Finite Group Databasebeta

← #21454085

Subgroups — #21454085

Order 7808.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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#16839703C212yesmaximal
2#16839701C211yesmaximal, characteristic
3#16839696C212yesmaximal
4#16839695C212yesmaximal
5#16839693C212yesmaximal
6#16839681C212yesmaximal
7#16839631C211yesmaximal, characteristic
8#16839629C212yesmaximal
9C61×#395C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×C4×Dic61C2211yescharacteristic
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2211yescharacteristic
31C2×Q8×C61—41no—
32C2×Q8×C61—42no—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—42no—
44C4⋊Dic61—41no—
45C4⋊Dic61—41no—
46#11758196—42no—
47#11758196—42no—
48#11758196—42no—
49#11758196—42no—
50#11758196—42no—
51C4×Dic61Q814yescomplemented
52C23×C61C2411yescharacteristic
53Q8×C61—44no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61C2×Q812yes—
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—24no—
77C2×Dic61C2×Q814yes—
78C22×C61C22×Q811yescharacteristic
79C22×C61H(5,𝔽2)11yescharacteristic
80C22×C61H(5,𝔽2)12yes—
81C22×C612−1+411yescharacteristic
82C22×C612−1+412yes—
83C4×C61—22no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61—42no—
87C4×C61—42no—
88Dic61—24no—
89Dic61—42no—
90Dic61—42no—
91Dic61—42no—
92#2843—611nomaximal, Sylow
93C2×C61#54412yes—
94C2×C61#54411yescharacteristic
95C2×C61#56011yescharacteristic
96C2×C61#56311yescharacteristic
97C2×C61#56312yes—
98#400—611no—
99#400—612no—
100#398—612no—
101#398—612no—
102#398—612no—
103#395—612no—
104#395D6111yescharacteristic
105#384—611no—
106#383—612no—
107C61#284311yescharacteristic, complemented, Sylow
108C22×Q8C2×D6111yescharacteristic
109C2×C4⋊C4—612no—
110C2×C4⋊C4—612no—
111C2×C4⋊C4—611no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—612no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6112yes—
118C2×C42—611no—
119#95—612no—
120#95—612no—
121#95—612no—
122#95—612no—
123#95—612no—
124#95—612no—
125#95—611no—
126#95—612no—
127#95C2×D6112yes—
128#95C2×D6111yescharacteristic
129C2×Q8—41no—
130C2×Q8—42no—
131C22×C4—612no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4—612no—
135C22×C4C22×D6112yes—
136C22×C4C22×D6112yes—
137C22×C4C22×D6111yescharacteristic
138C22×C4C22×D6111yescharacteristic
139C22×C4C22×D6111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—2442no—
143C4⋊C4—2442no—
144C4⋊C4—2442no—
145C4⋊C4—2442no—
146C4⋊C4—2442no—
147C4⋊C4—2441no—
148C4⋊C4—2441no—
149C42—614no—
150C23C23×D6111yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—614no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1224no—
174C2×C4—1222no—
175C2×C4Q8×D6112yes—
176C22C2×Q8×D6111yescharacteristic
177C22#1451982211yescharacteristic
178C22#1451982212yes—
179C22#1451982411yescharacteristic
180C22#1451982512yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—1224no—
187C4—2442no—
188C4—2442no—
189C4—2442no—
190C2#1684038912yes—
191C2#1684039111yescharacteristic
192C2#1684050111yescharacteristic
193C2#1684051111yescharacteristic
194C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2843
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic61Q8semidirect
107. C61#2843semidirect