Finite Group Databasebeta

← #21461094

Subgroups — #21461094

Order 7808.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#16840733C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#16840605C214yesmaximal, complemented
4C2×#14519748C211yesmaximal, characteristic
5C2×#11758213—21no—
6C2×D61⋊C8—21no—
7#14519834—21no—
8#14519834—21no—
9C22⋊#92420C2212yes—
10C22⋊#92420C2212yes—
11C22×C22⋊D61C412yes—
12C22×C4×D61C2211yescharacteristic
13#14519748—21no—
14#14519748—21no—
15#14519748—21no—
16#14519748—21no—
17C2×C4⋊Dic61C411yescharacteristic
18C2×C22⋊Dic61C2212yes—
19C22×D4×C61C411yescharacteristic
20C24×C61C2×C412yes—
21C23×D61C2×C411yescharacteristic
22C2×D4×C61—21no—
23C2×D4×C61—21no—
24C2×D4×C61—42no—
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—44no—
29C22×Dic61C2×C412yes—
30C22×Dic61C2311yescharacteristic
31C2×C4×D61—42no—
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×#92420—22no—
37C2×#92420—22no—
38#11758213—42no—
39D61⋊C8—42no—
40C22⋊Dic61—22no—
41C22⋊Dic61—22no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C23×C61—22no—
45C23×C61—24no—
46C23×C61—42no—
47C23×C61—42no—
48C23×C61C22×C411yescharacteristic
49C22×D61—22no—
50C22×D61—22no—
51C22×D61—41no—
52C22×D61C22⋊C411yescharacteristic
53C22×D61C22⋊C411yescharacteristic
54D4×C61—42no—
55D4×C61—42no—
56C2×C4×C61—22no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C22⋊D61—44no—
60C22⋊D61—44no—
61C2×Dic61—22no—
62C2×Dic61—41no—
63C2×Dic61—42no—
64C2×Dic61C2×D411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—41no—
69C4×D61—41no—
70#92420—42no—
71#92420—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—42no—
75C22×C61—42no—
76C22×C61—42no—
77C22×C61—84no—
78C22×C61C2×C22⋊C411yescharacteristic
79C22×C61#13112yes—
80C2×D61—21no—
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—44no—
86C2×D61#10012yes—
87C4×C61—21no—
88C4×C61#9912yes—
89Dic61—21no—
90Dic61—21no—
91Dic61—42no—
92#1471—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—82no—
95C2×C61#40811yescharacteristic
96C2×C61C2×#9911yescharacteristic
97C2×C61C2×#10011yescharacteristic
98D61—22no—
99D61—41no—
100C2×#121—611no—
101#407—611no—
102C2×C22⋊C8—611no—
103#323—614no—
104C61#147111yescharacteristic, complemented, Sylow
105C22×D4—612no—
106C22×D4#692311yescharacteristic
107C23×C4—611no—
108C2×M16—1221no—
109C22×C8—1221no—
110#121—1221no—
111#121—1221no—
112#121—1221no—
113#121—1221no—
114C2×C4⋊C4—611no—
115C2×C22⋊C4—612no—
116C22⋊C8—612no—
117C22⋊C8—612no—
118C22⋊C8—1221no—
119C22⋊C8—1221no—
120C24—611no—
121C24C2×#692312yes—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—42no—
125C2×D4—1222no—
126C2×D4—1222no—
127C2×D4—2444no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—612no—
134C22×C4—2442no—
135C22×C4C2×#692311yescharacteristic
136M16—2442no—
137C2×C8—1222no—
138C2×C8—1222no—
139C2×C8—2442no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C23—22no—
145C23—24no—
146C23—42no—
147C23—42no—
148C23—611no—
149C23—611no—
150C23—1222no—
151C23—1222no—
152C23—2441no—
153C23C22×#692311yescharacteristic
154D4—42no—
155D4—42no—
156D4—2444no—
157D4—2444no—
158C2×C4—22no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4C22⋊#692311yescharacteristic
169C2×C4C22⋊#692311yescharacteristic
170C8—2442no—
171C8—2442no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—84no—
178C22—612no—
179C22—1221no—
180C22—1221no—
181C22—1221no—
182C22—1221no—
183C22—1221no—
184C22—2444no—
185C22C2×C22⋊#692311yescharacteristic
186C22#1451986412yes—
187C4—21no—
188C4—1221no—
189C4—1221no—
190C4—2442no—
191C4#1451983512yes—
192C2—22no—
193C2—82no—
194C2—1222no—
195C2—2441no—
196C2#1684073611yescharacteristic
197C2C2×#1451983511yescharacteristic
198C2D61⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC22×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×D4#6923
hypocenterC61#1471
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840733C2semidirect
2. D61⋊(C22⋊C8)C2semidirect
3. #16840605C2semidirect
104. C61#1471semidirect