Finite Group Databasebeta

← #21444156

Subgroups — #21444156

Order 7808.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#14519739C211yesmaximal, characteristic
2#16839724C212yesmaximal, complemented
3#16839488C211yesmaximal, characteristic, complemented
4#16839485C212yesmaximal, complemented
5C61×#324C211yesmaximal, characteristic, complemented
6C22×D244C411yescharacteristic
7C22×C4×D61C411yescharacteristic
8C22×C4×D61C2211yescharacteristic
9C2×#11758189—22no—
10#14519739—22no—
11#14519739—22no—
12C2×#11758198C411yescharacteristic
13C2×#11758198C2211yescharacteristic
14C2×C4×Dic61C411yescharacteristic
15C22⋊#92418C2212yes—
16#14519689—22no—
17C2×C4⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yes—
19C23×D61C2×C411yescharacteristic
20C23×D61C2×C411yescharacteristic
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61C2×C411yescharacteristic
26C2×D244—22no—
27C2×D244—22no—
28C2×D244—22no—
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—42no—
32C2×C4×D61—42no—
33C2×C4×D61D412yes—
34C2×C4×D61D412yes—
35C2×C8×C61—22no—
36C4⋊C4×C61—22no—
37#11758198—22no—
38#11758198—22no—
39C4×Dic61—21no—
40C4×Dic61—21no—
41C2×#92418—22no—
42#11758189—44no—
43C23×C61C22×C411yescharacteristic
44C22×D61—21no—
45C22×D61—21no—
46C22×D61—21no—
47C22×D61—21no—
48C22×D61—41no—
49C22×D61—41no—
50C22×D61—41no—
51C22×D61—41no—
52C22×D61C22⋊C412yes—
53C22×D61M1612yescomplemented
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61M1612yescomplemented
60C2×C4×C61C2×D412yes—
61C2×Dic61—22no—
62C2×Dic61—21no—
63C2×Dic61—41no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66D244—28no—
67C4×D61—24no—
68C4×D61—42no—
69C4×D61—42no—
70C4×D61—42no—
71C8×C61—42no—
72#92418—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61C2×C22⋊C411yescharacteristic
76C22×C61C2×M1611yescharacteristic
77C22×C61C2×M1611yescharacteristic
78C2×D61—22no—
79C2×D61—22no—
80C2×D61—22no—
81C2×D61—22no—
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—42no—
88C4×C61—22no—
89C4×C61—22no—
90C4×C61—41no—
91Dic61—21no—
92Dic61—41no—
93Dic61#9912yes—
94#1465—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#40711yescharacteristic
98C2×C61C2×#9911yescharacteristic
99C2×C61#41311yescharacteristic
100D61—42no—
101D61—42no—
102C2×C4×D4—611no—
103#407—612no—
104#324—611no—
105#324D6111yescharacteristic, complemented
106#323—612no—
107C61#146511yescharacteristic, complemented, Sylow
108C22×D4—611no—
109C23×C4—611no—
110C23×C4—611no—
111C2×M16—1222no—
112C4×D4—1222no—
113C4×D4—1222no—
114C2×C4⋊C4C2×D6111yescharacteristic
115C2×C22⋊C4—611no—
116C2×C22⋊C4—611no—
117C2×C42—611no—
118C22⋊C8—612no—
119C22⋊C8—1222no—
120C22⋊C8C2×D6112yes—
121C24—611no—
122C24—611no—
123C2×D4—1222no—
124C2×D4—1222no—
125C2×D4—1222no—
126C22×C4—611no—
127C22×C4—612no—
128C22×C4—612no—
129C22×C4—611no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4—2442no—
133C22×C4—2442no—
134C22×C4C4×D6111yescharacteristic
135C22×C4C4×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137M16—2444no—
138C2×C8—22no—
139C2×C8—1222no—
140C4⋊C4—22no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C42—1221no—
144C42—1221no—
145C23—612no—
146C23—612no—
147C23—1221no—
148C23—1221no—
149C23—1221no—
150C23—1221no—
151C23—2441no—
152C23—2441no—
153C23—2441no—
154C23—2441no—
155C23C2×C4×D6111yescharacteristic
156D4—1228no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—1224no—
165C2×C4—1222no—
166C2×C4—1221no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4—2441no—
171C2×C4#1175818912yescomplemented
172C2×C4D4×D6112yes—
173C8—42no—
174C8—2442no—
175C22—21no—
176C22—21no—
177C22—1222no—
178C22—1222no—
179C22—1222no—
180C22—1222no—
181C22—2442no—
182C22—2442no—
183C22—2442no—
184C22—2442no—
185C22—2441no—
186C22—2441no—
187C22C22⋊C4×D6111yescharacteristic
188C22M16×D6111yescharacteristic
189C22C2×#1175818911yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—612no—
194C4—1221no—
195C4—2441no—
196C2—21no—
197C2—21no—
198C2—2442no—
199C2—2442no—
200C2#1683972411yescharacteristic
201C2#99×D6111yescharacteristic
202C2#1683974511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61C2×C22⋊C4
hypercenter#324D61
hypocenterC61#1465
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #16839724C2semidirect
3. #16839488C2semidirect
4. #16839485C2semidirect
5. C61×#324C2semidirect
53. C22×D61M16semidirect
59. C2×C4×C61M16semidirect
105. #324D61semidirect
107. C61#1465semidirect
171. C2×C4#11758189semidirect