Finite Group Databasebeta

← #21444652

Subgroups — #21444652

Order 7808.

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

normal subgroups only

This group has 168 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#16839889C211yesmaximal, characteristic, complemented
2C4×#11758200C211yesmaximal, characteristic
3D4×#92418C211yesmaximal, characteristic
4#16839512C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839484C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic
8C2×#11758200C411yescharacteristic
9C22×#92418—21no—
10C4×Dic122C2211yescharacteristic
11#14519708C411yescharacteristic
12C4⋊#92418C2211yescharacteristic
13#14519706—21no—
14#14519700C411yescharacteristic
15#14519698C411yescharacteristic
16C22⋊#92418—21no—
17#14519687—21no—
18C4×#92418C2211yescharacteristic
19C4×#92418C2211yescharacteristic
20C4×D4×C61C2211yescharacteristic
21C4⋊C8×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×Dic122C2×C411yescharacteristic
26C2×C8×C61—21no—
27C2×C8×C61—21no—
28C4⋊C4×C61C2×C411yescharacteristic
29C22⋊C4×C61—21no—
30C42×C61C2311yescharacteristic
31#11758200—22no—
32C4⋊Dic61C2×C411yescharacteristic
33#11758196—21no—
34C4×Dic61—21no—
35C2×#92418—21no—
36C2×#92418—42no—
37C2×#92418C2×C411yescharacteristic
38C2×#92418C2×C411yescharacteristic
39C2×#92418D411yescharacteristic
40C2×#92418D411yescharacteristic
41C23×C61—21no—
42D4×C61—21no—
43D4×C61M1612yes—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C22×C411yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61#4111yescharacteristic
50C2×Dic61—21no—
51C2×Dic61—21no—
52Dic122—21no—
53Dic122—21no—
54C8×C61—41no—
55C8×C61—41no—
56#92418—21no—
57#92418—21no—
58#92418—21no—
59#92418—41no—
60#92418SD1612yescomplemented
61C22×C61—22no—
62C22×C61—41no—
63C22×C61—41no—
64C22×C61C4×D411yescharacteristic
65C4×C61—21no—
66C4×C61—41no—
67C4×C61C2×M1611yescharacteristic
68C4×C61#13111yescharacteristic
69C4×C61C2×SD1611yescharacteristic
70C4×C61#13511yescharacteristic
71Dic61—41no—
72Dic61—41no—
73#1582—611nomaximal, Sylow
74C2×C61—42no—
75C2×C61#43511yescharacteristic
76C2×C61C4×SD1611yescharacteristic
77C2×C61#44411yescharacteristic
78#446—611no—
79C4×SD16—611no—
80C8×D4—611no—
81#334—611no—
82Q8⋊C8—611no—
83D4⋊C8D6111yescharacteristic
84#322—611no—
85C61#158211yescharacteristic, complemented, Sylow
86C2×SD16—611no—
87C22×C8—1221no—
88C4×Q8—611no—
89C4×D4C2×D6111yescharacteristic
90#106—611no—
91C4⋊C8—611no—
92C4⋊C8—1221no—
93C4⋊C8C2×D6111yescharacteristic
94#103—611no—
95#102—611no—
96C22⋊C8—1221no—
97#97—1221no—
98C4×C8—611no—
99C4×C8—611no—
100C4×C8C2×D6111yescharacteristic
101C2×Q8—611no—
102C2×D4C4×D6111yescharacteristic
103C22×C4—21no—
104SD16—1222no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—611no—
108C2×C8—611no—
109C2×C8—611no—
110C2×C8—611no—
111C2×C8—1221no—
112C2×C8—2442no—
113C4⋊C4—611no—
114C4⋊C4—1221no—
115C4⋊C4C4×D6111yescharacteristic
116C22⋊C4—21no—
117C42—1221no—
118C42C22×D6111yescharacteristic
119C23—21no—
120Q8—1221no—
121Q8—1221no—
122D4—21no—
123D4#1175818912yes—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—1221no—
128C2×C4—1221no—
129C2×C4C2×C4×D6111yescharacteristic
130C2×C4D4×D6111yescharacteristic
131C2×C4#1175822411yescharacteristic
132C8—41no—
133C8—41no—
134C8—612no—
135C8—1221no—
136C8—1221no—
137C8—1221no—
138C8—2441no—
139C22—22no—
140C22—41no—
141C22—41no—
142C22#1451973711yescharacteristic
143C4—21no—
144C4—41no—
145C4—2441no—
146C4—2441no—
147C4C2×#1175818911yescharacteristic
148C4#1451978511yescharacteristic
149C4SD16×D6111yescharacteristic
150C4#1451979611yescharacteristic
151C2—42no—
152C2#1683983011yescharacteristic
153C2#1683985311yescharacteristic
154C2#1683988111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C4×D4
hypercenterD4⋊C8D61
hypocenterC61#1582
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #16839889C2semidirect
4. #16839512C2semidirect
5. #16839494C2semidirect
6. #16839484C2semidirect
60. #92418SD16semidirect
85. C61#1582semidirect