Finite Group Databasebeta

← #21461395

Subgroups — #21461395

Order 7808.

158 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840778C211yesmaximal, characteristic
2#16840765C211yesmaximal, characteristic
3#16840626C211yesmaximal, characteristic, complemented
4#16840625C211yesmaximal, characteristic, complemented
5#16840624C211yesmaximal, characteristic, complemented
6#16840623C211yesmaximal, characteristic, complemented
7#16839812C211yesmaximal, characteristic
8C2×#11758217—21no—
9#14519844—21no—
10C4⋊#92420C2211yescharacteristic
11C4⋊#92420C2211yescharacteristic
12C4⋊#92420C2211yescharacteristic
13C4⋊#92420C2211yescharacteristic
14C22⋊#92420—21no—
15C4×#92420—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519706C411yescharacteristic
18#14519706C411yescharacteristic
19C22⋊#92418C411yescharacteristic
20C8×Dic61C2211yescharacteristic
21C8×Dic61C2211yescharacteristic
22C22⋊C8×C61C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61D411yescharacteristic
25C22×Dic61Q811yescharacteristic
26#11758217—42no—
27C2×#92420—21no—
28C2×#92420—21no—
29C2×#92420—21no—
30C2×#92420—21no—
31C2×C8×C61C2×C411yescharacteristic
32C2×C8×C61C2×C411yescharacteristic
33C4×Dic61C2×C411yescharacteristic
34C4×Dic61D411yescharacteristic
35C4×Dic61Q811yescharacteristic
36C4×Dic61C2311yescharacteristic
37C2×#92418C2×C411yescharacteristic
38C2×#92418C2×C411yescharacteristic
39C23×C61C4⋊C411yescharacteristic
40C2×C4×C61—21no—
41C2×C4×C61—21no—
42C2×C4×C61C4⋊C411yescharacteristic
43C2×C4×C61C22×C411yescharacteristic
44C2×Dic61—22no—
45C2×Dic61—21no—
46C2×Dic61—21no—
47C2×Dic61C4⋊C411yescharacteristic
48C2×Dic61C4⋊C411yescharacteristic
49C2×Dic61C2×D411yescharacteristic
50C2×Dic61C2×Q811yescharacteristic
51#92420—41no—
52#92420—41no—
53#92420—41no—
54#92420—41no—
55C8×C61—21no—
56C8×C61—21no—
57#92418—21no—
58#92418—21no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61C2×C4⋊C411yescharacteristic
63C4×C61—21no—
64C4×C61#13111yescharacteristic
65C4×C61#13111yescharacteristic
66Dic61—21no—
67Dic61—21no—
68Dic61#10812yes—
69Dic61AGL(1,ℤ/8)11yescharacteristic
70Dic61#13711yescharacteristic
71#1574—611nomaximal, Sylow
72C2×C61—41no—
73C2×C61#42411yescharacteristic
74C2×C61#42811yescharacteristic
75C2×C61C2×#10811yescharacteristic
76#431—611no—
77#431—611no—
78#423—611no—
79#335—611no—
80#335—611no—
81#334—611no—
82#334—611no—
83C61#157411yescharacteristic, complemented, Sylow
84C2×M16—1221no—
85C2×C42—611no—
86C4⋊C8—611no—
87C4⋊C8—611no—
88C4⋊C8—611no—
89C4⋊C8—611no—
90C4⋊C8—611no—
91C4⋊C8—611no—
92C4⋊C8—1221no—
93C22⋊C8—611no—
94C22⋊C8—1221no—
95C22⋊C8#692311yescharacteristic
96C4×C8—611no—
97C4×C8—611no—
98C4×C8—1221no—
99C22×C4—611no—
100C22×C4—611no—
101C22×C4C2×#692311yescharacteristic
102M16—2442no—
103C2×C8—611no—
104C2×C8—611no—
105C2×C8—1221no—
106C2×C8—1221no—
107C2×C8—1221no—
108C2×C8—1221no—
109C2×C8C2×#692311yescharacteristic
110C2×C8C2×#692311yescharacteristic
111C42—611no—
112C42—611no—
113C42—611no—
114C42—611no—
115C23C4⋊#692311yescharacteristic
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—611no—
119C2×C4—611no—
120C2×C4—611no—
121C2×C4—611no—
122C2×C4—1221no—
123C2×C4—1221no—
124C2×C4—1222no—
125C2×C4C4⋊#692311yescharacteristic
126C2×C4C22×#692311yescharacteristic
127C8—21no—
128C8—21no—
129C8—1221no—
130C8—1221no—
131C8—2441no—
132C8—2441no—
133C8—2441no—
134C8—2441no—
135C22—21no—
136C22—21no—
137C22—21no—
138C22C2×C4⋊#692311yescharacteristic
139C4—21no—
140C4—611no—
141C4—611no—
142C4—612no—
143C4—1221no—
144C4—1221no—
145C4#1451986411yescharacteristic
146C4#1451986411yescharacteristic
147C2—41no—
148C2#1684076811yescharacteristic
149C2#1684077311yescharacteristic
150C2D61⋊#10811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22⋊C8#6923
hypocenterC61#1574
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #16840626C2semidirect
4. #16840625C2semidirect
5. #16840624C2semidirect
6. #16840623C2semidirect
83. C61#1574semidirect