Finite Group Databasebeta

← #21461430

Subgroups — #21461430

Order 7808.

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

normal subgroups only

This group has 152 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#16840812C211yesmaximal, characteristic
2Q8×#92420C211yesmaximal, characteristic
3#16840625C211yesmaximal, characteristic
4#16840612C211yesmaximal, characteristic
5Q8⋊#92420C211yesmaximal, characteristic
6#92420⋊C8C211yesmaximal, characteristic
7#16839854C211yesmaximal, characteristic
8C4⋊#92420—21no—
9C4⋊#92420—21no—
10C4⋊#92420C2211yescharacteristic
11C4⋊#92420C2211yescharacteristic
12#14519832—21no—
13C4×#92420—21no—
14C4×#92420C2211yescharacteristic
15C4×#92420C2211yescharacteristic
16C2×#11758202C411yescharacteristic
17Q8×Dic61C2211yescharacteristic
18#14519742C2211yescharacteristic
19#14519710C411yescharacteristic
20#14519702C411yescharacteristic
21C8×Dic61C2211yescharacteristic
22#103×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×Dic122C2×C411yescharacteristic
25C2×#92420—21no—
26C2×#92420—21no—
27C2×#92420—21no—
28C2×#92420D411yescharacteristic
29C2×#92420D411yescharacteristic
30C2×C8×C61C2×C411yescharacteristic
31C4⋊C4×C61C2×C411yescharacteristic
32#11758202—22no—
33C4⋊Dic61—21no—
34C4⋊Dic61C2×C411yescharacteristic
35#11758196—21no—
36C4×Dic61—21no—
37C4×Dic61—21no—
38C4×Dic61C2311yescharacteristic
39C2×#92418C2×C411yescharacteristic
40Q8×C61—21no—
41Q8×C61M1612yes—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61C22×C411yescharacteristic
45C2×Dic61—21no—
46C2×Dic61—21no—
47C2×Dic61C2×D411yescharacteristic
48C2×Dic61#4111yescharacteristic
49Dic122—21no—
50Dic122—21no—
51#92420—21no—
52#92420—41no—
53#92420—41no—
54#92420—41no—
55#92420Q1612yescomplemented
56C8×C61—21no—
57#92418—21no—
58C22×C61C4×D411yescharacteristic
59C4×C61—22no—
60C4×C61—41no—
61C4×C61C2×M1611yescharacteristic
62C4×C61#13111yescharacteristic
63Dic61—21no—
64Dic61—41no—
65Dic61—41no—
66Dic61C2×Q1611yescharacteristic
67Dic61#13511yescharacteristic
68#1584—611nomaximal, Sylow
69C2×C61#43511yescharacteristic
70C2×C61C4×Q1611yescharacteristic
71C2×C61#44411yescharacteristic
72#446—611no—
73C8×Q8—611no—
74C4×Q16—611no—
75#335—611no—
76Q8⋊C8—611no—
77Q8⋊C8—611no—
78#322—611no—
79C61#158411yescharacteristic, complemented, Sylow
80C2×Q16—611no—
81C4×Q8—611no—
82C4×Q8—611no—
83#107—611no—
84C4⋊C8—611no—
85C4⋊C8—611no—
86C4⋊C8—1221no—
87C4⋊C8—1221no—
88#103—611no—
89#103#692311yescharacteristic
90#97—1221no—
91C4×C8—611no—
92C4×C8—611no—
93C4×C8—611no—
94C4×C8—1221no—
95C2×Q8—611no—
96C2×Q8C2×#692311yescharacteristic
97Q16—1222no—
98C2×C8—611no—
99C2×C8—611no—
100C2×C8—611no—
101C2×C8—1221no—
102C2×C8—1221no—
103C2×C8—1221no—
104C2×C8C2×#692311yescharacteristic
105C4⋊C4—611no—
106C4⋊C4—1221no—
107C4⋊C4—1221no—
108C4⋊C4C2×#692311yescharacteristic
109C42—611no—
110C42—1221no—
111C42—1221no—
112Q8—21no—
113Q8—1221no—
114Q8—1221no—
115Q8#1175821312yes—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—611no—
119C2×C4—611no—
120C2×C4—1221no—
121C2×C4—1221no—
122C2×C4C22×#692311yescharacteristic
123C8—21no—
124C8—612no—
125C8—1221no—
126C8—1221no—
127C8—2441no—
128C8—2441no—
129C8—2441no—
130C22D4×#692311yescharacteristic
131C4—22no—
132C4—41no—
133C4—611no—
134C4—611no—
135C4—1221no—
136C4—2441no—
137C4—2441no—
138C4C2×#1175821311yescharacteristic
139C4#1451986411yescharacteristic
140C2#1684079111yescharacteristic
141C2Q16×#692311yescharacteristic
142C2#1684080711yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#103×C61C4
socleC22×C61C4×D4
hypercenter#103#6923
hypocenterC61#1584
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
55. #92420Q16semidirect
79. C61#1584semidirect