Finite Group Databasebeta

← #21447862

Subgroups — #21447862

Order 7808.

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

normal subgroups only

This group has 166 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×#14519721C211yesmaximal, characteristic
2#16840140C211yesmaximal, characteristic, complemented
3D8×Dic61C211yesmaximal, characteristic
4#16839580C211yesmaximal, characteristic, complemented
5#16839567C211yesmaximal, characteristic, complemented
6#16839566C211yesmaximal, characteristic, complemented
7C2×SD32×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758202—21no—
10#14519775—21no—
11D4×Dic61—21no—
12#14519721—22no—
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519698—21no—
16C8×Dic61C2211yescharacteristic
17C2×Q16×C61C2211yescharacteristic
18C2×D8×C61C2211yescharacteristic
19SD32×C61—22no—
20C2×C16×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×D4×C61—21no—
23C22×Dic61—41no—
24C2×Dic122—21no—
25Q16×C61—21no—
26Q16×C61—21no—
27D8×C61—21no—
28D8×C61D412yes—
29C2×C8×C61C2311yescharacteristic
30C22⋊Dic61—41no—
31#11758202—42no—
32C4⋊Dic61—21no—
33#11758196—41no—
34#11758196—41no—
35C4×Dic61D411yescharacteristic
36C2×#92418D411yescharacteristic
37Dic244—21no—
38Dic244—21no—
39C16×C61—21no—
40#11758185—21no—
41C23×C61—41no—
42Q8×C61—41no—
43Q8×C61—41no—
44D4×C61—22no—
45D4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C2×D411yescharacteristic
48C2×Dic61—41no—
49C2×Dic61—41no—
50C2×Dic61—82no—
51C2×Dic61D811yescharacteristic
52C2×Dic61D811yescharacteristic
53Dic122—41no—
54Dic122—41no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57#92418—21no—
58C22×C61—42no—
59C22×C61—81no—
60C22×C61—81no—
61C22×C61C2×D811yescharacteristic
62C4×C61—81no—
63C4×C61#12111yescharacteristic
64C4×C61AGL(1,ℤ/8)11yescharacteristic
65Dic61—21no—
66Dic61—81no—
67Dic61—81no—
68Dic61SD3212yescomplemented
69#2208—611nomaximal, Sylow
70C2×C61—82no—
71C2×C61#45911yescharacteristic
72C2×C61C2×SD3211yescharacteristic
73C2×C61#51011yescharacteristic
74C2×SD32—611no—
75C2×SD32D6111yescharacteristic
76#494—611no—
77C4×D8—611no—
78C4⋊C16—611no—
79#358—611no—
80#358—611no—
81C61#220811yescharacteristic, complemented, Sylow
82C2×Q16—611no—
83C2×Q16—1221no—
84C2×Q16C2×D6111yescharacteristic
85C2×D8C2×D6111yescharacteristic
86C4⋊Q8—1221no—
87C4×D4—1221no—
88SD32—22no—
89SD32—1222no—
90C2×C16—611no—
91C2×C16C2×D6111yescharacteristic
92#107—611no—
93#102—1221no—
94C4×C8—611no—
95C2×Q8—21no—
96C2×Q8—1221no—
97C2×D4—21no—
98C22×C4—2441no—
99Q16—21no—
100Q16—21no—
101Q16—1221no—
102Q16—1221no—
103Q16—2442no—
104D8—21no—
105D8C22⋊D6112yes—
106C2×C8—611no—
107C2×C8C22×D6111yescharacteristic
108C4⋊C4—1221no—
109C4⋊C4—2441no—
110C4⋊C4—2441no—
111C22⋊C4—2441no—
112C42—611no—
113C16—21no—
114C16—1221no—
115C23—41no—
116Q8—41no—
117Q8—41no—
118Q8—2441no—
119Q8—2441no—
120D4—22no—
121D4—41no—
122C2×C4—41no—
123C2×C4—611no—
124C2×C4—611no—
125C2×C4—4882no—
126C2×C4—2441no—
127C2×C4—2441no—
128C2×C4D4×D6111yescharacteristic
129C8—1221no—
130C8#1175822411yescharacteristic
131C8C2×C22⋊D6111yescharacteristic
132C22—42no—
133C22—81no—
134C22—81no—
135C22D8×D6111yescharacteristic
136C4—81no—
137C4—612no—
138C4—1221no—
139C4—4881no—
140C4—4881no—
141C4#1451974911yescharacteristic
142C4#1451980111yescharacteristic
143C2—82no—
144C2#1683995511yescharacteristic
145C2SD32×D6111yescharacteristic
146C2#1684020111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×SD32×C61C2
socleC22×C61C2×D8
hypercenterC2×SD32D61
hypocenterC61#2208
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
2. #16840140C2semidirect
4. #16839580C2semidirect
5. #16839567C2semidirect
6. #16839566C2semidirect
68. Dic61SD32semidirect
81. C61#2208semidirect