Finite Group Databasebeta

← #21445916

Subgroups — #21445916

Order 7808.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14519736C211yesmaximal, characteristic
2C4×C22⋊Dic61C211yesmaximal, characteristic
3#16839523C214yesmaximal, complemented
4C61×#407C211yesmaximal, characteristic
5#14519736—21no—
6#14519736—21no—
7#14519736C412yescomplemented
8#14519736C2212yes—
9C2×C4⋊Dic61C411yescharacteristic, complemented
10C2×C4⋊Dic61C411yescharacteristic, complemented
11C2×C22⋊Dic61—21no—
12C2×C22⋊Dic61—21no—
13C2×C4×Dic61—21no—
14C2×C4×Dic61C2212yes—
15#14519684—21no—
16C23×C4×C61C2211yescharacteristic
17C2×M16×C61C2212yes—
18C22⋊C8×C61—21no—
19C22⋊C8×C61—21no—
20C24×C61D411yescharacteristic
21C22×C4×C61—24no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C22×Dic61—22no—
31M16×C61—24no—
32C2×C8×C61—22no—
33C22⋊Dic61—24no—
34C22⋊Dic61—22no—
35C22⋊Dic61—22no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61C2×C412yes—
39C4⋊Dic61C2×C412yes—
40C4×Dic61—22no—
41C4×Dic61—22no—
42C4×Dic61—24no—
43C23×C61—22no—
44C23×C61—22no—
45C23×C61—41no—
46C23×C61C22⋊C411yescharacteristic
47C23×C61C22⋊C411yescharacteristic
48C23×C61C2×D411yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61#4114yes—
59C2×Dic61—24no—
60C2×Dic61—22no—
61C2×Dic61—22no—
62C2×Dic61—42no—
63C2×Dic61—42no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66C8×C61—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—44no—
75C22×C61#10412yes—
76C22×C61C2×C22⋊C411yescharacteristic
77C22×C61#12312yes—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61#11712yes—
81C4×C61#12312yes—
82Dic61—44no—
83Dic61—42no—
84Dic61—42no—
85#1826—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61—22no—
88C2×C61—41no—
89C2×C61#38111yescharacteristic
90C2×C61C2×#10411yescharacteristic
91C2×C61#42111yescharacteristic
92C2×#117—611no—
93#407D6111yescharacteristic
94C4×C22⋊C4—611no—
95#339—614no—
96C61#182611yescharacteristic, complemented, Sylow
97C23×C4C2×D6111yescharacteristic
98C2×M16C2×D6112yes—
99#117—612no—
100#117—612no—
101#117—1221no—
102#117—1221no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4—611no—
105C2×C22⋊C4—1221no—
106C2×C22⋊C4—1221no—
107C2×C42—612no—
108C2×C42—1221no—
109C22⋊C8—21no—
110C22⋊C8—21no—
111#95—1221no—
112C24D24411yescharacteristic
113C22×C4—24no—
114C22×C4—1221no—
115C22×C4—1221no—
116C22×C4—1222no—
117C22×C4C4×D6111yescharacteristic
118C22×C4C4×D6111yescharacteristic
119C22×C4D24411yescharacteristic
120C22×C4C22⋊D6111yescharacteristic
121C22×C4C22⋊D6111yescharacteristic
122C22×C4C22×D6111yescharacteristic
123M16—24no—
124C2×C8—22no—
125C4⋊C4—612no—
126C4⋊C4—612no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C22⋊C4—1224no—
130C22⋊C4—1222no—
131C22⋊C4—1222no—
132C42—1222no—
133C42—1222no—
134C42—1224no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23#1175819811yescharacteristic
139C23#1175819811yescharacteristic
140C23C2×D24411yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—1224no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4—2442no—
152C2×C4—2442no—
153C2×C4#1175819811yescharacteristic
154C2×C4#1175819811yescharacteristic
155C2×C4C2×C4×D6111yescharacteristic
156C2×C4#1175822414yes—
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—42no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#1451970312yes—
168C22C2×#1175819811yescharacteristic
169C22#1451976112yes—
170C4—21no—
171C4—21no—
172C4—2444no—
173C4—2442no—
174C4—2442no—
175C4#1451973312yes—
176C4#1451975812yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#1683962311yescharacteristic
181C2C2×#1451970311yescharacteristic
182C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1826
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #16839523C2semidirect
7. #14519736C4semidirect
9. C2×C4⋊Dic61C4semidirect
10. C2×C4⋊Dic61C4semidirect
96. C61#1826semidirect