Finite Group Databasebeta

← #21446798

Subgroups — #21446798

Order 7808.

244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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#16840315C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic
3#16839608C211yesmaximal, characteristic
4#16839523C211yesmaximal, characteristic
5#16839522C211yesmaximal, characteristic
6#16839521C211yesmaximal, characteristic
7C61×#339C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9#14519776C412yescomplemented
10#14519768C412yescomplemented
11#14519754—22no—
12C4×Dic122—22no—
13#14519736C2211yescharacteristic
14C2×C4×Dic61C2211yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16#14519706—22no—
17#14519684—22no—
18C2×M16×C61C2211yescharacteristic
19#117×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61C2311yescharacteristic
23C22×Dic61—21no—
24C22×Dic61D412yes—
25C2×Dic122—22no—
26M16×C61—21no—
27M16×C61—21no—
28C2×C8×C61—21no—
29C4⋊C4×C61C2×C412yes—
30C22⋊C4×C61—21no—
31C42×C61—21no—
32C42×C61—21no—
33C42×C61Q812yescomplemented
34C22⋊Dic61—21no—
35C4⋊Dic61—22no—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—21no—
40C4×Dic61—21no—
41C4×Dic61C2×C411yescharacteristic
42C4×Dic61C2×C411yescharacteristic
43C4×Dic61D412yes—
44C4×Dic61Q812yescomplemented
45#11758194—21no—
46#11758194—21no—
47C2×#92418—21no—
48C23×C61C2×D411yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—42no—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×Q811yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—22no—
59C2×Dic61—22no—
60C2×Dic61—42no—
61C2×Dic61—42no—
62C2×Dic61C22⋊C412yes—
63C2×Dic61C22⋊C412yes—
64Dic122—44no—
65C8×C61—41no—
66#92418—41no—
67C22×C61—22no—
68C22×C61C2×C22⋊C411yescharacteristic
69C22×C61C22⋊Q811yescharacteristic
70C22×C61C22⋊Q811yescharacteristic
71C4×C61—42no—
72C4×C61—42no—
73C4×C61C4×Q811yescharacteristic
74C4×C61C4×Q811yescharacteristic
75C4×C61#12411yescharacteristic
76C4×C61C4⋊Q811yescharacteristic
77Dic61—22no—
78Dic61—22no—
79Dic61—42no—
80Dic61—42no—
81#1995—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—21no—
84C2×C61#39111yescharacteristic
85C2×C61#42112yes—
86#533—611no—
87#423—611no—
88#376—611no—
89#339—611no—
90#339—611no—
91#339—611no—
92#339D6111yescharacteristic
93C61#199511yescharacteristic, complemented, Sylow
94C2×M16—611no—
95C2×M16C2×D6111yescharacteristic
96C4⋊Q8—612no—
97#125—612no—
98C22⋊Q8—1222no—
99C4×Q8—1222no—
100#117—611no—
101#117C2×D6111yescharacteristic
102C2×C42—611no—
103C2×C42—611no—
104C2×C42C2×D6111yescharacteristic
105C4⋊C8—1222no—
106#95—1222no—
107C2×Q8—1222no—
108C22×C4—21no—
109C22×C4—612no—
110C22×C4—1221no—
111C22×C4C22×D6111yescharacteristic
112M16—21no—
113M16—21no—
114M16—1221no—
115M16—1221no—
116C2×C8—21no—
117C2×C8—1221no—
118C4⋊C4—612no—
119C4⋊C4—1222no—
120C4⋊C4—1222no—
121C4⋊C4—1222no—
122C4⋊C4C4×D6112yes—
123C22⋊C4—21no—
124C22⋊C4—1221no—
125C42—21no—
126C42—21no—
127C42—611no—
128C42—611no—
129C42—612no—
130C42—612no—
131C42—1221no—
132C42—1221no—
133C42Dic12212yescomplemented
134C23D4×D6111yescharacteristic
135Q8—2444no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—612no—
140C2×C4—612no—
141C2×C4—1222no—
142C2×C4—1222no—
143C2×C4—2442no—
144C2×C4—2442no—
145C2×C4C2×Dic12211yescharacteristic
146C2×C4C2×C4×D6111yescharacteristic
147C2×C4#1175822211yescharacteristic
148C2×C4D4×D6111yescharacteristic
149C2×C4#1175822411yescharacteristic
150C2×C4Q8×D6111yescharacteristic
151C8—41no—
152C8—2441no—
153C22—22no—
154C22C22⋊C4×D6111yescharacteristic
155C22#1451975411yescharacteristic
156C22#1451975511yescharacteristic
157C4—42no—
158C4—42no—
159C4—1222no—
160C4—1222no—
161C4—2442no—
162C4—2442no—
163C4#1451974211yescharacteristic
164C4C4×Dic12211yescharacteristic
165C4#1451976311yescharacteristic
166C4#1451977611yescharacteristic
167C2—21no—
168C2—21no—
169C2#1683966611yescharacteristic
170C2#1683977712yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61C2×C22⋊C4
hypercenter#339D61
hypocenterC61#1995
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14519776C4semidirect
10. #14519768C4semidirect
33. C42×C61Q8semidirect
44. C4×Dic61Q8semidirect
93. C61#1995semidirect
133. C42Dic122semidirect