Finite Group Databasebeta

← #21448577

Subgroups — #21448577

Order 7808.

484 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 217 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#16839669C212yesmaximal, complemented
2#16839655C212yesmaximal
3#16839655C212yesmaximal
4#16839648C212yesmaximal, complemented
5#16839648C212yesmaximal, complemented
6#16839625C211yesmaximal, characteristic
7C4⋊C4×Dic61C212yesmaximal, complemented
8C4×C22⋊Dic61C211yesmaximal, characteristic
9C2×C22⋊Q8×C61C211yesmaximal, characteristic
10C2×C4⋊Dic61C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×C22⋊Dic61C2212yes—
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2211yescharacteristic
15C2×C4×Dic61C2212yes—
16C2×C4×Dic61C2211yescharacteristic
17C2×C4×Dic61C2211yescharacteristic
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C23×C4×C61C2211yescharacteristic
28C22⋊Q8×C61C418yescomplemented
29C2×C4⋊C4×C61C2212yes—
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2212yes—
32C24×C61C2311yescharacteristic
33C2×Q8×C61—41no—
34C2×Q8×C61—41no—
35C2×Q8×C61C2×C414yes—
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61C2×C414yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C4⋊C4×C61C2×C414yes—
48C4⋊C4×C61C2×C418yes—
49C22⋊C4×C61C2×C418yes—
50C22⋊Dic61—24no—
51C22⋊Dic61—41no—
52C22⋊Dic61—41no—
53C4⋊Dic61—24no—
54C4⋊Dic61—42no—
55C4×Dic61—24no—
56C4×Dic61—41no—
57C4×Dic61—42no—
58C4×Dic61—41no—
59C23×C61—22no—
60C23×C61—21no—
61C23×C61—21no—
62C23×C61—22no—
63C23×C61C22×C412yes—
64C23×C61C2411yescharacteristic
65Q8×C61—44no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—44no—
75C2×C4×C61C22×C414yes—
76C2×C4×C61C22×C414yes—
77C2×C4×C61C22×C412yes—
78C2×C4×C61C22×C412yes—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61#4114yes—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—22no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61C23×C411yescharacteristic
97C22×C61C2×#4112yes—
98C22×C61H(5,𝔽2)11yescharacteristic
99C22×C61H(5,𝔽2)11yescharacteristic
100C22×C612−1+412yes—
101C4×C61—24no—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61—24no—
105Dic61—24no—
106Dic61—42no—
107Dic61—42no—
108Dic61—42no—
109#2332—611nomaximal, Sylow
110C2×C61—42no—
111C2×C61C4×#4111yescharacteristic
112C2×C61#51811yescharacteristic
113C2×C61#51911yescharacteristic
114C2×C61#53912yes—
115C2×C61#54212yes—
116C2×C22⋊Q8D6111yescharacteristic
117#391—612no—
118#388—612no—
119#388—612no—
120#387—612no—
121#387—612no—
122#381—611no—
123C4×C4⋊C4—612no—
124C4×C22⋊C4—611no—
125C61#233211yescharacteristic, complemented, Sylow
126C22×Q8C2×D6111yescharacteristic
127C23×C4C2×D6111yescharacteristic
128C22⋊Q8Dic6118yescomplemented
129C2×C4⋊C4—612no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4C2×D6112yes—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—612no—
134C2×C22⋊C4—611no—
135C2×C22⋊C4—611no—
136C2×C22⋊C4C2×D6112yes—
137C2×C42—612no—
138C2×C42—611no—
139C2×C42—611no—
140C2×C42—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95—612no—
145#95—612no—
146#95—612no—
147#95—612no—
148C24C22×D6111yescharacteristic
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8C2×Dic6114yes—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—612no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4C2×Dic6114yes—
159C22×C4C22×D6111yescharacteristic
160C22×C4C22×D6111yescharacteristic
161C22×C4C22×D6112yes—
162C22×C4C22×D6112yes—
163C4⋊C4—1224no—
164C4⋊C4—2442no—
165C4⋊C4C2×Dic6114yes—
166C4⋊C4C2×Dic6118yes—
167C22⋊C4—1224no—
168C22⋊C4—2441no—
169C22⋊C4—2441no—
170C22⋊C4C2×Dic6118yes—
171C42—1224no—
172C42—2441no—
173C42—2441no—
174C42—2442no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C22×Dic6112yes—
180C23C23×D6111yescharacteristic
181Q8—44no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—44no—
191C2×C4—614no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4C22×Dic6114yes—
204C2×C4C22×Dic6114yes—
205C2×C4C22×Dic6112yes—
206C2×C4C22×Dic6112yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C23×Dic6111yescharacteristic
213C22#41×D6112yes—
214C22#1451982211yescharacteristic
215C22#1451982211yescharacteristic
216C22#1451982512yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—24no—
221C4—1224no—
222C4—2442no—
223C4—2442no—
224C4—2442no—
225C2—42no—
226C2#41×Dic6111yescharacteristic
227C2#1684023711yescharacteristic
228C2#1684024011yescharacteristic
229C2#1684035812yes—
230C2#1684038212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×C22⋊Q8×C61C2
socleC23×C61C24
hypercenterC2×C22⋊Q8D61
hypocenterC61#2332
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #16839669C2semidirect
4. #16839648C2semidirect
5. #16839648C2semidirect
7. C4⋊C4×Dic61C2semidirect
28. C22⋊Q8×C61C4semidirect
125. C61#2332semidirect
128. C22⋊Q8Dic61semidirect