Finite Group Databasebeta

← #44537238

Subgroups — #44537238

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×#21463329C211yesmaximal, characteristic, complemented
2C22×C4×D491C211yesmaximal, characteristic, complemented
3#30628322C212yesmaximal, complemented
4#30628313C211yesmaximal, characteristic, complemented
5#30628312C211yesmaximal, characteristic, complemented
6#30628311C211yesmaximal, characteristic, complemented
7#30628307C212yesmaximal, complemented
8#30628299C212yesmaximal, complemented
9(C22⋊D491)⋊C4C212yesmaximal, complemented
10#30628295C211yesmaximal, characteristic, complemented
11C22⋊Q8×C491C211yesmaximal, characteristic, complemented
12C23×D491C2211yescharacteristic
13#21463329—24no—
14C2×D1964C2212yes—
15C2×D1964C2212yes—
16C2×D1964C2211yescharacteristic, complemented
17C2×C22⋊D491C2212yes—
18C22×Dic491C2211yescharacteristic
19C2×C4×D491—24no—
20C2×C4×D491C2211yescharacteristic
21C2×C4×D491C2211yescharacteristic
22C2×C4×D491C2211yescharacteristic
23C2×C4×D491C2211yescharacteristic
24C2×C4×D491C2212yescomplemented
25C4⋊Dic491C2211yescharacteristic, complemented
26Dic491⋊C4C2212yescomplemented
27(C2×D491)⋊C4C2212yes—
28(C2×D491)⋊C4C2212yes—
29(C2×D491)⋊C4C2212yescomplemented
30(C2×D491)⋊C4C2212yescomplemented
31C4×Dic491C2212yescomplemented
32C2×Q8×C491C2211yescharacteristic, complemented
33C22×C4×C491C2211yescharacteristic
34C4⋊C4×C491C2211yescharacteristic, complemented
35C4⋊C4×C491C2212yescomplemented
36C22⋊C4×C491C2212yes—
37C22×D491—22no—
38C22×D491—22no—
39C22×D491—22no—
40C22×D491C2312yes—
41C22×D491C2311yescharacteristic
42C22×D491C2311yescharacteristic
43D1964—24no—
44D1964—24no—
45D1964—22no—
46C22⋊D491—24no—
47C2×Dic491—22no—
48C2×Dic491C2312yes—
49C2×Dic491C2311yescharacteristic
50C2×Dic491C2311yescharacteristic
51C4×D491—22no—
52C4×D491—22no—
53C4×D491—22no—
54C4×D491—24no—
55C4×D491D414yescomplemented
56C23×C491C2311yescharacteristic
57Q8×C491—22no—
58C2×C4×C491—22no—
59C2×C4×C491C2311yescharacteristic
60C2×C4×C491C2312yes—
61C2×C4×C491C2312yes—
62C2×C4×C491C2311yescharacteristic
63C22×C491—21no—
64C22×C491—21no—
65C22×C491#4112yescomplemented
66C22×C491C2411yescharacteristic
67C2×D491—28no—
68C2×D491—21no—
69C2×D491—21no—
70C2×D491—21no—
71C2×D491—21no—
72C2×D491—22no—
73C2×D491—22no—
74C2×D491—22no—
75C2×D491C2×D412yes—
76C2×D491#4112yescomplemented
77C4×C491—21no—
78C4×C491—22no—
79C4×C491—22no—
80C4×C491C2×D412yes—
81Dic491—21no—
82Dic491—22no—
83Dic491C2×D412yes—
84C2×C491—22no—
85C2×C491C22×D411yescharacteristic
86C2×C491C2×#4111yescharacteristic
87C2×C491C2×#4111yescharacteristic
88D491—22no—
89D491—22no—
90D491—42no—
91C491#52511yescharacteristic, complemented, Sylow
92#525—4911nomaximal, Sylow
93C2×#41—4911no—
94C23×C4—4911no—
95#123—4912no—
96C22⋊Q8—4911no—
97C22⋊Q8D49111yescharacteristic, complemented
98#121—4911no—
99#121—4911no—
100#120—4912no—
101C4×D4—4912no—
102C4×D4—4912no—
103#117—4911no—
104C24—4911no—
105#41—9824no—
106C2×Q8C2×D49111yescharacteristic, complemented
107C2×D4—4912no—
108C2×D4—4912no—
109C2×D4—4912no—
110C2×D4—4911no—
111C22×C4—9824no—
112C22×C4—4911no—
113C22×C4—4911no—
114C22×C4—4911no—
115C22×C4—4911no—
116C22×C4—4912no—
117C22×C4—4911no—
118C22×C4C2×D49111yescharacteristic
119C4⋊C4—4912no—
120C4⋊C4—4911no—
121C4⋊C4C2×D49111yescharacteristic, complemented
122C4⋊C4C2×D49112yescomplemented
123C22⋊C4—4912no—
124C22⋊C4—4912no—
125C22⋊C4—4912no—
126C22⋊C4—4912no—
127C22⋊C4C2×D49112yes—
128C42—4912no—
129C23—9822no—
130C23—9822no—
131C23—9822no—
132C23—4912no—
133C23—4911no—
134C23—4911no—
135C23C22×D49111yescharacteristic
136Q8—22no—
137D4—9824no—
138D4—9824no—
139D4—9824no—
140D4—9822no—
141C2×C4—22no—
142C2×C4—9822no—
143C2×C4—9822no—
144C2×C4—9824no—
145C2×C4—9822no—
146C2×C4—9822no—
147C2×C4—4912no—
148C2×C4—4911no—
149C2×C4—4911no—
150C2×C4—4914no—
151C2×C4C22×D49112yes—
152C2×C4C22×D49111yescharacteristic
153C2×C4C22×D49112yes—
154C2×C4C22×D49111yescharacteristic
155C22—21no—
156C22—21no—
157C22—9828no—
158C22—9822no—
159C22—9822no—
160C22—9822no—
161C22—9821no—
162C22—9821no—
163C22—9821no—
164C22—9821no—
165C22—4912no—
166C22—4912no—
167C22#2146332912yescomplemented
168C22C23×D49111yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—9821no—
173C4—9822no—
174C4—4912no—
175C4D4×D49112yes—
176C2—22no—
177C2—19642no—
178C2—9822no—
179C2—9822no—
180C2C2×D4×D49111yescharacteristic
181C2#41×D49111yescharacteristic
182C2C2×#2146332911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC22⋊Q8×C491C2
hypercenterC22⋊Q8D491
hypocenterC491#525
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#21463329C2semidirect
2. C22×C4×D491C2semidirect
3. #30628322C2semidirect
4. #30628313C2semidirect
5. #30628312C2semidirect
6. #30628311C2semidirect
7. #30628307C2semidirect
8. #30628299C2semidirect
9. (C22⋊D491)⋊C4C2semidirect
10. #30628295C2semidirect
11. C22⋊Q8×C491C2semidirect
16. C2×D1964C22semidirect
24. C2×C4×D491C22semidirect
25. C4⋊Dic491C22semidirect
26. Dic491⋊C4C22semidirect
29. (C2×D491)⋊C4C22semidirect
30. (C2×D491)⋊C4C22semidirect
31. C4×Dic491C22semidirect
32. C2×Q8×C491C22semidirect
34. C4⋊C4×C491C22semidirect
35. C4⋊C4×C491C22semidirect
55. C4×D491D4semidirect
65. C22×C491#41semidirect
76. C2×D491#41semidirect
91. C491#525semidirect
97. C22⋊Q8D491semidirect
106. C2×Q8C2×D491semidirect
121. C4⋊C4C2×D491semidirect
122. C4⋊C4C2×D491semidirect
167. C22#21463329semidirect

Maximal subgroups

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

subgroupindex
C2×#214633292
C22×C4×D4912
#306283222
#306283132
#306283122
#306283112
#306283072
#306282992
(C22⋊D491)⋊C42
#306282952
C22⋊Q8×C4912
#525491