Finite Group Databasebeta

← #21448045

Subgroups — #21448045

Order 7808.

140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840166C211yesmaximal, characteristic
2#16840140C211yesmaximal, characteristic
3#16839567C211yesmaximal, characteristic
4#16839566C211yesmaximal, characteristic
5#16839565C211yesmaximal, characteristic
6C16×Dic61C211yesmaximal, characteristic
7C61×#358C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758202—21no—
10#14519776—21no—
11#14519775—21no—
12C2×#11758185C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519710—21no—
15C8×Dic61C2211yescharacteristic
16C2×Q16×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×Q8×C61—21no—
20C2×Dic122—21no—
21C2×Dic122—41no—
22Q16×C61—21no—
23Q16×C61—21no—
24C2×C8×C61C2311yescharacteristic
25C4⋊C4×C61—21no—
26#11758202—42no—
27C4⋊Dic61—21no—
28#11758196—41no—
29#11758196—41no—
30#11758196—41no—
31C4×Dic61D411yescharacteristic
32C2×#92418D411yescharacteristic
33Dic244—21no—
34Dic244—21no—
35C16×C61—21no—
36#11758185—21no—
37Q8×C61—41no—
38Q8×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61D811yescharacteristic
45C2×Dic61D811yescharacteristic
46Dic122—41no—
47Dic122—41no—
48Dic122—82no—
49C8×C61#4111yescharacteristic
50C8×C61#4111yescharacteristic
51#92418SD1612yes—
52C22×C61C2×D811yescharacteristic
53C4×C61—81no—
54C4×C61—81no—
55C4×C61#12411yescharacteristic
56C4×C61C2×SD1611yescharacteristic
57Dic61—81no—
58Dic61—81no—
59Dic61SD3212yes—
60Dic61Q3212yes—
61#2241—611nomaximal, Sylow
62C2×C61#48611yescharacteristic
63C2×C61C2×SD3211yescharacteristic
64C2×C61C2×Q3211yescharacteristic
65#500—611no—
66#494—611no—
67#358—611no—
68#358—611no—
69#358—611no—
70#358D6111yescharacteristic
71C4×C16—611no—
72C61#224111yescharacteristic, complemented, Sylow
73C2×Q16—611no—
74C2×Q16—1221no—
75C2×Q16C2×D6111yescharacteristic
76C4⋊Q8—1221no—
77C4⋊Q8—1221no—
78C2×C16—611no—
79C2×C16C2×D6111yescharacteristic
80#107—611no—
81#107—1221no—
82#107C2×D6111yescharacteristic
83C4×C8—611no—
84C2×Q8—21no—
85C2×Q8—1221no—
86C2×Q8—2441no—
87Q16—21no—
88Q16—21no—
89Q16—1221no—
90Q16—1221no—
91Q16—2442no—
92C2×C8—611no—
93C2×C8C22×D6111yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—1221no—
96C4⋊C4—2441no—
97C4⋊C4—2441no—
98C4⋊C4—2441no—
99C42—611no—
100C16—21no—
101C16—1221no—
102Q8—41no—
103Q8—41no—
104Q8—4882no—
105Q8—2441no—
106Q8—2441no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—611no—
110C2×C4—611no—
111C2×C4—2441no—
112C2×C4—2441no—
113C2×C4D4×D6111yescharacteristic
114C8—612no—
115C8#1175822211yescharacteristic
116C8#1175822411yescharacteristic
117C22D8×D6111yescharacteristic
118C4—81no—
119C4—81no—
120C4—612no—
121C4—612no—
122C4—4881no—
123C4—4881no—
124C4#1451976311yescharacteristic
125C4SD16×D6111yescharacteristic
126C2#1684010711yescharacteristic
127C2SD32×D6111yescharacteristic
128C2Q32×D6111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2241
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
72. C61#2241semidirect