Finite Group Databasebeta

← #21461231

Subgroups — #21461231

Order 7808.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#16840784C211yesmaximal, characteristic, complemented
2#16840706C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840613C212yesmaximal
5#16840291C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C4⋊#92420—21no—
8#14519834C2212yes—
9#14519832—21no—
10(C2×#6923)⋊C4—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—42no—
33C22⋊C4×C61—21no—
34C22⋊C4×C61—21no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—21no—
37C22⋊Dic61—21no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C23×C61—21no—
50C22×D61C2×D411yescharacteristic
51C2×#6923—42no—
52C2×#6923—42no—
53C2×#6923—42no—
54Q8×C61—41no—
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C22⋊D61—41no—
61C22⋊D61—41no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—42no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68C4×D61—21no—
69C4×D61—21no—
70C4×D61—41no—
71C4×D61—41no—
72#92420—42no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—21no—
78C2×D61—21no—
79C2×D61AGL(1,ℤ/8)11yescharacteristic
80C2×D61#13711yescharacteristic
81#6923—82no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—41no—
86Dic61—21no—
87Dic61—21no—
88Dic61—21no—
89Dic61—41no—
90Dic61—41no—
91#1512—611nomaximal, Sylow
92C2×C61—81no—
93C2×C61#41011yescharacteristic
94C2×C61#41711yescharacteristic
95C2×C61#42111yescharacteristic
96D61—21no—
97D61—21no—
98#529—611no—
99#432—611no—
100#382—611no—
101#328—612no—
102#327—612no—
103C61#151211yescharacteristic, complemented, Sylow
104#126—1221no—
105#125—611no—
106#124#692311yescharacteristic, complemented
107#123—1221no—
108C22⋊Q8—611no—
109#121—611no—
110C4×Q8—611no—
111C4×D4—611no—
112C4×D4—1221no—
113#117—1221no—
114C2×C4⋊C4—1221no—
115C2×C42—611no—
116C4⋊C8—1221no—
117C22⋊C8—612no—
118#97—1221no—
119#95—612no—
120#95—1221no—
121C2×Q8C2×#692311yescharacteristic
122C2×D4—1221no—
123C2×D4C2×#692311yescharacteristic
124C22×C4—611no—
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—1221no—
128C22×C4—1222no—
129C2×C8—1222no—
130C4⋊C4—611no—
131C4⋊C4—611no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—2442no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C42—611no—
143C42—611no—
144C42—611no—
145C42—1221no—
146C42C2×#692311yescharacteristic
147C23—21no—
148C23—611no—
149Q8—41no—
150D4—41no—
151D4—2441no—
152D4—2441no—
153C2×C4—21no—
154C2×C4—611no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4C22⋊#692311yescharacteristic
168C2×C4C22⋊#692311yescharacteristic
169C2×C4C22×#692311yescharacteristic
170C8—2442no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—611no—
175C22—611no—
176C22—1221no—
177C22—1221no—
178C22C2×C22⋊#692311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—1221no—
184C4—1221no—
185C4—1221no—
186C4—4882no—
187C4—2441no—
188C4—2441no—
189C2—81no—
190C2—1221no—
191C2—1221no—
192C2#1684074211yescharacteristic
193C2#1684075311yescharacteristic
194C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1512
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. #16840784C2semidirect
2. #16840706C2semidirect
3. #16840616C2semidirect
13. #14519769C4semidirect
17. Q8×Dic61C4semidirect
18. D4×Dic61C4semidirect
22. #124×C61C4semidirect
103. C61#1512semidirect
106. #124#6923semidirect