Finite Group Databasebeta

← #21460681

Subgroups — #21460681

Order 7808.

228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16839621C211yesmaximal, characteristic
4C2×D61⋊C8C412yescomplemented
5C2×C4⋊#6923—21no—
6C2×C22⋊#6923—21no—
7#14519834—21no—
8C22⋊#92420—21no—
9(C2×#6923)⋊C4C412yescomplemented
10C22×C4×D61C2211yescharacteristic
11C2×#11758196—21no—
12C2×#11758198—21no—
13#14519684C411yescharacteristic, complemented
14#95×C61C411yescharacteristic, complemented
15C23×D61D411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61—21no—
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61—21no—
20C22×Dic61D411yescharacteristic
21C2×C4×D61—42no—
22C2×C4×D61C2×C411yescharacteristic
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61D411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C22⋊#6923—41no—
27C22⋊#6923—41no—
28C2×#92420—22no—
29C4⋊#6923—42no—
30D61⋊C8—42no—
31#11758198—41no—
32#11758198—41no—
33#11758196—42no—
34C23×C61C22⋊C411yescharacteristic
35C22×D61—41no—
36C22×D61—41no—
37C22×D61C22⋊C411yescharacteristic
38C22×D61C4⋊C411yescharacteristic
39C22×D61D811yescharacteristic
40C22×D61SD1611yescharacteristic
41C22×D61SD1611yescharacteristic
42C22×D61Q1611yescharacteristic
43C2×#6923—42no—
44C2×#6923—42no—
45C2×#6923—42no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61C4211yescharacteristic
51C2×C4×C61C4⋊C411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61—41no—
54C2×Dic61—41no—
55C2×Dic61—41no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C4⋊C411yescharacteristic
58C4×D61—22no—
59C4×D61—22no—
60C4×D61—41no—
61C4×D61—41no—
62#92420—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61#9511yescharacteristic
66C22×C61#10211yescharacteristic
67C22×C61#10311yescharacteristic
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—21no—
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61#10211yescharacteristic
77C2×D61#10311yescharacteristic
78C2×D61#10611yescharacteristic
79C2×D61#10711yescharacteristic
80#6923—82no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—81no—
84Dic61—21no—
85Dic61—81no—
86Dic61#9912yes—
87#1289—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—21no—
90C2×C61H(3,ℤ/4)11yescharacteristic
91C2×C61#34011yescharacteristic
92C2×C61#34211yescharacteristic
93D61—21no—
94D61—21no—
95D61—21no—
96D61—21no—
97C2×C22⋊C8—611no—
98#380—611no—
99#380—611no—
100C61#128911yescharacteristic, complemented, Sylow
101C23×C4—611no—
102C22×C8—612no—
103C2×C4⋊C4—1221no—
104C2×C4⋊C4—1221no—
105C2×C22⋊C4—1221no—
106C2×C22⋊C4—1221no—
107C22⋊C8—1221no—
108C22⋊C8—1221no—
109#95—612no—
110#95—611no—
111#95#692311yescharacteristic, complemented
112C24—611no—
113C22×C4—21no—
114C22×C4—611no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1222no—
120C22×C4—1221no—
121C22×C4—2442no—
122C22×C4C2×#692311yescharacteristic
123C2×C8—1222no—
124C2×C8—2442no—
125C4⋊C4—2442no—
126C4⋊C4—2442no—
127C22⋊C4—2441no—
128C22⋊C4—2441no—
129C22⋊C4—2441no—
130C22⋊C4—2441no—
131C23—611no—
132C23—611no—
133C23—611no—
134C23—611no—
135C23—611no—
136C23—611no—
137C23—2441no—
138C23—2441no—
139C23C22⋊#692311yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—1222no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2441no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4—2442no—
154C2×C4—2442no—
155C2×C4—2442no—
156C2×C4—2441no—
157C2×C4C4×#692311yescharacteristic
158C2×C4C4⋊#692311yescharacteristic
159C8—2442no—
160C22—21no—
161C22—21no—
162C22—611no—
163C22—611no—
164C22—611no—
165C22—611no—
166C22—1221no—
167C22—1221no—
168C22—1221no—
169C22—1221no—
170C22—2441no—
171C22—2441no—
172C22—2441no—
173C22—2441no—
174C22(C2×#6923)⋊C411yescharacteristic
175C22#1451983911yescharacteristic
176C22#1451984011yescharacteristic
177C4—21no—
178C4—21no—
179C4—81no—
180C4—612no—
181C4—1221no—
182C4—4881no—
183C4—4882no—
184C2—21no—
185C2—21no—
186C2—1221no—
187C2—1221no—
188C2—1221no—
189C2—1221no—
190C2#1684062911yescharacteristic
191C2#1684063511yescharacteristic
192C2#1684063911yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
Fitting#95×C61C4
socleC22×C61#95
hypercenter#95#6923
hypocenterC61#1289
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D61⋊C8C4semidirect
9. (C2×#6923)⋊C4C4semidirect
13. #14519684C4semidirect
14. #95×C61C4semidirect
100. C61#1289semidirect
111. #95#6923semidirect