Finite Group Databasebeta

← #21453901

Subgroups — #21453901

Order 7808.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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#16839703C212yesmaximal, complemented
2#16839690C212yesmaximal, complemented
3#16839676C212yesmaximal, complemented
4#16839676C212yesmaximal, complemented
5#16839674C212yesmaximal, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839642C212yesmaximal, complemented
8#16839634C211yesmaximal, characteristic, complemented
9C61×#392C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2211yescharacteristic
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2212yes—
27C22×D4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2211yescharacteristic
31C24×C61C2312yes—
32C24×C61C2311yescharacteristic
33C2×D4×C61—24no—
34C2×D4×C61—42no—
35C2×D4×C61—42no—
36C2×D4×C61—42no—
37C2×D4×C61—41no—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×Dic61—42no—
42C22×Dic61—41no—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×Dic122—42no—
48C2×Dic122—41no—
49C22⋊C4×C61—41no—
50C22⋊C4×C61—42no—
51C22⋊Dic61—22no—
52C22⋊Dic61—42no—
53C22⋊Dic61—42no—
54C22⋊Dic61—42no—
55C22⋊Dic61—42no—
56C22⋊Dic61—42no—
57#11758196—42no—
58#11758196—42no—
59C23×C61—22no—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61#4112yes—
71C23×C61C2411yescharacteristic
72D4×C61—48no—
73D4×C61—44no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×Dic61—22no—
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—
94Dic122—44no—
95C22×C61—24no—
96C22×C61—22no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61C2×#4111yescharacteristic
108C22×C61H(5,𝔽2)12yes—
109C22×C61H(5,𝔽2)12yes—
110C22×C61H(5,𝔽2)11yescharacteristic
111C22×C612−1+411yescharacteristic
112C4×C61—42no—
113C4×C61—41no—
114C4×C61—41no—
115Dic61—42no—
116Dic61—42no—
117Dic61—42no—
118Dic61—42no—
119#2824—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61—82no—
122C2×C61#53812yes—
123C2×C61#53911yescharacteristic
124C2×C61#56011yescharacteristic
125C2×C61H(3,𝔽4)11yescharacteristic
126C2×C61#56212yes—
127#400—612no—
128#397—612no—
129#394—612no—
130#394—612no—
131#393—612no—
132#393—611no—
133#392D6111yescharacteristic
134#386—612no—
135#385—611no—
136C61#282411yescharacteristic, complemented, Sylow
137C22×Q8—611no—
138C22×D4C2×D6112yes—
139C22×D4C2×D6111yescharacteristic
140C23×C4—611no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C22⋊C4—611no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4C2×D6112yes—
151#95—612no—
152#95—612no—
153#95—612no—
154#95—612no—
155#95—612no—
156#95—611no—
157#95C2×D6111yescharacteristic
158C24C22×D6112yes—
159C24C22×D6111yescharacteristic
160C2×Q8—2441no—
161C2×Q8—2442no—
162C2×D4—24no—
163C2×D4—42no—
164C2×D4—41no—
165C2×D4—42no—
166C2×D4—42no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—2441no—
172C22×C4—2442no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—1222no—
181C22⋊C4—2442no—
182C22⋊C4—2442no—
183C22⋊C4—2442no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C23—21no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23#1175822412yes—
198C23C23×D6111yescharacteristic
199Q8—2444no—
200D4—48no—
201D4—44no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
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—1222no—
221C2×C4—2444no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22C2×#1175822411yescharacteristic
235C22#1451982211yescharacteristic
236C22#1451982212yes—
237C22#1451982212yes—
238C22#1451982411yescharacteristic
239C4—41no—
240C4—41no—
241C4—42no—
242C4—2442no—
243C4—2442no—
244C4—2442no—
245C4—2442no—
246C2—42no—
247C2—82no—
248C2#1684034712yes—
249C2#1684035711yescharacteristic
250C2#1684049911yescharacteristic
251C2#1684050511yescharacteristic
252C2#1684050712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2824
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #16839703C2semidirect
2. #16839690C2semidirect
3. #16839676C2semidirect
4. #16839676C2semidirect
5. #16839674C2semidirect
6. #16839674C2semidirect
7. #16839642C2semidirect
8. #16839634C2semidirect
136. C61#2824semidirect