Finite Group Databasebeta

← #21447489

Subgroups — #21447489

Order 7808.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840325C211yesmaximal, characteristic
2#16839734C212yesmaximal, complemented
3#16839555C211yesmaximal, characteristic, complemented
4#16839554C212yesmaximal, complemented
5C61×#353C211yesmaximal, characteristic, complemented
6C2×#11758224C2211yescharacteristic
7C2×D4×D61C411yescharacteristic, complemented
8#14519773C2211yescharacteristic
9#14519765C411yescharacteristic, complemented
10#14519764C411yescharacteristic, complemented
11#14519749—22no—
12#14519745—22no—
13#14519734C411yescharacteristic, complemented
14#14519733—22no—
15#14519692C2212yescomplemented
16#14519691—22no—
17#127×C61C2211yescharacteristic
18#99×C61C2212yescomplemented
19C23×D61—21no—
20C2×D4×C61—22no—
21C2×D4×C61C2×C411yescharacteristic
22C2×D4×C61C2311yescharacteristic
23C2×C22⋊D61—22no—
24C2×C22⋊D61—21no—
25C2×C22⋊D61D412yes—
26C22×Dic61D412yes—
27#11758224—42no—
28D4×D61—42no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61C2×C411yescharacteristic
31C2×Dic122C2×C411yescharacteristic
32C22⋊C4×C61—22no—
33C42×C61C2×C411yescharacteristic
34C22⋊Dic61—22no—
35C22⋊Dic61—22no—
36#11758198—21no—
37#11758198—22no—
38#11758196—21no—
39#11758196—42no—
40C4×Dic61—42no—
41C4×Dic61C2×C411yescharacteristic
42C23×C61—21no—
43C23×C61C2×D412yes—
44C22×D61—21no—
45C22×D61—42no—
46C22×D61—82no—
47C22×D61C22⋊C411yescharacteristic
48D4×C61—41no—
49D4×C61—41no—
50D4×C61—82no—
51C2×C4×C61—21no—
52C2×C4×C61—42no—
53C2×C4×C61C22×C411yescharacteristic
54C22⋊D61—42no—
55C22⋊D61—42no—
56C22⋊D61—82no—
57C2×Dic61—22no—
58C2×Dic61—22no—
59C2×Dic61—21no—
60C2×Dic61—42no—
61C2×Dic61C22⋊C412yes—
62C2×Dic61C22⋊C411yescharacteristic
63D244—41no—
64C4×D61—22no—
65Dic122—41no—
66C22×C61—22no—
67C22×C61—42no—
68C22×C61—42no—
69C22×C61—41no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—41no—
73C2×D61—42no—
74C2×D61—41no—
75C2×D61—84no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—82no—
79Dic61—22no—
80Dic61—41no—
81Dic61—82no—
82Dic61#9912yes—
83#2128—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—42no—
86C2×C61—81no—
87C2×C61C2×#9911yescharacteristic
88D61—41no—
89D61—81no—
90#535—611no—
91#410—612no—
92#353—611no—
93#353—612no—
94#353D6111yescharacteristic, complemented
95C61#212811yescharacteristic, complemented, Sylow
96C2×#41—611no—
97C22×D4—611no—
98#127—611no—
99#127C2×D6111yescharacteristic
100#124—611no—
101#124—611no—
102#121—1222no—
103#120—1222no—
104#117—611no—
105#117—1222no—
106#99—612no—
107#99—1222no—
108#99C2×D6112yescomplemented
109C24—1221no—
110#41—2442no—
111C2×Q8—611no—
112C2×D4—22no—
113C2×D4—612no—
114C2×D4—611no—
115C2×D4—1221no—
116C2×D4—1222no—
117C2×D4—2442no—
118C2×D4C4×D6111yescharacteristic
119C2×D4C22×D6111yescharacteristic
120C22×C4—612no—
121C22×C4—611no—
122C4⋊C4—1221no—
123C4⋊C4—2442no—
124C22⋊C4—22no—
125C22⋊C4—1222no—
126C22⋊C4—1221no—
127C22⋊C4—1222no—
128C22⋊C4—1222no—
129C42—611no—
130C42—2442no—
131C42C4×D6111yescharacteristic
132C23—21no—
133C23—611no—
134C23—1221no—
135C23—4882no—
136C23—2442no—
137C23D4×D6112yes—
138Q8—2441no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—4882no—
143D4—2441no—
144D4—2442no—
145D4—2442no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—611no—
149C2×C4—612no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—2442no—
155C2×C4C2×C4×D6111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—1221no—
161C22—4884no—
162C22—2442no—
163C22—2441no—
164C22—2441no—
165C22C22⋊C4×D6111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—612no—
170C4—1222no—
171C4—4882no—
172C4—2441no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—4881no—
177C2—2441no—
178C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#353C2
socleC2×C61C2×#99
hypercenter#353D61
hypocenterC61#2128
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #16839734C2semidirect
3. #16839555C2semidirect
4. #16839554C2semidirect
5. C61×#353C2semidirect
7. C2×D4×D61C4semidirect
9. #14519765C4semidirect
10. #14519764C4semidirect
13. #14519734C4semidirect
15. #14519692C22semidirect
18. #99×C61C22semidirect
94. #353D61semidirect
95. C61#2128semidirect
108. #99C2×D61semidirect