Finite Group Databasebeta

← #7582744

Subgroups — #7582744

Order 512.

1435 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59633C211yesmaximal, characteristic
2#36553C211yesmaximal, characteristic, complemented
3#31778C211yesmaximal, characteristic, complemented
4#31738C211yesmaximal, characteristic, complemented
5#30797C211yesmaximal, characteristic, complemented
6#30717C211yesmaximal, characteristic
7#29480C211yesmaximal, characteristic, complemented
8#29465C211yesmaximal, characteristic, complemented
9#29011C211yesmaximal, characteristic, complemented
10#28898C211yesmaximal, characteristic, complemented
11#28091C211yesmaximal, characteristic, complemented
12#27795C211yesmaximal, characteristic, complemented
13#27329C211yesmaximal, characteristic, complemented
14#27194C211yesmaximal, characteristic, complemented
15#27152C211yesmaximal, characteristic, complemented
16#27056C211yesmaximal, characteristic, complemented
17#26862C211yesmaximal, characteristic, complemented
18#26805C211yesmaximal, characteristic, complemented
19#26805C211yesmaximal, characteristic, complemented
20#26731C211yesmaximal, characteristic, complemented
21#26727C211yesmaximal, characteristic, complemented
22#26709C211yesmaximal, characteristic, complemented
23#26230C211yesmaximal, characteristic
24#24951C211yesmaximal, characteristic, complemented
25#23298C211yesmaximal, characteristic, complemented
26#23167C211yesmaximal, characteristic, complemented
27#23142C211yesmaximal, characteristic, complemented
28#23063C211yesmaximal, characteristic, complemented
29#22931C211yesmaximal, characteristic, complemented
30#21578C211yesmaximal, characteristic, complemented
31C4×#480C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#468C2211yescharacteristic
38#2855—21no—
39#2855C2211yescharacteristic
40#2808—21no—
41#2803—21no—
42#2602—21no—
43#2588—21no—
44#2587—21no—
45#2585—21no—
46#2574—21no—
47#2557—21no—
48#2544—21no—
49#2541C2211yescharacteristic
50#2511C2211yescharacteristic
51#2507C2211yescharacteristic
52#2505—21no—
53#2497C2211yescharacteristic
54#2492C2211yescharacteristic
55#2491C2211yescharacteristic
56#2491C2211yescharacteristic
57#2490C2211yescharacteristic
58#2490C2211yescharacteristic
59#2485C2211yescharacteristic
60#2459—21no—
61#2450—21no—
62#2445—21no—
63#2445C2211yescharacteristic
64#2445C2211yescharacteristic
65#2440C2211yescharacteristic
66#2417C2211yescharacteristic
67#2374—21no—
68#2370C2211yescharacteristic
69#2369C2211yescharacteristic
70#2369C2211yescharacteristic
71#2363C2211yescharacteristic
72#2363C2211yescharacteristic
73#2360C2211yescharacteristic
74#2360C2211yescharacteristic
75#2355C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2345C2211yescharacteristic
78C4×#123—21no—
79C4×#123C2211yescharacteristic
80C4×#121C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2100C2211yescharacteristic
84#2094C2211yescharacteristic
85#2087C2211yescharacteristic
86#2083C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2075C2211yescharacteristic
90#2071C2211yescharacteristic
91#2067C2211yescharacteristic
92#2066C2211yescharacteristic
93#2065C2211yescharacteristic
94#2065C2211yescharacteristic
95#2059C2211yescharacteristic
96#2057C2211yescharacteristic
97#2057C2211yescharacteristic
98#2055C2211yescharacteristic
99#2041C2211yescharacteristic
100#2036C2211yescharacteristic
101#2035C2211yescharacteristic
102#2035C2211yescharacteristic
103#2033C2211yescharacteristic
104#2033C2211yescharacteristic
105#2033C2211yescharacteristic
106#2033C2211yescharacteristic
107#2033C2211yescharacteristic
108#2026C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2014C2211yescharacteristic
112#2000C2211yescharacteristic
113#2000C2211yescharacteristic
114#2000C2211yescharacteristic
115#1990C2211yescharacteristic
116#1989C2211yescharacteristic
117#1988C2211yescharacteristic
118#1982C2211yescharacteristic
119#1973C2211yescharacteristic
120#1973C2211yescharacteristic
121#1968C2211yescharacteristic
122#1957C2211yescharacteristic
123#1954C2211yescharacteristic
124#1947C2211yescharacteristic
125#1947C2211yescharacteristic
126#1943C2211yescharacteristic
127#1942C2211yescharacteristic
128#1941C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1895C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1873C2211yescharacteristic
174#1870C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1825C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191#1771C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1749C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127—21no—
209C2×#127C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#124—21no—
212C2×#124—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123D411yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C42—21no—
235C22×C42C2311yescharacteristic
236#501—24no—
237#480—24no—
238#480—24no—
239#480—24no—
240#477—24no—
241#468—24no—
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#392—21no—
320#392—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388D411yescharacteristic
370#388D411yescharacteristic
371#387—21no—
372#387—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#387D411yescharacteristic
387#387D411yescharacteristic
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385D411yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382—21no—
406#381—21no—
407#381D411yescharacteristic
408#380—21no—
409#380—21no—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
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⋊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⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C2×#95—21no—
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526#127—41no—
527#127—41no—
528#127—82no—
529#125—22no—
530#125—41no—
531#124—82no—
532#124—82no—
533#123—24no—
534#123—44no—
535#123—82no—
536C22⋊Q8—22no—
537C22⋊Q8—41no—
538C22⋊Q8—41no—
539C22⋊Q8—41no—
540C22⋊Q8—82no—
541#121—22no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—41no—
546#121—41no—
547#121—41no—
548#121—41no—
549C4×Q8—22no—
550C4×Q8—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—82no—
558C4×D4—82no—
559C4×D4—82no—
560#117—41no—
561#117—41no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
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—41no—
590C2×C4⋊C4—41no—
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⋊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×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—41no—
659C2×C42—41no—
660C2×C42—82no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—22no—
670#107—22no—
671#107—22no—
672#107—22no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107#4114yes—
677#107#4114yes—
678#106—22no—
679#106—22no—
680#106—41no—
681#106—41no—
682C4⋊C8—22no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—41no—
689#103—41no—
690#103—41no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—22no—
713#97—41no—
714#97—41no—
715C4×C8—41no—
716C4×C8—41no—
717C4×C8—41no—
718C4×C8—41no—
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#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#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764C24—21no—
765C24—21no—
766C24C22×D411yescharacteristic
767C24C22×D411yescharacteristic
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—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
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—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
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×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C2511yescharacteristic
873SD16—82no—
874SD16—82no—
875M16—82no—
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—
899C2×C8C2×#4112yes—
900C4⋊C4—22no—
901C4⋊C4—21no—
902C4⋊C4—21no—
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—41no—
925C4⋊C4—41no—
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—42no—
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#13714yes—
951C4⋊C4C2×#4112yes—
952C4⋊C4C2×#4112yes—
953C4⋊C4C2×#4112yes—
954C4⋊C4C2×#4112yes—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—81no—
976C22⋊C4—81no—
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—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—41no—
1001C42—41no—
1002C42—42no—
1003C42—42no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
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—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23#57612yes—
1043C23C23×D411yescharacteristic
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—162no—
1049Q8—162no—
1050D4—44no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—84no—
1060D4—84no—
1061D4—162no—
1062D4—162no—
1063D4—162no—
1064D4—162no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—44no—
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—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—82no—
1150C2×C4—84no—
1151C2×C4—84no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4—162no—
1155C2×C4C2×#13712yes—
1156C2×C4C2×#13712yes—
1157C2×C4C2×#13712yes—
1158C2×C4C22×#4111yescharacteristic
1159C2×C4C22×#4111yescharacteristic
1160C2×C4#58511yescharacteristic
1161C2×C4#58511yescharacteristic
1162C2×C4#58511yescharacteristic
1163C2×C4#58511yescharacteristic
1164C8—22no—
1165C8—22no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22D4×#4111yescharacteristic
1201C22D4×#4111yescharacteristic
1202C22#348511yescharacteristic
1203C22C22×#13711yescharacteristic
1204C22C2×#57611yescharacteristic
1205C22#358411yescharacteristic
1206C22#358511yescharacteristic
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—42no—
1216C4—42no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—42no—
1222C4—42no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4#348011yescharacteristic
1234C4#351011yescharacteristic
1235C4#352411yescharacteristic
1236C4#356611yescharacteristic
1237C2—42no—
1238C2—81no—
1239C2—161no—
1240C2—161no—
1241C2#5917511yescharacteristic
1242C2#6144011yescharacteristic
1243C2#6146911yescharacteristic
1244C2#6148911yescharacteristic
1245C2#6151911yescharacteristic
1246C2#6172611yescharacteristic
1247C2#6175111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2541C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36553C2semidirect
3. #31778C2semidirect
4. #31738C2semidirect
5. #30797C2semidirect
7. #29480C2semidirect
8. #29465C2semidirect
9. #29011C2semidirect
10. #28898C2semidirect
11. #28091C2semidirect
12. #27795C2semidirect
13. #27329C2semidirect
14. #27194C2semidirect
15. #27152C2semidirect
16. #27056C2semidirect
17. #26862C2semidirect
18. #26805C2semidirect
19. #26805C2semidirect
20. #26731C2semidirect
21. #26727C2semidirect
22. #26709C2semidirect
24. #24951C2semidirect
25. #23298C2semidirect
26. #23167C2semidirect
27. #23142C2semidirect
28. #23063C2semidirect
29. #22931C2semidirect
30. #21578C2semidirect
31. C4×#480C2semidirect

Maximal subgroups

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

subgroupindex
#596332
#365532
#317782
#317382
#307972
#307172
#294802
#294652
#290112
#288982
#280912
#277952
#273292
#271942
#271522
#270562
#268622
#268052
#267312
#267272
#267092
#262302
#249512
#232982
#231672
#231422
#230632
#229312
#215782
C4×#4802