Finite Group Databasebeta

← #24919612

Subgroups — #24919612

Order 10624.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128415C211yesmaximal, characteristic, complemented
2#19128345C211yesmaximal, characteristic, complemented
3#19128059C211yesmaximal, characteristic, complemented
4#19128043C211yesmaximal, characteristic, complemented
5#19128024C211yesmaximal, characteristic, complemented
6#19127979C211yesmaximal, characteristic, complemented
7#19127945C211yesmaximal, characteristic, complemented
8#19127934C211yesmaximal, characteristic, complemented
9#19127914C211yesmaximal, characteristic, complemented
10#19127843C211yesmaximal, characteristic, complemented
11#19127813C211yesmaximal, characteristic, complemented
12#19127775C211yesmaximal, characteristic, complemented
13#19127706C211yesmaximal, characteristic, complemented
14#19127694C211yesmaximal, characteristic, complemented
15#447×C83C211yesmaximal, characteristic, complemented
16C2×#13050589C2211yescharacteristic
17C2×#13050578C2211yescharacteristic, complemented
18C2×#13050574C2211yescharacteristic
19C2×C8×D83C2211yescharacteristic, complemented
20#14581791C2211yescharacteristic, complemented
21#14581779—21no—
22#14581779C2211yescharacteristic
23#14581778—21no—
24#14581773—21no—
25#14581771C2211yescharacteristic
26#14581764—21no—
27#14581764—21no—
28#14581763C2211yescharacteristic
29#14581763C2211yescharacteristic, complemented
30#14581761—21no—
31D4×Dic83C2211yescharacteristic
32D4×Dic83C2211yescharacteristic, complemented
33C4×C22⋊D83C2211yescharacteristic
34#14581751C2211yescharacteristic
35#14581750C2211yescharacteristic, complemented
36#14581748—21no—
37C2×C22⋊Dic83—21no—
38#14581726C2211yescharacteristic, complemented
39#14581725C2211yescharacteristic, complemented
40#14581724C2211yescharacteristic, complemented
41Dic83⋊C8C2211yescharacteristic, complemented
42#14581717C2211yescharacteristic, complemented
43#14581717C2211yescharacteristic, complemented
44#14581715C2211yescharacteristic, complemented
45#14581713C2211yescharacteristic
46#14581713C2211yescharacteristic
47#14581713C2211yescharacteristic
48#14581713C2211yescharacteristic
49#14581713C2211yescharacteristic, complemented
50(C2×D83)⋊C8C2211yescharacteristic, complemented
51#14581702C2211yescharacteristic, complemented
52C22×D4×C83C2211yescharacteristic
53C2×D8×C83C2211yescharacteristic
54C2×D8×C83C2211yescharacteristic
55#121×C83C2211yescharacteristic
56#102×C83C2211yescharacteristic
57#102×C83C2211yescharacteristic
58C22⋊C8×C83C2211yescharacteristic
59#13050589—22no—
60#13050589—41no—
61C2×Dic166—21no—
62C2×Dic166C2311yescharacteristic
63C2×C22⋊D83—21no—
64C2×C22⋊D83—21no—
65C2×C22⋊D83—21no—
66C2×C22⋊D83D411yescharacteristic
67C22×Dic83—21no—
68C22×Dic83—21no—
69C22×Dic83—21no—
70C2×C4×D83C2311yescharacteristic
71#13050578—41no—
72#13050574—41no—
73C2×C83⋊C8C2311yescharacteristic
74C2×C83⋊C8C2311yescharacteristic
75C8×D83—41no—
76C4⋊Dic83C2311yescharacteristic
77C4⋊Dic83C2311yescharacteristic
78C4⋊Dic83C2311yescharacteristic
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81Dic83⋊C4D411yescharacteristic
82C22⋊Dic83—21no—
83C22⋊Dic83—21no—
84C22⋊Dic83—21no—
85C22⋊Dic83—21no—
86C22⋊Dic83—21no—
87C22⋊Dic83—21no—
88C22⋊Dic83—21no—
89C22⋊Dic83—21no—
90C22⋊Dic83D411yescharacteristic
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4D411yescharacteristic
93C4×Dic83—21no—
94C4×Dic83—21no—
95C4×Dic83C2311yescharacteristic
96C24×C83—21no—
97C2×D4×C83—22no—
98C2×D4×C83—21no—
99C2×D4×C83—21no—
100C2×D4×C83—41no—
101C2×D4×C83C2311yescharacteristic
102C2×D4×C83C2311yescharacteristic
103C2×D4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105D8×C83—22no—
106D8×C83—41no—
107C2×C8×C83C2311yescharacteristic
108C2×C8×C83C2311yescharacteristic
109C4⋊C4×C83C2311yescharacteristic
110C22⋊C4×C83—21no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—42no—
115C23×C83—42no—
116C23×C83—81no—
117C23×C83C2×D411yescharacteristic
118C22×D83C2×D411yescharacteristic
119D4×C83—21no—
120D4×C83—21no—
121D4×C83—21no—
122D4×C83—21no—
123D4×C83—21no—
124D4×C83—42no—
125D4×C83—81no—
126D4×C83#4112yes—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2411yescharacteristic
132C22⋊D83—41no—
133C22⋊D83—42no—
134C22⋊D83—81no—
135C22⋊D83—81no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—42no—
141C2×Dic83—42no—
142C2×Dic83—81no—
143C2×Dic83C2×D411yescharacteristic
144C2×Dic83C2×D411yescharacteristic
145C2×Dic83C2×D411yescharacteristic
146C4×D83—21no—
147C4×D83—21no—
148Dic166—21no—
149Dic166—21no—
150Dic166—81no—
151C8×C83—21no—
152C8×C83—21no—
153C83⋊C8—21no—
154C83⋊C8—21no—
155C22×C83—22no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—41no—
160C22×C83—41no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—84no—
168C22×C83C22×D411yescharacteristic
169C2×D83—21no—
170C2×D83—21no—
171C2×D83—21no—
172C4×C83—21no—
173C4×C83—41no—
174C4×C83C2×#4111yescharacteristic
175C4×C83H(5,𝔽2)11yescharacteristic
176Dic83—21no—
177Dic83—21no—
178Dic83—21no—
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182Dic83—41no—
183C2×C83—41no—
184C2×C83—42no—
185C2×C83—81no—
186C2×C83—81no—
187C2×C83#54611yescharacteristic
188C2×C83#57511yescharacteristic
189C2×C83#57611yescharacteristic
190D83—41no—
191#3319—831nomaximal, Sylow
192C83#331911yescharacteristic, complemented, Sylow
193#555—831no—
194#546—831no—
195#489—831no—
196#485—831no—
197#482—831no—
198#474—831no—
199#468—831no—
200#466—831no—
201#463—831no—
202#449—831no—
203#447D8311yescharacteristic, complemented
204#442—831no—
205#435—831no—
206#418—831no—
207#416—831no—
208C2×#41—831no—
209C22×D4C2×D8311yescharacteristic
210C2×SD16—831no—
211C2×D8C2×D8311yescharacteristic
212C2×D8C2×D8311yescharacteristic
213C2×M16—831no—
214C22×C8—831no—
215C4⋊Q8—831no—
216#124—831no—
217#124—1661no—
218#124—1661no—
219#123—1661no—
220C22⋊Q8—831no—
221#121—831no—
222#121—831no—
223#121—1661no—
224#121—1661no—
225#121C2×D8311yescharacteristic
226#120—1661no—
227C4×D4—831no—
228C4×D4—831no—
229C4×D4—831no—
230#117—831no—
231#117—831no—
232#117—1661no—
233C2×C22⋊C4—1661no—
234#107—831no—
235#107—831no—
236#106—831no—
237C4⋊C8—831no—
238#103—831no—
239#103—831no—
240#103—831no—
241#102—831no—
242#102—831no—
243#102—831no—
244#102—831no—
245#102—831no—
246#102C2×D8311yescharacteristic
247#102C2×D8311yescharacteristic
248C22⋊C8—831no—
249C22⋊C8C2×D8311yescharacteristic
250#97—831no—
251C24—21no—
252#41—3321no—
253#41—1662no—
254C2×Q8—831no—
255C2×Q8—1661no—
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—831no—
261C2×D4—1661no—
262C2×D4—1661no—
263C2×D4—1661no—
264C2×D4C22×D8311yescharacteristic
265C2×D4C22×D8311yescharacteristic
266C2×D4C22×D8311yescharacteristic
267C22×C4—831no—
268C22×C4—1661no—
269C22×C4—1661no—
270C22×C4—1661no—
271C22×C4C22×D8311yescharacteristic
272SD16—3321no—
273D8—22no—
274D8—41no—
275M16—3321no—
276C2×C8—3321no—
277C2×C8—831no—
278C2×C8—831no—
279C2×C8C22×D8311yescharacteristic
280C2×C8C22×D8311yescharacteristic
281C4⋊C4—831no—
282C4⋊C4—831no—
283C4⋊C4—831no—
284C4⋊C4—831no—
285C4⋊C4—1661no—
286C4⋊C4—1661no—
287C4⋊C4C22×D8311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—831no—
290C22⋊C4—831no—
291C22⋊C4—1661no—
292C22⋊C4—1661no—
293C22⋊C4—1661no—
294C22⋊C4—1661no—
295C22⋊C4—1661no—
296C22⋊C4—1661no—
297C22⋊C4—1661no—
298C22⋊C4—1661no—
299C22⋊C4—1661no—
300C42—831no—
301C42—1661no—
302C42—1661no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—831no—
310C23D4×D8311yescharacteristic
311Q8—6641no—
312Q8—1661no—
313Q8—1661no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—81no—
321D4—3322no—
322D4—3321no—
323D4—6641no—
324D4—6641no—
325D4#1305058912yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3322no—
330C2×C4—3322no—
331C2×C4—831no—
332C2×C4—831no—
333C2×C4—831no—
334C2×C4—6641no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4—1661no—
338C2×C4—1661no—
339C2×C4—1661no—
340C2×C4—1661no—
341C2×C4D4×D8311yescharacteristic
342C2×C4C23×D8311yescharacteristic
343C8—21no—
344C8—21no—
345C8—1661no—
346C8—1661no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—84no—
360C22—1661no—
361C22—1661no—
362C22—1661no—
363C22C2×D4×D8311yescharacteristic
364C4—21no—
365C4—41no—
366C4—3321no—
367C4—3321no—
368C4—3321no—
369C4—3321no—
370C4—1661no—
371C4—1661no—
372C4—1661no—
373C4C2×#1305058911yescharacteristic
374C4#1458183711yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—3321no—
380C2#1912833811yescharacteristic
381C2#1912849711yescharacteristic
382C2#1912850211yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#447×C83C2
socleC22×C83C22×D4
hypercenter#447D83
hypocenterC83#3319
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #19128415C2semidirect
2. #19128345C2semidirect
3. #19128059C2semidirect
4. #19128043C2semidirect
5. #19128024C2semidirect
6. #19127979C2semidirect
7. #19127945C2semidirect
8. #19127934C2semidirect
9. #19127914C2semidirect
10. #19127843C2semidirect
11. #19127813C2semidirect
12. #19127775C2semidirect
13. #19127706C2semidirect
14. #19127694C2semidirect
15. #447×C83C2semidirect
17. C2×#13050578C22semidirect
19. C2×C8×D83C22semidirect
20. #14581791C22semidirect
29. #14581763C22semidirect
32. D4×Dic83C22semidirect
35. #14581750C22semidirect
38. #14581726C22semidirect
39. #14581725C22semidirect
40. #14581724C22semidirect
41. Dic83⋊C8C22semidirect
42. #14581717C22semidirect
43. #14581717C22semidirect
44. #14581715C22semidirect
49. #14581713C22semidirect
50. (C2×D83)⋊C8C22semidirect
51. #14581702C22semidirect
192. C83#3319semidirect
203. #447D83semidirect

Maximal subgroups

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

subgroupindex
#191284152
#191283452
#191280592
#191280432
#191280242
#191279792
#191279452
#191279342
#191279142
#191278432
#191278132
#191277752
#191277062
#191276942
#447×C832
#331983