Finite Group Databasebeta

← #21448531

Subgroups — #21448531

Order 7808.

612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×#14519764C211yesmaximal, characteristic
2C2×C4×Dic122C211yesmaximal, characteristic, complemented
3#16839667C211yesmaximal, characteristic, complemented
4#16839665C211yesmaximal, characteristic
5#16839650C214yesmaximal, complemented
6#16839635C214yesmaximal, complemented
7#16839631C211yesmaximal, characteristic, complemented
8#16839608C211yesmaximal, characteristic, complemented
9C2×C4×D4×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519764C418yescomplemented
12C4×Dic122—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2214yes—
17C2×C22⋊Dic61C2214yes—
18C2×C4×Dic61C2212yes—
19C2×C4×Dic61C2211yescharacteristic
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2214yes—
24C22×D4×C61C2211yescharacteristic
25C23×C4×C61C2212yes—
26C4×D4×C61—24no—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C42×C61C2211yescharacteristic
30C24×C61C2312yes—
31C2×D4×C61—22no—
32C2×D4×C61—22no—
33C2×D4×C61C2×C414yes—
34C22×C4×C61—24no—
35C22×C4×C61—44no—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C2×Dic122—22no—
45C2×Dic122—22no—
46C2×Dic122C2×C414yescomplemented
47C4⋊C4×C61—22no—
48C22⋊C4×C61—24no—
49C42×C61D414yes—
50C22⋊Dic61—44no—
51C22⋊Dic61C2×C4116yescomplemented
52C4⋊Dic61—22no—
53#11758196—24no—
54#11758196—44no—
55C4×Dic61—24no—
56C4×Dic61—22no—
57C4×Dic61C2×C414yescomplemented
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—24no—
61C23×C61—24no—
62C23×C61C22×C414yes—
63C23×C61C2411yescharacteristic
64D4×C61—28no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—24no—
69C2×C4×C61—48no—
70C2×C4×C61C22×C412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D412yes—
74C2×C4×C61#4112yes—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61C22×C414yes—
85C2×Dic61C22×C414yes—
86Dic122—28no—
87C22×C61—24no—
88C22×C61—28no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—44no—
92C22×C61C23×C411yescharacteristic
93C22×C61C22×D411yescharacteristic
94C22×C61C2×#4111yescharacteristic
95C22×C61H(5,𝔽2)12yes—
96C22×C612−1+412yes—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—42no—
100C4×C61C4×D414yes—
101Dic61—24no—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105#2326—611nomaximal, Sylow
106C2×C61—44no—
107C2×C61C2×C4×D411yescharacteristic
108C2×C61#52012yes—
109C2×C61#53511yescharacteristic
110C2×C61#53611yescharacteristic
111C2×C61#54212yes—
112C2×#124—611no—
113C2×C4×Q8—611no—
114C2×C4×D4D6111yescharacteristic
115#391—611no—
116#390—611no—
117#388—614no—
118#385—614no—
119#384—611no—
120#376—611no—
121C61#232611yescharacteristic, complemented, Sylow
122C22×Q8—611no—
123C22×D4C2×D6111yescharacteristic
124C23×C4C2×D6112yes—
125#124—618no—
126C4×Q8—1224no—
127C4×D4—24no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—614no—
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C22⋊C4—614no—
133C2×C22⋊C4—614no—
134C2×C22⋊C4C2×D6112yes—
135C2×C42—611no—
136C2×C42—612no—
137C2×C42—611no—
138C2×C42C2×D6111yescharacteristic
139#95—612no—
140#95—612no—
141#95—614no—
142C24C22×D6112yes—
143C2×Q8—614no—
144C2×Q8—1222no—
145C2×Q8—1222no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4C4×D6114yes—
149C22×C4—24no—
150C22×C4—44no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—612no—
154C22×C4—612no—
155C22×C4C22×D6112yes—
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6111yescharacteristic
158C22×C4C22×D6111yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—1224no—
161C4⋊C4—1222no—
162C4⋊C4—2444no—
163C22⋊C4—24no—
164C22⋊C4—6116no—
165C22⋊C4—2444no—
166C42—614no—
167C42—1222no—
168C42—1224no—
169C42C22⋊D6114yes—
170C23—22no—
171C23—22no—
172C23—24no—
173C23—24no—
174C23C2×C4×D6114yes—
175C23C23×D6111yescharacteristic
176Q8—1228no—
177D4—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—48no—
183C2×C4—614no—
184C2×C4—614no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1224no—
193C2×C4—1222no—
194C2×C4C2×C4×D6112yes—
195C2×C4#1175822212yes—
196C2×C4C2×C22⋊D6112yes—
197C2×C4C2×C22⋊D6112yes—
198C2×C4C2×C22⋊D6112yes—
199C22—24no—
200C22—28no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22C22×C4×D6111yescharacteristic
205C22C22×C22⋊D6111yescharacteristic
206C22C2×#1175822211yescharacteristic
207C22#1451982212yes—
208C22#1451982412yes—
209C4—22no—
210C4—22no—
211C4—42no—
212C4—1224no—
213C4—1224no—
214C4—2442no—
215C4—2442no—
216C4C4×C22⋊D6114yes—
217C2—44no—
218C2C2×C4×C22⋊D6111yescharacteristic
219C2#1684024112yes—
220C2#1684032911yescharacteristic
221C2#1684033311yescharacteristic
222C2#1684037712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×C4×D4×C61C2
socleC23×C61C24
hypercenterC2×C4×D4D61
hypocenterC61#2326
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic122C2semidirect
3. #16839667C2semidirect
5. #16839650C2semidirect
6. #16839635C2semidirect
7. #16839631C2semidirect
8. #16839608C2semidirect
11. #14519764C4semidirect
46. C2×Dic122C2×C4semidirect
51. C22⋊Dic61C2×C4semidirect
57. C4×Dic61C2×C4semidirect
121. C61#2326semidirect