C4—41no—
1147C4—41no—
1148C4—42no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4#351811yescharacteristic
1160C4#352311yescharacteristic
1161C4#354111yescharacteristic
1162C4#355011yescharacteristic
1163C2—81no—
1164C2—161no—
1165C2#4529111yescharacteristic
1166C2#6117411yescharacteristic
1167C2#6122211yescharacteristic
1168C2#6185311yescharacteristic
1169C2#6186111yescharacteristic
1170C2#6217711yescharacteristic
1171C2#6218811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45274C2semidirect
3. #32240C2semidirect
4. #32227C2semidirect
5. #31821C2semidirect
6. #31820C2semidirect
9. #31436C2semidirect
10. #31429C2semidirect
11. #27823C2semidirect
12. #27642C2semidirect
13. #27121C2semidirect
14. #27117C2semidirect
15. #27005C2semidirect
16. #27000C2semidirect
19. #26458C2semidirect
20. #26454C2semidirect
21. #26452C2semidirect
22. #26293C2semidirect
23. #25470C2semidirect
24. #24697C2semidirect
25. #24346C2semidirect
28. #23071C2semidirect
29. #22521C2semidirect
30. #22101C2semidirect
31. #21843C2semidirect

Maximal subgroups

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

subgroupindex
#452742
#450372
#322402
#322272
#318212
#318202
#317672
#317662
#314362
#314292
#278232
#276422
#271212
#271172
#270052
#270002
#267332
#267242
#264582
#264542
#264522
#262932
#254702
#246972
#243462
#243092
#237142
#230712
#225212
#221012
#218432