Finite Group Databasebeta

← #21451231

Subgroups — #21451231

Order 7808.

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

normal subgroups only

This group has 412 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#16839692C211yesmaximal, characteristic
2#16839683C212yesmaximal
3#16839669C212yesmaximal
4#16839667C211yesmaximal, characteristic
5#16839661C212yesmaximal
6#16839649C212yesmaximal
7#16839643C212yesmaximal
8#16839613C212yesmaximal
9C61×#395C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C4×Dic61C2212yes—
17C2×C4×Dic61C2211yescharacteristic
18C2×C4×Dic61C2212yes—
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—24no—
32C2×Q8×C61—41no—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—22no—
43C2×Dic122—41no—
44C2×Dic122—41no—
45C4⋊C4×C61—24no—
46C4⋊C4×C61—41no—
47C4⋊Dic61—42no—
48C4⋊Dic61—41no—
49C4⋊Dic61—42no—
50#11758196—24no—
51#11758196Q818yescomplemented
52C4×Dic61—24no—
53C4×Dic61—41no—
54C4×Dic61—42no—
55C23×C61C2411yescharacteristic
56Q8×C61—44no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61C2×Q814yes—
68C2×C4×C61#4114yes—
69C2×C4×C61#4112yes—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61C2×Q814yes—
81C2×Dic61C2×Q814yes—
82Dic122—44no—
83C22×C61C22×Q812yes—
84C22×C61C2×#4112yes—
85C22×C61C2×#4111yescharacteristic
86C22×C61H(5,𝔽2)11yescharacteristic
87C22×C61H(5,𝔽2)11yescharacteristic
88C4×C61—22no—
89C4×C61—24no—
90C4×C61—24no—
91C4×C61—41no—
92C4×C61—41no—
93Dic61—24no—
94Dic61—24no—
95Dic61—42no—
96Dic61—42no—
97#2586—611nomaximal, Sylow
98C2×C61#53312yes—
99C2×C61#53811yescharacteristic
100C2×C61#55111yescharacteristic
101C2×C61#55412yes—
102C2×C61Q8211yescharacteristic
103#398—611no—
104#395—612no—
105#395D6111yescharacteristic
106#391—612no—
107#391—611no—
108#389—612no—
109#387—612no—
110#387—612no—
111C4×C4⋊C4—612no—
112C61#258611yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C22×Q8C2×D6111yescharacteristic
115C2×C4⋊C4—612no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—612no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4C2×D6112yes—
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42—612no—
123C2×C42—611no—
124C2×C42—612no—
125#95—612no—
126#95—612no—
127#95—611no—
128#95—612no—
129#95—612no—
130#95—612no—
131#95—612no—
132#95C2×D6112yes—
133#95C2×D6111yescharacteristic
134C2×Q8—24no—
135C2×Q8—41no—
136C2×Q8—1222no—
137C2×Q8—2441no—
138C2×Q8—2441no—
139C22×C4—612no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4C22×D6111yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C22×C4C22×D6112yes—
146C22×C4C22×D6112yes—
147C22×C4C22×D6111yescharacteristic
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—618no—
151C4⋊C4—1224no—
152C4⋊C4—2442no—
153C4⋊C4—2442no—
154C4⋊C4—2441no—
155C42—1224no—
156C42—2442no—
157C42—2441no—
158C23C23×D6111yescharacteristic
159Q8—44no—
160Q8—2444no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—614no—
172C2×C4—614no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4#1175822414yes—
184C2×C4Q8×D6114yes—
185C2×C4#1175822612yes—
186C22C2×Q8×D6112yes—
187C22C2×#1175822412yes—
188C22C2×#1175822611yescharacteristic
189C22#1451982211yescharacteristic
190C22#1451982311yescharacteristic
191C4—24no—
192C4—22no—
193C4—24no—
194C4—41no—
195C4—41no—
196C4—1224no—
197C4—1224no—
198C4—2442no—
199C4—2442no—
200C2#1684031712yes—
201C2#1684035211yescharacteristic
202C2#1684044311yescharacteristic
203C2#1684047012yes—
204C2#1684049211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2586
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. #11758196Q8semidirect
112. C61#2586semidirect