Finite Group Databasebeta

← #21445704

Subgroups — #21445704

Order 7808.

224 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14519712C211yesmaximal, characteristic
2#16839798C211yesmaximal, characteristic
3#16839717C211yesmaximal, characteristic
4C2×#14519687C211yesmaximal, characteristic
5#16839523C211yesmaximal, characteristic
6#16839521C211yesmaximal, characteristic
7C61×#405C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519712C414yescomplemented
13#14519710C412yescomplemented
14#14519708C412yescomplemented
15#14519687—21no—
16#14519687C414yescomplemented
17C8×Dic61—21no—
18C2×M16×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20#117×C61C2211yescharacteristic
21#97×C61—21no—
22C4×C8×C61—21no—
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25M16×C61—21no—
26M16×C61C2×C412yes—
27C2×C8×C61—21no—
28C2×C8×C61C2×C412yes—
29C2×C8×C61D411yescharacteristic
30C2×C8×C61D411yescharacteristic
31C2×C8×C61Q812yes—
32C4⋊C4×C61C2×C412yes—
33C22⋊C4×C61—21no—
34C42×C61—21no—
35C22⋊Dic61—21no—
36C4⋊Dic61C2×C412yes—
37C4×Dic61—21no—
38C4×Dic61—21no—
39C4×Dic61C2×C412yes—
40#11758194—21no—
41#11758194C2×C412yes—
42C2×#92418—21no—
43C2×#92418C2×C412yes—
44C2×#92418C2×C411yescharacteristic
45C2×#92418C2×C411yescharacteristic
46C2×#92418C2×C412yes—
47C23×C61#4111yescharacteristic
48C2×C4×C61—22no—
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×Q811yescharacteristic
54C2×C4×C61#4111yescharacteristic
55C2×Dic61—22no—
56C2×Dic61—22no—
57C2×Dic61—42no—
58C8×C61—22no—
59C8×C61C4⋊C412yes—
60C8×C61C4⋊C412yes—
61#92418—22no—
62#92418C4212yes—
63#92418C4212yes—
64C22×C61—22no—
65C22×C61#11711yescharacteristic
66C22×C61C4×D411yescharacteristic
67C22×C61C4×Q811yescharacteristic
68C4×C61—42no—
69C4×C61C2×C4211yescharacteristic
70C4×C61C2×C4⋊C411yescharacteristic
71C4×C61C4×D411yescharacteristic
72C4×C61C4×Q811yescharacteristic
73Dic61—42no—
74Dic61—42no—
75#1773—611nomaximal, Sylow
76C2×C61—21no—
77C2×C61—21no—
78C2×C61C4×C4⋊C411yescharacteristic
79C2×C61#44412yes—
80C2×#108—611no—
81#427—611no—
82#405—611no—
83#405D6111yescharacteristic
84C2×#97—611no—
85#339—611no—
86#339—611no—
87C61#177311yescharacteristic, complemented, Sylow
88C2×M16—611no—
89C2×M16C2×D6111yescharacteristic
90C22×C8—611no—
91C22×C8C2×D6111yescharacteristic
92#117—611no—
93#117C2×D6111yescharacteristic
94C2×C42—611no—
95#108—614no—
96#107—612no—
97#106—612no—
98#97—21no—
99#97—614no—
100#97—1221no—
101C4×C8—21no—
102C4×C8—1221no—
103C22×C4—1221no—
104C22×C4C22×D6111yescharacteristic
105M16—21no—
106M16—612no—
107M16—1221no—
108M16C4×D6112yes—
109C2×C8—21no—
110C2×C8—612no—
111C2×C8—611no—
112C2×C8—611no—
113C2×C8—612no—
114C2×C8—1221no—
115C2×C8Dic12212yes—
116C2×C8C4×D6112yes—
117C2×C8C22⋊D6111yescharacteristic
118C2×C8C22⋊D6111yescharacteristic
119C4⋊C4—612no—
120C4⋊C4C4×D6112yes—
121C22⋊C4—21no—
122C22⋊C4—1221no—
123C42—21no—
124C42—612no—
125C42—1221no—
126C42—1221no—
127C23#1175822211yescharacteristic
128C2×C4—22no—
129C2×C4—1222no—
130C2×C4—1222no—
131C2×C4—2442no—
132C2×C4C2×Dic12211yescharacteristic
133C2×C4C2×C4×D6111yescharacteristic
134C2×C4C2×C4×D6111yescharacteristic
135C2×C4C2×C4×D6111yescharacteristic
136C2×C4#1175822211yescharacteristic
137C2×C4C2×C22⋊D6111yescharacteristic
138C8—22no—
139C8—612no—
140C8—612no—
141C8—1222no—
142C8#1175819612yes—
143C8#1175819612yes—
144C22—22no—
145C22#1451973411yescharacteristic
146C22C4×C22⋊D6111yescharacteristic
147C22C4×Dic12211yescharacteristic
148C4—42no—
149C4—2442no—
150C4—2442no—
151C4C42×D6111yescharacteristic
152C4C2×#1175819611yescharacteristic
153C4C4×C22⋊D6111yescharacteristic
154C4C4×Dic12211yescharacteristic
155C2—21no—
156C2—21no—
157C2C4×#1175819611yescharacteristic
158C2#1683988212yes—
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC4×C61C2×C42
FrattiniC22×C4C22×D61
FittingC61×#405C2
socleC22×C61C4×D4
hypercenter#405D61
hypocenterC61#1773
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
12. #14519712C4semidirect
13. #14519710C4semidirect
14. #14519708C4semidirect
16. #14519687C4semidirect
87. C61#1773semidirect