Finite Group Databasebeta

← #21462093

Subgroups — #21462093

Order 7808.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#16840743C212yesmaximal, complemented
2#16840668C212yesmaximal, complemented
3#16840667C212yesmaximal, complemented
4#16840313C211yesmaximal, characteristic
5#14519856—22no—
6#14519836—22no—
7#14519836C2214yes—
8C2×#11758226C411yescharacteristic, complemented
9C2×#11758226C2211yescharacteristic
10#14519774C2211yescharacteristic
11#14519766C411yescharacteristic, complemented
12#14519766C2211yescharacteristic
13#14519752—22no—
14#14519739—22no—
15C42×D61C411yescharacteristic, complemented
16C4⋊Q8×C61C411yescharacteristic, complemented
17C2×Q8×C61C2×C411yescharacteristic
18C2×Q8×C61C2×C411yescharacteristic
19#11758226—41no—
20#11758226—41no—
21#11758226—41no—
22#11758226—41no—
23C2×D244—21no—
24C2×D244—22no—
25C2×D244C2×C411yescharacteristic
26C2×D244D412yes—
27C2×D244C2311yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D412yes—
32C22⋊#6923—24no—
33C4⋊#6923—42no—
34C4×#6923—42no—
35C4⋊C4×C61—22no—
36C42×C61C2×C411yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41C22×D61—21no—
42C22×D61C22⋊C411yescharacteristic
43C22×D61C2×D412yes—
44C2×#6923—44no—
45Q8×C61—41no—
46Q8×C61—41no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61C22⋊C412yes—
50C2×C4×C61C22×C411yescharacteristic
51C2×Dic61—21no—
52C2×Dic61C22⋊C411yescharacteristic
53D244—42no—
54D244—41no—
55D244—41no—
56D244—44no—
57D244—42no—
58C4×D61—22no—
59C4×D61—22no—
60C4×D61—21no—
61C4×D61—21no—
62C4×D61—42no—
63C4×D61—41no—
64C4×D61—41no—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—21no—
67C2×D61—22no—
68C2×D61—41no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—41no—
72#6923—84no—
73C4×C61—22no—
74C4×C61—21no—
75C4×C61—22no—
76C4×C61—41no—
77Dic61—41no—
78Dic61#9911yescharacteristic
79Dic61#9911yescharacteristic
80#2126—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61C2×#9911yescharacteristic
83D61—42no—
84D61—41no—
85D61—81no—
86#532—611no—
87#410—612no—
88#354—612no—
89#353—612no—
90C61#212611yescharacteristic, complemented, Sylow
91C2×#41—611no—
92C2×#41—611no—
93C4⋊Q8#692311yescharacteristic, complemented
94#127—611no—
95#124—611no—
96#124—611no—
97#121—1222no—
98C4×D4—1222no—
99#117—1222no—
100C2×C42—611no—
101#99—614no—
102#99—1222no—
103#41—2441no—
104#41—2441no—
105#41—2441no—
106#41—2441no—
107C2×Q8C2×#692311yescharacteristic
108C2×Q8C2×#692311yescharacteristic
109C2×D4—612no—
110C2×D4—611no—
111C2×D4—611no—
112C2×D4—1222no—
113C2×D4—1221no—
114C22×C4—612no—
115C22×C4—611no—
116C22×C4—1221no—
117C22×C4—1221no—
118C4⋊C4—22no—
119C4⋊C4—2442no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1224no—
123C42—611no—
124C42—1221no—
125C42—2442no—
126C42C2×#692311yescharacteristic
127C23—611no—
128C23—612no—
129C23—1221no—
130Q8—41no—
131Q8—41no—
132D4—2442no—
133D4—2441no—
134D4—2441no—
135D4—2444no—
136D4—2442no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—611no—
140C2×C4—1222no—
141C2×C4—1222no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—2442no—
146C2×C4—2441no—
147C2×C4—2441no—
148C2×C4—2444no—
149C2×C4C22⋊#692312yes—
150C2×C4C22×#692311yescharacteristic
151C22—1222no—
152C22—1221no—
153C22—2442no—
154C22—2441no—
155C22—2442no—
156C22—2441no—
157C22C2×C22⋊#692311yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—41no—
162C4—611no—
163C4—611no—
164C4—4884no—
165C4—2441no—
166C2—21no—
167C2—4881no—
168C2—2442no—
169C2—2441no—
170C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC2×C61C2×#99
hypercenterC4⋊Q8#6923
hypocenterC61#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #16840743C2semidirect
2. #16840668C2semidirect
3. #16840667C2semidirect
8. C2×#11758226C4semidirect
11. #14519766C4semidirect
15. C42×D61C4semidirect
16. C4⋊Q8×C61C4semidirect
90. C61#2126semidirect
93. C4⋊Q8#6923semidirect