Finite Group Databasebeta

← #21447983

Subgroups — #21447983

Order 7808.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840164C211yesmaximal, characteristic
2#16839589C211yesmaximal, characteristic
3#16839587C211yesmaximal, characteristic
4C4⋊#11758185C211yesmaximal, characteristic
5#16839566C211yesmaximal, characteristic
6#16839566C211yesmaximal, characteristic
7C4×Q16×C61C211yesmaximal, characteristic
8#14519769—21no—
9C2×#11758185C2211yescharacteristic
10C2×#11758185C2211yescharacteristic
11#14519711C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519709—21no—
14C2×Q16×C61C2211yescharacteristic
15C4×Q8×C61—21no—
16#107×C61C2211yescharacteristic
17#103×C61—21no—
18C4×C8×C61C2211yescharacteristic
19C2×Q8×C61—21no—
20Q16×C61—21no—
21Q16×C61Q812yes—
22C2×C8×C61D411yescharacteristic
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25C4⋊C4×C61—41no—
26C42×C61—41no—
27C42×C61D411yescharacteristic
28C4⋊Dic61—21no—
29C4⋊Dic61—21no—
30#11758196—41no—
31#11758196—41no—
32#11758185—21no—
33#11758185—21no—
34Q8×C61—22no—
35Q8×C61—41no—
36C2×C4×C61—41no—
37C2×C4×C61—41no—
38C2×C4×C61D811yescharacteristic
39C2×C4×C61D811yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61—41no—
43C8×C61—21no—
44C8×C61C2×Q811yescharacteristic
45C8×C61#4111yescharacteristic
46C22×C61C2×D811yescharacteristic
47C4×C61—21no—
48C4×C61—21no—
49C4×C61—42no—
50C4×C61—81no—
51C4×C61C22⋊Q811yescharacteristic
52C4×C61#13711yescharacteristic
53Dic61—81no—
54Dic61—81no—
55#2229—611nomaximal, Sylow
56C2×C61#47411yescharacteristic
57C2×C61#50811yescharacteristic
58C2×C61#51011yescharacteristic
59#499—611no—
60C4×Q16D6111yescharacteristic
61#367—611no—
62#366—611no—
63C4⋊C16—611no—
64#358—611no—
65#358—611no—
66C61#222911yescharacteristic, complemented, Sylow
67C2×Q16C2×D6111yescharacteristic
68#125—1221no—
69C4×Q8—21no—
70C2×C16—611no—
71C2×C16—611no—
72#107—611no—
73#107—611no—
74#107C2×D6111yescharacteristic
75#106—1221no—
76#103—21no—
77C4×C8C2×D6111yescharacteristic
78C2×Q8—21no—
79Q16—21no—
80Q16Dic12212yes—
81C2×C8C22⋊D6111yescharacteristic
82C2×C8C22×D6111yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—41no—
85C4⋊C4—1221no—
86C4⋊C4—1221no—
87C4⋊C4—2441no—
88C4⋊C4—2441no—
89C42—41no—
90C42C22⋊D6111yescharacteristic
91C16—1221no—
92C16—1221no—
93Q8—22no—
94Q8—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2441no—
98C2×C4—2441no—
99C2×C4#1175819911yescharacteristic
100C2×C4#1175819911yescharacteristic
101C2×C4C2×C22⋊D6111yescharacteristic
102C8—21no—
103C8C2×Dic12211yescharacteristic
104C8#1175822211yescharacteristic
105C22C2×#1175819911yescharacteristic
106C4—21no—
107C4—21no—
108C4—42no—
109C4—81no—
110C4—4881no—
111C4—4881no—
112C4#1451975611yescharacteristic
113C4#1451980711yescharacteristic
114C2#1684004211yescharacteristic
115C2#1684019211yescharacteristic
116C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC4×Q16×C61C2
socleC22×C61C2×D8
hypercenterC4×Q16D61
hypocenterC61#2229
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
66. C61#2229semidirect