Finite Group Databasebeta

← #21447884

Subgroups — #21447884

Order 7808.

158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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
2C2×#14519722C211yesmaximal, characteristic
3#16840147C211yesmaximal, characteristic
4#16839856C211yesmaximal, characteristic, complemented
5#16839580C211yesmaximal, characteristic, complemented
6#16839562C211yesmaximal, characteristic
7C61×#358C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×#11758201—21no—
10C2×D488C2211yescharacteristic
11#14519766—21no—
12#14519742—21no—
13#14519723—22no—
14#14519722—22no—
15C2×#11758185C2211yescharacteristic
16#14519700—21no—
17C8×Dic61C2211yescharacteristic
18C2×Q16×C61C2211yescharacteristic
19C2×C16×C61C2211yescharacteristic
20#107×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×D244—21no—
23C2×Dic122—21no—
24Q16×C61—21no—
25Q16×C61—21no—
26C2×C8×C61C2311yescharacteristic
27C4⋊C4×C61—21no—
28#11758201—42no—
29#11758198—41no—
30#11758198—41no—
31#11758196—41no—
32C4×Dic61—41no—
33C4×Dic61D411yescharacteristic
34C2×#92418D411yescharacteristic
35Dic244—21no—
36Dic244D412yes—
37D488—21no—
38D488—21no—
39C16×C61—21no—
40#11758185—21no—
41C22×D61—41no—
42Q8×C61—41no—
43Q8×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C2×D411yescharacteristic
47C2×Dic61—41no—
48C2×Dic61D811yescharacteristic
49C2×Dic61D811yescharacteristic
50D244—41no—
51D244—41no—
52Dic122—22no—
53Dic122—41no—
54C8×C61C2×D411yescharacteristic
55C8×C61#4111yescharacteristic
56#92418—21no—
57C22×C61C2×D811yescharacteristic
58C2×D61—81no—
59C2×D61—81no—
60C2×D61—81no—
61C4×C61—81no—
62C4×C61—81no—
63C4×C61#12111yescharacteristic
64C4×C61AGL(1,ℤ/8)11yescharacteristic
65Dic61—21no—
66Dic61—21no—
67Dic61—42no—
68#2211—611nomaximal, Sylow
69C2×C61#45911yescharacteristic
70C2×C61#50811yescharacteristic
71C2×C61#51011yescharacteristic
72D61—161no—
73C2×Q32—611no—
74C2×SD32—611no—
75#495—611no—
76C4×Q16—611no—
77C4⋊C16—611no—
78#358D6111yescharacteristic, complemented
79#357—611no—
80C61#221111yescharacteristic, complemented, Sylow
81C2×Q16—611no—
82C2×Q16C2×D6111yescharacteristic
83C2×SD16—1221no—
84C2×D8—611no—
85#124—1221no—
86C4×Q8—1221no—
87Q32—1222no—
88SD32—1222no—
89C2×C16—611no—
90C2×C16C2×D6111yescharacteristic
91#107C2×D6111yescharacteristic
92#103—1221no—
93C4×C8—611no—
94C2×Q8—21no—
95C2×Q8—1221no—
96C2×D4—1221no—
97Q16—21no—
98Q16—21no—
99Q16—612no—
100Q16—1221no—
101SD16—2442no—
102D8—1221no—
103D8—1221no—
104C2×C8—611no—
105C2×C8C22×D6111yescharacteristic
106C4⋊C4—21no—
107C4⋊C4—2441no—
108C22⋊C4—2441no—
109C22⋊C4—2441no—
110C42—611no—
111C42—2441no—
112C16—21no—
113C16—1221no—
114C23—2441no—
115Q8—41no—
116Q8—41no—
117Q8—1222no—
118Q8—2441no—
119D4—2441no—
120D4—2441no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—611no—
124C2×C4—611no—
125C2×C4—2441no—
126C2×C4D4×D6111yescharacteristic
127C8—1221no—
128C8#1175822211yescharacteristic
129C8D4×D6111yescharacteristic
130C22—4881no—
131C22—4881no—
132C22—4881no—
133C22D8×D6111yescharacteristic
134C4—81no—
135C4—81no—
136C4—1221no—
137C4—1221no—
138C4—2442no—
139C4#1451975011yescharacteristic
140C4#1451980411yescharacteristic
141C2—9761no—
142C2#1683995611yescharacteristic
143C2#1684019311yescharacteristic
144C2#1684020411yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2211
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
1. C2×#14519723C2semidirect
4. #16839856C2semidirect
5. #16839580C2semidirect
7. C61×#358C2semidirect
78. #358D61semidirect
80. C61#2211semidirect