Finite Group Databasebeta

← #21462119

Subgroups — #21462119

Order 7808.

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

normal subgroups only

This group has 262 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#16840749C212yesmaximal, complemented
2#16840671C212yesmaximal, complemented
3#16840670C212yesmaximal, complemented
4#16840325C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519838C2214yescomplemented
7#14519837—22no—
8C2×#11758224C2211yescharacteristic
9C2×D4×D61C411yescharacteristic
10#14519773C411yescharacteristic
11#14519765C2211yescharacteristic
12#14519764C2211yescharacteristic
13#14519749—22no—
14#14519745—22no—
15#14519734C411yescharacteristic
16#127×C61C411yescharacteristic
17C23×D61—21no—
18C2×D4×C61—22no—
19C2×D4×C61C2×C411yescharacteristic
20C2×D4×C61C2×C411yescharacteristic
21C2×C22⋊D61—22no—
22C2×C22⋊D61—21no—
23C2×C22⋊D61D412yes—
24C22×Dic61D412yes—
25#11758224—42no—
26D4×D61—42no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61C2×C411yescharacteristic
29C2×Dic122C2311yescharacteristic
30#11758217—24no—
31#11758217—42no—
32C2×#92420—42no—
33C42×C61C2×C411yescharacteristic
34C22⋊Dic61—22no—
35#11758198—21no—
36#11758198—22no—
37#11758196—21no—
38C4×Dic61C2×C411yescharacteristic
39C23×C61—21no—
40C23×C61C22⋊C412yes—
41C22×D61—21no—
42C22×D61—42no—
43C22×D61—82no—
44C22×D61C22⋊C411yescharacteristic
45D4×C61—41no—
46D4×C61—41no—
47D4×C61—82no—
48C2×C4×C61—21no—
49C2×C4×C61C22×C411yescharacteristic
50C22⋊D61—42no—
51C22⋊D61—42no—
52C22⋊D61—82no—
53C2×Dic61—22no—
54C2×Dic61—22no—
55C2×Dic61—21no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C2×D412yes—
58D244—41no—
59C4×D61—22no—
60Dic122—41no—
61#92420—44no—
62C22×C61—22no—
63C22×C61—42no—
64C22×C61—42no—
65C22×C61—41no—
66C22×C61C2×C22⋊C411yescharacteristic
67C2×D61—21no—
68C2×D61—41no—
69C2×D61—42no—
70C2×D61—41no—
71C2×D61—84no—
72C4×C61—21no—
73C4×C61—41no—
74Dic61—22no—
75Dic61—41no—
76Dic61#9912yes—
77#2134—611nomaximal, Sylow
78C2×C61—21no—
79C2×C61—42no—
80C2×C61—81no—
81C2×C61C2×#9911yescharacteristic
82D61—41no—
83D61—81no—
84#535—611no—
85#413—612no—
86#355—612no—
87#355—612no—
88C61#213411yescharacteristic, complemented, Sylow
89C2×#41—611no—
90C22×D4—611no—
91C2×M16—1222no—
92#127—611no—
93#127#692311yescharacteristic
94#124—611no—
95#124—611no—
96#121—1222no—
97#120—1222no—
98#117—611no—
99#101—614no—
100#100—1222no—
101C24—1221no—
102#41—2442no—
103C2×Q8—611no—
104C2×D4—22no—
105C2×D4—612no—
106C2×D4—611no—
107C2×D4—1221no—
108C2×D4—1222no—
109C2×D4—2442no—
110C2×D4C2×#692311yescharacteristic
111C2×D4C2×#692311yescharacteristic
112C22×C4—612no—
113C22×C4—611no—
114M16—1224no—
115M16—2442no—
116C2×C8—2442no—
117C4⋊C4—1221no—
118C22⋊C4—1222no—
119C22⋊C4—1221no—
120C22⋊C4—1222no—
121C42—611no—
122C42C2×#692311yescharacteristic
123C23—21no—
124C23—611no—
125C23—1221no—
126C23—4882no—
127C23—2442no—
128C23C22⋊#692312yes—
129Q8—2441no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—4882no—
134D4—2441no—
135D4—2442no—
136D4—2442no—
137C2×C4—21no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—1222no—
141C2×C4—1222no—
142C2×C4—1222no—
143C2×C4—1221no—
144C2×C4C22×#692311yescharacteristic
145C8—2444no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—1221no—
151C22—4884no—
152C22—2442no—
153C22—2441no—
154C22—2441no—
155C22C2×C22⋊#692311yescharacteristic
156C4—21no—
157C4—41no—
158C4—612no—
159C4—1222no—
160C4—2441no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—4881no—
165C2—2441no—
166C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC2×C61C2×#99
hypercenter#127#6923
hypocenterC61#2134
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #16840749C2semidirect
2. #16840671C2semidirect
3. #16840670C2semidirect
6. #14519838C22semidirect
88. C61#2134semidirect