Finite Group Databasebeta

← #21447909

Subgroups — #21447909

Order 7808.

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

normal subgroups only

This group has 154 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
2C2×C16×D61C211yesmaximal, characteristic
3#16840004C211yesmaximal, characteristic
4#16840000C211yesmaximal, characteristic
5#16839587C211yesmaximal, characteristic, complemented
6#16839567C211yesmaximal, characteristic, complemented
7C61×#358C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×C8×D61C2211yescharacteristic
10#14519757—21no—
11#14519753—21no—
12#14519723—22no—
13C2×#11758185C2211yescharacteristic
14C16×D61—22no—
15#14519711C2211yescharacteristic
16#14519701—21no—
17#14519700—21no—
18C2×Q16×C61C2211yescharacteristic
19C2×C16×C61C2211yescharacteristic
20#107×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×C4×D61D411yescharacteristic
23C2×Dic122—21no—
24Q16×C61—21no—
25Q16×C61—21no—
26C2×C8×C61C2311yescharacteristic
27C4⋊C4×C61—21no—
28#11758198—41no—
29#11758198—41no—
30C4⋊Dic61—21no—
31C4⋊Dic61—41no—
32#11758196—41no—
33C2×#92418D411yescharacteristic
34Dic244—21no—
35Dic244—21no—
36C8×D61—21no—
37C8×D61—21no—
38C16×C61—21no—
39#11758185D412yes—
40C22×D61D811yescharacteristic
41Q8×C61—41no—
42Q8×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61C2×D411yescharacteristic
46C2×Dic61—41no—
47C2×Dic61—41no—
48C2×Dic61D811yescharacteristic
49C4×D61—21no—
50C4×D61—21no—
51Dic122—41no—
52Dic122—41no—
53C8×C61C2×D411yescharacteristic
54C8×C61#4111yescharacteristic
55#92418—21no—
56C22×C61C2×D811yescharacteristic
57C2×D61—21no—
58C2×D61—21no—
59C2×D61Q3212yescomplemented
60C4×C61—81no—
61C4×C61—81no—
62C4×C61#12111yescharacteristic
63C4×C61#13511yescharacteristic
64Dic61—21no—
65Dic61—81no—
66Dic61—81no—
67#2216—611nomaximal, Sylow
68C2×C61#46611yescharacteristic
69C2×C61C2×Q3211yescharacteristic
70C2×C61#50811yescharacteristic
71D61—22no—
72C2×Q32—611no—
73C22×C16—611no—
74#467—611no—
75#467—611no—
76#366—611no—
77#358—611no—
78#358D6111yescharacteristic, complemented
79C61#221611yescharacteristic, complemented, Sylow
80C2×Q16—611no—
81C2×Q16C2×D6111yescharacteristic
82C22×C8—611no—
83C22⋊Q8—1221no—
84C22⋊Q8—1221no—
85Q32—1222no—
86C2×C16—611no—
87C2×C16—1222no—
88C2×C16C2×D6111yescharacteristic
89#107—611no—
90#107C2×D6111yescharacteristic
91#103—1221no—
92#103—1221no—
93C2×Q8—21no—
94C2×Q8—1221no—
95C22×C4—611no—
96Q16—21no—
97Q16—21no—
98Q16—1221no—
99Q16—1221no—
100C2×C8—611no—
101C2×C8—1221no—
102C2×C8—1221no—
103C2×C8C22×D6111yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—1221no—
106C4⋊C4—2441no—
107C4⋊C4—2441no—
108C22⋊C4—2441no—
109C22⋊C4—2441no—
110C16—21no—
111C16—612no—
112C23—611no—
113Q8—41no—
114Q8—41no—
115Q8—2441no—
116Q8—2441no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—611no—
120C2×C4—1221no—
121C2×C4—1221no—
122C2×C4—2441no—
123C2×C4—2441no—
124C2×C4D4×D6111yescharacteristic
125C8—1221no—
126C8#1175822211yescharacteristic
127C8D4×D6111yescharacteristic
128C22—612no—
129C22—1221no—
130C22—1221no—
131C22D8×D6111yescharacteristic
132C4—81no—
133C4—81no—
134C4—1221no—
135C4—4881no—
136C4—4881no—
137C4#1451975011yescharacteristic
138C4#1451979811yescharacteristic
139C2—1222no—
140C2#1683999711yescharacteristic
141C2Q32×D6111yescharacteristic
142C2#1684019311yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2216
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
5. #16839587C2semidirect
6. #16839567C2semidirect
7. C61×#358C2semidirect
59. C2×D61Q32semidirect
78. #358D61semidirect
79. C61#2216semidirect