Finite Group Databasebeta

← #21462219

Subgroups — #21462219

Order 7808.

146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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#16840806C211yesmaximal, characteristic, complemented
2#16840804C211yesmaximal, characteristic, complemented
3#16840691C211yesmaximal, characteristic, complemented
4#16840677C211yesmaximal, characteristic, complemented
5#16840676C211yesmaximal, characteristic, complemented
6C16×#6923C211yesmaximal, characteristic, complemented
7#16840193C211yesmaximal, characteristic
8#14519865—21no—
9#14519864—21no—
10D61⋊C16C2211yescharacteristic
11#14519848C2211yescharacteristic
12#14519848C2211yescharacteristic
13#14519842—21no—
14#14519841—21no—
15C8×#6923C2211yescharacteristic
16#14519800C2211yescharacteristic
17#14519796C2211yescharacteristic
18#14519723C411yescharacteristic, complemented
19#14519722C411yescharacteristic, complemented
20#14519718C411yescharacteristic, complemented
21C16×D61C2211yescharacteristic
22SD32×C61C411yescharacteristic, complemented
23#11758226—21no—
24#11758224—21no—
25#11758217—41no—
26C2×#92420—41no—
27C4×#6923D411yescharacteristic
28#11758213—21no—
29#11758213—21no—
30#11758213—41no—
31D61⋊C8—41no—
32D61⋊C8D411yescharacteristic
33Q16×C61C2×C411yescharacteristic
34D8×C61C2×C411yescharacteristic
35#11758201—21no—
36#11758200—21no—
37Dic244C2×C411yescharacteristic
38D488C2×C411yescharacteristic
39C8×D61C2311yescharacteristic
40#11758187—21no—
41C16×C61C2×C411yescharacteristic
42#11758185C2×C411yescharacteristic
43C2×#6923—21no—
44Q8×C61—21no—
45D4×C61—21no—
46C22⋊D61—41no—
47C2×Dic61—41no—
48D244—21no—
49D244—41no—
50C4×D61—41no—
51C4×D61C2×D411yescharacteristic
52Dic122—21no—
53#92420—41no—
54#92420—41no—
55#92420D811yescharacteristic
56#92420D811yescharacteristic
57C8×C61C22×C411yescharacteristic
58#92418#4111yescharacteristic
59C22×C61—41no—
60C2×D61—41no—
61C2×D61#13511yescharacteristic
62#6923—22no—
63C4×C61—41no—
64C4×C61C4×D411yescharacteristic
65Dic61—41no—
66Dic61C2×D811yescharacteristic
67#2178—611nomaximal, Sylow
68C2×C61—81no—
69C2×C61C4×D811yescharacteristic
70D61—21no—
71D61—81no—
72#508—611no—
73#443—611no—
74#443—611no—
75#368—611no—
76#359—611no—
77#359—611no—
78C4×C16—611no—
79C61#217811yescharacteristic, complemented, Sylow
80#135—611no—
81#135—611no—
82#131—1221no—
83#131—1221no—
84Q32—611no—
85SD32—611no—
86SD32#692311yescharacteristic, complemented
87D16—611no—
88C2×C16—611no—
89C2×C16—611no—
90#108—611no—
91#108—611no—
92#104—1221no—
93#104—1221no—
94C4×C8—611no—
95#41—1221no—
96#41—1221no—
97Q16—611no—
98Q16C2×#692311yescharacteristic
99SD16—1221no—
100SD16—1221no—
101D8—611no—
102D8C2×#692311yescharacteristic
103M16—1221no—
104M16—1221no—
105M16—2441no—
106M16—2441no—
107C2×C8—611no—
108C2×C8—611no—
109C2×C8—2441no—
110C2×C8—2441no—
111C42—611no—
112C16—611no—
113C16—1221no—
114C16C2×#692311yescharacteristic
115Q8—21no—
116Q8—1221no—
117D4—21no—
118D4—1221no—
119D4—2441no—
120D4—2441no—
121C2×C4—611no—
122C2×C4—1221no—
123C2×C4—2441no—
124C2×C4—2441no—
125C8—611no—
126C8—611no—
127C8—611no—
128C8—2441no—
129C8—2441no—
130C8C22×#692311yescharacteristic
131C22—41no—
132C22—611no—
133C22—2441no—
134C4—41no—
135C4—611no—
136C4—1222no—
137C4—2441no—
138C4D4×#692311yescharacteristic
139C2—81no—
140C2—1221no—
141C2—4881no—
142C2D8×#692311yescharacteristic
subgroupG/H
centerC2D8×#6923
commutatorC8×C61C22×C4
FrattiniC8C22×#6923
FittingSD32×C61C4
socleC2×C61C4×D8
hypercenterSD32#6923
hypocenterC61#2178
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #16840806C2semidirect
2. #16840804C2semidirect
3. #16840691C2semidirect
4. #16840677C2semidirect
5. #16840676C2semidirect
6. C16×#6923C2semidirect
18. #14519723C4semidirect
19. #14519722C4semidirect
20. #14519718C4semidirect
22. SD32×C61C4semidirect
79. C61#2178semidirect
86. SD32#6923semidirect