Finite Group Databasebeta

← #21453802

Subgroups — #21453802

Order 7808.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#16839701C211yesmaximal, characteristic
2#16839696C212yesmaximal
3#16839695C212yesmaximal
4#16839667C211yesmaximal, characteristic
5#16839666C212yesmaximal
6#16839659C212yesmaximal
7#16839647C212yesmaximal
8#16839644C212yesmaximal
9C61×#400C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×C4×Dic61C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#95×C61C2212yes—
29#95×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—41no—
41C2×Dic122—41no—
42C2×Dic122Q814yes—
43C4⋊C4×C61—41no—
44C4⋊C4×C61—41no—
45C4⋊Dic61—24no—
46C4⋊Dic61—41no—
47#11758196—24no—
48#11758196—24no—
49#11758196—42no—
50#11758196—42no—
51C4×Dic61—41no—
52C4×Dic61—42no—
53C23×C61C2411yescharacteristic
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—22no—
77C2×Dic61C2×Q814yes—
78C2×Dic61#4114yes—
79Dic122—44no—
80C22×C61C22×Q811yescharacteristic
81C22×C61C2×#4112yes—
82C22×C61H(5,𝔽2)11yescharacteristic
83C22×C61H(5,𝔽2)11yescharacteristic
84C22×C612−1+412yes—
85C4×C61—22no—
86C4×C61—42no—
87C4×C61—42no—
88C4×C61—41no—
89C4×C61—41no—
90Dic61—24no—
91Dic61—24no—
92Dic61—42no—
93Dic61—42no—
94#2809—611nomaximal, Sylow
95C2×C61#53912yes—
96C2×C61#54311yescharacteristic
97C2×C61#55511yescharacteristic
98C2×C61#55712yes—
99C2×C61#56311yescharacteristic
100#400—611no—
101#400D6111yescharacteristic
102#398—612no—
103#398—612no—
104#391—611no—
105#391—612no—
106#389—612no—
107#387—612no—
108#387—612no—
109C61#280911yescharacteristic, complemented, Sylow
110C22×Q8—611no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—612no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C42—612no—
120C2×C42—611no—
121#95—611no—
122#95—612no—
123#95—612no—
124#95—612no—
125#95—612no—
126#95—612no—
127#95—612no—
128#95C2×D6111yescharacteristic
129#95C2×D6112yes—
130#95C2×D6112yes—
131C2×Q8—614no—
132C2×Q8—2441no—
133C2×Q8—2441no—
134C22×C4—612no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4—612no—
138C22×C4C22×D6111yescharacteristic
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6112yes—
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—1224no—
146C4⋊C4—1224no—
147C4⋊C4—1224no—
148C4⋊C4—2442no—
149C4⋊C4—2442no—
150C4⋊C4—2441no—
151C42—2441no—
152C42—2442no—
153C23C23×D6111yescharacteristic
154Q8—2444no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—614no—
168C2×C4—614no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4Q8×D6112yes—
180C22C2×Q8×D6111yescharacteristic
181C22#41×D6112yes—
182C22#1451982211yescharacteristic
183C22#1451982311yescharacteristic
184C22#1451982412yes—
185C4—22no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—42no—
190C4—1224no—
191C4—1224no—
192C4—2442no—
193C4—2442no—
194C2#1684035312yes—
195C2#1684038711yescharacteristic
196C2#1684047411yescharacteristic
197C2#1684048912yes—
198C2#1684051511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2809
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
109. C61#2809semidirect