Finite Group Databasebeta

← #21456767

Subgroups — #21456767

Order 7808.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840319C211yesmaximal, characteristic
2#16840141C212yesmaximal, complemented
3#16840112C212yesmaximal, complemented
4#16839969C214yesmaximal, complemented
5#16839918C214yesmaximal
6#16839815C211yesmaximal, characteristic
7C2×C4⋊Q8×C61C211yesmaximal, characteristic
8C2×#11758202C2218yes—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519769—21no—
12#14519756—21no—
13#14519756C2212yes—
14C4×Dic122—21no—
15C4×Dic122C2212yes—
16#14519736—21no—
17C4⋊#92418C2212yes—
18#14519701C2218yes—
19C22⋊#92418C2212yes—
20C4×#92418C2212yes—
21C22×Q8×C61C2212yes—
22C4⋊Q8×C61—21no—
23C4⋊Q8×C61—21no—
24C4⋊Q8×C61C2212yes—
25C4⋊Q8×C61C2212yes—
26C2×C4⋊C4×C61—21no—
27C2×C4⋊C4×C61—21no—
28C2×C42×C61C2211yescharacteristic
29C2×Q8×C61—22no—
30C2×Q8×C61—44no—
31C2×Q8×C61C2314yes—
32C22×C4×C61—22no—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×Dic122—21no—
37C2×Dic122C2312yes—
38C4⋊C4×C61—22no—
39C4⋊C4×C61—22no—
40C4⋊C4×C61—22no—
41C4⋊C4×C61—22no—
42C42×C61D411yescharacteristic
43C42×C61D411yescharacteristic
44C42×C61C2311yescharacteristic
45C42×C61C2311yescharacteristic
46C22⋊Dic61—22no—
47#11758202—48no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61C2312yes—
52#11758196—22no—
53#11758196—22no—
54C4×Dic61—22no—
55C2×#92418C2314yes—
56C23×C61C2×D411yescharacteristic
57Q8×C61—28no—
58Q8×C61—44no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—24no—
62C2×C4×C61—44no—
63C2×C4×C61Q1614yescomplemented
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2411yescharacteristic
70C2×Dic61—22no—
71C2×Dic61—22no—
72Dic122—24no—
73Dic122—42no—
74#92418—24no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61C2×Q1612yes—
78C22×C61C22×D411yescharacteristic
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—44no—
82C4×C61C2×Q1612yes—
83C4×C61C2×Q1612yes—
84C4×C61#13712yes—
85C4×C61H(5,𝔽2)12yes—
86Dic61—42no—
87Dic61—42no—
88#3209—611nomaximal, Sylow
89C2×C61—22no—
90C2×C61#53511yescharacteristic
91C2×C61C22×Q1611yescharacteristic
92C2×C61C2×#13711yescharacteristic
93#533—611no—
94C2×C4⋊Q8D6111yescharacteristic
95#494—612no—
96#487—612no—
97#462—614no—
98#451—614no—
99#431—611no—
100C61#320911yescharacteristic, complemented, Sylow
101C22×Q8C2×D6112yes—
102C2×Q16—618no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—611no—
106C4⋊Q8—611no—
107C4⋊Q8C2×D6112yes—
108C4⋊Q8C2×D6112yes—
109#125—1221no—
110C22⋊Q8—612no—
111C22⋊Q8—1221no—
112C4×Q8—612no—
113C4×Q8—1221no—
114#117—1221no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C42C2×D6111yescharacteristic
118C4⋊C8—612no—
119#103—618no—
120C22⋊C8—612no—
121C4×C8—612no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—612no—
125C2×Q8—1221no—
126C2×Q8C22×D6114yes—
127C22×C4—22no—
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22⋊D6111yescharacteristic
130C22×C4C22×D6111yescharacteristic
131Q16—2448no—
132C2×C8—614no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—612no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C22⋊C4—1222no—
144C42—1222no—
145C42C22⋊D6111yescharacteristic
146C42C22⋊D6111yescharacteristic
147C42C22×D6111yescharacteristic
148C42C22×D6111yescharacteristic
149C23C2×C22⋊D6111yescharacteristic
150Q8—28no—
151Q8—44no—
152Q8—1224no—
153Q8—2442no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—1222no—
159C2×C4—1222no—
160C2×C4#1175820214yescomplemented
161C2×C4C2×C22⋊D6111yescharacteristic
162C2×C4C2×C22⋊D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C2×C4C2×C22⋊D6111yescharacteristic
166C2×C4C23×D6111yescharacteristic
167C8—1224no—
168C22—21no—
169C22—21no—
170C22C2×#1175820212yes—
171C22C22×C22⋊D6111yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—2442no—
176C4—2442no—
177C4C2×#1175820212yes—
178C4C2×#1175820212yes—
179C4#1451980812yes—
180C4#1451982212yes—
181C2—22no—
182C2#1684032911yescharacteristic
183C2C22×#1175820211yescharacteristic
184C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4⋊Q8×C61C2
socleC22×C61C22×D4
hypercenterC2×C4⋊Q8D61
hypocenterC61#3209
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16840141C2semidirect
3. #16840112C2semidirect
4. #16839969C2semidirect
63. C2×C4×C61Q16semidirect
100. C61#3209semidirect
160. C2×C4#11758202semidirect