Finite Group Databasebeta

← #21461279

Subgroups — #21461279

Order 7808.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840785C211yesmaximal, characteristic, complemented
2C4×#11758213C211yesmaximal, characteristic, complemented
3#16840618C212yesmaximal, complemented
4#16840617C212yesmaximal, complemented
5#124×D61C211yesmaximal, characteristic
6C2×#11758213—21no—
7#14519844—21no—
8#14519834—21no—
9#14519832C2212yescomplemented
10#14519832C2212yescomplemented
11C4×#92420—21no—
12C2×Q8×D61C411yescharacteristic
13C2×D4×D61C411yescharacteristic
14#14519766C2211yescharacteristic
15#14519765C411yescharacteristic
16#14519764C2211yescharacteristic
17#14519763—21no—
18#14519763—21no—
19C22⋊C4×D61—21no—
20C22⋊C4×D61—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic
23C23×D61—21no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27Q8×D61—42no—
28D4×D61—42no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×Dic122—21no—
35C2×Dic122C2×C411yescharacteristic
36C2×#92420—22no—
37C2×#92420—22no—
38#11758213—24no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C42×C61C2×C411yescharacteristic
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—21no—
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61—21no—
52C22×D61—21no—
53C22×D61—42no—
54C22×D61—42no—
55C22×D61—42no—
56C22×D61C22⋊C411yescharacteristic
57Q8×C61—41no—
58D4×C61—41no—
59C2×C4×C61—21no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C22⋊D61—42no—
64C2×Dic61—21no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68D244—41no—
69C4×D61—22no—
70C4×D61—22no—
71C4×D61—41no—
72C4×D61—42no—
73Dic122—42no—
74Dic122—41no—
75#92420—24no—
76#92420—42no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61C2×C22⋊C411yescharacteristic
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—84no—
87C2×D61#10412yes—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—41no—
92Dic61—21no—
93Dic61—21no—
94Dic61—41no—
95Dic61#10012yes—
96#1527—611nomaximal, Sylow
97C2×C61—81no—
98C2×C61C2×#10011yescharacteristic
99C2×C61C2×#10411yescharacteristic
100C2×C61#42111yescharacteristic
101D61—22no—
102D61—81no—
103C2×#124—611no—
104#432—611no—
105C4×M16—611no—
106#329—612no—
107#329—612no—
108C61#152711yescharacteristic, complemented, Sylow
109C22×Q8—611no—
110C22×D4—611no—
111C2×M16—1221no—
112#124—611no—
113#124—611no—
114#124—611no—
115#124—1221no—
116#124—1221no—
117#124#692311yescharacteristic
118C2×C22⋊C4—1221no—
119C2×C22⋊C4—1221no—
120C2×C42—611no—
121C4⋊C8—1221no—
122C22⋊C8—1221no—
123#97—612no—
124#97—612no—
125C4×C8—1221no—
126C24—1221no—
127C2×Q8—611no—
128C2×Q8—1221no—
129C2×Q8—2442no—
130C2×Q8C2×#692311yescharacteristic
131C2×D4—611no—
132C2×D4—1221no—
133C2×D4—2442no—
134C2×D4C2×#692311yescharacteristic
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
139M16—1224no—
140C2×C8—1222no—
141C2×C8—1222no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C22⋊C4—1221no—
150C42—611no—
151C42—611no—
152C42—611no—
153C42C2×#692311yescharacteristic
154C23—21no—
155C23—611no—
156C23—1221no—
157C23—2442no—
158C23—2442no—
159C23—2442no—
160Q8—41no—
161Q8—2441no—
162Q8—2442no—
163D4—41no—
164D4—2441no—
165D4—2442no—
166C2×C4—21no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—2441no—
174C2×C4—2442no—
175C2×C4C22⋊#692311yescharacteristic
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22×#692311yescharacteristic
178C8—1224no—
179C8—2442no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—612no—
184C22—1221no—
185C22—1221no—
186C22—4884no—
187C22—2441no—
188C22—2441no—
189C22—2441no—
190C22C2×C22⋊#692311yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—612no—
196C4—1221no—
197C4—1221no—
198C4—2441no—
199C2—81no—
200C2—1222no—
201C2—4881no—
202C2D61⋊#10011yescharacteristic
203C2D61⋊#10411yescharacteristic
204C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1527
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840785C2semidirect
2. C4×#11758213C2semidirect
3. #16840618C2semidirect
4. #16840617C2semidirect
9. #14519832C22semidirect
10. #14519832C22semidirect
108. C61#1527semidirect