Finite Group Databasebeta

← #21444603

Subgroups — #21444603

Order 7808.

160 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#16839818C211yesmaximal, characteristic
2#16839813C211yesmaximal, characteristic
3C4⋊C8×D61C211yesmaximal, characteristic
4#16839514C211yesmaximal, characteristic, complemented
5#16839513C211yesmaximal, characteristic, complemented
6#16839512C211yesmaximal, characteristic, complemented
7C61×#335C211yesmaximal, characteristic, complemented
8C2×C8×D61—21no—
9C42×D61C2211yescharacteristic
10C4⋊#92418C2211yescharacteristic
11C4⋊#92418C2211yescharacteristic
12#14519706—21no—
13#14519706C411yescharacteristic
14#14519706C411yescharacteristic
15#14519689—21no—
16#14519689C411yescharacteristic
17#14519689C411yescharacteristic
18#14519687—21no—
19C4×#92418C2211yescharacteristic
20C4⋊C8×C61C2211yescharacteristic
21C4⋊C8×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61D411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C2×C8×C61—21no—
27C2×C8×C61—21no—
28C2×C8×C61C2×C411yescharacteristic
29C2×C8×C61C2×C411yescharacteristic
30C42×C61C2311yescharacteristic
31C4×Dic61C2×C411yescharacteristic
32C4×Dic61D411yescharacteristic
33C4×Dic61Q811yescharacteristic
34C2×#92418—21no—
35C2×#92418—21no—
36C2×#92418C2×C411yescharacteristic
37C2×#92418C2×C411yescharacteristic
38C8×D61—42no—
39C22×D61C4⋊C411yescharacteristic
40C2×C4×C61C22×C411yescharacteristic
41C2×C4×C61C2×D411yescharacteristic
42C2×C4×C61C2×Q811yescharacteristic
43C2×Dic61C4⋊C411yescharacteristic
44C2×Dic61C4⋊C411yescharacteristic
45C2×Dic61C4⋊C411yescharacteristic
46C4×D61—22no—
47C4×D61—21no—
48C4×D61—21no—
49C4×D61—21no—
50C4×D61—21no—
51C8×C61—21no—
52C8×C61—21no—
53C8×C61—41no—
54C8×C61—41no—
55#92418—21no—
56#92418—21no—
57#92418—41no—
58#92418—41no—
59C22×C61C2×C4⋊C411yescharacteristic
60C2×D61—21no—
61C2×D61—21no—
62C2×D61#10812yes—
63C4×C61—21no—
64C4×C61#13111yescharacteristic
65C4×C61#13111yescharacteristic
66C4×C61AGL(1,ℤ/8)11yescharacteristic
67C4×C61#13711yescharacteristic
68Dic61—21no—
69Dic61—21no—
70Dic61—21no—
71#1573—611nomaximal, Sylow
72C2×C61#42411yescharacteristic
73C2×C61#42811yescharacteristic
74C2×C61C2×#10811yescharacteristic
75D61—22no—
76#432—611no—
77#431—611no—
78C2×C4⋊C8—611no—
79#335—611no—
80#335D6111yescharacteristic, complemented
81#334—611no—
82#334—611no—
83C61#157311yescharacteristic, complemented, Sylow
84C22×C8—1221no—
85C2×C42—611no—
86C4⋊C8—611no—
87C4⋊C8—611no—
88C4⋊C8—611no—
89C4⋊C8—611no—
90C4⋊C8—1221no—
91C4⋊C8C2×D6111yescharacteristic
92C4⋊C8C2×D6111yescharacteristic
93C22⋊C8—611no—
94C22⋊C8—611no—
95C22⋊C8—1221no—
96#97—1221no—
97C4×C8—611no—
98C4×C8C2×D6111yescharacteristic
99C22×C4—611no—
100C22×C4—611no—
101C22×C4—611no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—611no—
105C2×C8—611no—
106C2×C8—1221no—
107C2×C8—1221no—
108C2×C8—2442no—
109C2×C8C4×D6111yescharacteristic
110C2×C8C4×D6111yescharacteristic
111C42—611no—
112C42—611no—
113C42—611no—
114C42C22×D6111yescharacteristic
115C23—611no—
116C2×C4—611no—
117C2×C4—611no—
118C2×C4—611no—
119C2×C4—1222no—
120C2×C4—1221no—
121C2×C4—1221no—
122C2×C4—1221no—
123C2×C4—1221no—
124C2×C4C2×C4×D6111yescharacteristic
125C2×C4D4×D6111yescharacteristic
126C2×C4Q8×D6111yescharacteristic
127C8—21no—
128C8—21no—
129C8—41no—
130C8—41no—
131C8—1221no—
132C8—1221no—
133C8—2441no—
134C8—2441no—
135C22—612no—
136C22—1221no—
137C22—1221no—
138C22C4⋊C4×D6111yescharacteristic
139C4—21no—
140C4—1221no—
141C4—1221no—
142C4—1221no—
143C4#1451978311yescharacteristic
144C4#1451978511yescharacteristic
145C4#1451980111yescharacteristic
146C4#1451980911yescharacteristic
147C2—1222no—
148C2#1683978711yescharacteristic
149C2#1683980311yescharacteristic
150C2#108×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#335C2
socleC22×C61C2×C4⋊C4
hypercenter#335D61
hypocenterC61#1573
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
4. #16839514C2semidirect
5. #16839513C2semidirect
6. #16839512C2semidirect
7. C61×#335C2semidirect
80. #335D61semidirect
83. C61#1573semidirect