Finite Group Databasebeta

← #21461569

Subgroups — #21461569

Order 7808.

360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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×#14519837C212yesmaximal
2C4×#11758217C212yesmaximal, complemented
3#16840642C212yesmaximal, complemented
4C2×#14519737C211yesmaximal, characteristic
5C2×#11758217C2214yes—
6#14519837C418yescomplemented
7#14519832—22no—
8C4×#92420—22no—
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⋊D61C2×C414yes—
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61—42no—
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C411yescharacteristic
30C22×Dic61C2311yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—42no—
34#11758217—24no—
35#11758217C2×C418yescomplemented
36C2×#92420—24no—
37C22⋊C4×C61—22no—
38#11758198—22no—
39#11758196—22no—
40C4×Dic61D412yes—
41C4×Dic61D412yes—
42C23×C61—21no—
43C23×C61—21no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61C4212yes—
47C23×C61C22×C411yescharacteristic
48C22×D61—21no—
49C22×D61—21no—
50C22×D61—41no—
51C22×D61—41no—
52C22×D61C4212yes—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C412yes—
57C22⋊D61—28no—
58C2×Dic61—22no—
59C2×Dic61—21no—
60C2×Dic61—42no—
61C2×Dic61—42no—
62C2×Dic61—41no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22×C412yes—
66C2×Dic61C2×D412yes—
67C2×Dic61#4112yes—
68C4×D61—42no—
69C4×D61—42no—
70#92420—28no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—22no—
74C22×C61—42no—
75C22×C61—42no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61C2×C4211yescharacteristic
79C22×C61C2×C22⋊C411yescharacteristic
80C22×C61#11711yescharacteristic
81C2×D61—22no—
82C2×D61—42no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—42no—
86C4×C61—22no—
87C4×C61—41no—
88Dic61—21no—
89Dic61—41no—
90Dic61#10012yescomplemented
91Dic61C4×D414yes—
92C4×#100—611nomaximal, Sylow
93C2×C61—21no—
94C2×C61—21no—
95C2×C61—42no—
96C2×C61C4×C22⋊C411yescharacteristic
97C2×C61C2×#10011yescharacteristic
98C2×C61#41311yescharacteristic
99D61—42no—
100C2×C4×D4—611no—
101C2×#100—612no—
102C4×M16—612no—
103#343—612no—
104C61C4×#10011yescharacteristic, complemented, Sylow
105C22×D4—611no—
106C23×C4—611no—
107C23×C4—611no—
108C2×M16—614no—
109C4×D4—1222no—
110C4×D4—1222no—
111C2×C4⋊C4—611no—
112C2×C22⋊C4—611no—
113C2×C22⋊C4#692311yescharacteristic
114C2×C42—611no—
115#100—618no—
116#97—1222no—
117C4×C8—1222no—
118C24—611no—
119C24C2×#692311yescharacteristic
120C2×D4—614no—
121C2×D4—1222no—
122C2×D4—1222no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—611no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4—1221no—
129C22×C4—1221no—
130C22×C4—2442no—
131C22×C4—2442no—
132C22×C4C2×#692311yescharacteristic
133C22×C4C2×#692311yescharacteristic
134M16—618no—
135M16—1224no—
136C2×C8—1224no—
137C4⋊C4—1222no—
138C22⋊C4—22no—
139C22⋊C4—1222no—
140C42—612no—
141C42—612no—
142C23—21no—
143C23—21no—
144C23—41no—
145C23—41no—
146C23—612no—
147C23—1221no—
148C23—1221no—
149C23—2441no—
150C23—2441no—
151C23C4×#692312yes—
152C23C22×#692311yescharacteristic
153D4—1228no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—612no—
158C2×C4—611no—
159C2×C4—612no—
160C2×C4—612no—
161C2×C4—611no—
162C2×C4—1222no—
163C2×C4—1221no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2441no—
169C2×C4C22⋊#692312yes—
170C8—1228no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22—1222no—
179C22—2442no—
180C22—2442no—
181C22—2441no—
182C22—2441no—
183C22C2×C4×#692311yescharacteristic
184C22C2×C22⋊#692311yescharacteristic
185C22#1451985611yescharacteristic
186C4—22no—
187C4—41no—
188C4—612no—
189C4—614no—
190C4—1221no—
191C4—2441no—
192C2—21no—
193C2—21no—
194C2—42no—
195C2—2442no—
196C2C4×C22⋊#692311yescharacteristic
197C2D61⋊#10011yescharacteristic
198C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC22×C61C2×C42
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61C4×#100
LCSG ▷ C22×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
2. C4×#11758217C2semidirect
3. #16840642C2semidirect
6. #14519837C4semidirect
35. #11758217C2×C4semidirect
90. Dic61#100semidirect
104. C61C4×#100semidirect