Finite Group Databasebeta

← #21461334

Subgroups — #21461334

Order 7808.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#16840779C211yesmaximal, characteristic
2#16840765C211yesmaximal, characteristic
3#16840621C214yesmaximal, complemented
4C2×#14519776C211yesmaximal, characteristic
5C2×#11758217—21no—
6#14519844C2212yes—
7#14519844C2212yes—
8C4⋊#92420—21no—
9C22⋊#92420—21no—
10C4×#92420—21no—
11C22×Dic122—21no—
12#14519776—21no—
13#14519776—21no—
14#14519776C412yes—
15#14519776C2212yes—
16C2×C4⋊Dic61C411yescharacteristic
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×Dic61—21no—
23C22×Dic61D411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×Dic122—22no—
26C2×Dic122—22no—
27C2×Dic122—44no—
28#11758217—42no—
29C2×#92420—22no—
30C2×#92420—22no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61C2×C412yes—
33C4⋊Dic61—21no—
34C4⋊Dic61C2×C412yes—
35#11758196—22no—
36#11758196—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61C2311yescharacteristic
41C23×C61C22⋊C411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—42no—
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22×C411yescharacteristic
47C2×Dic61—22no—
48C2×Dic61—22no—
49C2×Dic61—42no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61SD1612yes—
53C2×Dic61Q1612yes—
54C2×Dic61C2×D411yescharacteristic
55C2×Dic61C2×D411yescharacteristic
56Dic122—44no—
57Dic122—44no—
58#92420—42no—
59#92420—42no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61#10312yes—
63C22×C61C2×C22⋊C411yescharacteristic
64C4×C61—21no—
65C4×C61—42no—
66C4×C61#10112yes—
67Dic61—21no—
68Dic61—42no—
69Dic61#10312yes—
70Dic61C2×SD1611yescharacteristic
71Dic61C2×Q1611yescharacteristic
72Dic61AGL(1,ℤ/8)12yes—
73#1549—611nomaximal, Sylow
74C2×C61—22no—
75C2×C61C2×#10111yescharacteristic
76C2×C61C2×#10311yescharacteristic
77C2×C61#41811yescharacteristic
78C2×C4⋊Q8—611no—
79#431—611no—
80#423—611no—
81#332—614no—
82C61#154911yescharacteristic, complemented, Sylow
83C22×Q8—1221no—
84C2×M16—1221no—
85C4⋊Q8—612no—
86C4⋊Q8—612no—
87C4⋊Q8—1221no—
88C4⋊Q8—1221no—
89C2×C4⋊C4—611no—
90C2×C4⋊C4—1221no—
91C2×C4⋊C4#692311yescharacteristic
92C2×C42—611no—
93C4⋊C8—612no—
94C4⋊C8—612no—
95C4⋊C8—1221no—
96C22⋊C8—1221no—
97C4×C8—1221no—
98C2×Q8—1222no—
99C2×Q8—1222no—
100C2×Q8—2444no—
101C22×C4—21no—
102C22×C4—611no—
103C22×C4—611no—
104C22×C4—1221no—
105C22×C4C2×#692311yescharacteristic
106M16—2442no—
107C2×C8—1222no—
108C2×C8—1222no—
109C4⋊C4—21no—
110C4⋊C4—612no—
111C4⋊C4—1222no—
112C4⋊C4—1222no—
113C4⋊C4—1221no—
114C4⋊C4C2×#692312yes—
115C42—611no—
116C42—611no—
117C42—611no—
118C42—611no—
119C23C22⋊#692311yescharacteristic
120Q8—2444no—
121Q8—2444no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—612no—
126C2×C4—612no—
127C2×C4—611no—
128C2×C4—611no—
129C2×C4—611no—
130C2×C4—611no—
131C2×C4—1222no—
132C2×C4—1222no—
133C2×C4—2442no—
134C2×C4C22⋊#692311yescharacteristic
135C2×C4C22×#692311yescharacteristic
136C8—2442no—
137C8—2442no—
138C22—21no—
139C22—21no—
140C22#1451984012yes—
141C22C2×C22⋊#692311yescharacteristic
142C4—21no—
143C4—42no—
144C4—612no—
145C4—611no—
146C4—611no—
147C4—612no—
148C4—1221no—
149C4—2442no—
150C4#1451983812yes—
151C2—22no—
152C2C2×#1451983811yescharacteristic
153C2C2×#1451984011yescharacteristic
154C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1549
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840621C2semidirect
82. C61#1549semidirect