Finite Group Databasebeta

← #21447925

Subgroups — #21447925

Order 7808.

150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14519717C211yesmaximal, characteristic
3#16840003C211yesmaximal, characteristic
4#16839589C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6#16839565C211yesmaximal, characteristic, complemented
7C61×#467C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9#14519756—21no—
10#14519723—22no—
11#14519717—22no—
12C2×#11758185C2211yescharacteristic
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519702—21no—
16C2×Q16×C61C2211yescharacteristic
17C22×C8×C61C2211yescharacteristic
18C22⋊Q8×C61—21no—
19#107×C61C2211yescharacteristic
20#103×C61—21no—
21C2×Q8×C61—21no—
22C22×C4×C61D411yescharacteristic
23C2×Dic122—21no—
24Q16×C61—21no—
25Q16×C61—21no—
26C2×C8×C61—21no—
27C2×C8×C61—21no—
28C2×C8×C61D411yescharacteristic
29C2×C8×C61C2311yescharacteristic
30C4⋊C4×C61—21no—
31C4⋊C4×C61—41no—
32C22⋊C4×C61—41no—
33C22⋊Dic61—41no—
34C4⋊Dic61—21no—
35#11758196—41no—
36Dic244—21no—
37Dic244—21no—
38#11758185—21no—
39#11758185D412yes—
40C23×C61D811yescharacteristic
41Q8×C61—41no—
42Q8×C61—41no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61D811yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×Dic61—41no—
50C2×Dic61—41no—
51Dic122—41no—
52Dic122—41no—
53C8×C61—21no—
54C8×C61C2×D411yescharacteristic
55C8×C61#4111yescharacteristic
56C22×C61—21no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61C2×D811yescharacteristic
60C4×C61—21no—
61C4×C61—81no—
62C4×C61—81no—
63C4×C61#12111yescharacteristic
64C4×C61#13511yescharacteristic
65Dic61—81no—
66Dic61—81no—
67#2219—611nomaximal, Sylow
68C2×C61—41no—
69C2×C61#46611yescharacteristic
70C2×C61#51011yescharacteristic
71C2×C61#51011yescharacteristic
72C2×Q32—611no—
73C2×M32—611no—
74#467—611no—
75#467D6111yescharacteristic
76#367—611no—
77#358—611no—
78#358—611no—
79C61#221911yescharacteristic, complemented, Sylow
80C2×Q16—611no—
81C2×Q16C2×D6111yescharacteristic
82C22×C8C2×D6111yescharacteristic
83C22⋊Q8—21no—
84C22⋊Q8—1221no—
85Q32—1222no—
86M32—1222no—
87C2×C16—611no—
88C2×C16—611no—
89#107—611no—
90#107C2×D6111yescharacteristic
91#103—21no—
92#103—1221no—
93C2×Q8—21no—
94C2×Q8—1221no—
95C22×C4C22⋊D6111yescharacteristic
96Q16—21no—
97Q16—21no—
98Q16—1221no—
99Q16—1221no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8C22⋊D6111yescharacteristic
103C2×C8C22×D6111yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—41no—
106C4⋊C4—1221no—
107C4⋊C4—2441no—
108C22⋊C4—41no—
109C22⋊C4—2441no—
110C16—612no—
111C16—1221no—
112C23#1175819911yescharacteristic
113Q8—41no—
114Q8—41no—
115Q8—2441no—
116Q8—2441no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2441no—
122C2×C4—2441no—
123C2×C4#1175819911yescharacteristic
124C2×C4C2×C22⋊D6111yescharacteristic
125C8—21no—
126C8D4×D6111yescharacteristic
127C8#1175822411yescharacteristic
128C22—21no—
129C22—21no—
130C22—21no—
131C22C2×#1175819911yescharacteristic
132C4—21no—
133C4—81no—
134C4—81no—
135C4—4881no—
136C4—4881no—
137C4#1451974911yescharacteristic
138C4#1451979711yescharacteristic
139C2—41no—
140C2#1683999611yescharacteristic
141C2#1684020211yescharacteristic
142C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#467C2
socleC22×C61C2×D8
hypercenter#467D61
hypocenterC61#2219
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
1. C2×#14519723C2semidirect
4. #16839589C2semidirect
5. #16839566C2semidirect
6. #16839565C2semidirect
79. C61#2219semidirect