Finite Group Databasebeta

← #21461794

Subgroups — #21461794

Order 7808.

432 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C23×#92420C211yesmaximal, characteristic, complemented
2C2×#14519834C212yesmaximal, complemented
3C2×C22⋊#92420C211yesmaximal, characteristic, complemented
4#16840628C212yesmaximal, complemented
5C2×#14519737C211yesmaximal, characteristic
6C22×#92420—22no—
7C22×#92420—24no—
8C22×#92420C2212yes—
9C22×#92420C2212yes—
10#14519834—24no—
11C22⋊#92420—22no—
12C22×C22⋊D61C411yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519737—22no—
16#14519737—22no—
17C2×#11758196C411yescharacteristic
18C2×#11758198C411yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20C2×C22⋊C4×C61C411yescharacteristic
21C24×C61C2×C411yescharacteristic
22C23×D61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61—22no—
26C2×C22⋊D61—22no—
27C2×C22⋊D61C814yescomplemented
28C22×Dic61—22no—
29C22×Dic61—22no—
30C22×Dic61C2×C411yescharacteristic
31C22×Dic61C2×C411yescharacteristic
32C22×Dic61D412yes—
33C22×Dic61D412yes—
34C22×Dic61C2311yescharacteristic
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61—22no—
39C2×#92420—28no—
40C2×#92420—22no—
41C2×#92420—22no—
42C2×#92420—22no—
43C2×#92420—22no—
44C2×#92420—22no—
45C2×#92420D414yescomplemented
46C22⋊C4×C61—22no—
47#11758198—22no—
48#11758196—22no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C23×C61—22no—
52C23×C61—22no—
53C23×C61C22⋊C412yes—
54C23×C61C2×C812yes—
55C23×C61M1612yes—
56C23×C61C22×C411yescharacteristic
57C22×D61—21no—
58C22×D61—22no—
59C22×D61—21no—
60C22×D61—22no—
61C22×D61C2×C812yescomplemented
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C22⋊D61—28no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—22no—
71C2×Dic61—24no—
72C2×Dic61—22no—
73C2×Dic61C22⋊C412yes—
74C2×Dic61C2×C812yescomplemented
75C2×Dic61C2×D412yes—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61#4112yes—
79C4×D61—41no—
80C4×D61—42no—
81C4×D61—41no—
82#92420—24no—
83#92420—42no—
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—24no—
87C22×C61—24no—
88C22×C61C22⋊C814yescomplemented
89C22×C61C2×C22⋊C411yescharacteristic
90C22×C61C4×D412yes—
91C22×C61C22×C811yescharacteristic
92C22×C61C2×M1611yescharacteristic
93C22×C61#13112yes—
94C2×D61—22no—
95C2×D61—24no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—42no—
99C4×C61—41no—
100C4×C61—41no—
101Dic61—22no—
102Dic61—22no—
103Dic61#12011yescharacteristic
104Dic61#12112yes—
105Dic61#12311yescharacteristic
106#1869—611nomaximal, Sylow
107C2×C61—24no—
108C2×C61#38611yescharacteristic
109C2×C61C2×C22⋊C811yescharacteristic
110C2×C61#40811yescharacteristic
111C2×C61C8×D412yes—
112C2×C61#43512yes—
113D61—42no—
114C23×C8—611no—
115C2×C4×D4—611no—
116C2×C22⋊C8—611no—
117C2×C22⋊C8—612no—
118#336—612no—
119C61#186911yescharacteristic, complemented, Sylow
120C22×D4—611no—
121C23×C4—611no—
122C23×C4—611no—
123C22×C8—612no—
124C22×C8—612no—
125C22×C8—1224no—
126C22×C8—1222no—
127C4×D4—1222no—
128C4×D4—1222no—
129C2×C4⋊C4—611no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4#692311yescharacteristic
132C2×C42—611no—
133C22⋊C8—1224no—
134C22⋊C8—1222no—
135C24—611no—
136C24C2×#692311yescharacteristic
137C2×D4—614no—
138C2×D4—1222no—
139C2×D4—1222no—
140C22×C4—611no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1222no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4—1222no—
149C22×C4—1222no—
150C22×C4—1222no—
151C22×C4C2×#692311yescharacteristic
152C22×C4C2×#692311yescharacteristic
153C2×C8—614no—
154C2×C8—1222no—
155C2×C8—1222no—
156C2×C8—1228no—
157C2×C8—1222no—
158C2×C8—1222no—
159C2×C8—1222no—
160C4⋊C4—1222no—
161C22⋊C4—22no—
162C22⋊C4—1222no—
163C42—1221no—
164C42—1221no—
165C23—22no—
166C23—22no—
167C23—612no—
168C23—1221no—
169C23—1222no—
170C23—1221no—
171C23—1222no—
172C23D61⋊C812yes—
173C23#1175821312yes—
174C23C22⋊#692312yes—
175C23C22×#692311yescharacteristic
176D4—1228no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—612no—
184C2×C4—612no—
185C2×C4—612no—
186C2×C4—612no—
187C2×C4—1222no—
188C2×C4—1224no—
189C2×C4—1222no—
190C2×C4—1221no—
191C2×C4—1222no—
192C2×C4—1221no—
193C2×C4—2441no—
194C2×C4—2442no—
195C2×C4—2441no—
196C8—1224no—
197C8—2442no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—1222no—
203C22—1224no—
204C22—2441no—
205C22—2441no—
206C22—2442no—
207C22#1451983414yescomplemented
208C22C2×C22⋊#692311yescharacteristic
209C22D4×#692312yes—
210C22C2×D61⋊C811yescharacteristic
211C22C2×#1175821311yescharacteristic
212C22#1451986412yes—
213C4—41no—
214C4—41no—
215C4—611no—
216C4—612no—
217C4—611no—
218C4—1222no—
219C4—1222no—
220C2—24no—
221C2—2442no—
222C2#1684071011yescharacteristic
223C2C2×#1451983411yescharacteristic
224C2#1684073511yescharacteristic
225C2#1684078912yes—
226C2#1684079112yes—
subgroupG/H
center, FrattiniC23C22×#6923
commutatorC22×C61C22×C8
FittingC2×C22⋊C4×C61C4
socleC23×C61C22×C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1869
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#92420C2semidirect
2. C2×#14519834C2semidirect
3. C2×C22⋊#92420C2semidirect
4. #16840628C2semidirect
27. C2×C22⋊D61C8semidirect
45. C2×#92420D4semidirect
61. C22×D61C2×C8semidirect
74. C2×Dic61C2×C8semidirect
88. C22×C61C22⋊C8semidirect
119. C61#1869semidirect
207. C22#14519834semidirect