Finite Group Databasebeta

← #6589287

Subgroups — #6589287

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 1197 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35968C211yesmaximal, characteristic, complemented
2#35963C211yesmaximal, characteristic, complemented
3#33284C211yesmaximal, characteristic, complemented
4#33075C211yesmaximal, characteristic, complemented
5#33038C211yesmaximal, characteristic
6#29088C211yesmaximal, characteristic, complemented
7#29072C211yesmaximal, characteristic, complemented
8#27831C211yesmaximal, characteristic, complemented
9#27786C211yesmaximal, characteristic, complemented
10#27431C211yesmaximal, characteristic, complemented
11#27427C211yesmaximal, characteristic, complemented
12#27157C211yesmaximal, characteristic, complemented
13#27143C211yesmaximal, characteristic, complemented
14#26917C211yesmaximal, characteristic, complemented
15#26917C211yesmaximal, characteristic, complemented
16#26844C211yesmaximal, characteristic, complemented
17#26837C211yesmaximal, characteristic, complemented
18#26702C211yesmaximal, characteristic, complemented
19#26698C211yesmaximal, characteristic, complemented
20#26467C211yesmaximal, characteristic, complemented
21#26451C211yesmaximal, characteristic, complemented
22#24686C211yesmaximal, characteristic, complemented
23#24631C211yesmaximal, characteristic
24#23228C211yesmaximal, characteristic, complemented
25#23219C211yesmaximal, characteristic, complemented
26#23108C211yesmaximal, characteristic
27#23072C211yesmaximal, characteristic, complemented
28#23072C211yesmaximal, characteristic, complemented
29#23071C211yesmaximal, characteristic, complemented
30#21678C211yesmaximal, characteristic, complemented
31#20504C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41#2667—21no—
42#2651—21no—
43#2647C2211yescharacteristic
44#2641C2211yescharacteristic
45#2597—21no—
46#2593—21no—
47#2589—21no—
48#2587—21no—
49#2569—21no—
50#2565C2211yescharacteristic
51#2552C2211yescharacteristic
52#2550C2211yescharacteristic
53#2548C2211yescharacteristic
54#2531—21no—
55#2526—21no—
56#2513C2211yescharacteristic
57#2512C2211yescharacteristic
58#2497—21no—
59#2479—21no—
60#2468—21no—
61#2454C2211yescharacteristic
62#2454C2211yescharacteristic
63#2454C2211yescharacteristic
64#2452C2211yescharacteristic
65#2448C2211yescharacteristic
66#2448C2211yescharacteristic
67#2438—21no—
68#2423—21no—
69#2402C2211yescharacteristic
70#2396—21no—
71#2395—21no—
72#2370C2211yescharacteristic
73#2370C2211yescharacteristic
74#2370C2211yescharacteristic
75#2370C2211yescharacteristic
76#2367C2211yescharacteristic
77#2367C2211yescharacteristic
78#2366C2211yescharacteristic
79#2365C2211yescharacteristic
80#2357C2211yescharacteristic
81#2357C2211yescharacteristic
82#2354C2211yescharacteristic
83#2354C2211yescharacteristic
84#2276C2211yescharacteristic
85#2275C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2073C2211yescharacteristic
91#2071C2211yescharacteristic
92#2067C2211yescharacteristic
93#2067C2211yescharacteristic
94#2059C2211yescharacteristic
95#2057C2211yescharacteristic
96#2055C2211yescharacteristic
97#2055C2211yescharacteristic
98#2054C2211yescharacteristic
99#2054C2211yescharacteristic
100#2042C2211yescharacteristic
101#2042C2211yescharacteristic
102#2026C2211yescharacteristic
103#2026C2211yescharacteristic
104#2025C2211yescharacteristic
105#2025C2211yescharacteristic
106#2025C2211yescharacteristic
107#2023C2211yescharacteristic
108#2012C2211yescharacteristic
109#2012C2211yescharacteristic
110#1992C2211yescharacteristic
111#1992C2211yescharacteristic
112#1991C2211yescharacteristic
113#1991C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1987C2211yescharacteristic
117#1983C2211yescharacteristic
118#1983C2211yescharacteristic
119#1982C2211yescharacteristic
120#1972C2211yescharacteristic
121#1970C2211yescharacteristic
122#1961C2211yescharacteristic
123#1957C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1948C2211yescharacteristic
127#1948C2211yescharacteristic
128#1939C2211yescharacteristic
129#1939C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1935C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1921C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic
180#1832C2211yescharacteristic
181#1805C2211yescharacteristic
182#1803C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186C4×#107C2211yescharacteristic
187C4×#106C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1771C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1763C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
228#489—24no—
229#488—24no—
230#478—24no—
231#478—24no—
232#478—24no—
233#459—24no—
234#440—24no—
235#440—24no—
236C4×SD16—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
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×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
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#400—21no—
289#400—21no—
290#400D411yescharacteristic
291#400D411yescharacteristic
292#400D411yescharacteristic
293#400D411yescharacteristic
294#399—21no—
295#399—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398D411yescharacteristic
307#398D411yescharacteristic
308#398D411yescharacteristic
309#398D411yescharacteristic
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#393—21no—
328#391—21no—
329#391—21no—
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#390—21no—
333#390—21no—
334#390—21no—
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#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#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#386—21no—
395#386—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#384—21no—
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—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⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—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×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—41no—
505C2×D8—41no—
506C2×D8—41no—
507C2×D8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—41no—
518#127—22no—
519#127—22no—
520#126—82no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—41no—
527#125—41no—
528#125—41no—
529#124—22no—
530#124—22no—
531#124—41no—
532#124—41no—
533C22⋊Q8—82no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—82no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—82no—
551C4×D4#4114yes—
552#117—82no—
553#117—82no—
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⋊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⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
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⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
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×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—41no—
662#107#4114yes—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—22no—
667#106—41no—
668C4⋊C8—22no—
669C4⋊C8—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—41no—
679#103—41no—
680#103#4114yes—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#97—22no—
701#97—22no—
702#97—22no—
703#97—22no—
704#97—41no—
705C4×C8—22no—
706C4×C8—22no—
707C4×C8—41no—
708C4×C8—41no—
709C4×C8—41no—
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—
757C24—21no—
758C24—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—81no—
767C2×Q8C2×#4112yes—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C2×#4112yes—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—24no—
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—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
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×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C2511yescharacteristic
835SD16—28no—
836D8—82no—
837D8—82no—
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—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8C2×#4112yes—
861C2×C8C2×#4112yes—
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—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
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—81no—
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⋊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—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
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—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42C2×#4112yes—
985C422−1+412yes—
986C23—22no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23C23×D411yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—41no—
1011Q8—41no—
1012Q8—84no—
1013D4—22no—
1014D4—22no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—84no—
1026D4—162no—
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—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
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—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—84no—
1107C2×C4—84no—
1108C2×C4—162no—
1109C2×C4—162no—
1110C2×C4—162no—
1111C2×C4#54812yes—
1112C2×C4#54812yes—
1113C2×C4C22×#4111yescharacteristic
1114C2×C4C22×#4111yescharacteristic
1115C2×C4C22×#4111yescharacteristic
1116C2×C4C2×2−1+411yescharacteristic
1117C2×C4#58511yescharacteristic
1118C2×C4#58511yescharacteristic
1119C8—22no—
1120C8—22no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22C2×#54811yescharacteristic
1149C22D4×#4111yescharacteristic
1150C22D4×#4111yescharacteristic
1151C22#358411yescharacteristic
1152C22#358411yescharacteristic
1153C22#358511yescharacteristic
1154C22#358511yescharacteristic
1155C4—22no—
1156C4—22no—
1157C4—42no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4#344411yescharacteristic
1183C4#351011yescharacteristic
1184C4#351511yescharacteristic
1185C4#351811yescharacteristic
1186C2—82no—
1187C2—161no—
1188C2—161no—
1189C2#3614211yescharacteristic
1190C2#6134311yescharacteristic
1191C2#6134911yescharacteristic
1192C2#6150211yescharacteristic
1193C2#6150711yescharacteristic
1194C2#6153411yescharacteristic
1195C2#6154811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
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
1. #35968C2semidirect
2. #35963C2semidirect
3. #33284C2semidirect
4. #33075C2semidirect
6. #29088C2semidirect
7. #29072C2semidirect
8. #27831C2semidirect
9. #27786C2semidirect
10. #27431C2semidirect
11. #27427C2semidirect
12. #27157C2semidirect
13. #27143C2semidirect
14. #26917C2semidirect
15. #26917C2semidirect
16. #26844C2semidirect
17. #26837C2semidirect
18. #26702C2semidirect
19. #26698C2semidirect
20. #26467C2semidirect
21. #26451C2semidirect
22. #24686C2semidirect
24. #23228C2semidirect
25. #23219C2semidirect
27. #23072C2semidirect
28. #23072C2semidirect
29. #23071C2semidirect
30. #21678C2semidirect
31. #20504C2semidirect

Maximal subgroups

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

subgroupindex
#359682
#359632
#332842
#330752
#330382
#290882
#290722
#278312
#277862
#274312
#274272
#271572
#271432
#269172
#268442
#268372
#267022
#266982
#264672
#264512
#246862
#246312
#232282
#232192
#231082
#230722
#230712
#216782
#205042