Finite Group Databasebeta

← #21451467

Subgroups — #21451467

Order 7808.

396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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#16839704C212yesmaximal
2#16839683C212yesmaximal
3#16839668C212yesmaximal
4#16839666C212yesmaximal
5#16839649C212yesmaximal
6#16839646C212yesmaximal
7#16839630C211yesmaximal, characteristic
8C4×C4⋊Dic61C211yesmaximal, characteristic
9C61×#376C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C4×Dic61C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519684C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2211yescharacteristic
26C2×C42×C61C2212yes—
27C2×C42×C61C2211yescharacteristic
28#95×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×Dic122—24no—
41C2×Dic122—24no—
42C2×Dic122—42no—
43C42×C61—24no—
44C42×C61Q814yescomplemented
45C4⋊Dic61—24no—
46C4⋊Dic61—42no—
47#11758196—24no—
48#11758196—24no—
49C4×Dic61—41no—
50C4×Dic61—41no—
51C23×C61C2411yescharacteristic
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—21no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61C2×Q812yes—
62C2×C4×C61C2×Q812yes—
63C2×C4×C61C2×Q812yes—
64C2×C4×C61#4114yes—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61#4114yes—
77Dic122—48no—
78C22×C61C22×Q811yescharacteristic
79C22×C61C2×#4112yes—
80C22×C61C2×#4112yes—
81C22×C61H(5,𝔽2)11yescharacteristic
82C22×C612−1+411yescharacteristic
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—22no—
86C4×C61—24no—
87C4×C61—42no—
88Dic61—24no—
89Dic61—42no—
90Dic61—42no—
91Dic61—42no—
92#2605—611nomaximal, Sylow
93C2×C61#53311yescharacteristic
94C2×C61#53311yescharacteristic
95C2×C61#54411yescharacteristic
96C2×C61#55112yes—
97C2×C61#55612yes—
98#400—612no—
99#395—612no—
100#391—612no—
101#391—612no—
102#387—612no—
103#387—612no—
104#383—611no—
105C4×C4⋊C4—611no—
106#376D6111yescharacteristic
107C61#260511yescharacteristic, complemented, Sylow
108C22×Q8—612no—
109C2×C4⋊C4—612no—
110C2×C4⋊C4—612no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—612no—
113C2×C42—611no—
114C2×C42—611no—
115C2×C42C2×D6112yes—
116C2×C42C2×D6111yescharacteristic
117#95—612no—
118#95—611no—
119#95—612no—
120#95—611no—
121#95—612no—
122#95—612no—
123#95—612no—
124#95—612no—
125#95—612no—
126#95C2×D6112yes—
127#95C2×D6111yescharacteristic
128#95C2×D6111yescharacteristic
129C2×Q8—1224no—
130C2×Q8—1224no—
131C2×Q8—2442no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4—612no—
135C22×C4—612no—
136C22×C4C22×D6112yes—
137C22×C4C22×D6111yescharacteristic
138C22×C4C22×D6111yescharacteristic
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6112yes—
141C4⋊C4—1224no—
142C4⋊C4—1224no—
143C4⋊C4—1224no—
144C4⋊C4—2442no—
145C42—24no—
146C42—2441no—
147C42—2441no—
148C42Dic12214yescomplemented
149C23C23×D6111yescharacteristic
150Q8—2448no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—614no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4C2×Dic12212yes—
173C2×C4C2×Dic12212yes—
174C2×C4C2×Dic12212yes—
175C2×C4#1175822214yes—
176C22C22×Dic12211yescharacteristic
177C22#41×D6112yes—
178C22C2×#1175822212yes—
179C22#1451982311yescharacteristic
180C22#1451982411yescharacteristic
181C4—22no—
182C4—22no—
183C4—22no—
184C4—24no—
185C4—42no—
186C4—1224no—
187C4—2442no—
188C4—2442no—
189C4—2442no—
190C2#1684031511yescharacteristic
191C2#1684031911yescharacteristic
192C2#1684039011yescharacteristic
193C2#1684043612yes—
194C2#1684048012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#376C2
hypercenter#376D61
hypocenterC61#2605
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
44. C42×C61Q8semidirect
107. C61#2605semidirect
148. C42Dic122semidirect