Finite Group Databasebeta

← #21461795

Subgroups — #21461795

Order 7808.

432 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×D61⋊C8C211yesmaximal, characteristic, complemented
2C2×#14519834C212yesmaximal, complemented
3C2×#14519834C211yesmaximal, characteristic, complemented
4#16840628C212yesmaximal, complemented
5C2×#14519739C211yesmaximal, characteristic
6C2×D61⋊C8—22no—
7C2×D61⋊C8—24no—
8C22×#92420C2212yes—
9C22×#92420C2212yes—
10#14519834—22no—
11#14519834—24no—
12C22×D244C411yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519739—22no—
16#14519739—22no—
17C2×#11758198C411yescharacteristic
18C2×#11758198C411yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20C2×C4⋊C4×C61C411yescharacteristic
21C23×D61C2×C411yescharacteristic
22C23×D61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61C2×C411yescharacteristic
27C22×Dic61C2311yescharacteristic
28C2×D244—22no—
29C2×D244—22no—
30C2×D244C814yescomplemented
31C2×C4×D61—22no—
32C2×C4×D61—22no—
33C2×C4×D61—22no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—22no—
37C2×C4×D61D412yes—
38C2×C4×D61D412yes—
39C2×#92420—22no—
40C2×#92420—22no—
41C2×#92420—22no—
42C2×#92420—22no—
43C2×#92420—22no—
44C2×#92420D414yescomplemented
45D61⋊C8—28no—
46C4⋊C4×C61—22no—
47#11758198—22no—
48#11758198—22no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C23×C61C22×C411yescharacteristic
52C22×D61—22no—
53C22×D61—22no—
54C22×D61—21no—
55C22×D61—22no—
56C22×D61—21no—
57C22×D61—22no—
58C22×D61C22⋊C412yes—
59C22×D61C2×C812yes—
60C22×D61C2×C812yescomplemented
61C22×D61M1612yes—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61C22⋊C412yes—
68C2×C4×C61C2×C812yescomplemented
69C2×Dic61—21no—
70C2×Dic61—22no—
71C2×Dic61C2×D412yes—
72C2×Dic61C2×D411yescharacteristic
73C2×Dic61C2×D411yescharacteristic
74C2×Dic61#4112yes—
75D244—28no—
76C4×D61—22no—
77C4×D61—24no—
78C4×D61—22no—
79C4×D61—41no—
80C4×D61—42no—
81C4×D61—41no—
82#92420—24no—
83#92420—42no—
84C22×C61C2×C22⋊C411yescharacteristic
85C22×C61C4×D412yes—
86C22×C61C22×C811yescharacteristic
87C22×C61C2×M1611yescharacteristic
88C22×C61#13112yes—
89C2×D61—22no—
90C2×D61—22no—
91C2×D61—24no—
92C2×D61—24no—
93C2×D61—22no—
94C2×D61—24no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—42no—
98C2×D61C22⋊C814yescomplemented
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—41no—
102Dic61—41no—
103Dic61#12011yescharacteristic
104Dic61#12112yes—
105Dic61#12311yescharacteristic
106#1869—611nomaximal, Sylow
107C2×C61#38611yescharacteristic
108C2×C61C2×C22⋊C811yescharacteristic
109C2×C61#40811yescharacteristic
110C2×C61C8×D412yes—
111C2×C61#43512yes—
112D61—24no—
113D61—42no—
114C23×C8—611no—
115C2×C4×D4—611no—
116C2×C22⋊C8—612no—
117C2×C22⋊C8—611no—
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#692311yescharacteristic
130C2×C22⋊C4—611no—
131C2×C22⋊C4—611no—
132C2×C42—611no—
133C22⋊C8—1224no—
134C22⋊C8—1222no—
135C24—611no—
136C24—611no—
137C2×D4—614no—
138C2×D4—1222no—
139C2×D4—1222no—
140C22×C4—611no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—611no—
144C22×C4—1222no—
145C22×C4—1222no—
146C22×C4—1222no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1222no—
150C22×C4C2×#692311yescharacteristic
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—22no—
161C22⋊C4—1222no—
162C22⋊C4—1222no—
163C42—1221no—
164C42—1221no—
165C23—612no—
166C23—612no—
167C23—612no—
168C23—612no—
169C23—1222no—
170C23—1222no—
171C23—1221no—
172C23—1222no—
173C23—1221no—
174C23—1222no—
175C23C22×#692311yescharacteristic
176D4—1228no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—612no—
185C2×C4—612no—
186C2×C4—1222no—
187C2×C4—1224no—
188C2×C4—1222no—
189C2×C4—1221no—
190C2×C4—1222no—
191C2×C4—2441no—
192C2×C4—2442no—
193C2×C4—2441no—
194C2×C4D61⋊C812yescomplemented
195C2×C4C22⋊#692312yes—
196C8—1224no—
197C8—2442no—
198C22—614no—
199C22—1222no—
200C22—1222no—
201C22—1224no—
202C22—1224no—
203C22—1222no—
204C22—1224no—
205C22—2441no—
206C22—2441no—
207C22—2442no—
208C22C2×C22⋊#692311yescharacteristic
209C22D4×#692312yes—
210C22C2×D61⋊C811yescharacteristic
211C22D61⋊M1611yescharacteristic
212C22#1451986512yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—611no—
217C4—612no—
218C4—611no—
219C4—2441no—
220C2—1224no—
221C2—2442no—
222C2#1684071011yescharacteristic
223C2D61⋊(C22⋊C8)11yescharacteristic
224C2#1684073711yescharacteristic
225C2#1684079012yes—
226C2#1684079212yes—
subgroupG/H
center, FrattiniC23C22×#6923
commutatorC22×C61C22×C8
FittingC2×C4⋊C4×C61C4
socleC23×C61C22×C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1869
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊C8C2semidirect
2. C2×#14519834C2semidirect
3. C2×#14519834C2semidirect
4. #16840628C2semidirect
30. C2×D244C8semidirect
44. C2×#92420D4semidirect
60. C22×D61C2×C8semidirect
68. C2×C4×C61C2×C8semidirect
98. C2×D61C22⋊C8semidirect
119. C61#1869semidirect
194. C2×C4D61⋊C8semidirect