Finite Group Databasebeta

← #21448024

Subgroups — #21448024

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#16839800C211yesmaximal, characteristic
2#16839589C211yesmaximal, characteristic, complemented
3#16839587C211yesmaximal, characteristic, complemented
4#16839566C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6C22⋊#11758185C211yesmaximal, characteristic
7C61×#467C211yesmaximal, characteristic
8#14519736—21no—
9C2×#11758185C2211yescharacteristic
10C2×#11758185C2211yescharacteristic
11#14519711C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519709—21no—
14C2×Q16×C61C2211yescharacteristic
15C22×C8×C61C2211yescharacteristic
16C22⋊Q8×C61—21no—
17#107×C61C2211yescharacteristic
18#103×C61—21no—
19C2×Q8×C61—21no—
20C22×C4×C61D411yescharacteristic
21Q16×C61—21no—
22Q16×C61—21no—
23C2×C8×C61—21no—
24C2×C8×C61—21no—
25C2×C8×C61D411yescharacteristic
26C2×C8×C61C2311yescharacteristic
27C4⋊C4×C61—21no—
28C4⋊C4×C61—41no—
29C22⋊C4×C61—41no—
30C22⋊Dic61—41no—
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4×Dic61—41no—
34#11758185—21no—
35#11758185—21no—
36C23×C61D811yescharacteristic
37Q8×C61—41no—
38Q8×C61—41no—
39C2×C4×C61—21no—
40C2×C4×C61—21no—
41C2×C4×C61—41no—
42C2×C4×C61—41no—
43C2×C4×C61D811yescharacteristic
44C2×C4×C61C2×D411yescharacteristic
45C2×Dic61—41no—
46C2×Dic61—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—81no—
56C4×C61—81no—
57C4×C61#12311yescharacteristic
58C4×C61#13711yescharacteristic
59Dic61—81no—
60Dic61—81no—
61#2237—611nomaximal, Sylow
62C2×C61—41no—
63C2×C61#48011yescharacteristic
64C2×C61#50811yescharacteristic
65C2×C61#51011yescharacteristic
66#467D6111yescharacteristic
67#427—611no—
68#367—611no—
69#366—611no—
70#358—611no—
71#358—611no—
72C22⋊C16—611no—
73C61#223711yescharacteristic, complemented, Sylow
74C2×Q16C2×D6111yescharacteristic
75C22×C8C2×D6111yescharacteristic
76C22⋊Q8—21no—
77#117—1221no—
78C2×C16—611no—
79C2×C16—611no—
80#107—611no—
81#107—611no—
82#107C2×D6111yescharacteristic
83#106—1221no—
84#103—21no—
85C2×Q8—21no—
86C22×C4C22⋊D6111yescharacteristic
87Q16—21no—
88Q16—21no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C22⋊D6111yescharacteristic
92C2×C8C22×D6111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—1221no—
96C4⋊C4—1221no—
97C22⋊C4—41no—
98C22⋊C4—2441no—
99C42—2441no—
100C16—1221no—
101C16—1221no—
102C23#1175819911yescharacteristic
103Q8—41no—
104Q8—41no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—2441no—
110C2×C4—2441no—
111C2×C4#1175819911yescharacteristic
112C2×C4C2×C22⋊D6111yescharacteristic
113C8—21no—
114C8#1175822411yescharacteristic
115C8#1175822411yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×#1175819911yescharacteristic
120C4—21no—
121C4—81no—
122C4—81no—
123C4—4881no—
124C4—4881no—
125C4#1451975811yescharacteristic
126C4#1451980711yescharacteristic
127C2—41no—
128C2#1684007311yescharacteristic
129C2#1684019211yescharacteristic
130C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#467C2
socleC22×C61C2×D8
hypercenter#467D61
hypocenterC61#2237
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #16839589C2semidirect
3. #16839587C2semidirect
4. #16839566C2semidirect
5. #16839566C2semidirect
73. C61#2237semidirect