Finite Group Databasebeta

← #21450770

Subgroups — #21450770

Order 7808.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519754C214yesmaximal, complemented
3C2×D4×Dic61C211yesmaximal, characteristic
4#16839698C214yesmaximal, complemented
5#16839665C211yesmaximal, characteristic
6#16839632C211yesmaximal, characteristic, complemented
7#16839631C211yesmaximal, characteristic, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C23×Dic61C2212yes—
12#14519776—24no—
13#14519754—216no—
14D4×Dic61—24no—
15C2×C4⋊Dic61C2214yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2214yes—
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2214yes—
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2214yes—
29C2×C42×C61C2211yescharacteristic
30C24×C61C2312yes—
31C2×D4×C61—22no—
32C2×D4×C61—22no—
33C2×D4×C61Q814yescomplemented
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—24no—
38C22×Dic61—28no—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C2×Dic122—28no—
45C2×Dic122—24no—
46C4⋊C4×C61—22no—
47C22⋊C4×C61—28no—
48C42×C61—22no—
49C22⋊Dic61—24no—
50C22⋊Dic61—28no—
51C4⋊Dic61—22no—
52C4⋊Dic61—28no—
53C4⋊Dic61—22no—
54#11758196—28no—
55#11758196—24no—
56#11758196D418yescomplemented
57C4×Dic61—22no—
58C4×Dic61D414yes—
59C23×C61—24no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—24no—
63C23×C61C2×Q814yes—
64C23×C61C2411yescharacteristic
65D4×C61—28no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—24no—
69C2×C4×C61—22no—
70C2×C4×C61C2×D414yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×Q812yes—
73C2×C4×C61#4112yes—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80C2×Dic61—22no—
81C2×Dic61—48no—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D414yes—
84C2×Dic61C2×D412yes—
85C2×Dic61C2×D414yes—
86Dic122—48no—
87C22×C61—24no—
88C22×C61—28no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—44no—
92C22×C61C22×D411yescharacteristic
93C22×C61C22×D412yes—
94C22×C61C22×Q811yescharacteristic
95C22×C61C2×#4111yescharacteristic
96C22×C612−1+412yes—
97C4×C61—24no—
98C4×C61—42no—
99C4×C61C22⋊Q814yescomplemented
100Dic61—22no—
101Dic61—24no—
102Dic61—42no—
103Dic61—42no—
104Dic61#12714yes—
105#2542—611nomaximal, Sylow
106C2×C61—44no—
107C2×C61C2×C22⋊Q811yescharacteristic
108C2×C61C2×#12711yescharacteristic
109C2×C61#53611yescharacteristic
110C2×C61#54712yes—
111C2×C61D4×Q812yes—
112C2×C4⋊Q8—611no—
113C2×C22⋊Q8—614no—
114C2×C4×D4—611no—
115#399—614no—
116#390—611no—
117#390D6111yescharacteristic
118#384—611no—
119#384—611no—
120C4×C4⋊C4—611no—
121C61#254211yescharacteristic, complemented, Sylow
122C22×Q8—612no—
123C22×D4C2×D6111yescharacteristic
124C23×C4—612no—
125C4⋊Q8—1224no—
126C22⋊Q8—12216no—
127C4×D4—1224no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4—614no—
131C2×C4⋊C4—614no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4—612no—
136C2×C22⋊C4—614no—
137C2×C22⋊C4C2×D6114yes—
138C2×C42—611no—
139C2×C42—611no—
140C2×C42C2×D6111yescharacteristic
141#95—612no—
142C24C22×D6112yes—
143C2×Q8—1228no—
144C2×Q8—1224no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4Dic12214yescomplemented
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—1224no—
154C22×C4—1228no—
155C22×C4C22×D6112yes—
156C22×C4C22×D6112yes—
157C22×C4C22×D6111yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—618no—
160C4⋊C4—1228no—
161C4⋊C4—1224no—
162C4⋊C4—1222no—
163C4⋊C4—1228no—
164C4⋊C4—1222no—
165C22⋊C4—28no—
166C22⋊C4—1224no—
167C22⋊C4—1228no—
168C42—22no—
169C42—614no—
170C42—1222no—
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic12214yes—
176C23C23×D6111yescharacteristic
177Q8—2448no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—612no—
184C2×C4—614no—
185C2×C4—612no—
186C2×C4—614no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1224no—
192C2×C4—1224no—
193C2×C4—1222no—
194C2×C4—2448no—
195C2×C4C2×Dic12212yes—
196C2×C4D4×D6114yes—
197C2×C4D4×D6112yes—
198C2×C4#1175822412yes—
199C22—24no—
200C22—28no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22C2×D4×D6111yescharacteristic
205C22C2×D4×D6112yes—
206C22C22×Dic12211yescharacteristic
207C22C2×#1175822411yescharacteristic
208C22#1451982412yes—
209C4—24no—
210C4—42no—
211C4—614no—
212C4—1222no—
213C4—1224no—
214C4—2442no—
215C4—2442no—
216C4#1451975414yescomplemented
217C2—44no—
218C2C2×#1451975411yescharacteristic
219C2#127×D6111yescharacteristic
220C2#1684033211yescharacteristic
221C2#1684041212yes—
222C2D4×Dic12212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2542
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
2. C2×#14519754C2semidirect
4. #16839698C2semidirect
6. #16839632C2semidirect
7. #16839631C2semidirect
8. C4×#11758196C2semidirect
33. C2×D4×C61Q8semidirect
56. #11758196D4semidirect
99. C4×C61C22⋊Q8semidirect
121. C61#2542semidirect
147. C2×D4Dic122semidirect
216. C4#14519754semidirect