Finite Group Databasebeta

← #16840409

Subgroups — #16840409

Order 3904.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11758222C211yesmaximal, characteristic, complemented
2C2×D4×D61C211yesmaximal, characteristic, complemented
3#14519764C211yesmaximal, characteristic, complemented
4#14519759C212yesmaximal, complemented
5#14519757C211yesmaximal, characteristic, complemented
6#14519748C212yesmaximal, complemented
7#14519745C212yesmaximal, complemented
8#14519739C211yesmaximal, characteristic, complemented
9C4×C22⋊D61C211yesmaximal, characteristic, complemented
10C22⋊C4×D61C212yesmaximal, complemented
11#121×C61C211yesmaximal, characteristic, complemented
12C23×D61C2212yes—
13C2×D4×C61C2211yescharacteristic
14C2×D4×C61C2212yescomplemented
15C22×C4×C61C2211yescharacteristic, complemented
16C2×C22⋊D61C2212yes—
17C2×C22⋊D61C2211yescharacteristic
18C2×C22⋊D61C2212yescomplemented
19D4×D61—24no—
20#11758222—24no—
21C2×D244C2211yescharacteristic
22C2×C4×D61C2211yescharacteristic
23C2×C4×D61C2212yescomplemented
24C2×C4×D61C2212yescomplemented
25C2×Dic122C2211yescharacteristic, complemented
26C4⋊C4×C61C2211yescharacteristic, complemented
27C22⋊C4×C61C2212yescomplemented
28C22⋊Dic61C2212yescomplemented
29C22⋊Dic61C2211yescharacteristic, complemented
30C22⋊Dic61C2212yescomplemented
31#11758198C2211yescharacteristic
32#11758198C2212yes—
33#11758198C2212yescomplemented
34C4⋊Dic61C2212yescomplemented
35#11758196C2211yescharacteristic, complemented
36C4×Dic61C2211yescharacteristic, complemented
37C23×C61C2312yes—
38C23×C61C2311yescharacteristic
39C22×D61—24no—
40C22×D61—24no—
41C22×D61—42no—
42C22×D61C2312yes—
43C22×D61C2311yescharacteristic
44D4×C61—22no—
45D4×C61—42no—
46C2×C4×C61—22no—
47C2×C4×C61C2311yescharacteristic
48C2×C4×C61C2312yes—
49C2×C4×C61C2311yescharacteristic
50C22⋊D61—24no—
51C22⋊D61—24no—
52C22⋊D61—22no—
53C2×Dic61C2311yescharacteristic
54C2×Dic61C2311yescharacteristic
55C2×Dic61C2311yescharacteristic
56C2×Dic61C2312yes—
57D244D414yescomplemented
58C4×D61—24no—
59C4×D61—22no—
60C4×D61—42no—
61Dic122—22no—
62C22×C61—21no—
63C22×C61—22no—
64C22×C61—21no—
65C22×C61—22no—
66C22×C61—21no—
67C22×C61—22no—
68C22×C61C2411yescharacteristic
69C2×D61—21no—
70C2×D61—22no—
71C2×D61—22no—
72C2×D61—21no—
73C2×D61—48no—
74C2×D61C2×D414yes—
75C2×D61#4112yescomplemented
76C4×C61—21no—
77C4×C61—22no—
78C4×C61C2×D412yes—
79Dic61—22no—
80Dic61—21no—
81Dic61—21no—
82Dic61—21no—
83C2×C61—42no—
84C2×C61—41no—
85C2×C61C22×D411yescharacteristic
86C2×C61C2×#4111yescharacteristic
87C2×C61H(5,𝔽2)11yescharacteristic
88D61—22no—
89D61—24no—
90#546—611nomaximal, Sylow
91C61#54611yescharacteristic, complemented, Sylow
92C2×#41—611no—
93C22×D4—611no—
94#124—611no—
95#123—612no—
96C22⋊Q8—611no—
97#121—612no—
98#121D6111yescharacteristic, complemented
99#120—612no—
100C4×D4—611no—
101C4×D4—611no—
102C2×C22⋊C4—612no—
103C24—612no—
104#41—1224no—
105C2×Q8—611no—
106C2×D4—611no—
107C2×D4—612no—
108C2×D4—612no—
109C2×D4—611no—
110C2×D4—1224no—
111C2×D4C2×D6111yescharacteristic
112C2×D4C2×D6112yescomplemented
113C22×C4—612no—
114C22×C4—611no—
115C22×C4—612no—
116C22×C4C2×D6111yescharacteristic, complemented
117C4⋊C4—611no—
118C4⋊C4—612no—
119C4⋊C4C2×D6111yescharacteristic, complemented
120C22⋊C4—612no—
121C22⋊C4—611no—
122C22⋊C4—612no—
123C22⋊C4—611no—
124C22⋊C4—612no—
125C22⋊C4—612no—
126C22⋊C4C2×D6112yescomplemented
127C42—611no—
128C23—611no—
129C23—612no—
130C23—1224no—
131C23—1224no—
132C23—2442no—
133C23C22×D6112yes—
134C23C22×D6111yescharacteristic
135Q8—1222no—
136D4—22no—
137D4—42no—
138D4—614no—
139D4—1222no—
140D4—1224no—
141D4—1224no—
142C2×C4—22no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—612no—
146C2×C4—611no—
147C2×C4—1224no—
148C2×C4—1222no—
149C2×C4—2442no—
150C2×C4C22×D6112yes—
151C2×C4C22×D6111yescharacteristic
152C2×C4C22×D6111yescharacteristic
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—614no—
160C22—612no—
161C22—1221no—
162C22—1222no—
163C22—1222no—
164C22—1221no—
165C22—2448no—
166C22C23×D6111yescharacteristic
167C4—21no—
168C4—22no—
169C4—1221no—
170C4—1222no—
171C4—1221no—
172C4—1221no—
173C4D4×D6112yes—
174C2—42no—
175C2—41no—
176C2—1222no—
177C2—1224no—
178C2C2×D4×D6111yescharacteristic
179C2#41×D6111yescharacteristic
180C2#1451982211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
Fitting#121×C61C2
hypercenter#121D61
hypocenterC61#546
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#11758222C2semidirect
2. C2×D4×D61C2semidirect
3. #14519764C2semidirect
4. #14519759C2semidirect
5. #14519757C2semidirect
6. #14519748C2semidirect
7. #14519745C2semidirect
8. #14519739C2semidirect
9. C4×C22⋊D61C2semidirect
10. C22⋊C4×D61C2semidirect
11. #121×C61C2semidirect
14. C2×D4×C61C22semidirect
15. C22×C4×C61C22semidirect
18. C2×C22⋊D61C22semidirect
23. C2×C4×D61C22semidirect
24. C2×C4×D61C22semidirect
25. C2×Dic122C22semidirect
26. C4⋊C4×C61C22semidirect
27. C22⋊C4×C61C22semidirect
28. C22⋊Dic61C22semidirect
29. C22⋊Dic61C22semidirect
30. C22⋊Dic61C22semidirect
33. #11758198C22semidirect
34. C4⋊Dic61C22semidirect
35. #11758196C22semidirect
36. C4×Dic61C22semidirect
57. D244D4semidirect
75. C2×D61#41semidirect
91. C61#546semidirect
98. #121D61semidirect
112. C2×D4C2×D61semidirect
116. C22×C4C2×D61semidirect
119. C4⋊C4C2×D61semidirect
126. C22⋊C4C2×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#117582222
C2×D4×D612
#145197642
#145197592
#145197572
#145197482
#145197452
#145197392
C4×C22⋊D612
C22⋊C4×D612
#121×C612
#54661