Finite Group Databasebeta

← #21461282

Subgroups — #21461282

Order 7808.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840785C211yesmaximal, characteristic
2C4×#11758213C211yesmaximal, characteristic
3#16840619C212yesmaximal, complemented
4#16840619C212yesmaximal, complemented
5#125×D61C211yesmaximal, characteristic
6C2×#11758213—21no—
7#14519844—21no—
8#14519834—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11C4×#92420—21no—
12#14519769C411yescharacteristic
13#14519768C2211yescharacteristic
14#14519768C2211yescharacteristic
15#14519767—21no—
16#14519767—21no—
17C4⋊C4×D61—21no—
18C4⋊C4×D61—21no—
19C4⋊C4×D61C411yescharacteristic
20C4⋊C4×D61C411yescharacteristic
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic
23C2×C4×D61—21no—
24C2×C4×D61—21no—
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61D411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×#92420—22no—
29C2×#92420—22no—
30#11758213—24no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C411yescharacteristic
34C4⋊C4×C61C2×C411yescharacteristic
35C42×C61C2×C411yescharacteristic
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61C2×C411yescharacteristic
39C4⋊Dic61C2×C411yescharacteristic
40#11758196—21no—
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C22×D61C22⋊C411yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22×C411yescharacteristic
55C2×Dic61—21no—
56C2×Dic61—21no—
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C2×Dic61C2×D411yescharacteristic
60C4×D61—22no—
61C4×D61—22no—
62C4×D61—41no—
63C4×D61—42no—
64C4×D61—42no—
65#92420—24no—
66#92420—42no—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—21no—
69C2×D61—21no—
70C2×D61#10412yes—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—41no—
75C4×C61—41no—
76Dic61—21no—
77Dic61—21no—
78Dic61—41no—
79Dic61—41no—
80Dic61#10112yes—
81#1528—611nomaximal, Sylow
82C2×C61C2×#10111yescharacteristic
83C2×C61C2×#10411yescharacteristic
84C2×C61#42111yescharacteristic
85D61—22no—
86C2×#125—611no—
87#432—611no—
88C4×M16—611no—
89#330—612no—
90#330—612no—
91C61#152811yescharacteristic, complemented, Sylow
92C2×M16—1221no—
93#125—611no—
94#125—611no—
95#125—611no—
96#125—1221no—
97#125—1221no—
98#125#692311yescharacteristic
99C2×C4⋊C4—611no—
100C2×C4⋊C4—611no—
101C2×C4⋊C4—1221no—
102C2×C4⋊C4—1221no—
103C2×C42—611no—
104C4⋊C8—1221no—
105C22⋊C8—1221no—
106#97—612no—
107#97—612no—
108C4×C8—1221no—
109C22×C4—611no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4—1221no—
113C22×C4—1221no—
114M16—1224no—
115C2×C8—1222no—
116C2×C8—1222no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—611no—
120C4⋊C4—611no—
121C4⋊C4—1221no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4C2×#692311yescharacteristic
130C4⋊C4C2×#692311yescharacteristic
131C42—611no—
132C42—611no—
133C42—611no—
134C42C2×#692311yescharacteristic
135C23—611no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—1222no—
142C2×C4—1222no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—2441no—
146C2×C4—2442no—
147C2×C4—2442no—
148C2×C4C22⋊#692311yescharacteristic
149C2×C4C22⋊#692311yescharacteristic
150C2×C4C22×#692311yescharacteristic
151C8—1224no—
152C8—2442no—
153C22—612no—
154C22—1221no—
155C22—1221no—
156C22C2×C22⋊#692311yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—612no—
163C4—1221no—
164C4—1221no—
165C4—2441no—
166C4—2441no—
167C2—1222no—
168C2D61⋊#10111yescharacteristic
169C2D61⋊#10411yescharacteristic
170C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1528
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #16840619C2semidirect
4. #16840619C2semidirect
91. C61#1528semidirect