Finite Group Databasebeta

← #21460692

Subgroups — #21460692

Order 7808.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×#14519834C211yesmaximal, characteristic
2C2×(C2×#6923)⋊C4C211yesmaximal, characteristic
3#16839619C211yesmaximal, characteristic
4C23×#6923—21no—
5C22×#92420—21no—
6#14519834—21no—
7#14519834C412yescomplemented
8(C2×#6923)⋊C4—21no—
9(C2×#6923)⋊C4C412yescomplemented
10C22×C4×D61C2211yescharacteristic
11C2×C4⋊Dic61C411yescharacteristic, complemented
12C2×#11758198—21no—
13#14519684—21no—
14C2×C4⋊C4×C61C411yescharacteristic, complemented
15C23×D61D411yescharacteristic
16C22×#6923—22no—
17C22×#6923—22no—
18C22×#6923—22no—
19C22×#6923—41no—
20C22×#6923—41no—
21C22×#6923—41no—
22C22×#6923—41no—
23C22×C4×C61—21no—
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C2×C4×D61—41no—
28C2×C4×D61—41no—
29C2×C4×D61C2×C411yescharacteristic
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61Q811yescharacteristic
33C2×#92420—22no—
34C2×#92420—41no—
35C2×#92420—41no—
36C4⋊C4×C61—41no—
37#11758198—41no—
38#11758198—41no—
39C4⋊Dic61—41no—
40C23×C61C22⋊C411yescharacteristic
41C22×D61—21no—
42C22×D61—21no—
43C22×D61—21no—
44C22×D61—21no—
45C22×D61C22⋊C411yescharacteristic
46C22×D61C4⋊C411yescharacteristic
47C22×D61D811yescharacteristic
48C22×D61SD1611yescharacteristic
49C22×D61SD1611yescharacteristic
50C22×D61Q1611yescharacteristic
51C2×#6923—24no—
52C2×#6923—42no—
53C2×#6923—42no—
54C2×#6923—42no—
55C2×#6923—42no—
56C2×#6923—42no—
57C2×#6923—42no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C4211yescharacteristic
64C2×C4×C61C4⋊C411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C4⋊C411yescharacteristic
72C4×D61—41no—
73C4×D61—41no—
74C4×D61—41no—
75C4×D61—41no—
76#92420—42no—
77C22×C61#9511yescharacteristic
78C22×C61#9911yescharacteristic
79C22×C61#9911yescharacteristic
80C22×C61#10211yescharacteristic
81C22×C61#10311yescharacteristic
82C22×C61#10411yescharacteristic
83C22×C61#10411yescharacteristic
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—21no—
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61#10211yescharacteristic
97C2×D61#10311yescharacteristic
98C2×D61#10611yescharacteristic
99C2×D61#10711yescharacteristic
100#6923—44no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—81no—
104Dic61—21no—
105Dic61—21no—
106Dic61—81no—
107#1294—611nomaximal, Sylow
108C2×C61#32711yescharacteristic
109C2×C61#32711yescharacteristic
110C2×C61#32811yescharacteristic
111C2×C61#32811yescharacteristic
112C2×C61#33911yescharacteristic
113C2×C61#34011yescharacteristic
114C2×C61#34211yescharacteristic
115D61—21no—
116D61—21no—
117D61—21no—
118D61—21no—
119C2×C22⋊C8—611no—
120#380—611no—
121C2×#95—611no—
122C61#129411yescharacteristic, complemented, Sylow
123C23×C4—611no—
124C23×C4—1221no—
125C22×C8—1221no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4#692311yescharacteristic, complemented
128C2×C22⋊C4—1221no—
129C22⋊C8—612no—
130C22⋊C8—1221no—
131#95—612no—
132#95—1221no—
133#95—1221no—
134C24—611no—
135C22×C4—21no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—1222no—
142C22×C4—1222no—
143C22×C4—1222no—
144C22×C4—1221no—
145C22×C4—2441no—
146C22×C4—2441no—
147C22×C4—2441no—
148C22×C4—2441no—
149C22×C4—2441no—
150C22×C4—2441no—
151C22×C4C2×#692311yescharacteristic
152C2×C8—1222no—
153C2×C8—2441no—
154C2×C8—2441no—
155C4⋊C4—41no—
156C4⋊C4—2441no—
157C22⋊C4—2441no—
158C22⋊C4—2441no—
159C23—611no—
160C23—611no—
161C23—611no—
162C23—611no—
163C23—611no—
164C23—611no—
165C23—1221no—
166C23—1221no—
167C23—1221no—
168C23—1221no—
169C23C22⋊#692311yescharacteristic
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1224no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4C4×#692311yescharacteristic
194C2×C4C4⋊#692311yescharacteristic
195C8—2442no—
196C22—611no—
197C22—611no—
198C22—611no—
199C22—611no—
200C22—1221no—
201C22—1221no—
202C22—1221no—
203C22—1221no—
204C22—1221no—
205C22—1221no—
206C22—1221no—
207C22—1221no—
208C22—1221no—
209C22—1221no—
210C22—1221no—
211C22—1221no—
212C22(C2×#6923)⋊C411yescharacteristic
213C22#1451983511yescharacteristic
214C22#1451983611yescharacteristic
215C22#1451983911yescharacteristic
216C22#1451984011yescharacteristic
217C22#1451984111yescharacteristic
218C22#1451984211yescharacteristic
219C4—21no—
220C4—21no—
221C4—81no—
222C4—1221no—
223C4—1221no—
224C4—4881no—
225C4—2444no—
226C2—1221no—
227C2—1221no—
228C2—1221no—
229C2—1221no—
230C2#1684061311yescharacteristic
231C2#1684061411yescharacteristic
232C2#1684061511yescharacteristic
233C2#1684061611yescharacteristic
234C2#1684063211yescharacteristic
235C2#1684063511yescharacteristic
236C2#1684064011yescharacteristic
subgroupG/H
centerC23C22⋊#6923
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
FittingC2×C4⋊C4×C61C4
socleC23×C61C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1294
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #14519834C4semidirect
9. (C2×#6923)⋊C4C4semidirect
11. C2×C4⋊Dic61C4semidirect
14. C2×C4⋊C4×C61C4semidirect
122. C61#1294semidirect
127. C2×C4⋊C4#6923semidirect