Finite Group Databasebeta

← #21461220

Subgroups — #21461220

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#16840616C212yesmaximal, complemented
4#16840613C212yesmaximal
5#16840291C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C2×C4×#6923—21no—
8#14519844—21no—
9#14519834C2212yes—
10#14519832—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic, complemented
14#14519759—21no—
15#14519753C2211yescharacteristic
16#14519748C2211yescharacteristic
17Q8×Dic61C411yescharacteristic, complemented
18D4×Dic61C411yescharacteristic, complemented
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61—21no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4⋊#6923—24no—
33C4×#6923—42no—
34C22⋊C4×C61—21no—
35C22⋊C4×C61—21no—
36C42×C61C2×C411yescharacteristic
37C22⋊Dic61—21no—
38C22⋊Dic61—21no—
39#11758198—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C23×C61—21no—
51C22×D61C2×D411yescharacteristic
52C2×#6923—24no—
53C2×#6923—42no—
54C2×#6923—42no—
55Q8×C61—41no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—41no—
62C22⋊D61—41no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—42no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69C4×D61—21no—
70C4×D61—21no—
71C4×D61—22no—
72C4×D61—41no—
73#92420—42no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61AGL(1,ℤ/8)11yescharacteristic
81C2×D61#13711yescharacteristic
82#6923—44no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87Dic61—21no—
88Dic61—21no—
89Dic61—41no—
90Dic61—41no—
91Dic61#10412yes—
92#1509—611nomaximal, Sylow
93C2×C61—81no—
94C2×C61#41011yescharacteristic
95C2×C61#41711yescharacteristic
96C2×C61C2×#10411yescharacteristic
97D61—21no—
98D61—21no—
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—611no—
107#124#692311yescharacteristic, complemented
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×Q8C2×#692311yescharacteristic
123C2×D4—1221no—
124C2×D4C2×#692311yescharacteristic
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—1221no—
129C22×C4—1222no—
130C2×C8—1222no—
131C4⋊C4—611no—
132C4⋊C4—611no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1224no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C42—611no—
144C42—611no—
145C42—611no—
146C42—1221no—
147C42—2442no—
148C42C2×#692311yescharacteristic
149C23—21no—
150C23—611no—
151Q8—41no—
152D4—41no—
153D4—2441no—
154D4—2441no—
155C2×C4—21no—
156C2×C4—611no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—1222no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1224no—
163C2×C4—1221no—
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—41no—
174C22—41no—
175C22—41no—
176C22—611no—
177C22—611no—
178C22—1221no—
179C22—1221no—
180C22C2×C22⋊#692311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—612no—
186C4—1221no—
187C4—1221no—
188C4—2444no—
189C4—2441no—
190C4—2441no—
191C2—81no—
192C2—1221no—
193C2—1221no—
194C2#1684074211yescharacteristic
195C2#1684075311yescharacteristic
196C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1509
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×C4⋊#6923C2semidirect
3. #16840616C2semidirect
13. #14519769C4semidirect
17. Q8×Dic61C4semidirect
18. D4×Dic61C4semidirect
22. #124×C61C4semidirect
104. C61#1509semidirect
107. #124#6923semidirect