Finite Group Databasebeta

← #44537235

Subgroups — #44537235

Order 31424.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#21463327C211yesmaximal, characteristic, complemented
2C22×C4×D491C211yesmaximal, characteristic, complemented
3#30628319C212yesmaximal, complemented
4#30628317C211yesmaximal, characteristic, complemented
5#30628316C211yesmaximal, characteristic, complemented
6#30628308C211yesmaximal, characteristic, complemented
7#30628305C212yesmaximal, complemented
8D4×Dic491C212yesmaximal, complemented
9(C22⋊D491)⋊C4C212yesmaximal, complemented
10#30628295C211yesmaximal, characteristic, complemented
11#121×C491C211yesmaximal, characteristic, complemented
12C23×D491C2211yescharacteristic
13#21463327—24no—
14C2×Dic982C2211yescharacteristic, complemented
15C2×C22⋊D491C2212yes—
16C2×C22⋊D491C2212yes—
17C22×Dic491C2211yescharacteristic
18C22×Dic491C2212yescomplemented
19C2×C4×D491—24no—
20C2×C4×D491C2211yescharacteristic
21C2×C4×D491C2211yescharacteristic
22C2×C4×D491C2211yescharacteristic
23C2×C4×D491C2211yescharacteristic
24C4⋊Dic491C2211yescharacteristic, complemented
25C4⋊Dic491C2212yescomplemented
26Dic491⋊C4C2212yescomplemented
27C22⋊Dic491C2212yes—
28C22⋊Dic491C2212yescomplemented
29(C2×D491)⋊C4C2212yes—
30(C2×D491)⋊C4C2212yes—
31C4×Dic491C2212yescomplemented
32C2×D4×C491C2212yes—
33C2×D4×C491C2211yescharacteristic, complemented
34C22×C4×C491C2211yescharacteristic
35C4⋊C4×C491C2211yescharacteristic, complemented
36C22⋊C4×C491C2212yescomplemented
37C22×D491—22no—
38C22×D491—22no—
39C22×D491—22no—
40C22×D491C2311yescharacteristic
41C22×D491C2311yescharacteristic
42Dic982—22no—
43C22⋊D491—24no—
44C22⋊D491—24no—
45C2×Dic491—22no—
46C2×Dic491—24no—
47C2×Dic491C2312yes—
48C2×Dic491C2312yes—
49C2×Dic491C2311yescharacteristic
50C2×Dic491C2311yescharacteristic
51C4×D491—22no—
52C4×D491—22no—
53C4×D491—22no—
54C4×D491D414yescomplemented
55C23×C491C2312yes—
56C23×C491C2311yescharacteristic
57D4×C491—24no—
58D4×C491—22no—
59C2×C4×C491—22no—
60C2×C4×C491C2311yescharacteristic
61C2×C4×C491C2312yes—
62C2×C4×C491C2311yescharacteristic
63C22×C491—21no—
64C22×C491—21no—
65C22×C491—22no—
66C22×C491—22no—
67C22×C491—22no—
68C22×C491#4112yescomplemented
69C22×C491C2411yescharacteristic
70C2×D491—28no—
71C2×D491—21no—
72C2×D491—21no—
73C2×D491—21no—
74C2×D491—21no—
75C2×D491C2×D412yes—
76C2×D491#4112yescomplemented
77C4×C491—21no—
78C4×C491—22no—
79C4×C491C2×D412yes—
80Dic491—21no—
81Dic491—22no—
82Dic491—22no—
83Dic491C2×D412yes—
84C2×C491—22no—
85C2×C491—42no—
86C2×C491C22×D411yescharacteristic
87C2×C491C2×#4111yescharacteristic
88C2×C491C2×#4111yescharacteristic
89D491—22no—
90D491—22no—
91C491#52511yescharacteristic, complemented, Sylow
92#525—4911nomaximal, Sylow
93C2×#41—4911no—
94C23×C4—4911no—
95#123—4912no—
96C22⋊Q8—4911no—
97C22⋊Q8—4911no—
98#121—4911no—
99#121D49111yescharacteristic, complemented
100#120—4912no—
101C4×D4—4912no—
102C4×D4—4912no—
103#117—4911no—
104C24—4911no—
105#41—9824no—
106C2×Q8—4911no—
107C2×D4—4912no—
108C2×D4—4912no—
109C2×D4C2×D49112yes—
110C2×D4C2×D49111yescharacteristic, complemented
111C22×C4—9824no—
112C22×C4—4911no—
113C22×C4—4912no—
114C22×C4—4911no—
115C22×C4—4911no—
116C22×C4—4911no—
117C22×C4—4911no—
118C22×C4C2×D49111yescharacteristic
119C4⋊C4—4912no—
120C4⋊C4—4911no—
121C4⋊C4—4912no—
122C4⋊C4C2×D49111yescharacteristic, complemented
123C22⋊C4—4912no—
124C22⋊C4—4912no—
125C22⋊C4—4912no—
126C22⋊C4—4912no—
127C22⋊C4C2×D49112yescomplemented
128C42—4912no—
129C23—9822no—
130C23—9822no—
131C23—9822no—
132C23—4911no—
133C23—4911no—
134C23C22×D49112yes—
135C23C22×D49111yescharacteristic
136Q8—9822no—
137D4—24no—
138D4—22no—
139D4—9824no—
140D4—9824no—
141C2×C4—22no—
142C2×C4—9822no—
143C2×C4—9822no—
144C2×C4—9822no—
145C2×C4—9824no—
146C2×C4—9822no—
147C2×C4—4912no—
148C2×C4—4911no—
149C2×C4—4912no—
150C2×C4—4911no—
151C2×C4—4914no—
152C2×C4C22×D49112yes—
153C2×C4C22×D49111yescharacteristic
154C2×C4C22×D49111yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—9828no—
161C22—9821no—
162C22—9821no—
163C22—9821no—
164C22—9821no—
165C22—4912no—
166C22—4912no—
167C22#2146332712yescomplemented
168C22C23×D49111yescharacteristic
169C4—21no—
170C4—22no—
171C4—9821no—
172C4—9822no—
173C4—9822no—
174C4—4912no—
175C4D4×D49112yes—
176C2—22no—
177C2—42no—
178C2—9822no—
179C2—9822no—
180C2C2×D4×D49111yescharacteristic
181C2#41×D49111yescharacteristic
182C2C2×#2146332711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#121×C491C2
hypercenter#121D491
hypocenterC491#525
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#21463327C2semidirect
2. C22×C4×D491C2semidirect
3. #30628319C2semidirect
4. #30628317C2semidirect
5. #30628316C2semidirect
6. #30628308C2semidirect
7. #30628305C2semidirect
8. D4×Dic491C2semidirect
9. (C22⋊D491)⋊C4C2semidirect
10. #30628295C2semidirect
11. #121×C491C2semidirect
14. C2×Dic982C22semidirect
18. C22×Dic491C22semidirect
24. C4⋊Dic491C22semidirect
25. C4⋊Dic491C22semidirect
26. Dic491⋊C4C22semidirect
28. C22⋊Dic491C22semidirect
31. C4×Dic491C22semidirect
33. C2×D4×C491C22semidirect
35. C4⋊C4×C491C22semidirect
36. C22⋊C4×C491C22semidirect
54. C4×D491D4semidirect
68. C22×C491#41semidirect
76. C2×D491#41semidirect
91. C491#525semidirect
99. #121D491semidirect
110. C2×D4C2×D491semidirect
122. C4⋊C4C2×D491semidirect
127. C22⋊C4C2×D491semidirect
167. C22#21463327semidirect

Maximal subgroups

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

subgroupindex
C2×#214633272
C22×C4×D4912
#306283192
#306283172
#306283162
#306283082
#306283052
D4×Dic4912
(C22⋊D491)⋊C42
#306282952
#121×C4912
#525491