Finite Group Databasebeta

← #21461126

Subgroups — #21461126

Order 7808.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840781C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#16840610C214yesmaximal, complemented
4#16840313C211yesmaximal, characteristic
5C2×D61⋊C8—21no—
6#14519844—21no—
7C4⋊#92420—21no—
8C4⋊#92420C2212yes—
9#14519834—21no—
10C4×#92420C2212yes—
11C2×#11758226—21no—
12#14519774C411yescharacteristic
13#14519766—21no—
14#14519752—21no—
15#14519752C412yes—
16#14519739—21no—
17#14519739C2212yes—
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic
20C2×Q8×C61—21no—
21#11758226—42no—
22#11758226—42no—
23C2×D244—22no—
24C2×D244—21no—
25C2×D244—21no—
26C2×D244C2×C412yes—
27C2×C4×D61—22no—
28C2×C4×D61C2×C411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×#92420—22no—
32C2×#92420—22no—
33D61⋊C8—42no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C412yes—
36C42×C61C2×C411yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61C2311yescharacteristic
42C22×D61—22no—
43C22×D61C22⋊C411yescharacteristic
44Q8×C61—42no—
45C2×C4×C61—22no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×Dic61C22⋊C411yescharacteristic
50C2×Dic61C2×D411yescharacteristic
51C2×Dic61C2×D411yescharacteristic
52D244—24no—
53D244—42no—
54D244—44no—
55D244—42no—
56C4×D61—22no—
57C4×D61—41no—
58C4×D61—42no—
59C4×D61—42no—
60C4×D61D812yes—
61C4×D61SD1612yes—
62#92420—42no—
63#92420—42no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—21no—
66C2×D61—21no—
67C2×D61—42no—
68C2×D61—42no—
69C2×D61—42no—
70C2×D61#10212yes—
71C4×C61—21no—
72C4×C61—42no—
73C4×C61#10212yes—
74C4×C61#13112yes—
75Dic61—21no—
76Dic61—21no—
77Dic61C2×D811yescharacteristic
78Dic61C2×SD1611yescharacteristic
79#1480—611nomaximal, Sylow
80C2×C61#40811yescharacteristic
81C2×C61C2×#10211yescharacteristic
82C2×C61#42111yescharacteristic
83D61—22no—
84D61—82no—
85#532—611no—
86#431—611no—
87C2×C4⋊C8—611no—
88D4⋊C8—614no—
89C61#148011yescharacteristic, complemented, Sylow
90C2×#41—1221no—
91C22×C8—1221no—
92C4⋊Q8#692311yescharacteristic
93#127—611no—
94#124—1221no—
95#121—612no—
96#121—1221no—
97C4×D4—612no—
98C4×D4—1221no—
99C2×C42—611no—
100C4⋊C8—612no—
101C4⋊C8—1221no—
102C4⋊C8—1221no—
103C22⋊C8—1221no—
104C4×C8—612no—
105#41—2442no—
106#41—2442no—
107C2×Q8—21no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1221no—
111C2×D4—1221no—
112C22×C4—611no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4—1222no—
116C2×C8—1222no—
117C2×C8—1222no—
118C2×C8—2442no—
119C4⋊C4—21no—
120C4⋊C4C2×#692312yes—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42—611no—
124C42—611no—
125C42—611no—
126C42C2×#692311yescharacteristic
127C23—611no—
128C23—1222no—
129Q8—42no—
130D4—1224no—
131D4—2442no—
132D4—2444no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—611no—
136C2×C4—612no—
137C2×C4—612no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—1222no—
141C2×C4—2441no—
142C2×C4—2442no—
143C2×C4—2442no—
144C2×C4C22⋊#692311yescharacteristic
145C2×C4C22⋊#692311yescharacteristic
146C2×C4C22×#692311yescharacteristic
147C8—2442no—
148C8—2442no—
149C22—612no—
150C22—1221no—
151C22—1221no—
152C22—2442no—
153C22—2442no—
154C22—2442no—
155C22C2×C22⋊#692311yescharacteristic
156C4—21no—
157C4—42no—
158C4—611no—
159C4—611no—
160C4—1221no—
161C4—1221no—
162C4#1451983912yes—
163C4#1451986512yes—
164C2—1222no—
165C2—4882no—
166C2#1684073711yescharacteristic
167C2C2×#1451983911yescharacteristic
168C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1480
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #16840781C2semidirect
2. D61⋊(C4⋊C8)C2semidirect
3. #16840610C2semidirect
89. C61#1480semidirect