Finite Group Databasebeta

← #21453762

Subgroups — #21453762

Order 7808.

480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#16839704C212yesmaximal, complemented
2#16839674C212yesmaximal, complemented
3#16839674C212yesmaximal, complemented
4#16839666C212yesmaximal, complemented
5#16839665C211yesmaximal, characteristic
6#16839642C211yesmaximal, characteristic
7#16839635C212yesmaximal, complemented
8#16839634C212yesmaximal, complemented
9C61×#386C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C23×Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C23×C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C24×C61C2311yescharacteristic
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C2×D4×C61Q814yescomplemented
36C22×C4×C61—41no—
37C22×C4×C61—42no—
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×Dic61—41no—
42C22×Dic61—42no—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×Dic122—24no—
48C2×Dic122—42no—
49C2×Dic122—42no—
50C22⋊C4×C61—41no—
51C22⋊C4×C61—42no—
52C22⋊Dic61—24no—
53C22⋊Dic61—24no—
54C22⋊Dic61—41no—
55C22⋊Dic61—42no—
56C4⋊Dic61—41no—
57#11758196—42no—
58#11758196—42no—
59C4×Dic61—41no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61—22no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—21no—
68C23×C61C2×Q812yes—
69C23×C61C2×Q812yes—
70C23×C61C2411yescharacteristic
71D4×C61—44no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—44no—
81C2×C4×C61C2×Q812yes—
82C2×Dic61—22no—
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#4114yes—
95Dic122—48no—
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—24no—
99C22×C61—24no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61C22×Q811yescharacteristic
107C22×C61C2×#4112yes—
108C22×C61H(5,𝔽2)11yescharacteristic
109C22×C61H(5,𝔽2)12yes—
110C22×C61H(5,𝔽2)11yescharacteristic
111C4×C61—22no—
112C4×C61—42no—
113C4×C61—42no—
114Dic61—24no—
115Dic61—42no—
116Dic61—42no—
117Dic61—42no—
118#2804—611nomaximal, Sylow
119C2×C61—42no—
120C2×C61—42no—
121C2×C61#53812yes—
122C2×C61#54311yescharacteristic
123C2×C61#55412yes—
124C2×C61#55911yescharacteristic
125C2×C61H(3,𝔽4)11yescharacteristic
126#400—612no—
127#393—612no—
128#393—612no—
129#391—612no—
130#390—611no—
131#386—611no—
132#386D6111yescharacteristic
133#385—612no—
134#385—612no—
135C61#280411yescharacteristic, complemented, Sylow
136C22×Q8—612no—
137C22×D4C2×D6111yescharacteristic
138C23×C4—611no—
139C23×C4C2×D6111yescharacteristic
140C2×C4⋊C4—612no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—611no—
143C2×C22⋊C4—612no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—611no—
147C2×C22⋊C4C2×D6112yes—
148C2×C22⋊C4C2×D6111yescharacteristic
149C2×C42—611no—
150#95—612no—
151#95—612no—
152#95—612no—
153#95—612no—
154#95—612no—
155#95—612no—
156#95C2×D6112yes—
157C24C22×D6111yescharacteristic
158C24C22×D6111yescharacteristic
159C2×Q8—1224no—
160C2×Q8—2442no—
161C2×Q8—2442no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4Dic12214yescomplemented
165C22×C4—42no—
166C22×C4—41no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—2442no—
172C22×C4—2441no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C4⋊C4—2441no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—1224no—
182C22⋊C4—1224no—
183C22⋊C4—2442no—
184C22⋊C4—2441no—
185C42—2441no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23C2×Dic12212yes—
195C23C2×Dic12212yes—
196C23C23×D6111yescharacteristic
197Q8—2448no—
198D4—44no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—614no—
209C2×C4—1222no—
210C2×C4—1222no—
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—2444no—
221C2×C4C2×Dic12212yes—
222C22—24no—
223C22—24no—
224C22—22no—
225C22—22no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22C22×Dic12211yescharacteristic
233C22#41×D6112yes—
234C22#1451982212yes—
235C22#1451982211yescharacteristic
236C22#1451982211yescharacteristic
237C4—22no—
238C4—42no—
239C4—42no—
240C4—1224no—
241C4—2442no—
242C4—2442no—
243C4—2442no—
244C2—42no—
245C2—42no—
246C2#1684034412yes—
247C2#1684038811yescharacteristic
248C2#1684047112yes—
249C2#1684049611yescharacteristic
250C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2804
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839674C2semidirect
3. #16839674C2semidirect
4. #16839666C2semidirect
7. #16839635C2semidirect
8. #16839634C2semidirect
35. C2×D4×C61Q8semidirect
135. C61#2804semidirect
164. C2×D4Dic122semidirect