Finite Group Databasebeta

← #21447680

Subgroups — #21447680

Order 7808.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14519721C211yesmaximal, characteristic
2#16839856C211yesmaximal, characteristic, complemented
3D8×Dic61C211yesmaximal, characteristic
4#16839587C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839537C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9#14519742—21no—
10D4×Dic61—21no—
11#14519721C414yescomplemented
12C2×#11758185C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519700—21no—
15#14519698—21no—
16C8×Dic61C2211yescharacteristic
17C2×D8×C61C2211yescharacteristic
18C2×C16×C61C2211yescharacteristic
19#107×C61C2211yescharacteristic
20C2×D4×C61—21no—
21C22×Dic61—41no—
22C2×Dic122—21no—
23D8×C61—21no—
24D8×C61C2×C412yes—
25C2×C8×C61C2311yescharacteristic
26C4⋊C4×C61—21no—
27C22⋊Dic61—41no—
28C4⋊Dic61—21no—
29#11758196—41no—
30C4×Dic61—41no—
31C4×Dic61D411yescharacteristic
32C2×#92418D411yescharacteristic
33Dic244—21no—
34Dic244C2×C412yescomplemented
35C16×C61—21no—
36#11758185C2×C412yescomplemented
37C23×C61—41no—
38D4×C61—22no—
39D4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61—82no—
45C2×Dic61D811yescharacteristic
46C2×Dic61D811yescharacteristic
47Dic122—22no—
48Dic122—41no—
49C8×C61C22×C411yescharacteristic
50C8×C61#4111yescharacteristic
51#92418—21no—
52C22×C61—42no—
53C22×C61—81no—
54C22×C61—81no—
55C22×C61C2×D811yescharacteristic
56C4×C61—81no—
57C4×C61C4×D411yescharacteristic
58C4×C61#13511yescharacteristic
59Dic61—21no—
60Dic61—21no—
61Dic61—42no—
62Dic61—81no—
63#2175—611nomaximal, Sylow
64C2×C61—82no—
65C2×C61C4×D811yescharacteristic
66C2×C61#50911yescharacteristic
67C2×C61#51011yescharacteristic
68C2×SD32—611no—
69C4×Q16—611no—
70C4×D8—611no—
71#366—611no—
72#358—611no—
73#357D6111yescharacteristic
74#346—611no—
75C61#217511yescharacteristic, complemented, Sylow
76C2×Q16—611no—
77C2×D8C2×D6111yescharacteristic
78C4×Q8—1221no—
79C4×D4—1221no—
80SD32—614no—
81C2×C16—611no—
82C2×C16C2×D6111yescharacteristic
83#107—611no—
84#107C2×D6111yescharacteristic
85#103—1221no—
86#102—1221no—
87C4×C8—611no—
88C2×Q8—1221no—
89C2×D4—21no—
90C22×C4—2441no—
91Q16—612no—
92Q16—1221no—
93D8—21no—
94D8C4×D6112yes—
95C2×C8—611no—
96C2×C8C22×D6111yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—1221no—
99C4⋊C4—2441no—
100C22⋊C4—2441no—
101C42—611no—
102C42—2441no—
103C16—21no—
104C16—612no—
105C23—41no—
106Q8—1222no—
107Q8—2441no—
108D4—22no—
109D4—41no—
110C2×C4—41no—
111C2×C4—611no—
112C2×C4—611no—
113C2×C4—4882no—
114C2×C4—2441no—
115C2×C4—2441no—
116C2×C4D4×D6111yescharacteristic
117C8—1221no—
118C8C2×C4×D6111yescharacteristic
119C8#1175822411yescharacteristic
120C22—42no—
121C22—81no—
122C22—81no—
123C22D8×D6111yescharacteristic
124C4—81no—
125C4—1221no—
126C4—1221no—
127C4—4881no—
128C4—2442no—
129C4#1451973711yescharacteristic
130C4#1451979811yescharacteristic
131C2—82no—
132C2#1683984211yescharacteristic
133C2#1684019611yescharacteristic
134C2#1684020111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2175
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. #16839856C2semidirect
4. #16839587C2semidirect
5. #16839567C2semidirect
6. #16839537C2semidirect
11. #14519721C4semidirect
34. Dic244C2×C4semidirect
36. #11758185C2×C4semidirect
75. C61#2175semidirect