Finite Group Databasebeta

← #21461289

Subgroups — #21461289

Order 7808.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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
1#16840784C211yesmaximal, characteristic, complemented
2#16840721C211yesmaximal, characteristic, complemented
3#16840617C214yesmaximal, complemented
4#16840310C211yesmaximal, characteristic
5C2×D61⋊C8—21no—
6C4⋊#92420—21no—
7#14519834—21no—
8#14519832—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11C2×#11758224C412yes—
12#14519777C411yescharacteristic
13#14519764C2212yes—
14#14519748—21no—
15#14519748—21no—
16D4×Dic61—21no—
17D4×Dic61—21no—
18C42×D61C2211yescharacteristic
19#127×C61C411yescharacteristic
20C2×D4×C61—21no—
21C2×D4×C61—21no—
22C2×D4×C61C2×C412yes—
23C2×C22⋊D61—22no—
24C22×Dic61—22no—
25#11758224—44no—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×Dic122C2×C412yes—
30C2×#92420—22no—
31C2×#92420—22no—
32D61⋊C8—24no—
33C42×C61C2×C411yescharacteristic
34C22⋊Dic61—22no—
35C22⋊Dic61—22no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61C2311yescharacteristic
41C23×C61—22no—
42C22×D61C22⋊C411yescharacteristic
43D4×C61—42no—
44D4×C61—42no—
45D4×C61—42no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C22⋊D61—44no—
50C2×Dic61—22no—
51C2×Dic61—44no—
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61C2×D411yescharacteristic
54C2×Dic61C2×D411yescharacteristic
55C4×D61—22no—
56C4×D61—22no—
57C4×D61—41no—
58Dic122—42no—
59#92420—24no—
60#92420—42no—
61C22×C61—42no—
62C22×C61—42no—
63C22×C61—42no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—21no—
66C2×D61—21no—
67C2×D61#10012yes—
68C4×C61—21no—
69C4×C61—21no—
70C4×C61#10412yes—
71Dic61—21no—
72Dic61—21no—
73Dic61—21no—
74Dic61—42no—
75#1530—611nomaximal, Sylow
76C2×C61—82no—
77C2×C61C2×#10011yescharacteristic
78C2×C61C2×#10411yescharacteristic
79C2×C61#42111yescharacteristic
80D61—22no—
81#532—611no—
82#432—611no—
83C2×#97—611no—
84#329—614no—
85C61#153011yescharacteristic, complemented, Sylow
86C2×#41—612no—
87C22×C8—1221no—
88C4⋊Q8—611no—
89#127#692311yescharacteristic
90#124—612no—
91#121—1221no—
92#121—1221no—
93C4×D4—1221no—
94C4×D4—1221no—
95C2×C42—611no—
96C4⋊C8—1221no—
97C22⋊C8—1221no—
98#97—612no—
99#97—612no—
100#97—1221no—
101#41—2444no—
102C2×Q8—612no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4—1222no—
106C2×D4C2×#692312yes—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4—1222no—
111C2×C8—1222no—
112C2×C8—1224no—
113C2×C8—1222no—
114C4⋊C4—1221no—
115C4⋊C4—1221no—
116C22⋊C4—1222no—
117C22⋊C4—1222no—
118C42—611no—
119C42—611no—
120C42—611no—
121C42C2×#692311yescharacteristic
122C23—22no—
123C23—611no—
124Q8—2442no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—2444no—
129C2×C4—611no—
130C2×C4—611no—
131C2×C4—611no—
132C2×C4—1222no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4—2441no—
136C2×C4—2444no—
137C2×C4C22⋊#692311yescharacteristic
138C2×C4C22⋊#692311yescharacteristic
139C2×C4C22×#692311yescharacteristic
140C8—1224no—
141C8—2442no—
142C22—42no—
143C22—42no—
144C22—42no—
145C22—612no—
146C22—1221no—
147C22—1221no—
148C22C2×C22⋊#692311yescharacteristic
149C4—21no—
150C4—21no—
151C4—1221no—
152C4—1221no—
153C4—1221no—
154C4—2442no—
155C4#1451984112yes—
156C2—82no—
157C2—1222no—
158C2D61⋊#10011yescharacteristic
159C2C2×#1451984111yescharacteristic
160C2#1684076011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#127#6923
hypocenterC61#1530
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. #16840721C2semidirect
3. #16840617C2semidirect
85. C61#1530semidirect