Finite Group Databasebeta

← #44537291

Subgroups — #44537291

Order 31424.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#21463328C211yesmaximal, characteristic, complemented
2C2×D4×D491C211yesmaximal, characteristic, complemented
3#30628333C212yesmaximal, complemented
4#30628323C212yesmaximal, complemented
5#30628312C211yesmaximal, characteristic, complemented
6#30628311C211yesmaximal, characteristic, complemented
7#30628308C211yesmaximal, characteristic, complemented
8#30628307C212yesmaximal, complemented
9#30628305C212yesmaximal, complemented
10#30628295C211yesmaximal, characteristic, complemented
11#121×C491C211yesmaximal, characteristic, complemented
12C23×D491C2212yes—
13#21463328—24no—
14C2×Dic982C2211yescharacteristic, complemented
15C2×D1964C2211yescharacteristic
16C2×D1964C2211yescharacteristic
17C2×D1964C2212yescomplemented
18C2×C22⋊D491C2212yes—
19C2×C22⋊D491C2211yescharacteristic
20C2×C22⋊D491C2211yescharacteristic, complemented
21C2×C22⋊D491C2212yescomplemented
22C2×C22⋊D491C2212yescomplemented
23D4×D491—24no—
24C2×C4×D491C2211yescharacteristic
25C2×C4×D491C2211yescharacteristic, complemented
26C4⋊Dic491C2211yescharacteristic, complemented
27C22⋊Dic491C2212yescomplemented
28(C2×D491)⋊C4C2212yes—
29(C2×D491)⋊C4C2212yescomplemented
30(C2×D491)⋊C4C2212yescomplemented
31C4×Dic491C2212yescomplemented
32C2×D4×C491C2211yescharacteristic
33C2×D4×C491C2212yescomplemented
34C22×C4×C491C2211yescharacteristic, complemented
35C4⋊C4×C491C2211yescharacteristic, complemented
36C22⋊C4×C491C2212yescomplemented
37C22×D491—24no—
38C22×D491—42no—
39C22×D491—42no—
40C22×D491C2312yes—
41C22×D491C2311yescharacteristic
42C22×D491C2311yescharacteristic
43Dic982—22no—
44D1964—22no—
45D1964—22no—
46D1964—42no—
47C22⋊D491—22no—
48C22⋊D491—24no—
49C22⋊D491—22no—
50C22⋊D491—42no—
51C22⋊D491—42no—
52C2×Dic491C2312yes—
53C2×Dic491C2311yescharacteristic
54C2×Dic491C2311yescharacteristic
55C4×D491—22no—
56C4×D491D414yescomplemented
57C23×C491C2311yescharacteristic
58C23×C491C2312yes—
59D4×C491—22no—
60D4×C491—42no—
61C2×C4×C491—22no—
62C2×C4×C491C2311yescharacteristic
63C2×C4×C491C2312yes—
64C2×C4×C491C2311yescharacteristic
65C22×C491—21no—
66C22×C491—22no—
67C22×C491—21no—
68C22×C491—22no—
69C22×C491—21no—
70C22×C491—22no—
71C22×C491C2411yescharacteristic
72C2×D491—21no—
73C2×D491—21no—
74C2×D491—21no—
75C2×D491—22no—
76C2×D491—21no—
77C2×D491—22no—
78C2×D491—21no—
79C2×D491—22no—
80C2×D491—48no—
81C2×D491C2×D412yes—
82C4×C491—21no—
83C4×C491—22no—
84C4×C491C2×D412yes—
85Dic491—21no—
86Dic491—22no—
87Dic491C2×D412yes—
88C2×C491—42no—
89C2×C491—41no—
90C2×C491C22×D411yescharacteristic
91C2×C491H(5,𝔽2)11yescharacteristic
92C2×C491H(5,𝔽2)11yescharacteristic
93D491—22no—
94D491—41no—
95D491—42no—
96C491#53511yescharacteristic, complemented, Sylow
97#535—4911nomaximal, Sylow
98C2×#41—4911no—
99C22×D4—4911no—
100#127—4912no—
101#124—4912no—
102#121—4911no—
103#121—4911no—
104#121—4911no—
105#121D49111yescharacteristic, complemented
106#120—4912no—
107#120—4912no—
108#117—4911no—
109C24—4912no—
110#41—9824no—
111C2×Q8—4911no—
112C2×D4—9824no—
113C2×D4—4912no—
114C2×D4—4912no—
115C2×D4—4911no—
116C2×D4—4912no—
117C2×D4—4911no—
118C2×D4—4912no—
119C2×D4—4911no—
120C2×D4—4911no—
121C2×D4C2×D49111yescharacteristic
122C2×D4C2×D49112yescomplemented
123C22×C4—4911no—
124C22×C4—4911no—
125C22×C4C2×D49111yescharacteristic, complemented
126C4⋊C4—4911no—
127C4⋊C4C2×D49111yescharacteristic, complemented
128C22⋊C4—4912no—
129C22⋊C4—4912no—
130C22⋊C4—4912no—
131C22⋊C4—4912no—
132C22⋊C4C2×D49112yescomplemented
133C42—4912no—
134C23—19642no—
135C23—19642no—
136C23—9824no—
137C23—4912no—
138C23—4911no—
139C23—4911no—
140C23C22×D49112yes—
141C23C22×D49111yescharacteristic
142Q8—9822no—
143D4—22no—
144D4—42no—
145D4—19642no—
146D4—19642no—
147D4—19642no—
148D4—9822no—
149D4—9822no—
150D4—9824no—
151D4—9822no—
152D4—9822no—
153C2×C4—22no—
154C2×C4—9822no—
155C2×C4—4912no—
156C2×C4—4911no—
157C2×C4—4911no—
158C2×C4—4914no—
159C2×C4C22×D49112yes—
160C2×C4C22×D49111yescharacteristic
161C2×C4C22×D49111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—19648no—
169C22—9821no—
170C22—9822no—
171C22—9821no—
172C22—9822no—
173C22—9821no—
174C22—9822no—
175C22—9821no—
176C22—9821no—
177C22—4912no—
178C22C23×D49111yescharacteristic
179C4—21no—
180C4—22no—
181C4—9821no—
182C4—9822no—
183C4—4912no—
184C4D4×D49112yes—
185C2—42no—
186C2—41no—
187C2—19642no—
188C2—19641no—
189C2—9822no—
190C2C2×D4×D49111yescharacteristic
191C2#3062838211yescharacteristic
192C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#121×C491C2
hypercenter#121D491
hypocenterC491#535
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#21463328C2semidirect
2. C2×D4×D491C2semidirect
3. #30628333C2semidirect
4. #30628323C2semidirect
5. #30628312C2semidirect
6. #30628311C2semidirect
7. #30628308C2semidirect
8. #30628307C2semidirect
9. #30628305C2semidirect
10. #30628295C2semidirect
11. #121×C491C2semidirect
14. C2×Dic982C22semidirect
17. C2×D1964C22semidirect
20. C2×C22⋊D491C22semidirect
21. C2×C22⋊D491C22semidirect
22. C2×C22⋊D491C22semidirect
25. C2×C4×D491C22semidirect
26. C4⋊Dic491C22semidirect
27. C22⋊Dic491C22semidirect
29. (C2×D491)⋊C4C22semidirect
30. (C2×D491)⋊C4C22semidirect
31. C4×Dic491C22semidirect
33. C2×D4×C491C22semidirect
34. C22×C4×C491C22semidirect
35. C4⋊C4×C491C22semidirect
36. C22⋊C4×C491C22semidirect
56. C4×D491D4semidirect
96. C491#535semidirect
105. #121D491semidirect
122. C2×D4C2×D491semidirect
125. C22×C4C2×D491semidirect
127. C4⋊C4C2×D491semidirect
132. C22⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
C2×#214633282
C2×D4×D4912
#306283332
#306283232
#306283122
#306283112
#306283082
#306283072
#306283052
#306282952
#121×C4912
#535491