Finite Group Databasebeta

← #21446794

Subgroups — #21446794

Order 7808.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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
3C42×Dic61C211yesmaximal, 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×Dic61—22no—
15C2×C4×Dic61C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519706—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—28no—
40C4×Dic61—21no—
41C4×Dic61—21no—
42C4×Dic61C2×C411yescharacteristic
43C4×Dic61C2×C411yescharacteristic
44C4×Dic61D412yes—
45C4×Dic61Q812yescomplemented
46#11758194—21no—
47#11758194—21no—
48C2×#92418—21no—
49C23×C61C2×D411yescharacteristic
50C2×C4×C61—24no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61C2×Q811yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×Dic61—24no—
60C2×Dic61—22no—
61C2×Dic61—24no—
62C2×Dic61—22no—
63C2×Dic61C22⋊C412yes—
64C2×Dic61C22⋊C412yes—
65Dic122—44no—
66C8×C61—41no—
67#92418—41no—
68C22×C61—22no—
69C22×C61C2×C22⋊C411yescharacteristic
70C22×C61C22⋊Q811yescharacteristic
71C22×C61C22⋊Q811yescharacteristic
72C4×C61—24no—
73C4×C61—42no—
74C4×C61C4×Q811yescharacteristic
75C4×C61C4×Q811yescharacteristic
76C4×C61#12411yescharacteristic
77C4×C61C4⋊Q811yescharacteristic
78Dic61—24no—
79Dic61—22no—
80Dic61—42no—
81Dic61#10414yes—
82#1994—611nomaximal, Sylow
83C2×C61—21no—
84C2×C61—21no—
85C2×C61#39111yescharacteristic
86C2×C61C2×#10412yes—
87#533—611no—
88#423—611no—
89C43—611no—
90#339—611no—
91#339—611no—
92#339—611no—
93#339D6111yescharacteristic
94C61#199411yescharacteristic, complemented, Sylow
95C2×M16—611no—
96C2×M16C2×D6111yescharacteristic
97C4⋊Q8—612no—
98#125—612no—
99C22⋊Q8—1222no—
100C4×Q8—1222no—
101#117—611no—
102#117C2×D6111yescharacteristic
103C2×C42—611no—
104C2×C42—611no—
105C2×C42—1222no—
106C2×C42C2×D6111yescharacteristic
107C4⋊C8—1222no—
108C2×Q8—1222no—
109C22×C4—21no—
110C22×C4—612no—
111C22×C4—1221no—
112C22×C4C22×D6111yescharacteristic
113M16—21no—
114M16—21no—
115M16—1221no—
116M16—1221no—
117C2×C8—21no—
118C2×C8—1221no—
119C4⋊C4—612no—
120C4⋊C4—1222no—
121C4⋊C4—1222no—
122C4⋊C4—1222no—
123C4⋊C4C4×D6112yes—
124C22⋊C4—21no—
125C22⋊C4—1221no—
126C42—21no—
127C42—21no—
128C42—611no—
129C42—611no—
130C42—612no—
131C42—612no—
132C42—1228no—
133C42—1221no—
134C42—1221no—
135C42Dic12212yescomplemented
136C23D4×D6111yescharacteristic
137Q8—2444no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—612no—
142C2×C4—612no—
143C2×C4—1224no—
144C2×C4—1224no—
145C2×C4—1222no—
146C2×C4—1222no—
147C2×C4C2×Dic12211yescharacteristic
148C2×C4C2×C4×D6111yescharacteristic
149C2×C4#1175822211yescharacteristic
150C2×C4D4×D6111yescharacteristic
151C2×C4#1175822411yescharacteristic
152C2×C4Q8×D6111yescharacteristic
153C8—41no—
154C8—2441no—
155C22—22no—
156C22C22⋊C4×D6111yescharacteristic
157C22#1451975411yescharacteristic
158C22#1451975511yescharacteristic
159C4—24no—
160C4—42no—
161C4—614no—
162C4—1224no—
163C4—1222no—
164C4—2442no—
165C4#1451974211yescharacteristic
166C4C4×Dic12211yescharacteristic
167C4#1451976311yescharacteristic
168C4#1451977611yescharacteristic
169C2—21no—
170C2—21no—
171C2#1683966611yescharacteristic
172C2#104×D6112yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61C2×C22⋊C4
hypercenter#339D61
hypocenterC61#1994
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
45. C4×Dic61Q8semidirect
94. C61#1994semidirect
135. C42Dic122semidirect