Finite Group Databasebeta

← #21461390

Subgroups — #21461390

Order 7808.

150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 60 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#16840783C211yesmaximal, characteristic
2#16840778C211yesmaximal, characteristic
3#16840626C211yesmaximal, characteristic, complemented
4#16840625C211yesmaximal, characteristic, complemented
5#16840624C211yesmaximal, characteristic, complemented
6#16840623C211yesmaximal, characteristic, complemented
7#16839812C211yesmaximal, characteristic
8C4⋊#92420C2211yescharacteristic
9C4⋊#92420C2211yescharacteristic
10C4⋊#92420C2211yescharacteristic
11C4⋊#92420C2211yescharacteristic
12C22⋊#92420—21no—
13C22⋊#92420—21no—
14#14519832—21no—
15C4×#92420—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519706C411yescharacteristic
18#14519706C411yescharacteristic
19C22⋊#92418C411yescharacteristic
20C8×Dic61C2211yescharacteristic
21C8×Dic61C2211yescharacteristic
22C22⋊C8×C61C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61D411yescharacteristic
25C22×Dic61Q811yescharacteristic
26C2×#92420—21no—
27C2×#92420—21no—
28C2×#92420—21no—
29C2×#92420—21no—
30C2×C8×C61C2×C411yescharacteristic
31C2×C8×C61C2×C411yescharacteristic
32C4×Dic61C2×C411yescharacteristic
33C4×Dic61D411yescharacteristic
34C4×Dic61Q811yescharacteristic
35C4×Dic61C2311yescharacteristic
36C2×#92418C2×C411yescharacteristic
37C2×#92418C2×C411yescharacteristic
38C23×C61C4⋊C411yescharacteristic
39C2×C4×C61—21no—
40C2×C4×C61—21no—
41C2×C4×C61C4⋊C411yescharacteristic
42C2×C4×C61C22×C411yescharacteristic
43C2×Dic61—21no—
44C2×Dic61—21no—
45C2×Dic61—41no—
46C2×Dic61C4⋊C411yescharacteristic
47C2×Dic61C4⋊C411yescharacteristic
48C2×Dic61C2×D411yescharacteristic
49C2×Dic61C2×Q811yescharacteristic
50#92420—41no—
51#92420—41no—
52#92420—41no—
53#92420—41no—
54C8×C61—21no—
55C8×C61—21no—
56#92418—21no—
57#92418—21no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61C2×C4⋊C411yescharacteristic
62C4×C61—21no—
63C4×C61#13111yescharacteristic
64C4×C61#13111yescharacteristic
65Dic61—21no—
66Dic61—21no—
67Dic61—21no—
68Dic61#13511yescharacteristic
69Dic61#13511yescharacteristic
70#1572—611nomaximal, Sylow
71C2×C61—41no—
72C2×C61#42411yescharacteristic
73C2×C61#42711yescharacteristic
74C2×C61#43011yescharacteristic
75#432—611no—
76#431—611no—
77#431—611no—
78#335—611no—
79#335—611no—
80#334—611no—
81#334—611no—
82C61#157211yescharacteristic, complemented, Sylow
83C2×C42—611no—
84C4⋊C8—611no—
85C4⋊C8—611no—
86C4⋊C8—611no—
87C4⋊C8—611no—
88C4⋊C8—611no—
89C4⋊C8—611no—
90C22⋊C8—611no—
91C22⋊C8—1221no—
92C22⋊C8—1221no—
93C22⋊C8#692311yescharacteristic
94#97—1221no—
95C4×C8—611no—
96C4×C8—611no—
97C4×C8—1221no—
98C22×C4—611no—
99C22×C4—611no—
100C22×C4C2×#692311yescharacteristic
101C2×C8—611no—
102C2×C8—611no—
103C2×C8—1221no—
104C2×C8—1221no—
105C2×C8—1221no—
106C2×C8—1221no—
107C2×C8C2×#692311yescharacteristic
108C2×C8C2×#692311yescharacteristic
109C42—611no—
110C42—611no—
111C42—611no—
112C42—611no—
113C23C4⋊#692311yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—611no—
117C2×C4—611no—
118C2×C4—611no—
119C2×C4—611no—
120C2×C4—1221no—
121C2×C4—1221no—
122C2×C4—2441no—
123C2×C4C4⋊#692311yescharacteristic
124C2×C4C22×#692311yescharacteristic
125C8—21no—
126C8—21no—
127C8—1221no—
128C8—1221no—
129C8—2441no—
130C8—2441no—
131C8—2441no—
132C8—2441no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22C2×C4⋊#692311yescharacteristic
137C4—21no—
138C4—611no—
139C4—611no—
140C4—1221no—
141C4—1221no—
142C4—1221no—
143C4#1451986411yescharacteristic
144C4#1451986411yescharacteristic
145C2—41no—
146C2#1684076811yescharacteristic
147C2#1684077211yescharacteristic
148C2#1684077711yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22⋊C8#6923
hypocenterC61#1572
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #16840626C2semidirect
4. #16840625C2semidirect
5. #16840624C2semidirect
6. #16840623C2semidirect
82. C61#1572semidirect