Finite Group Databasebeta

← #21453781

Subgroups — #21453781

Order 7808.

392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 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#16839695C212yesmaximal
2#16839694C212yesmaximal
3#16839682C212yesmaximal
4#16839668C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic
6#16839666C212yesmaximal
7#16839661C212yesmaximal
8#16839648C212yesmaximal
9C61×#389C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2212yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×Dic122—22no—
41C2×Dic122—41no—
42C2×Dic122—41no—
43C2×Dic122—41no—
44C2×Dic122—41no—
45C2×Dic122Q814yescomplemented
46C4⋊C4×C61—24no—
47C4⋊C4×C61—41no—
48C4⋊C4×C61Q814yescomplemented
49C42×C61—41no—
50C4⋊Dic61—42no—
51C4⋊Dic61—42no—
52C4⋊Dic61—41no—
53C4⋊Dic61—41no—
54#11758196—42no—
55#11758196—42no—
56C4×Dic61—42no—
57C23×C61C2411yescharacteristic
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×Q812yes—
70C2×C4×C61C2×Q814yes—
71C2×C4×C61C2×Q812yes—
72C2×C4×C61#4112yes—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61C2×Q814yes—
85Dic122—44no—
86Dic122—44no—
87C22×C61C22×Q811yescharacteristic
88C22×C61C22×Q811yescharacteristic
89C22×C61C2×#4111yescharacteristic
90C22×C61H(5,𝔽2)11yescharacteristic
91C22×C61H(5,𝔽2)11yescharacteristic
92C22×C61H(5,𝔽2)11yescharacteristic
93C22×C612−1+411yescharacteristic
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—24no—
98C4×C61—42no—
99Dic61—24no—
100Dic61—42no—
101Dic61—42no—
102Dic61—42no—
103#2806—611nomaximal, Sylow
104C2×C61#53811yescharacteristic
105C2×C61#54311yescharacteristic
106C2×C61#54411yescharacteristic
107C2×C61#55411yescharacteristic
108C2×C61#55711yescharacteristic
109C2×C61Q8211yescharacteristic
110C2×C61#56211yescharacteristic
111#398—612no—
112#398—612no—
113#395—612no—
114#391—611no—
115#391—611no—
116#391—612no—
117#389—612no—
118#389D6111yescharacteristic
119#387—612no—
120C61#280611yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C22×Q8—611no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4C2×D6112yes—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C42—612no—
133C2×C42C2×D6111yescharacteristic
134#95—612no—
135#95—612no—
136#95—612no—
137#95—612no—
138#95—612no—
139#95—612no—
140#95—612no—
141#95C2×D6112yes—
142C2×Q8—614no—
143C2×Q8—1222no—
144C2×Q8—2441no—
145C2×Q8—2441no—
146C2×Q8—2441no—
147C2×Q8—2441no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4C22×D6112yes—
153C22×C4C22×D6111yescharacteristic
154C22×C4C22×D6112yes—
155C22×C4C22×D6111yescharacteristic
156C22×C4C22×D6111yescharacteristic
157C4⋊C4—24no—
158C4⋊C4—41no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C4⋊C4—2442no—
162C4⋊C4—2441no—
163C4⋊C4—2441no—
164C4⋊C4—2442no—
165C4⋊C4Dic12214yescomplemented
166C42—41no—
167C42—2442no—
168C23C23×D6111yescharacteristic
169Q8—2444no—
170Q8—2444no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—614no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4C2×Dic12214yes—
195C2×C4C2×Dic12212yes—
196C2×C4#1175822412yes—
197C2×C4Q8×D6112yes—
198C22C2×Q8×D6111yescharacteristic
199C22C22×Dic12211yescharacteristic
200C22C2×#1175822411yescharacteristic
201C22#1451982211yescharacteristic
202C22#1451982311yescharacteristic
203C22#1451982311yescharacteristic
204C22#1451982511yescharacteristic
205C4—24no—
206C4—22no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1224no—
211C4—2442no—
212C4—2442no—
213C4—2442no—
214C2#1684034911yescharacteristic
215C2#1684038711yescharacteristic
216C2#1684039311yescharacteristic
217C2#1684046911yescharacteristic
218C2#1684048711yescharacteristic
219C2Q8×Dic12211yescharacteristic
220C2#1684051011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2806
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
45. C2×Dic122Q8semidirect
48. C4⋊C4×C61Q8semidirect
120. C61#2806semidirect
165. C4⋊C4Dic122semidirect