Finite Group Databasebeta

← #21461684

Subgroups — #21461684

Order 7808.

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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#16840765C212yesmaximal, complemented
2C2×#14519837C212yesmaximal
3#16840642C212yesmaximal, complemented
4C2×#14519737C211yesmaximal, characteristic
5C2×#11758217C2214yes—
6#14519844—22no—
7C4⋊#92420—22no—
8#14519837—24no—
9C22×C22⋊D61C2211yescharacteristic
10C23×Dic61C411yescharacteristic
11C22×C4×D61C411yescharacteristic
12#14519737—22no—
13#14519737—22no—
14C2×#11758196C2211yescharacteristic
15C2×#11758198C411yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17C2×C22⋊C4×C61C411yescharacteristic
18C24×C61C2×C411yescharacteristic
19C23×D61C2×C411yescharacteristic
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61C2×C411yescharacteristic
22C2×C22⋊D61—22no—
23C2×C22⋊D61—22no—
24C2×C22⋊D61D412yes—
25C2×C22⋊D61Q812yes—
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—42no—
29C22×Dic61C2×C411yescharacteristic
30C22×Dic61C2×C411yescharacteristic
31C22×Dic61C2311yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—42no—
35#11758217—24no—
36#11758217—24no—
37C2×#92420—24no—
38C22⋊C4×C61—22no—
39#11758198—22no—
40#11758196—22no—
41C4×Dic61D412yes—
42C4×Dic61D412yes—
43C23×C61—21no—
44C23×C61—21no—
45C23×C61—41no—
46C23×C61—41no—
47C23×C61C4⋊C412yes—
48C23×C61C22×C411yescharacteristic
49C22×D61—21no—
50C22×D61—21no—
51C22×D61—41no—
52C22×D61—41no—
53C22×D61C4⋊C412yes—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C22⋊C412yes—
58C22⋊D61—24no—
59C22⋊D61—24no—
60C2×Dic61—22no—
61C2×Dic61—21no—
62C2×Dic61—42no—
63C2×Dic61—42no—
64C2×Dic61—41no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68C2×Dic61C2×D412yes—
69C2×Dic61C2×Q811yescharacteristic
70C2×Dic61#4112yes—
71C4×D61—42no—
72C4×D61—42no—
73#92420—44no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—22no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C22×C61C2×C4⋊C411yescharacteristic
83C22×C61#11711yescharacteristic
84C2×D61—22no—
85C2×D61—42no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—42no—
89C4×C61—22no—
90C4×C61—41no—
91Dic61—21no—
92Dic61—41no—
93Dic61#10012yescomplemented
94Dic61#12112yes—
95Dic61C22⋊Q812yes—
96#1800—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61—42no—
100C2×C61#38011yescharacteristic
101C2×C61C2×#10011yescharacteristic
102C2×C61#41311yescharacteristic
103D61—42no—
104C2×C4×D4—611no—
105#423—612no—
106C2×#100—612no—
107#343—612no—
108C61#180011yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C23×C4—611no—
111C23×C4—611no—
112C2×M16—614no—
113C4×D4—1222no—
114C4×D4—1222no—
115C2×C4⋊C4—611no—
116C2×C22⋊C4—611no—
117C2×C22⋊C4#692311yescharacteristic
118C2×C42—611no—
119C4⋊C8—1222no—
120C4⋊C8—1222no—
121#100—1224no—
122C24—611no—
123C24C2×#692311yescharacteristic
124C2×D4—612no—
125C2×D4—612no—
126C2×D4—1222no—
127C2×D4—1222no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4—2442no—
136C22×C4—2442no—
137C22×C4C2×#692311yescharacteristic
138C22×C4C2×#692311yescharacteristic
139M16—1224no—
140M16—1224no—
141C2×C8—1224no—
142C4⋊C4—1222no—
143C22⋊C4—22no—
144C22⋊C4—1222no—
145C42—612no—
146C42—612no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—612no—
152C23—1221no—
153C23—1221no—
154C23—2441no—
155C23—2441no—
156C23C4⋊#692312yes—
157C23C22×#692311yescharacteristic
158D4—1224no—
159D4—1224no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—611no—
164C2×C4—612no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—612no—
168C2×C4—611no—
169C2×C4—1222no—
170C2×C4—1221no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4—2441no—
176C2×C4C22⋊#692312yes—
177C8—2444no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—1222no—
186C22—2442no—
187C22—2442no—
188C22—2441no—
189C22—2441no—
190C22C2×C22⋊#692311yescharacteristic
191C22C2×C4⋊#692311yescharacteristic
192C22#1451985611yescharacteristic
193C4—22no—
194C4—41no—
195C4—612no—
196C4—612no—
197C4—612no—
198C4—1221no—
199C4—2441no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—2442no—
204C2#1684070411yescharacteristic
205C2D61⋊#10011yescharacteristic
206C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1800
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840765C2semidirect
3. #16840642C2semidirect
93. Dic61#100semidirect
108. C61#1800semidirect