Finite Group Databasebeta

← #21448028

Subgroups — #21448028

Order 7808.

132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840003C211yesmaximal, characteristic
2#16839800C211yesmaximal, characteristic
3#16839590C211yesmaximal, characteristic, complemented
4#16839588C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839567C211yesmaximal, characteristic, complemented
7C61×C22⋊C16C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9#14519756—21no—
10#14519736—21no—
11#14519711C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519709—21no—
15#14519702—21no—
16C22×C8×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18C2×C16×C61C2211yescharacteristic
19C22×C4×C61D411yescharacteristic
20C2×Dic122—21no—
21C2×C8×C61—21no—
22C2×C8×C61—21no—
23C2×C8×C61D411yescharacteristic
24C2×C8×C61C2311yescharacteristic
25C22⋊Dic61—41no—
26C22⋊Dic61—41no—
27C4⋊Dic61—21no—
28C4⋊Dic61—21no—
29C4⋊Dic61—21no—
30#11758196—41no—
31C4×Dic61—41no—
32Dic244—21no—
33Dic244—21no—
34C16×C61—21no—
35C16×C61—21no—
36C23×C61D811yescharacteristic
37C2×C4×C61—21no—
38C2×C4×C61—21no—
39C2×C4×C61D811yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61—41no—
45Dic122—41no—
46Dic122—41no—
47C8×C61—21no—
48C8×C61#4111yescharacteristic
49C8×C61#4111yescharacteristic
50C22×C61—21no—
51C22×C61—21no—
52C22×C61—21no—
53C22×C61C2×D811yescharacteristic
54C4×C61—21no—
55C4×C61#12311yescharacteristic
56C4×C61#13711yescharacteristic
57Dic61—81no—
58Dic61—81no—
59Dic61—81no—
60Dic61—81no—
61#2237—611nomaximal, Sylow
62C2×C61—41no—
63C2×C61#48011yescharacteristic
64C2×C61#50811yescharacteristic
65C2×C61#51011yescharacteristic
66#467—611no—
67#427—611no—
68#367—611no—
69#366—611no—
70#358—611no—
71#358—611no—
72C22⋊C16D6111yescharacteristic
73C61#223711yescharacteristic, complemented, Sylow
74C2×Q16—611no—
75C22×C8C2×D6111yescharacteristic
76C22⋊Q8—1221no—
77#117—1221no—
78C2×C16C2×D6111yescharacteristic
79C2×C16C2×D6111yescharacteristic
80#107—611no—
81#107—611no—
82#107—611no—
83#106—1221no—
84#103—1221no—
85C2×Q8—1221no—
86C22×C4D24411yescharacteristic
87Q16—1221no—
88Q16—1221no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8D24411yescharacteristic
92C2×C8C22×D6111yescharacteristic
93C4⋊C4—1221no—
94C4⋊C4—1221no—
95C4⋊C4—1221no—
96C4⋊C4—2441no—
97C22⋊C4—2441no—
98C22⋊C4—2441no—
99C42—2441no—
100C16—21no—
101C16—21no—
102C23D48811yescharacteristic
103Q8—2441no—
104Q8—2441no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—2441no—
108C2×C4—2441no—
109C2×C4—2441no—
110C2×C4—2441no—
111C2×C4D48811yescharacteristic
112C2×C4C2×D24411yescharacteristic
113C8—21no—
114C8#1175822411yescharacteristic
115C8#1175822411yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×D48811yescharacteristic
120C4—21no—
121C4—4881no—
122C4—4881no—
123C4—4881no—
124C4—4881no—
125C4#1451976111yescharacteristic
126C4#1451981011yescharacteristic
127C2—41no—
128C2#1684007611yescharacteristic
129C2#1684019411yescharacteristic
130C2#1684020511yescharacteristic
subgroupG/H
centerC22C2×D488
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×C22⋊C16C2
socleC22×C61C2×D8
hypercenterC22⋊C16D61
hypocenterC61#2237
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. #16839590C2semidirect
4. #16839588C2semidirect
5. #16839567C2semidirect
6. #16839567C2semidirect
73. C61#2237semidirect