Finite Group Databasebeta

← #21461222

Subgroups — #21461222

Order 7808.

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

normal subgroups only

This group has 242 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×C4⋊#6923C211yesmaximal, characteristic, complemented
3#16840615C212yesmaximal, complemented
4#16840614C212yesmaximal
5#16840297C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C2×C4×#6923—21no—
8#14519844—21no—
9#14519834C2212yes—
10#14519832—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519772—21no—
13#14519765C411yescharacteristic, complemented
14#14519762—21no—
15#14519757C2211yescharacteristic
16#14519752C2211yescharacteristic
17#14519742C411yescharacteristic, complemented
18#14519739—21no—
19#14519739C411yescharacteristic, complemented
20#14519735—21no—
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×D244—21no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61C2311yescharacteristic
30C2×Dic122C2×C411yescharacteristic
31C2×#92420—22no—
32C4⋊#6923—24no—
33C4×#6923—42no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61C2×C411yescharacteristic
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C22×D61—21no—
51C22×D61C2×D411yescharacteristic
52C2×#6923—24no—
53C2×#6923—42no—
54C2×#6923—42no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64D244—41no—
65D244—41no—
66D244—41no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—22no—
70C4×D61—41no—
71C4×D61—42no—
72Dic122—41no—
73#92420—42no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—41no—
78C2×D61—41no—
79C2×D61—41no—
80C2×D61AGL(1,ℤ/8)11yescharacteristic
81C2×D61#13711yescharacteristic
82#6923—44no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61—41no—
88Dic61—21no—
89Dic61—21no—
90Dic61—41no—
91Dic61#10412yes—
92#1509—611nomaximal, Sylow
93C2×C61#41011yescharacteristic
94C2×C61#41711yescharacteristic
95C2×C61C2×#10411yescharacteristic
96D61—21no—
97D61—21no—
98D61—81no—
99#529—611no—
100#432—611no—
101C4×C4⋊C4—611no—
102#328—612no—
103#327—612no—
104C61#150911yescharacteristic, complemented, Sylow
105#126—1221no—
106#125#692311yescharacteristic, complemented
107#124—611no—
108#123—1221no—
109C22⋊Q8—611no—
110#121—611no—
111C4×Q8—611no—
112C4×D4—611no—
113C4×D4—1221no—
114#117—1221no—
115C2×C4⋊C4—1221no—
116C2×C42—611no—
117C2×C42—1221no—
118C4⋊C8—1221no—
119C22⋊C8—612no—
120#97—1221no—
121#95—612no—
122C2×Q8—611no—
123C2×D4—611no—
124C2×D4—1221no—
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—1221no—
129C22×C4—1222no—
130C2×C8—1222no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1224no—
136C4⋊C4C2×#692311yescharacteristic
137C4⋊C4C2×#692311yescharacteristic
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C42—611no—
144C42—611no—
145C42—611no—
146C42—1221no—
147C42—2442no—
148C42C2×#692311yescharacteristic
149C23—611no—
150C23—1221no—
151Q8—2441no—
152D4—2441no—
153D4—2441no—
154D4—2441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—611no—
160C2×C4—1222no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—1224no—
164C2×C4—1221no—
165C2×C4—2441no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22⋊#692311yescharacteristic
171C2×C4C22×#692311yescharacteristic
172C8—2442no—
173C22—611no—
174C22—611no—
175C22—1221no—
176C22—1221no—
177C22—2441no—
178C22—2441no—
179C22—2441no—
180C22C2×C22⋊#692311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—612no—
187C4—1221no—
188C4—1221no—
189C4—2444no—
190C4—2441no—
191C2—1221no—
192C2—1221no—
193C2—4881no—
194C2#1684074311yescharacteristic
195C2#1684075311yescharacteristic
196C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #16840785C2semidirect
2. C4×C4⋊#6923C2semidirect
3. #16840615C2semidirect
13. #14519765C4semidirect
17. #14519742C4semidirect
19. #14519739C4semidirect
22. #125×C61C4semidirect
104. C61#1509semidirect
106. #125#6923semidirect