Finite Group Databasebeta

← #6589271

Subgroups — #6589271

Order 512.

1364 conjugacy classes of subgroups.

The subgroup lattice has 1153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35871C211yesmaximal, characteristic
2#35870C211yesmaximal, characteristic, complemented
3#33285C211yesmaximal, characteristic, complemented
4#33077C211yesmaximal, characteristic, complemented
5#33040C211yesmaximal, characteristic
6#29091C211yesmaximal, characteristic
7#29075C211yesmaximal, characteristic
8#27827C211yesmaximal, characteristic, complemented
9#27782C211yesmaximal, characteristic, complemented
10#27435C211yesmaximal, characteristic
11#27423C211yesmaximal, characteristic
12#27151C211yesmaximal, characteristic, complemented
13#27149C211yesmaximal, characteristic, complemented
14#26919C211yesmaximal, characteristic
15#26919C211yesmaximal, characteristic
16#26845C211yesmaximal, characteristic
17#26836C211yesmaximal, characteristic
18#26694C211yesmaximal, characteristic, complemented
19#26690C211yesmaximal, characteristic, complemented
20#26466C211yesmaximal, characteristic, complemented
21#26451C211yesmaximal, characteristic, complemented
22#24686C211yesmaximal, characteristic
23#24630C211yesmaximal, characteristic
24#23233C211yesmaximal, characteristic, complemented
25#23217C211yesmaximal, characteristic, complemented
26#23112C211yesmaximal, characteristic
27#23076C211yesmaximal, characteristic
28#23073C211yesmaximal, characteristic, complemented
29#23069C211yesmaximal, characteristic, complemented
30#21678C211yesmaximal, characteristic, complemented
31#20504C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41#2665—21no—
42#2655—21no—
43#2647C2211yescharacteristic
44#2642C2211yescharacteristic
45#2590—21no—
46#2589—21no—
47#2587—21no—
48#2585—21no—
49#2565C2211yescharacteristic
50#2551C2211yescharacteristic
51#2550C2211yescharacteristic
52#2549—21no—
53#2546C2211yescharacteristic
54#2533—21no—
55#2533—21no—
56#2528—21no—
57#2524—21no—
58#2514C2211yescharacteristic
59#2511C2211yescharacteristic
60#2492—21no—
61#2454C2211yescharacteristic
62#2452C2211yescharacteristic
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2446C2211yescharacteristic
66#2446C2211yescharacteristic
67#2438—21no—
68#2429—21no—
69#2402—21no—
70#2402C2211yescharacteristic
71#2396—21no—
72#2370C2211yescharacteristic
73#2370C2211yescharacteristic
74#2369C2211yescharacteristic
75#2369C2211yescharacteristic
76#2365C2211yescharacteristic
77#2365C2211yescharacteristic
78#2365C2211yescharacteristic
79#2365C2211yescharacteristic
80#2357C2211yescharacteristic
81#2356C2211yescharacteristic
82#2355C2211yescharacteristic
83#2354C2211yescharacteristic
84#2276C2211yescharacteristic
85#2275C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2073C2211yescharacteristic
91#2071C2211yescharacteristic
92#2068C2211yescharacteristic
93#2068C2211yescharacteristic
94#2059C2211yescharacteristic
95#2057C2211yescharacteristic
96#2055C2211yescharacteristic
97#2055C2211yescharacteristic
98#2055C2211yescharacteristic
99#2055C2211yescharacteristic
100#2043C2211yescharacteristic
101#2043C2211yescharacteristic
102#2026C2211yescharacteristic
103#2024C2211yescharacteristic
104#2024C2211yescharacteristic
105#2024C2211yescharacteristic
106#2024C2211yescharacteristic
107#2024C2211yescharacteristic
108#2013C2211yescharacteristic
109#2013C2211yescharacteristic
110#1993C2211yescharacteristic
111#1992C2211yescharacteristic
112#1991C2211yescharacteristic
113#1990C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1987C2211yescharacteristic
117#1981C2211yescharacteristic
118#1981C2211yescharacteristic
119#1981C2211yescharacteristic
120#1973C2211yescharacteristic
121#1968C2211yescharacteristic
122#1960C2211yescharacteristic
123#1956C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1947C2211yescharacteristic
128#1939C2211yescharacteristic
129#1939C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1933C2211yescharacteristic
142#1933C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1865C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1832C2211yescharacteristic
181#1805C2211yescharacteristic
182#1803C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186C4×#107C2211yescharacteristic
187C4×#107C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228#491—24no—
229#487—24no—
230#478—24no—
231#477—24no—
232#477—24no—
233#461—24no—
234#440—24no—
235#440—24no—
236C4×SD16—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
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×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
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#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400D411yescharacteristic
301#400D411yescharacteristic
302#400D411yescharacteristic
303#400D411yescharacteristic
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398D411yescharacteristic
315#398D411yescharacteristic
316#398D411yescharacteristic
317#398D411yescharacteristic
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#393—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#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#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#388—21no—
370#388—21no—
371#388—21no—
372#388—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#387—21no—
396#387—21no—
397#387—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#383—21no—
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#380—21no—
411#380—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445#376—21no—
446#376—21no—
447#376C2311yescharacteristic
448C2×#95—21no—
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#336C2311yescharacteristic
476#336C2311yescharacteristic
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×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—82no—
527#125—22no—
528#125—22no—
529#125—22no—
530#125—41no—
531C22⋊Q8—82no—
532C22⋊Q8—82no—
533C22⋊Q8—82no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—82no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4#4114yes—
551#117—82no—
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⋊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⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#107—22no—
644#107—22no—
645#107—22no—
646#107—22no—
647#107—41no—
648#107#4114yes—
649#106—22no—
650#106—22no—
651#106—41no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654C4⋊C8—22no—
655C4⋊C8—22no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103#4114yes—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#97—22no—
685#97—22no—
686#97—22no—
687#97—22no—
688#97—41no—
689C4×C8—22no—
690C4×C8—22no—
691C4×C8—41no—
692C4×C8—41no—
693C4×C8—41no—
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#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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
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
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8C2×#4112yes—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4C2×#4112yes—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—24no—
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—42no—
807C22×C4—42no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
829SD16—28no—
830SD16—82no—
831SD16—82no—
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×C8C2×#4112yes—
855C2×C8C2×#4112yes—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
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—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
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—42no—
909C4⋊C4—42no—
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⋊C4C2×#4112yes—
921C4⋊C4C2×#4112yes—
922C4⋊C4C2×#4112yes—
923C4⋊C4C2×#4112yes—
924C22⋊C4—24no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42C2×#4112yes—
965C422−1+412yes—
966C23—22no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C23×D411yescharacteristic
974Q8—22no—
975Q8—22no—
976Q8—41no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—84no—
987Q8—162no—
988Q8—162no—
989D4—22no—
990D4—22no—
991D4—41no—
992D4—41no—
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—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
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—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
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—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—84no—
1077C2×C4—162no—
1078C2×C4—162no—
1079C2×C4#54812yes—
1080C2×C4#54812yes—
1081C2×C4#57712yes—
1082C2×C4#57812yes—
1083C2×C4C22×#4111yescharacteristic
1084C2×C4C22×#4111yescharacteristic
1085C2×C4C22×#4111yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4#58511yescharacteristic
1088C2×C4#58511yescharacteristic
1089C8—22no—
1090C8—22no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22C2×#54811yescharacteristic
1105C22D4×#4111yescharacteristic
1106C22D4×#4111yescharacteristic
1107C22C2×#57711yescharacteristic
1108C22C2×#57811yescharacteristic
1109C22#358511yescharacteristic
1110C22#358611yescharacteristic
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—22no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4#344411yescharacteristic
1141C4#351011yescharacteristic
1142C4#351511yescharacteristic
1143C4#351811yescharacteristic
1144C2—82no—
1145C2#3614211yescharacteristic
1146C2#6134011yescharacteristic
1147C2#6134811yescharacteristic
1148C2#6149911yescharacteristic
1149C2#6151311yescharacteristic
1150C2#6152511yescharacteristic
1151C2#6155111yescharacteristic
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. #35870C2semidirect
3. #33285C2semidirect
4. #33077C2semidirect
8. #27827C2semidirect
9. #27782C2semidirect
12. #27151C2semidirect
13. #27149C2semidirect
18. #26694C2semidirect
19. #26690C2semidirect
20. #26466C2semidirect
21. #26451C2semidirect
24. #23233C2semidirect
25. #23217C2semidirect
28. #23073C2semidirect
29. #23069C2semidirect
30. #21678C2semidirect

Maximal subgroups

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

subgroupindex
#358712
#358702
#332852
#330772
#330402
#290912
#290752
#278272
#277822
#274352
#274232
#271512
#271492
#269192
#268452
#268362
#266942
#266902
#264662
#264512
#246862
#246302
#232332
#232172
#231122
#230762
#230732
#230692
#216782
#205042