Finite Group Databasebeta

← #21447879

Subgroups — #21447879

Order 7808.

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

normal subgroups only

This group has 158 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
1C2×#14519723C211yesmaximal, characteristic, complemented
2#16840145C211yesmaximal, characteristic
3Q16×Dic61C211yesmaximal, characteristic, complemented
4#16839580C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839563C211yesmaximal, characteristic
7C2×SD32×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758200—21no—
10#14519764—21no—
11Q8×Dic61—21no—
12#14519723—22no—
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519701—21no—
16C8×Dic61C2211yescharacteristic
17C2×Q16×C61C2211yescharacteristic
18C2×D8×C61C2211yescharacteristic
19SD32×C61—22no—
20C2×C16×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×D4×C61—21no—
23C2×Dic122—21no—
24Q16×C61—21no—
25Q16×C61D412yes—
26D8×C61—21no—
27D8×C61—21no—
28C2×C8×C61C2311yescharacteristic
29C22⋊Dic61—41no—
30C22⋊Dic61—41no—
31#11758200—42no—
32C4⋊Dic61—21no—
33C4⋊Dic61—41no—
34C4×Dic61—41no—
35C4×Dic61D411yescharacteristic
36C2×#92418D411yescharacteristic
37Dic244—21no—
38Dic244—21no—
39C16×C61—21no—
40#11758185—21no—
41C23×C61—41no—
42Q8×C61—22no—
43Q8×C61—41no—
44D4×C61—41no—
45D4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C2×D411yescharacteristic
48C2×Dic61—41no—
49C2×Dic61—41no—
50C2×Dic61D811yescharacteristic
51C2×Dic61D811yescharacteristic
52Dic122—41no—
53Dic122—41no—
54C8×C61C2×D411yescharacteristic
55C8×C61#4111yescharacteristic
56#92418—21no—
57C22×C61—81no—
58C22×C61—81no—
59C22×C61—81no—
60C22×C61C2×D811yescharacteristic
61C4×C61—42no—
62C4×C61#12111yescharacteristic
63C4×C61AGL(1,ℤ/8)11yescharacteristic
64Dic61—21no—
65Dic61—21no—
66Dic61—81no—
67Dic61—81no—
68#2211—611nomaximal, Sylow
69C2×C61—161no—
70C2×C61#45911yescharacteristic
71C2×C61#50811yescharacteristic
72C2×C61#51011yescharacteristic
73C2×Q32—611no—
74C2×SD32D6111yescharacteristic
75#495—611no—
76C4×Q16—611no—
77C4⋊C16—611no—
78#358—611no—
79#357—611no—
80C61#221111yescharacteristic, complemented, Sylow
81C2×Q16—611no—
82C2×Q16C2×D6111yescharacteristic
83C2×SD16—1221no—
84C2×D8C2×D6111yescharacteristic
85#124—1221no—
86C4×Q8—1221no—
87Q32—1222no—
88SD32—22no—
89C2×C16—611no—
90C2×C16C2×D6111yescharacteristic
91#107—611no—
92#103—1221no—
93C4×C8—611no—
94C2×Q8—21no—
95C2×Q8—1221no—
96C2×D4—21no—
97Q16—21no—
98Q16—1221no—
99Q16—1221no—
100Q16C22⋊D6112yes—
101SD16—2442no—
102D8—21no—
103D8—21no—
104C2×C8—611no—
105C2×C8C22×D6111yescharacteristic
106C4⋊C4—1221no—
107C4⋊C4—2441no—
108C22⋊C4—2441no—
109C22⋊C4—2441no—
110C42—611no—
111C42—2441no—
112C16—21no—
113C16—1221no—
114C23—41no—
115Q8—22no—
116Q8—41no—
117Q8—2441no—
118Q8—2441no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—611no—
123C2×C4—611no—
124C2×C4—2441no—
125C2×C4—2441no—
126C2×C4D4×D6111yescharacteristic
127C8—1221no—
128C8#1175822411yescharacteristic
129C8C2×C22⋊D6111yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22D8×D6111yescharacteristic
134C4—42no—
135C4—1221no—
136C4—1221no—
137C4—4881no—
138C4—4881no—
139C4#1451974911yescharacteristic
140C4#1451980111yescharacteristic
141C2—161no—
142C2#1683995511yescharacteristic
143C2#1684019311yescharacteristic
144C2#1684020111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×SD32×C61C2
socleC22×C61C2×D8
hypercenterC2×SD32D61
hypocenterC61#2211
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
3. Q16×Dic61C2semidirect
4. #16839580C2semidirect
5. #16839567C2semidirect
80. C61#2211semidirect