Finite Group Databasebeta

← #16840407

Subgroups — #16840407

Order 3904.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11758224C211yesmaximal, characteristic, complemented
2C2×D4×D61C211yesmaximal, characteristic, complemented
3#14519765C211yesmaximal, characteristic, complemented
4#14519761C212yesmaximal, complemented
5#14519757C211yesmaximal, characteristic, complemented
6#14519752C211yesmaximal, characteristic, complemented
7#14519751C212yesmaximal, complemented
8#14519747C212yesmaximal, complemented
9C4×D244C211yesmaximal, characteristic, complemented
10C2×#11758198C212yesmaximal, complemented
11C4×D4×C61C211yesmaximal, characteristic, complemented
12C23×D61C2212yes—
13C2×D4×C61C2211yescharacteristic
14C22×C4×C61C2212yescomplemented
15C2×C22⋊D61C2212yes—
16C2×C22⋊D61C2212yescomplemented
17C22×Dic61C2212yescomplemented
18#11758224—24no—
19D4×D61—24no—
20C2×D244C2211yescharacteristic
21C2×D244C2211yescharacteristic
22C2×D244C2212yescomplemented
23C2×C4×D61C2211yescharacteristic
24C2×C4×D61C2211yescharacteristic, complemented
25C2×Dic122C2211yescharacteristic, complemented
26C4⋊C4×C61C2211yescharacteristic, complemented
27C22⋊C4×C61C2212yescomplemented
28C42×C61C2211yescharacteristic, complemented
29#11758198C2211yescharacteristic
30#11758198C2212yes—
31#11758198C2212yescomplemented
32#11758198C2212yescomplemented
33#11758198C2211yescharacteristic, complemented
34#11758198C2212yescomplemented
35C4⋊Dic61C2211yescharacteristic, complemented
36C4⋊Dic61C2212yescomplemented
37C23×C61C2312yes—
38C22×D61—24no—
39C22×D61—24no—
40C22×D61—42no—
41C22×D61C2312yes—
42C22×D61C2311yescharacteristic
43C22×D61C2311yescharacteristic
44D4×C61D414yescomplemented
45C2×C4×C61—42no—
46C2×C4×C61C2312yes—
47C2×C4×C61C2311yescharacteristic
48C2×C4×C61C2311yescharacteristic
49C2×C4×C61C2311yescharacteristic
50C22⋊D61—24no—
51C22⋊D61—24no—
52C2×Dic61—24no—
53C2×Dic61C2311yescharacteristic
54C2×Dic61C2312yes—
55C2×Dic61C2311yescharacteristic
56D244—22no—
57D244—22no—
58D244—42no—
59C4×D61—22no—
60C4×D61—22no—
61Dic122—22no—
62C22×C61—22no—
63C22×C61—22no—
64C22×C61C2×D414yes—
65C22×C61C2411yescharacteristic
66C2×D61—21no—
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—22no—
70C2×D61—21no—
71C2×D61—22no—
72C2×D61—21no—
73C2×D61—22no—
74C2×D61—48no—
75C2×D61#4112yescomplemented
76C4×C61—21no—
77C4×C61—22no—
78C4×C61—21no—
79C4×C61C2×D412yes—
80Dic61—22no—
81Dic61—21no—
82Dic61—21no—
83C2×C61—24no—
84C2×C61C22×D411yescharacteristic
85C2×C61C2×#4111yescharacteristic
86C2×C61H(5,𝔽2)11yescharacteristic
87D61—22no—
88D61—41no—
89D61—42no—
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#121—611no—
99#120—612no—
100C4×D4—611no—
101C4×D4D6111yescharacteristic, complemented
102C2×C22⋊C4—612no—
103C24—612no—
104#41—1224no—
105C2×Q8—611no—
106C2×D4—612no—
107C2×D4—612no—
108C2×D4—611no—
109C2×D4—611no—
110C2×D4—612no—
111C2×D4—1224no—
112C2×D4C2×D6111yescharacteristic
113C22×C4—612no—
114C22×C4—611no—
115C22×C4—611no—
116C22×C4C2×D6112yescomplemented
117C4⋊C4—611no—
118C4⋊C4—612no—
119C4⋊C4C2×D6111yescharacteristic, complemented
120C22⋊C4—611no—
121C22⋊C4—612no—
122C22⋊C4—612no—
123C22⋊C4—612no—
124C22⋊C4—611no—
125C22⋊C4—612no—
126C22⋊C4C2×D6112yescomplemented
127C42C2×D6111yescharacteristic, complemented
128C23—611no—
129C23—612no—
130C23—611no—
131C23—1224no—
132C23—1224no—
133C23—2442no—
134C23C22×D6112yes—
135Q8—1222no—
136D4—1222no—
137D4—1224no—
138D4—1224no—
139D4—1222no—
140D4—2442no—
141D4D24414yescomplemented
142C2×C4—42no—
143C2×C4—611no—
144C2×C4—612no—
145C2×C4—611no—
146C2×C4—1224no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4C22×D6111yescharacteristic
150C2×C4C22×D6111yescharacteristic
151C2×C4C22×D6112yes—
152C2×C4C22×D6111yescharacteristic
153C22—22no—
154C22—22no—
155C22—612no—
156C22—1221no—
157C22—1221no—
158C22—1221no—
159C22—1222no—
160C22—1221no—
161C22—1222no—
162C22—1221no—
163C22—1222no—
164C22—2448no—
165C22C2×D24414yes—
166C22C23×D6111yescharacteristic
167C4—21no—
168C4—21no—
169C4—22no—
170C4—1221no—
171C4—1221no—
172C4—1222no—
173C4C2×D24412yes—
174C2—24no—
175C2—1222no—
176C2—2442no—
177C2—2441no—
178C2C22×D24411yescharacteristic
179C2#41×D6111yescharacteristic
180C2#1451982211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
FittingC4×D4×C61C2
hypercenterC4×D4D61
hypocenterC61#546
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11758224C2semidirect
2. C2×D4×D61C2semidirect
3. #14519765C2semidirect
4. #14519761C2semidirect
5. #14519757C2semidirect
6. #14519752C2semidirect
7. #14519751C2semidirect
8. #14519747C2semidirect
9. C4×D244C2semidirect
10. C2×#11758198C2semidirect
11. C4×D4×C61C2semidirect
14. C22×C4×C61C22semidirect
16. C2×C22⋊D61C22semidirect
17. C22×Dic61C22semidirect
22. C2×D244C22semidirect
24. C2×C4×D61C22semidirect
25. C2×Dic122C22semidirect
26. C4⋊C4×C61C22semidirect
27. C22⋊C4×C61C22semidirect
28. C42×C61C22semidirect
31. #11758198C22semidirect
32. #11758198C22semidirect
33. #11758198C22semidirect
34. #11758198C22semidirect
35. C4⋊Dic61C22semidirect
36. C4⋊Dic61C22semidirect
44. D4×C61D4semidirect
75. C2×D61#41semidirect
91. C61#546semidirect
101. C4×D4D61semidirect
116. C22×C4C2×D61semidirect
119. C4⋊C4C2×D61semidirect
126. C22⋊C4C2×D61semidirect
127. C42C2×D61semidirect
141. D4D244semidirect

Maximal subgroups

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

subgroupindex
C2×#117582242
C2×D4×D612
#145197652
#145197612
#145197572
#145197522
#145197512
#145197472
C4×D2442
C2×#117581982
C4×D4×C612
#54661