Finite Group Databasebeta

← #21461999

Subgroups — #21461999

Order 7808.

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

normal subgroups only

This group has 260 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
1D61⋊(C4⋊C8)C211yesmaximal, characteristic
2C4×C4⋊#6923C211yesmaximal, characteristic
3#16840635C212yesmaximal
4#16840635C212yesmaximal
5#125×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923—21no—
9#14519844—21no—
10C4⋊#92420—21no—
11(C2×#6923)⋊C4—21no—
12#14519769C411yescharacteristic, complemented
13#14519768C411yescharacteristic, complemented
14#14519768C411yescharacteristic, complemented
15#14519767—21no—
16#14519767—21no—
17C4⋊C4×D61—21no—
18C4⋊C4×D61—21no—
19C4⋊C4×D61C2211yescharacteristic
20C4⋊C4×D61C2211yescharacteristic
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×C4×D61—21no—
25C2×C4×D61—21no—
26C2×C4×D61D411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61C2311yescharacteristic
29C2×#92420—22no—
30C4⋊#6923—22no—
31C4⋊#6923Q814yes—
32C4×#6923—42no—
33D61⋊C8—24no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61C2×C411yescharacteristic
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C22×D61C2×D411yescharacteristic
53C2×#6923—24no—
54C2×#6923—42no—
55C2×#6923—42no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—42no—
70C4×D61—41no—
71C4×D61—41no—
72C4×D61C2×Q812yes—
73C4×D61#4112yes—
74#92420—42no—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61C22⋊Q812yes—
77C2×D61#13512yes—
78C2×D61AGL(1,ℤ/8)11yescharacteristic
79C2×D61#13711yescharacteristic
80#6923—44no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C4×Q812yes—
86Dic61—21no—
87Dic61—21no—
88Dic61—41no—
89Dic61—41no—
90Dic61#12411yescharacteristic
91Dic61C4⋊Q811yescharacteristic
92#1989—611nomaximal, Sylow
93C2×C61#39111yescharacteristic
94C2×C61#41611yescharacteristic
95C2×C61#41711yescharacteristic
96D61#47812yes—
97D61#47912yes—
98C2×#125—611no—
99C2×C4⋊C8—611no—
100C4×C4⋊C4—611no—
101#340—612no—
102#340—612no—
103C61#198911yescharacteristic, complemented, Sylow
104C22×C8—612no—
105#125—611no—
106#125—611no—
107#125—611no—
108#125—1221no—
109#125—1221no—
110#125#692311yescharacteristic, complemented
111C2×C4⋊C4—612no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4—1221no—
116C2×C42—611no—
117C2×C42—1221no—
118C4⋊C8—1221no—
119C4⋊C8—1221no—
120#95—1221no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1221no—
125C22×C4—1221no—
126C22×C4—1222no—
127C2×C8—1222no—
128C2×C8—1224no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—614no—
132C4⋊C4—611no—
133C4⋊C4—611no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4—1222no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4C2×#692311yescharacteristic
144C4⋊C4C2×#692311yescharacteristic
145C42—611no—
146C42—611no—
147C42—611no—
148C42—2442no—
149C42C2×#692311yescharacteristic
150C23—611no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—611no—
154C2×C4—612no—
155C2×C4—612no—
156C2×C4—611no—
157C2×C4—611no—
158C2×C4—1221no—
159C2×C4—1222no—
160C2×C4—1221no—
161C2×C4—1224no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—2442no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22⋊#692311yescharacteristic
171C2×C4C22×#692311yescharacteristic
172C8—2442no—
173C22—612no—
174C22—612no—
175C22—611no—
176C22—611no—
177C22C2×C22⋊#692311yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—611no—
183C4—611no—
184C4—1221no—
185C4—1221no—
186C4—2444no—
187C4—2441no—
188C4—2441no—
189C4Q8×#692312yes—
190C2—612no—
191C2—612no—
192C2(C2×#6923)⋊Q811yescharacteristic
193C2#1684075211yescharacteristic
194C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1989
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #14519769C4semidirect
13. #14519768C4semidirect
14. #14519768C4semidirect
22. #125×C61C4semidirect
103. C61#1989semidirect
110. #125#6923semidirect