Finite Group Databasebeta

← #21461098

Subgroups — #21461098

Order 7808.

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

normal subgroups only

This group has 270 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#16840732C211yesmaximal, characteristic
2C2×C22⋊#92420C211yesmaximal, characteristic
3#16840608C212yesmaximal, complemented
4#16840607C212yesmaximal, complemented
5C2×#14519754C211yesmaximal, characteristic
6C2×#11758217—21no—
7C22×#92420—21no—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10C22⋊#92420C2212yes—
11C22⋊#92420C2212yes—
12C22×Dic122C411yescharacteristic
13C23×Dic61C2211yescharacteristic
14#14519754—21no—
15#14519754—21no—
16#14519754—21no—
17#14519754—21no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C411yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×C22⋊Dic61C411yescharacteristic
22C2×C22⋊C4×C61C411yescharacteristic
23C24×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61—42no—
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C411yescharacteristic
30C22×Dic61D411yescharacteristic
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34C22×Dic61C2311yescharacteristic
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—42no—
38#11758217—42no—
39C2×#92420—22no—
40C2×#92420—22no—
41C2×#92420—42no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61C22⋊C411yescharacteristic
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—22no—
61C2×C4×C61—41no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61—22no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C2×D411yescharacteristic
75C2×Dic61C2×D411yescharacteristic
76Dic122—42no—
77Dic122—42no—
78#92420—42no—
79#92420—42no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—44no—
88C22×C61#10112yes—
89C22×C61C2×C22⋊C411yescharacteristic
90C22×C61#13112yes—
91C4×C61—41no—
92C4×C61—41no—
93Dic61—21no—
94Dic61—21no—
95Dic61—21no—
96Dic61—41no—
97Dic61—41no—
98Dic61#9912yes—
99#1472—611nomaximal, Sylow
100C2×C61—22no—
101C2×C61—22no—
102C2×C61—41no—
103C2×C61#40811yescharacteristic
104C2×C61C2×#9911yescharacteristic
105C2×C61C2×#10111yescharacteristic
106C2×C22⋊Q8—611no—
107#407—611no—
108C2×C22⋊C8—611no—
109#324—612no—
110#324—612no—
111C61#147211yescharacteristic, complemented, Sylow
112C22×Q8—611no—
113C23×C4—611no—
114C2×M16—1221no—
115C22×C8—1221no—
116C22⋊Q8—1221no—
117C22⋊Q8—1221no—
118C22⋊Q8—1221no—
119C22⋊Q8—1221no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—611no—
123C2×C22⋊C4—611no—
124C2×C22⋊C4#692311yescharacteristic
125C22⋊C8—612no—
126C22⋊C8—612no—
127C22⋊C8—1221no—
128C22⋊C8—1221no—
129C24C2×#692311yescharacteristic
130C2×Q8—1221no—
131C2×Q8—1221no—
132C2×Q8—2442no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—2442no—
142C22×C4C2×#692311yescharacteristic
143C22×C4C2×#692311yescharacteristic
144M16—2442no—
145C2×C8—1222no—
146C2×C8—1222no—
147C2×C8—2442no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C23—22no—
159C23—22no—
160C23—41no—
161C23C22⋊#692311yescharacteristic
162C23C22⋊#692311yescharacteristic
163C23C22×#692311yescharacteristic
164Q8—2442no—
165Q8—2442no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1222no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2441no—
184C8—2442no—
185C8—2442no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—44no—
194C22#1451983812yes—
195C22C2×C22⋊#692311yescharacteristic
196C22#1451986412yes—
197C4—41no—
198C4—41no—
199C4—612no—
200C4—1221no—
201C4—1221no—
202C4—1221no—
203C4—2441no—
204C4—2441no—
205C2—22no—
206C2—22no—
207C2—41no—
208C2#1684073511yescharacteristic
209C2D61⋊#9911yescharacteristic
210C2C2×#1451983811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1472
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840608C2semidirect
4. #16840607C2semidirect
111. C61#1472semidirect