Finite Group Databasebeta

← #21444596

Subgroups — #21444596

Order 7808.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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#16839818C211yesmaximal, characteristic
2#16839814C211yesmaximal, characteristic
3#16839813C211yesmaximal, characteristic
4#16839514C211yesmaximal, characteristic, complemented
5#16839514C211yesmaximal, characteristic, complemented
6#16839513C211yesmaximal, characteristic, complemented
7C61×#334C211yesmaximal, characteristic, complemented
8C42×D61C2211yescharacteristic
9C4⋊#92418C2211yescharacteristic
10C4⋊#92418C2211yescharacteristic
11#14519706C411yescharacteristic
12#14519706C411yescharacteristic
13#14519689—21no—
14#14519689—21no—
15#14519689C411yescharacteristic
16#14519689C411yescharacteristic
17#14519687—21no—
18C4×#92418C2211yescharacteristic
19C8×Dic61—21no—
20C4⋊C8×C61C2211yescharacteristic
21C4⋊C8×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61D411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C2×C8×C61—21no—
27C2×C8×C61—21no—
28C2×C8×C61C2×C411yescharacteristic
29C2×C8×C61C2×C411yescharacteristic
30C42×C61C2311yescharacteristic
31C4×Dic61C2×C411yescharacteristic
32C4×Dic61D411yescharacteristic
33C4×Dic61Q811yescharacteristic
34C2×#92418—21no—
35C2×#92418—21no—
36C2×#92418C2×C411yescharacteristic
37C2×#92418C2×C411yescharacteristic
38C22×D61C4⋊C411yescharacteristic
39C2×C4×C61C22×C411yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×C4×C61C2×Q811yescharacteristic
42C2×Dic61C4⋊C411yescharacteristic
43C2×Dic61C4⋊C411yescharacteristic
44C2×Dic61C4⋊C411yescharacteristic
45C4×D61—21no—
46C4×D61—21no—
47C4×D61—21no—
48C4×D61—21no—
49C4×D61—41no—
50C8×C61—21no—
51C8×C61—21no—
52C8×C61—41no—
53C8×C61—41no—
54#92418—21no—
55#92418—21no—
56#92418—41no—
57#92418—41no—
58C22×C61C2×C4⋊C411yescharacteristic
59C2×D61—21no—
60C2×D61—21no—
61C2×D61—21no—
62C4×C61—21no—
63C4×C61#13111yescharacteristic
64C4×C61#13111yescharacteristic
65C4×C61#13511yescharacteristic
66C4×C61#13511yescharacteristic
67Dic61—21no—
68Dic61—21no—
69Dic61—21no—
70#1572—611nomaximal, Sylow
71C2×C61#42411yescharacteristic
72C2×C61#42711yescharacteristic
73C2×C61#43011yescharacteristic
74D61—41no—
75#432—611no—
76#431—611no—
77#431—611no—
78#335—611no—
79#335—611no—
80#334—611no—
81#334D6111yescharacteristic, complemented
82C61#157211yescharacteristic, complemented, Sylow
83C2×C42—611no—
84C4⋊C8—611no—
85C4⋊C8—611no—
86C4⋊C8—611no—
87C4⋊C8—611no—
88C4⋊C8C2×D6111yescharacteristic
89C4⋊C8C2×D6111yescharacteristic
90C22⋊C8—611no—
91C22⋊C8—611no—
92C22⋊C8—1221no—
93C22⋊C8—1221no—
94#97—1221no—
95C4×C8—611no—
96C4×C8—1221no—
97C4×C8C2×D6111yescharacteristic
98C22×C4—611no—
99C22×C4—611no—
100C22×C4—611no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—611no—
104C2×C8—611no—
105C2×C8—1221no—
106C2×C8—1221no—
107C2×C8C4×D6111yescharacteristic
108C2×C8C4×D6111yescharacteristic
109C42—611no—
110C42—611no—
111C42—611no—
112C42C22×D6111yescharacteristic
113C23—611no—
114C2×C4—611no—
115C2×C4—611no—
116C2×C4—611no—
117C2×C4—1221no—
118C2×C4—1221no—
119C2×C4—1221no—
120C2×C4—1221no—
121C2×C4—2441no—
122C2×C4C2×C4×D6111yescharacteristic
123C2×C4D4×D6111yescharacteristic
124C2×C4Q8×D6111yescharacteristic
125C8—21no—
126C8—21no—
127C8—41no—
128C8—41no—
129C8—1221no—
130C8—1221no—
131C8—2441no—
132C8—2441no—
133C22—1221no—
134C22—1221no—
135C22—1221no—
136C22C4⋊C4×D6111yescharacteristic
137C4—21no—
138C4—1221no—
139C4—1221no—
140C4—1221no—
141C4#1451978311yescharacteristic
142C4#1451978511yescharacteristic
143C4#1451979811yescharacteristic
144C4#1451979811yescharacteristic
145C2—2441no—
146C2#1683978711yescharacteristic
147C2#1683979711yescharacteristic
148C2#1683980911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#334C2
socleC22×C61C2×C4⋊C4
hypercenter#334D61
hypocenterC61#1572
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
4. #16839514C2semidirect
5. #16839514C2semidirect
6. #16839513C2semidirect
7. C61×#334C2semidirect
81. #334D61semidirect
82. C61#1572semidirect