Finite Group Databasebeta

← #21461097

Subgroups — #21461097

Order 7808.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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#16840733C211yesmaximal, characteristic
2D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#16840607C214yesmaximal, complemented
4C2×#14519757C211yesmaximal, characteristic
5C2×#11758213—21no—
6C2×D61⋊C8—21no—
7#14519834—21no—
8#14519834—21no—
9C22⋊#92420C2212yes—
10C22⋊#92420C2212yes—
11C22×Dic122C411yescharacteristic
12C22×C4×D61C2211yescharacteristic
13#14519757—21no—
14#14519757—21no—
15#14519757—21no—
16#14519757—21no—
17C2×C4⋊Dic61C2212yes—
18C2×#11758198C412yes—
19C2×C4⋊C4×C61C411yescharacteristic
20C23×D61C2×C411yescharacteristic
21C22×C4×C61C2×C412yes—
22C22×C4×C61C2×C411yescharacteristic
23C22×Dic61C2×C412yes—
24C22×Dic61C2311yescharacteristic
25C2×C4×D61—42no—
26C2×C4×D61D411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—42no—
33C2×#92420—22no—
34C2×#92420—22no—
35#11758213—42no—
36D61⋊C8—42no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39#11758198—22no—
40#11758198—22no—
41C4⋊Dic61—22no—
42C4⋊Dic61—22no—
43C23×C61C22×C411yescharacteristic
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—41no—
47C22×D61C22⋊C411yescharacteristic
48C22×D61C22⋊C411yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—24no—
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—41no—
56C2×Dic61—42no—
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C4×D61—22no—
60C4×D61—22no—
61C4×D61—41no—
62C4×D61—41no—
63Dic122—42no—
64Dic122—42no—
65#92420—42no—
66#92420—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61C2×C22⋊C411yescharacteristic
70C22×C61#13112yes—
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—21no—
75C2×D61—21no—
76C2×D61—44no—
77C2×D61#10112yes—
78C4×C61—21no—
79C4×C61—42no—
80C4×C61#9912yes—
81Dic61—21no—
82Dic61—21no—
83Dic61—42no—
84#1472—611nomaximal, Sylow
85C2×C61—22no—
86C2×C61#40811yescharacteristic
87C2×C61C2×#9911yescharacteristic
88C2×C61C2×#10111yescharacteristic
89D61—22no—
90D61—41no—
91C2×C22⋊Q8—611no—
92#407—611no—
93C2×C22⋊C8—611no—
94#324—614no—
95C61#147211yescharacteristic, complemented, Sylow
96C22×Q8—611no—
97C23×C4—611no—
98C2×M16—1221no—
99C22×C8—1221no—
100C22⋊Q8—1221no—
101C22⋊Q8—1221no—
102C22⋊Q8—1221no—
103C22⋊Q8—1221no—
104C2×C4⋊C4—612no—
105C2×C4⋊C4#692311yescharacteristic
106C2×C22⋊C4—612no—
107C22⋊C8—612no—
108C22⋊C8—612no—
109C22⋊C8—1221no—
110C22⋊C8—1221no—
111C24—611no—
112C2×Q8—1221no—
113C2×Q8—1221no—
114C2×Q8—2442no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—612no—
121C22×C4—2442no—
122C22×C4C2×#692312yes—
123C22×C4C2×#692311yescharacteristic
124M16—2442no—
125C2×C8—1222no—
126C2×C8—1222no—
127C2×C8—2442no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C23—611no—
135C23—611no—
136C23—1222no—
137C23—1222no—
138C23—2441no—
139C23C22×#692311yescharacteristic
140Q8—2442no—
141Q8—2442no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—1222no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4—2442no—
154C2×C4C22⋊#692311yescharacteristic
155C2×C4C22⋊#692311yescharacteristic
156C8—2442no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—612no—
161C22—1221no—
162C22—1221no—
163C22—1221no—
164C22—1221no—
165C22—1221no—
166C22—2444no—
167C22C2×C22⋊#692311yescharacteristic
168C22#1451986412yes—
169C4—21no—
170C4—42no—
171C4—1221no—
172C4—1221no—
173C4—2442no—
174C4#1451983612yes—
175C2—22no—
176C2—1222no—
177C2—2441no—
178C2#1684073611yescharacteristic
179C2C2×#1451983611yescharacteristic
180C2D61⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1472
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840607C2semidirect
95. C61#1472semidirect