Finite Group Databasebeta

← #21446419

Subgroups — #21446419

Order 7808.

186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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#16839800C211yesmaximal, characteristic
2#16839788C211yesmaximal, characteristic
3#16839717C211yesmaximal, characteristic
4#16839527C211yesmaximal, characteristic
5#16839522C211yesmaximal, characteristic
6#16839522C211yesmaximal, characteristic
7C61×#336C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519736C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519711C411yescharacteristic, complemented
13#14519711C411yescharacteristic, complemented
14#14519709C411yescharacteristic, complemented
15#14519709C411yescharacteristic, complemented
16#14519706—21no—
17#14519706—21no—
18#14519687—21no—
19C8×Dic61—21no—
20C22×C8×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C2×C8×C61—21no—
26C2×C8×C61—21no—
27C2×C8×C61—21no—
28C2×C8×C61—21no—
29C2×C8×C61C2×C411yescharacteristic
30C2×C8×C61C2×C411yescharacteristic
31C2×C8×C61D411yescharacteristic
32C2×C8×C61D411yescharacteristic
33C42×C61—21no—
34C42×C61—21no—
35C22⋊Dic61—21no—
36C22⋊Dic61—21no—
37C4⋊Dic61C2×C411yescharacteristic
38C4⋊Dic61C2×C411yescharacteristic
39C4⋊Dic61C2×C411yescharacteristic
40C4⋊Dic61C2×C411yescharacteristic
41C4×Dic61—21no—
42C4×Dic61—21no—
43#11758194—21no—
44#11758194—21no—
45#11758194—21no—
46#11758194Q812yes—
47C2×#92418—21no—
48C2×#92418—21no—
49C23×C61#4111yescharacteristic
50C2×C4×C61—22no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C8×C61—21no—
64C8×C61—21no—
65C8×C61—21no—
66C8×C61—21no—
67#92418—22no—
68#92418—41no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61C4×D411yescharacteristic
72C22×C61#12511yescharacteristic
73C22×C61#12611yescharacteristic
74C4×C61—42no—
75C4×C61#11711yescharacteristic
76C4×C61C4×Q811yescharacteristic
77C4×C61C22⋊Q811yescharacteristic
78C4×C61#12311yescharacteristic
79Dic61—41no—
80Dic61—41no—
81Dic61—41no—
82Dic61—41no—
83#1922—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—21no—
86C2×C61#38711yescharacteristic
87C2×C61#44311yescharacteristic
88C2×C61#44411yescharacteristic
89#427—611no—
90#424—611no—
91#405—611no—
92#341—611no—
93#339—611no—
94#339—611no—
95#336D6111yescharacteristic
96C61#192211yescharacteristic, complemented, Sylow
97C2×M16—611no—
98C2×M16—611no—
99C22×C8C2×D6111yescharacteristic
100C22×C8C2×D6111yescharacteristic
101#117—611no—
102#117—611no—
103C2×C42C2×D6111yescharacteristic
104#107—611no—
105#107—611no—
106#106—611no—
107#106—611no—
108C4⋊C8—1221no—
109C4⋊C8—1221no—
110#97—1221no—
111C4×C8—1221no—
112C22×C4—21no—
113C22×C4C22×D6111yescharacteristic
114M16—612no—
115M16—1221no—
116M16—1221no—
117M16—1221no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1221no—
123C2×C8—1221no—
124C2×C8C4×D6111yescharacteristic
125C2×C8C4×D6111yescharacteristic
126C2×C8D24411yescharacteristic
127C2×C8D24411yescharacteristic
128C4⋊C4—611no—
129C4⋊C4—611no—
130C4⋊C4—611no—
131C4⋊C4—611no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C42—21no—
135C42—21no—
136C42—1221no—
137C42—1221no—
138C23#1175822211yescharacteristic
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—1221no—
146C2×C4C2×C4×D6111yescharacteristic
147C2×C4C2×D24411yescharacteristic
148C2×C4#1175822411yescharacteristic
149C2×C4#1175822411yescharacteristic
150C2×C4#1175822411yescharacteristic
151C2×C4Q8×D6111yescharacteristic
152C8—21no—
153C8—21no—
154C8—21no—
155C8—21no—
156C8—1222no—
157C8—2441no—
158C22—21no—
159C22—21no—
160C22C4×D24411yescharacteristic
161C22#1451976711yescharacteristic
162C22#1451977011yescharacteristic
163C4—42no—
164C4—2441no—
165C4—2441no—
166C4—2441no—
167C4—2441no—
168C4#1451973311yescharacteristic
169C4#1451974211yescharacteristic
170C4#1451975711yescharacteristic
171C4#1451976111yescharacteristic
172C2—21no—
173C2—21no—
174C2#1683964711yescharacteristic
175C2#1683988011yescharacteristic
176C2#1683988511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC22×C61C4×D4
hypercenter#336D61
hypocenterC61#1922
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #336

Complements

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

NH ≅ G/Ntype
12. #14519711C4semidirect
13. #14519711C4semidirect
14. #14519709C4semidirect
15. #14519709C4semidirect
96. C61#1922semidirect