Finite Group Databasebeta

← #16840328

Subgroups — #16840328

Order 3904.

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×#11758222C211yesmaximal, characteristic, complemented
2C2×D4×D61C211yesmaximal, characteristic, complemented
3#14519773C212yesmaximal, complemented
4#14519763C212yesmaximal, complemented
5#14519752C211yesmaximal, characteristic, complemented
6#14519751C211yesmaximal, characteristic, complemented
7#14519748C211yesmaximal, characteristic, complemented
8#14519747C212yesmaximal, complemented
9#14519745C212yesmaximal, complemented
10#14519735C211yesmaximal, characteristic, 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⋊D61C2211yescharacteristic, complemented
19C2×C22⋊D61C2212yescomplemented
20C2×C22⋊D61C2212yescomplemented
21D4×D61—24no—
22#11758222—24no—
23C2×D244C2211yescharacteristic
24C2×D244C2211yescharacteristic
25C2×D244C2212yescomplemented
26C2×C4×D61C2211yescharacteristic
27C2×C4×D61C2211yescharacteristic, complemented
28C2×Dic122C2211yescharacteristic, complemented
29C4⋊C4×C61C2211yescharacteristic, complemented
30C22⋊C4×C61C2212yescomplemented
31C22⋊Dic61C2212yescomplemented
32#11758198C2212yes—
33#11758198C2212yescomplemented
34#11758198C2212yescomplemented
35C4⋊Dic61C2211yescharacteristic, complemented
36C4×Dic61C2212yescomplemented
37C23×C61C2312yes—
38C23×C61C2311yescharacteristic
39C22×D61—24no—
40C22×D61—42no—
41C22×D61—42no—
42C22×D61C2312yes—
43C22×D61C2311yescharacteristic
44C22×D61C2311yescharacteristic
45D4×C61—22no—
46D4×C61—42no—
47C2×C4×C61—22no—
48C2×C4×C61C2312yes—
49C2×C4×C61C2311yescharacteristic
50C2×C4×C61C2311yescharacteristic
51C22⋊D61—22no—
52C22⋊D61—22no—
53C22⋊D61—24no—
54C22⋊D61—42no—
55C22⋊D61—42no—
56C2×Dic61C2312yes—
57C2×Dic61C2311yescharacteristic
58C2×Dic61C2311yescharacteristic
59D244—22no—
60D244—22no—
61D244—42no—
62C4×D61—22no—
63C4×D61D414yescomplemented
64Dic122—22no—
65C22×C61—21no—
66C22×C61—22no—
67C22×C61—21no—
68C22×C61—22no—
69C22×C61—21no—
70C22×C61—22no—
71C22×C61C2411yescharacteristic
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—21no—
75C2×D61—22no—
76C2×D61—21no—
77C2×D61—22no—
78C2×D61—21no—
79C2×D61—22no—
80C2×D61—48no—
81C2×D61C2×D412yes—
82C4×C61—21no—
83C4×C61—22no—
84C4×C61C2×D412yes—
85Dic61—21no—
86Dic61—22no—
87Dic61C2×D412yes—
88C2×C61—42no—
89C2×C61—41no—
90C2×C61C22×D411yescharacteristic
91C2×C61H(5,𝔽2)11yescharacteristic
92C2×C61H(5,𝔽2)11yescharacteristic
93D61—22no—
94D61—41no—
95D61—42no—
96#535—611nomaximal, Sylow
97C61#53511yescharacteristic, complemented, Sylow
98C2×#41—611no—
99C22×D4—611no—
100#127—612no—
101#124—612no—
102#121—611no—
103#121—611no—
104#121—611no—
105#121D6111yescharacteristic, complemented
106#120—612no—
107#120—612no—
108#117—611no—
109C24—612no—
110#41—1224no—
111C2×Q8—611no—
112C2×D4—611no—
113C2×D4—612no—
114C2×D4—611no—
115C2×D4—612no—
116C2×D4—612no—
117C2×D4—611no—
118C2×D4—611no—
119C2×D4—612no—
120C2×D4—1224no—
121C2×D4C2×D6111yescharacteristic
122C2×D4C2×D6112yescomplemented
123C22×C4—611no—
124C22×C4—611no—
125C22×C4C2×D6111yescharacteristic, complemented
126C4⋊C4—611no—
127C4⋊C4C2×D6111yescharacteristic, complemented
128C22⋊C4—612no—
129C22⋊C4—612no—
130C22⋊C4—612no—
131C22⋊C4—612no—
132C22⋊C4C2×D6112yescomplemented
133C42—612no—
134C23—611no—
135C23—612no—
136C23—611no—
137C23—1224no—
138C23—2442no—
139C23—2442no—
140C23C22×D6112yes—
141C23C22×D6111yescharacteristic
142Q8—1222no—
143D4—22no—
144D4—42no—
145D4—1222no—
146D4—1224no—
147D4—1222no—
148D4—1222no—
149D4—1222no—
150D4—2442no—
151D4—2442no—
152D4—2442no—
153C2×C4—22no—
154C2×C4—611no—
155C2×C4—614no—
156C2×C4—612no—
157C2×C4—611no—
158C2×C4—1222no—
159C2×C4C22×D6112yes—
160C2×C4C22×D6111yescharacteristic
161C2×C4C22×D6111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—612no—
169C22—1221no—
170C22—1221no—
171C22—1221no—
172C22—1222no—
173C22—1221no—
174C22—1222no—
175C22—1221no—
176C22—1222no—
177C22—2448no—
178C22C23×D6111yescharacteristic
179C4—21no—
180C4—22no—
181C4—612no—
182C4—1221no—
183C4—1222no—
184C4D4×D6112yes—
185C2—42no—
186C2—41no—
187C2—1222no—
188C2—2442no—
189C2—2441no—
190C2C2×D4×D6111yescharacteristic
191C2#1451982211yescharacteristic
192C2#1451982311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
Fitting#121×C61C2
hypercenter#121D61
hypocenterC61#535
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. #14519773C2semidirect
4. #14519763C2semidirect
5. #14519752C2semidirect
6. #14519751C2semidirect
7. #14519748C2semidirect
8. #14519747C2semidirect
9. #14519745C2semidirect
10. #14519735C2semidirect
11. #121×C61C2semidirect
14. C2×D4×C61C22semidirect
15. C22×C4×C61C22semidirect
18. C2×C22⋊D61C22semidirect
19. C2×C22⋊D61C22semidirect
20. C2×C22⋊D61C22semidirect
25. C2×D244C22semidirect
27. C2×C4×D61C22semidirect
28. C2×Dic122C22semidirect
29. C4⋊C4×C61C22semidirect
30. C22⋊C4×C61C22semidirect
31. C22⋊Dic61C22semidirect
33. #11758198C22semidirect
34. #11758198C22semidirect
35. C4⋊Dic61C22semidirect
36. C4×Dic61C22semidirect
63. C4×D61D4semidirect
97. C61#535semidirect
105. #121D61semidirect
122. C2×D4C2×D61semidirect
125. C22×C4C2×D61semidirect
127. C4⋊C4C2×D61semidirect
132. 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
#145197732
#145197632
#145197522
#145197512
#145197482
#145197472
#145197452
#145197352
#121×C612
#53561