Finite Group Databasebeta

← #44543604

Subgroups — #44543604

Order 31936.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22547810C211yesmaximal, characteristic, complemented
2C23×Dic499C211yesmaximal, characteristic, complemented
3#30630335C211yesmaximal, characteristic, complemented
4#30630332C211yesmaximal, characteristic, complemented
5#30630328C212yesmaximal, complemented
6#30630323C212yesmaximal, complemented
7#30630320C211yesmaximal, characteristic, complemented
8D4×Dic499C212yesmaximal, complemented
9(C22⋊D499)⋊C4C212yesmaximal, complemented
10#30630307C211yesmaximal, characteristic, complemented
11#120×C499C211yesmaximal, characteristic, complemented
12#22547810—24no—
13C2×Dic998C2211yescharacteristic, complemented
14C2×C22⋊D499C2212yes—
15C2×C22⋊D499C2211yescharacteristic
16C2×C22⋊D499C2211yescharacteristic, complemented
17C22×Dic499—24no—
18C22×Dic499C2212yes—
19C22×Dic499C2212yes—
20C22×Dic499C2211yescharacteristic
21C22×Dic499C2211yescharacteristic
22C22×Dic499C2211yescharacteristic, complemented
23C2×C4×D499C2211yescharacteristic, complemented
24C4⋊Dic499C2212yescomplemented
25Dic499⋊C4C2212yescomplemented
26Dic499⋊C4C2212yescomplemented
27C22⋊Dic499C2211yescharacteristic
28C22⋊Dic499C2212yes—
29C22⋊Dic499C2212yescomplemented
30(C2×D499)⋊C4C2212yescomplemented
31C4×Dic499C2212yescomplemented
32C24×C499C2211yescharacteristic
33C2×D4×C499C2212yes—
34C2×D4×C499C2211yescharacteristic
35C22⋊C4×C499C2211yescharacteristic
36C22⋊C4×C499C2212yes—
37C22×D499C2311yescharacteristic
38Dic998—22no—
39C22⋊D499—22no—
40C22⋊D499—24no—
41C22⋊D499—22no—
42C2×Dic499—22no—
43C2×Dic499—24no—
44C2×Dic499—24no—
45C2×Dic499—22no—
46C2×Dic499D414yescomplemented
47C2×Dic499C2312yes—
48C2×Dic499C2312yes—
49C2×Dic499C2311yescharacteristic
50C2×Dic499C2311yescharacteristic
51C2×Dic499C2311yescharacteristic
52C4×D499—22no—
53C23×C499—22no—
54C23×C499—24no—
55C23×C499C2311yescharacteristic
56C23×C499C2311yescharacteristic
57C23×C499C2312yes—
58D4×C499—22no—
59D4×C499—24no—
60C2×C4×C499C2312yes—
61C2×C4×C499C2311yescharacteristic
62C22×C499—28no—
63C22×C499—22no—
64C22×C499—22no—
65C22×C499—22no—
66C22×C499—21no—
67C22×C499—22no—
68C22×C499C2×D412yes—
69C22×C499#4114yescomplemented
70C22×C499C2411yescharacteristic
71C2×D499—21no—
72C2×D499—22no—
73C4×C499—21no—
74C4×C499—22no—
75Dic499—22no—
76Dic499—21no—
77Dic499—22no—
78Dic499C2×D412yes—
79Dic499C2×D412yes—
80C2×C499—22no—
81C2×C499—24no—
82C2×C499—41no—
83C2×C499C22×D411yescharacteristic
84C2×C499C2×#4112yes—
85D499—41no—
86C499#52511yescharacteristic, complemented, Sylow
87#525—4991nomaximal, Sylow
88C2×#41—4991no—
89C23×C4—4991no—
90#123—4991no—
91#123—4991no—
92C22⋊Q8—4992no—
93#121—4992no—
94#120—4991no—
95#120D49911yescharacteristic, complemented
96C4×D4—4992no—
97C4×D4—4992no—
98#117—4991no—
99C24C2×D49911yescharacteristic
100#41—9984no—
101C2×Q8—4991no—
102C2×D4—4992no—
103C2×D4—4991no—
104C2×D4—4991no—
105C2×D4C2×D49912yes—
106C2×D4C2×D49911yescharacteristic
107C22×C4—9984no—
108C22×C4—4992no—
109C22×C4—4992no—
110C22×C4—4991no—
111C22×C4—4991no—
112C22×C4—4991no—
113C22×C4—4991no—
114C4⋊C4—4992no—
115C4⋊C4—4992no—
116C4⋊C4—4992no—
117C22⋊C4—4991no—
118C22⋊C4—4992no—
119C22⋊C4—4992no—
120C22⋊C4—4992no—
121C22⋊C4C2×D49911yescharacteristic
122C22⋊C4C2×D49912yes—
123C42—4992no—
124C23—22no—
125C23—24no—
126C23—4991no—
127C23C22×D49911yescharacteristic
128C23C22×D49911yescharacteristic
129C23C22×D49912yes—
130Q8—9982no—
131D4—22no—
132D4—24no—
133D4—9982no—
134D4—9984no—
135D4—9982no—
136C2×C4—9982no—
137C2×C4—9982no—
138C2×C4—9984no—
139C2×C4—9984no—
140C2×C4—9982no—
141C2×C4—4992no—
142C2×C4—4992no—
143C2×C4—4991no—
144C2×C4—4994no—
145C2×C4—4991no—
146C2×C4—4991no—
147C2×C4C22×D49912yes—
148C2×C4C22×D49911yescharacteristic
149C22—28no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—22no—
155C22—9981no—
156C22—9982no—
157C22D4×D49912yes—
158C22#2254781014yescomplemented
159C22C23×D49911yescharacteristic
160C4—21no—
161C4—22no—
162C4—9982no—
163C4—9981no—
164C4—9982no—
165C4—4992no—
166C4—4992no—
167C2—22no—
168C2—24no—
169C2—41no—
170C2—19961no—
171C2C2×D4×D49911yescharacteristic
172C2C2×#2254781012yes—
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#120×C499C2
hypercenter#120D499
hypocenterC499#525
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#22547810C2semidirect
2. C23×Dic499C2semidirect
3. #30630335C2semidirect
4. #30630332C2semidirect
5. #30630328C2semidirect
6. #30630323C2semidirect
7. #30630320C2semidirect
8. D4×Dic499C2semidirect
9. (C22⋊D499)⋊C4C2semidirect
10. #30630307C2semidirect
11. #120×C499C2semidirect
13. C2×Dic998C22semidirect
16. C2×C22⋊D499C22semidirect
22. C22×Dic499C22semidirect
23. C2×C4×D499C22semidirect
24. C4⋊Dic499C22semidirect
25. Dic499⋊C4C22semidirect
26. Dic499⋊C4C22semidirect
29. C22⋊Dic499C22semidirect
30. (C2×D499)⋊C4C22semidirect
31. C4×Dic499C22semidirect
46. C2×Dic499D4semidirect
69. C22×C499#41semidirect
86. C499#525semidirect
95. #120D499semidirect
158. C22#22547810semidirect

Maximal subgroups

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

subgroupindex
C2×#225478102
C23×Dic4992
#306303352
#306303322
#306303282
#306303232
#306303202
D4×Dic4992
(C22⋊D499)⋊C42
#306303072
#120×C4992
#525499