Finite Group Databasebeta

← #21453995

Subgroups — #21453995

Order 7808.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C61⋊#401C212yesmaximal
2#16839704C212yesmaximal
3#16839703C212yesmaximal
4#16839701C211yesmaximal, characteristic
5#16839696C212yesmaximal
6#16839692C211yesmaximal, characteristic
7#16839681C212yesmaximal
8#16839646C212yesmaximal
9C61×#391C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16#14519684C2212yes—
17#14519684C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C2×Q8×C61—22no—
32C2×Q8×C61—41no—
33C2×Q8×C61—41no—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C4⋊C4×C61—41no—
44C42×C61—41no—
45C4⋊Dic61—41no—
46C4⋊Dic61—41no—
47#11758196—24no—
48#11758196—42no—
49#11758196—42no—
50#11758196—42no—
51C23×C61C2411yescharacteristic
52Q8×C61—44no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61#4112yes—
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—24no—
77C22×C61C2×#4111yescharacteristic
78C22×C61H(5,𝔽2)11yescharacteristic
79C22×C61H(5,𝔽2)11yescharacteristic
80C22×C612−1+412yes—
81C22×C612−1+412yes—
82C4×C61—22no—
83C4×C61—42no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61—42no—
87Dic61—42no—
88Dic61—42no—
89Dic61—42no—
90Dic61—42no—
91#2833—611nomaximal, Sylow
92C2×C61#53811yescharacteristic
93C2×C61#54112yes—
94C2×C61#56311yescharacteristic
95C2×C61#56311yescharacteristic
96C2×C61#56312yes—
97#401—612no—
98#400—611no—
99#400—612no—
100#400—612no—
101#398—611no—
102#398—612no—
103#395—612no—
104#391D6111yescharacteristic
105#387—612no—
106C61#283311yescharacteristic, complemented, Sylow
107C22×Q8C2×D6111yescharacteristic
108C2×C4⋊C4—612no—
109C2×C4⋊C4—612no—
110C2×C4⋊C4—612no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4C2×D6111yescharacteristic
115C2×C42C2×D6111yescharacteristic
116#95—612no—
117#95—612no—
118#95—612no—
119#95—612no—
120#95—612no—
121#95—612no—
122#95—612no—
123#95—612no—
124#95—611no—
125#95—611no—
126#95C2×D6112yes—
127#95C2×D6112yes—
128C2×Q8—22no—
129C2×Q8—41no—
130C2×Q8—41no—
131C22×C4—612no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4—612no—
135C22×C4C22×D6112yes—
136C22×C4C22×D6111yescharacteristic
137C22×C4C22×D6111yescharacteristic
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—1224no—
142C4⋊C4—2442no—
143C4⋊C4—2442no—
144C4⋊C4—2442no—
145C4⋊C4—2441no—
146C4⋊C4—2441no—
147C42—41no—
148C23C23×D6111yescharacteristic
149Q8—44no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
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—1224no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4#1175822212yes—
174C22C2×#1175822211yescharacteristic
175C22#1451982211yescharacteristic
176C22#1451982211yescharacteristic
177C22#1451982412yes—
178C22#1451982512yes—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—42no—
184C4—2442no—
185C4—2442no—
186C4—2442no—
187C4—2442no—
188C2#1684035011yescharacteristic
189C2#1684037012yes—
190C2#1684051111yescharacteristic
191C2#1684051211yescharacteristic
192C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2833
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
106. C61#2833semidirect