Finite Group Databasebeta

← #21448952

Subgroups — #21448952

Order 7808.

552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14519758C211yesmaximal, characteristic
2#16839665C211yesmaximal, characteristic
3#16839650C212yesmaximal, complemented
4#16839650C212yesmaximal, complemented
5#16839649C212yesmaximal, complemented
6#16839613C212yesmaximal, complemented
7C22⋊C4×Dic61C212yesmaximal, complemented
8C4×C22⋊Dic61C212yesmaximal, complemented
9C61×#386C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11#14519758C418yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C4×Dic61C2212yes—
20C2×C4×Dic61C2212yes—
21C2×C4×Dic61C2212yes—
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2211yescharacteristic
28C23×C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2211yescharacteristic
31#95×C61C2212yes—
32C24×C61C2311yescharacteristic
33C24×C61C2311yescharacteristic
34C2×D4×C61—41no—
35C2×D4×C61—41no—
36C2×D4×C61C2×C414yes—
37C22×C4×C61—24no—
38C22×C4×C61—41no—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×Dic61—41no—
43C22×Dic61—41no—
44C22×Dic61C2×C414yescomplemented
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22⋊C4×C61—24no—
50C22⋊C4×C61—41no—
51C22⋊Dic61—24no—
52C22⋊Dic61—24no—
53C22⋊Dic61C2×C418yes—
54C22⋊Dic61C2×C414yescomplemented
55C4⋊Dic61—41no—
56#11758196—24no—
57#11758196C2×C418yescomplemented
58C4×Dic61—24no—
59C4×Dic61—41no—
60C4×Dic61—42no—
61C4×Dic61—42no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—21no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61C22×C412yes—
71C23×C61C22×C412yes—
72C23×C61C2411yescharacteristic
73D4×C61—44no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—44no—
82C2×C4×C61C22×C412yes—
83C2×C4×C61#4114yes—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—44no—
94C2×Dic61C22×C414yes—
95C2×Dic61C22×C414yes—
96C2×Dic61#4114yes—
97C22×C61—24no—
98C22×C61—24no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61C23×C411yescharacteristic
108C22×C61C2×#4112yes—
109C22×C61C2×#4112yes—
110C22×C61H(5,𝔽2)11yescharacteristic
111C22×C61H(5,𝔽2)11yescharacteristic
112C4×C61—22no—
113C4×C61—24no—
114C4×C61—42no—
115Dic61—24no—
116Dic61—24no—
117Dic61—24no—
118Dic61—42no—
119#2374—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61—42no—
122C2×C61C4×#4112yes—
123C2×C61#51811yescharacteristic
124C2×C61#55111yescharacteristic
125C2×C61#55312yes—
126C2×C61#55911yescharacteristic
127C2×#123—611no—
128#390—611no—
129#388—612no—
130#388—612no—
131#387—612no—
132#386D6111yescharacteristic
133C4×C4⋊C4—612no—
134C4×C22⋊C4—612no—
135C4×C22⋊C4—612no—
136C61#237411yescharacteristic, complemented, Sylow
137C22×D4C2×D6111yescharacteristic
138C23×C4—611no—
139C23×C4C2×D6111yescharacteristic
140#123—618no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—611no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—611no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4C2×D6112yes—
149C2×C22⋊C4C2×D6111yescharacteristic
150C2×C42—612no—
151C2×C42—612no—
152C2×C42—612no—
153C2×C42—611no—
154#95—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95C2×D6112yes—
159C24C22×D6111yescharacteristic
160C24C22×D6111yescharacteristic
161C2×D4—41no—
162C2×D4—41no—
163C2×D4C4×D6114yes—
164C22×C4—24no—
165C22×C4—41no—
166C22×C4—612no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—614no—
170C22×C4—612no—
171C22×C4—2441no—
172C22×C4—2441no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6112yes—
176C4⋊C4—618no—
177C4⋊C4—1224no—
178C4⋊C4—2441no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—618no—
182C22⋊C4—614no—
183C22⋊C4—1224no—
184C22⋊C4—1224no—
185C42—1224no—
186C42—2442no—
187C42—2441no—
188C42—2442no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—21no—
194C23—21no—
195C23—21no—
196C23—21no—
197C23C2×C4×D6112yes—
198C23C2×C4×D6112yes—
199C23C23×D6111yescharacteristic
200D4—44no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—44no—
209C2×C4—614no—
210C2×C4—614no—
211C2×C4—614no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—2444no—
222C2×C4C2×C4×D6112yes—
223C2×C4#1175822414yes—
224C22—24no—
225C22—24no—
226C22—22no—
227C22—22no—
228C22—42no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22C22×C4×D6111yescharacteristic
235C22#41×D6112yes—
236C22C2×#1175822412yes—
237C22#1451982211yescharacteristic
238C22#1451982211yescharacteristic
239C4—22no—
240C4—24no—
241C4—42no—
242C4—1224no—
243C4—1224no—
244C4—1224no—
245C4—2442no—
246C2—42no—
247C2—42no—
248C2C4×#1175822412yes—
249C2#1684023511yescharacteristic
250C2#1684044311yescharacteristic
251C2#1684045912yes—
252C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#386C2
socleC23×C61C24
hypercenter#386D61
hypocenterC61#2374
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #16839650C2semidirect
4. #16839650C2semidirect
5. #16839649C2semidirect
6. #16839613C2semidirect
7. C22⋊C4×Dic61C2semidirect
8. C4×C22⋊Dic61C2semidirect
11. #14519758C4semidirect
44. C22×Dic61C2×C4semidirect
54. C22⋊Dic61C2×C4semidirect
57. #11758196C2×C4semidirect
136. C61#2374semidirect