Finite Group Databasebeta

← #21446420

Subgroups — #21446420

Order 7808.

186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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#16839789C211yesmaximal, characteristic
2#16839718C211yesmaximal, characteristic
3#16839527C211yesmaximal, characteristic
4#16839521C211yesmaximal, characteristic
5#16839521C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#427C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12C4⋊#92418—21no—
13C4⋊#92418—21no—
14#14519688—21no—
15C4×#92418—21no—
16C22×C8×C61C2211yescharacteristic
17#117×C61C2211yescharacteristic
18#117×C61C2211yescharacteristic
19#107×C61C411yescharacteristic, complemented
20#107×C61C411yescharacteristic, complemented
21#106×C61C411yescharacteristic, complemented
22#106×C61C411yescharacteristic, complemented
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25C2×C8×C61—21no—
26C2×C8×C61—21no—
27C2×C8×C61C2×C411yescharacteristic
28C2×C8×C61C2×C411yescharacteristic
29C4⋊C4×C61C2×C411yescharacteristic
30C4⋊C4×C61C2×C411yescharacteristic
31C4⋊C4×C61C2×C411yescharacteristic
32C4⋊C4×C61C2×C411yescharacteristic
33C22⋊C4×C61—21no—
34C22⋊C4×C61—21no—
35C42×C61—21no—
36C42×C61—21no—
37C4×Dic61—21no—
38C4×Dic61—21no—
39#11758194—21no—
40#11758194—21no—
41#11758194—21no—
42#11758194Q812yes—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418D411yescharacteristic
48C2×#92418D411yescharacteristic
49C23×C61#4111yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×Q811yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×Dic61—22no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C8×C61—21no—
64C8×C61—21no—
65#92418—22no—
66#92418—21no—
67#92418—21no—
68#92418—41no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61C4×D411yescharacteristic
72C22×C61#12511yescharacteristic
73C22×C61#12611yescharacteristic
74C4×C61—41no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61—41no—
78C4×C61#11711yescharacteristic
79C4×C61C4×Q811yescharacteristic
80C4×C61C22⋊Q811yescharacteristic
81C4×C61#12311yescharacteristic
82Dic61—42no—
83#1922—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—21no—
86C2×C61#38711yescharacteristic
87C2×C61#44311yescharacteristic
88C2×C61#44411yescharacteristic
89#427D6111yescharacteristic
90#424—611no—
91#405—611no—
92#341—611no—
93#339—611no—
94#339—611no—
95#336—611no—
96C61#192211yescharacteristic, complemented, Sylow
97C2×M16—611no—
98C2×M16—611no—
99C22×C8—611no—
100C22×C8C2×D6111yescharacteristic
101#117C2×D6111yescharacteristic
102#117C2×D6111yescharacteristic
103C2×C42—611no—
104#107Dic6111yescharacteristic, complemented
105#107Dic6111yescharacteristic, complemented
106#106Dic6111yescharacteristic, complemented
107#106Dic6111yescharacteristic, complemented
108C4⋊C8—1221no—
109C4⋊C8—1221no—
110#97—1221no—
111C4×C8—1221no—
112C22×C4—1221no—
113C22×C4C22×D6111yescharacteristic
114M16—612no—
115M16—1221no—
116M16—1221no—
117M16—1221no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—611no—
121C2×C8—611no—
122C2×C8—1221no—
123C2×C8—1221no—
124C2×C8—1221no—
125C2×C8—1221no—
126C2×C8C2×Dic6111yescharacteristic
127C2×C8C2×Dic6111yescharacteristic
128C4⋊C4C2×Dic6111yescharacteristic
129C4⋊C4C2×Dic6111yescharacteristic
130C4⋊C4C2×Dic6111yescharacteristic
131C4⋊C4C2×Dic6111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C42—21no—
135C42—21no—
136C42—1221no—
137C42—1221no—
138C23#1175822411yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—1222no—
144C2×C4—2441no—
145C2×C4—2441no—
146C2×C4#1175822211yescharacteristic
147C2×C4#1175822211yescharacteristic
148C2×C4D4×D6111yescharacteristic
149C2×C4Q8×D6111yescharacteristic
150C2×C4#1175822611yescharacteristic
151C2×C4C22×Dic6111yescharacteristic
152C8—21no—
153C8—21no—
154C8—1222no—
155C8—1221no—
156C8—1221no—
157C8—2441no—
158C22—21no—
159C22—21no—
160C22D4×Dic6111yescharacteristic
161C22#1451976711yescharacteristic
162C22#1451977211yescharacteristic
163C4—41no—
164C4—41no—
165C4—41no—
166C4—41no—
167C4—2442no—
168C4#1451973611yescharacteristic
169C4Q8×Dic6111yescharacteristic
170C4#1451975511yescharacteristic
171C4#1451976211yescharacteristic
172C2—21no—
173C2—21no—
174C2#1683964811yescharacteristic
175C2#1683987911yescharacteristic
176C2#1683988411yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#427C2
socleC22×C61C4×D4
hypercenter#427D61
hypocenterC61#1922
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
19. #107×C61C4semidirect
20. #107×C61C4semidirect
21. #106×C61C4semidirect
22. #106×C61C4semidirect
96. C61#1922semidirect
104. #107Dic61semidirect
105. #107Dic61semidirect
106. #106Dic61semidirect
107. #106Dic61semidirect