Finite Group Databasebeta

← #21448969

Subgroups — #21448969

Order 7808.

512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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#16839657C212yesmaximal, complemented
3#16839656C212yesmaximal, complemented
4#16839650C212yesmaximal, complemented
5#16839646C212yesmaximal, complemented
6#16839642C211yesmaximal, characteristic
7#16839634C212yesmaximal, complemented
8#16839620C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12#14519758C418yescomplemented
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C4×Dic61C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2212yes—
31C2×C42×C61C2211yescharacteristic
32C24×C61C2311yescharacteristic
33C24×C61C2311yescharacteristic
34C2×D4×C61—41no—
35C2×D4×C61—41no—
36C2×D4×C61C2×C414yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×Dic61—41no—
41C22×Dic61—41no—
42C22×Dic61—41no—
43C22×Dic61—42no—
44C22×Dic61C2×C414yescomplemented
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C4⋊C4×C61—41no—
50C22⋊C4×C61—42no—
51C22⋊C4×C61—42no—
52C42×C61—41no—
53C22⋊Dic61—42no—
54C22⋊Dic61—41no—
55C22⋊Dic61C2×C418yes—
56C22⋊Dic61C2×C414yescomplemented
57#11758196—42no—
58#11758196—42no—
59#11758196—42no—
60#11758196C2×C418yescomplemented
61C4×Dic61—42no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61—22no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—21no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61C22×C412yes—
71C23×C61C22×C412yes—
72C23×C61C2411yescharacteristic
73D4×C61—44no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C22×C412yes—
83C2×Dic61—22no—
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×Dic61—44no—
95C2×Dic61C22×C414yes—
96C2×Dic61C22×C414yes—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61—24no—
100C22×C61—24no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61C23×C411yescharacteristic
108C22×C61H(5,𝔽2)11yescharacteristic
109C22×C61H(5,𝔽2)11yescharacteristic
110C22×C61H(5,𝔽2)12yes—
111C22×C612−1+412yes—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—42no—
115Dic61—24no—
116Dic61—24no—
117Dic61—42no—
118Dic61—42no—
119#2376—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61—42no—
122C2×C61#51811yescharacteristic
123C2×C61#52012yes—
124C2×C61#56011yescharacteristic
125C2×C61#56212yes—
126C2×C61#56311yescharacteristic
127C2×#123—611no—
128#390D6111yescharacteristic
129#389—612no—
130#388—612no—
131#388—612no—
132#387—612no—
133#386—611no—
134#385—612no—
135#380—612no—
136C61#237611yescharacteristic, complemented, Sylow
137C22×D4C2×D6111yescharacteristic
138C23×C4—611no—
139C23×C4—611no—
140#123—618no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C22⋊C4—612no—
147C2×C22⋊C4—611no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4C2×D6112yes—
151C2×C22⋊C4C2×D6112yes—
152C2×C42—612no—
153C2×C42C2×D6111yescharacteristic
154#95—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95—612no—
159C24C22×D6111yescharacteristic
160C24C22×D6111yescharacteristic
161C2×D4—41no—
162C2×D4—41no—
163C2×D4C4×D6114yes—
164C22×C4—612no—
165C22×C4—612no—
166C22×C4—614no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4—2442no—
172C22×C4—2441no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C4⋊C4—41no—
177C4⋊C4—618no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—618no—
184C22⋊C4—614no—
185C22⋊C4—2442no—
186C22⋊C4—2441no—
187C42—41no—
188C42—2442no—
189C23—22no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23C2×C4×D6112yes—
198C23C2×C4×D6112yes—
199C23C23×D6111yescharacteristic
200D4—44no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—614no—
210C2×C4—614no—
211C2×C4—1222no—
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×C4—2444no—
223C2×C4C2×C4×D6112yes—
224C22—22no—
225C22—22no—
226C22—24no—
227C22—24no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22C22×C4×D6111yescharacteristic
235C22#1451982211yescharacteristic
236C22#1451982211yescharacteristic
237C22#1451982212yes—
238C22#1451982412yes—
239C4—22no—
240C4—42no—
241C4—42no—
242C4—1224no—
243C4—1224no—
244C4—2442no—
245C4—2442no—
246C2—42no—
247C2—42no—
248C2#1684023511yescharacteristic
249C2#1684024112yes—
250C2#1684049911yescharacteristic
251C2#1684050712yes—
252C2#1684051211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#390C2
socleC23×C61C24
hypercenter#390D61
hypocenterC61#2376
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #16839657C2semidirect
3. #16839656C2semidirect
4. #16839650C2semidirect
5. #16839646C2semidirect
7. #16839634C2semidirect
8. #16839620C2semidirect
12. #14519758C4semidirect
44. C22×Dic61C2×C4semidirect
56. C22⋊Dic61C2×C4semidirect
60. #11758196C2×C4semidirect
136. C61#2376semidirect