Finite Group Databasebeta

← #7086641

Subgroups — #7086641

Order 512.

1380 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59713C211yesmaximal, characteristic
2#39663C211yesmaximal, characteristic, complemented
3#32232C211yesmaximal, characteristic, complemented
4#32166C211yesmaximal, characteristic, complemented
5#32166C211yesmaximal, characteristic, complemented
6#32126C211yesmaximal, characteristic
7#31820C211yesmaximal, characteristic, complemented
8#31091C211yesmaximal, characteristic, complemented
9#30522C211yesmaximal, characteristic
10#30522C211yesmaximal, characteristic
11#29554C211yesmaximal, characteristic, complemented
12#29355C211yesmaximal, characteristic, complemented
13#29070C211yesmaximal, characteristic, complemented
14#29005C211yesmaximal, characteristic
15#28010C211yesmaximal, characteristic, complemented
16#27769C211yesmaximal, characteristic, complemented
17#27537C211yesmaximal, characteristic, complemented
18#27341C211yesmaximal, characteristic, complemented
19#27283C211yesmaximal, characteristic, complemented
20#27013C211yesmaximal, characteristic, complemented
21#26918C211yesmaximal, characteristic, complemented
22#26845C211yesmaximal, characteristic, complemented
23#26711C211yesmaximal, characteristic, complemented
24#26642C211yesmaximal, characteristic
25#25290C211yesmaximal, characteristic, complemented
26#24498C211yesmaximal, characteristic, complemented
27#23683C211yesmaximal, characteristic, complemented
28#23284C211yesmaximal, characteristic, complemented
29#23221C211yesmaximal, characteristic, complemented
30#22865C211yesmaximal, characteristic
31#22218C211yesmaximal, characteristic, complemented
32C2×#491C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#419C2211yescharacteristic
41#2862C2211yescharacteristic
42#2806—21no—
43#2788—21no—
44#2775—21no—
45#2774—21no—
46#2768—21no—
47#2727—21no—
48#2666—21no—
49#2604—21no—
50#2589—21no—
51#2586—21no—
52#2551C2211yescharacteristic
53#2546C2211yescharacteristic
54#2546C2211yescharacteristic
55#2545—21no—
56#2521—21no—
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2511C2211yescharacteristic
60#2497C2211yescharacteristic
61#2492C2211yescharacteristic
62#2491C2211yescharacteristic
63#2491C2211yescharacteristic
64#2474—21no—
65#2454C2211yescharacteristic
66#2451C2211yescharacteristic
67#2446C2211yescharacteristic
68#2441C2211yescharacteristic
69#2439—21no—
70#2434C2211yescharacteristic
71#2434C2211yescharacteristic
72#2429C2211yescharacteristic
73#2423C2211yescharacteristic
74#2373—21no—
75#2370C2211yescharacteristic
76#2369C2211yescharacteristic
77#2365C2211yescharacteristic
78#2363C2211yescharacteristic
79#2346C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81#2334—21no—
82C4×C4⋊Q8C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84C4×#126C2211yescharacteristic
85#2293C2211yescharacteristic
86#2100C2211yescharacteristic
87#2088C2211yescharacteristic
88#2083C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic
91#2072C2211yescharacteristic
92#2072C2211yescharacteristic
93#2072C2211yescharacteristic
94#2071C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2066C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2058C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2043C2211yescharacteristic
107#2043C2211yescharacteristic
108#2043C2211yescharacteristic
109#2043C2211yescharacteristic
110#2043C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2026C2211yescharacteristic
114#2024C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2023C2211yescharacteristic
119#2013C2211yescharacteristic
120#2013C2211yescharacteristic
121#2013C2211yescharacteristic
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1990C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1981C2211yescharacteristic
131#1981C2211yescharacteristic
132#1981C2211yescharacteristic
133#1981C2211yescharacteristic
134#1981C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1956C2211yescharacteristic
140#1956C2211yescharacteristic
141#1941C2211yescharacteristic
142#1940C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1926C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1921C2211yescharacteristic
168#1919C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1895C2211yescharacteristic
173#1894C2211yescharacteristic
174#1894C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1873C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1844C2211yescharacteristic
189#1803C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1770C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195#1767C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1744C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126D411yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235#491—42no—
236#487—24no—
237#487—24no—
238#485—42no—
239#479—42no—
240#448—24no—
241#440—42no—
242#440—42no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256#419—42no—
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×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#399—21no—
305#399—21no—
306#399—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388D411yescharacteristic
396#388D411yescharacteristic
397#388D411yescharacteristic
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#387D411yescharacteristic
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#383D411yescharacteristic
423#382—21no—
424#382—21no—
425#382—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454C43C2311yescharacteristic
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×Q8—21no—
491C22×Q8—22no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2411yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×M16—41no—
519C2×M16—41no—
520C2×M16—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—82no—
546#126—24no—
547#126—44no—
548#126—82no—
549#125—22no—
550#125—41no—
551#124—82no—
552#124—82no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557#121—22no—
558#121—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—82no—
568C4×D4—22no—
569C4×D4—41no—
570#117—22no—
571#117—41no—
572#117—82no—
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—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#107—22no—
673#107—22no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103#4114yes—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717C22⋊C8—22no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720#97—41no—
721#97—41no—
722#97—41no—
723C4×C8—22no—
724C4×C8—22no—
725C4×C8—41no—
726C4×C8—41no—
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#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778C24—21no—
779C24C22×D411yescharacteristic
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—44no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—82no—
817C2×Q8—82no—
818C2×Q8—82no—
819C2×Q8C2×#4112yes—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—42no—
827C2×D4—81no—
828C2×D4—81no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C2511yescharacteristic
870SD16—44no—
871SD16—44no—
872SD16—82no—
873SD16—82no—
874M16—82no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8C2×#4112yes—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4#13714yes—
961C4⋊C4C2×#4112yes—
962C4⋊C4H(5,𝔽2)12yes—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—41no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C42—22no—
988C42—22no—
989C42—22no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—41no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23C23×D411yescharacteristic
1030Q8—22no—
1031Q8—22no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—84no—
1047Q8—84no—
1048Q8—162no—
1049Q8—162no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—162no—
1055C2×C4—21no—
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—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
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—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4C2×#13712yes—
1141C2×C4C2×#13712yes—
1142C2×C4C2×#13712yes—
1143C2×C4#57712yes—
1144C2×C4#57712yes—
1145C2×C4C22×#4111yescharacteristic
1146C2×C4C2×H(5,𝔽2)11yescharacteristic
1147C2×C4#58511yescharacteristic
1148C2×C4#58511yescharacteristic
1149C2×C4#58511yescharacteristic
1150C2×C4#58511yescharacteristic
1151C8—22no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22D4×#4111yescharacteristic
1174C22#348811yescharacteristic
1175C22#350011yescharacteristic
1176C22C22×#13711yescharacteristic
1177C22C2×#57711yescharacteristic
1178C22C2×#57711yescharacteristic
1179C22#358611yescharacteristic
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—41no—
1186C4—42no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—42no—
1193C4—41no—
1194C4—41no—
1195C4—42no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4#350611yescharacteristic
1209C4#352111yescharacteristic
1210C4#354011yescharacteristic
1211C4#356811yescharacteristic
1212C2—81no—
1213C2—161no—
1214C2#4418211yescharacteristic
1215C2#6145711yescharacteristic
1216C2#6148111yescharacteristic
1217C2#6200211yescharacteristic
1218C2#6204211yescharacteristic
1219C2#6254011yescharacteristic
1220C2#6260311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39663C2semidirect
3. #32232C2semidirect
4. #32166C2semidirect
5. #32166C2semidirect
7. #31820C2semidirect
8. #31091C2semidirect
11. #29554C2semidirect
12. #29355C2semidirect
13. #29070C2semidirect
15. #28010C2semidirect
16. #27769C2semidirect
17. #27537C2semidirect
18. #27341C2semidirect
19. #27283C2semidirect
20. #27013C2semidirect
21. #26918C2semidirect
22. #26845C2semidirect
23. #26711C2semidirect
25. #25290C2semidirect
26. #24498C2semidirect
27. #23683C2semidirect
28. #23284C2semidirect
29. #23221C2semidirect
31. #22218C2semidirect

Maximal subgroups

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

subgroupindex
#597132
#396632
#322322
#321662
#321262
#318202
#310912
#305222
#295542
#293552
#290702
#290052
#280102
#277692
#275372
#273412
#272832
#270132
#269182
#268452
#267112
#266422
#252902
#244982
#236832
#232842
#232212
#228652
#222182