Finite Group Databasebeta

← #21451792

Subgroups — #21451792

Order 7808.

436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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#16839701C212yesmaximal, complemented
3#16839695C212yesmaximal, complemented
4#16839694C212yesmaximal, complemented
5#16839637C212yesmaximal
6#16839634C212yesmaximal
7#16839622C211yesmaximal, characteristic
8C2×#14519684C211yesmaximal, characteristic
9C61×#380C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—41no—
33C22×C4×C61—41no—
34C22×C4×C61Q814yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—22no—
40C22×Dic61—22no—
41C22×Dic61—41no—
42C22×Dic61—41no—
43C22×Dic61—41no—
44C22×Dic61—41no—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C4⋊C4×C61—41no—
50C4⋊C4×C61—41no—
51C22⋊C4×C61—24no—
52C22⋊Dic61—24no—
53C4⋊Dic61—41no—
54C4⋊Dic61—42no—
55C4⋊Dic61—41no—
56C4⋊Dic61—42no—
57#11758196—42no—
58#11758196—42no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61C2×Q812yes—
64C23×C61#4112yes—
65C23×C61#4112yes—
66C23×C61C2411yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—44no—
78C2×C4×C61C2×Q812yes—
79C2×C4×C61C2×Q812yes—
80C2×Dic61—22no—
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—44no—
93C2×Dic61—44no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61#12514yes—
101C22×C61C22×Q811yescharacteristic
102C22×C61C2×#4111yescharacteristic
103C22×C61C2×#4111yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C61H(5,𝔽2)11yescharacteristic
107C22×C612−1+411yescharacteristic
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61—42no—
112Dic61—42no—
113Dic61—42no—
114Dic61—42no—
115Dic61—42no—
116#2646—611nomaximal, Sylow
117C2×C61—24no—
118C2×C61C2×#12511yescharacteristic
119C2×C61#53811yescharacteristic
120C2×C61#53811yescharacteristic
121C2×C61#53911yescharacteristic
122C2×C61#53911yescharacteristic
123C2×C61#54311yescharacteristic
124C2×C61#54411yescharacteristic
125#400—612no—
126#400—612no—
127#398—612no—
128#398—612no—
129#385—612no—
130#385—612no—
131#380—611no—
132#380D6111yescharacteristic
133C2×#95—611no—
134C61#264611yescharacteristic, complemented, Sylow
135C23×C4—611no—
136C23×C4—611no—
137C23×C4C2×D6111yescharacteristic
138C2×C4⋊C4—611no—
139C2×C4⋊C4—611no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4C2×D6111yescharacteristic
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C22⋊C4—612no—
147C2×C22⋊C4C2×D6112yes—
148#95—612no—
149#95—612no—
150#95—612no—
151#95—612no—
152#95—612no—
153#95—612no—
154#95—612no—
155#95C2×D6112yes—
156C24C22×D6111yescharacteristic
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4—612no—
163C22×C4—1222no—
164C22×C4—1222no—
165C22×C4—2441no—
166C22×C4—2441no—
167C22×C4—2441no—
168C22×C4—2441no—
169C22×C4Dic12214yes—
170C22×C4C22×D6112yes—
171C22×C4C22×D6112yes—
172C22×C4C22×D6111yescharacteristic
173C22×C4C22×D6111yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C22⋊C4—24no—
183C22⋊C4—1224no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23C2×Dic12212yes—
189C23#1175822412yes—
190C23#1175822612yes—
191C23C23×D6111yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—2444no—
216C2×C4—2444no—
217C2×C4C2×Dic12212yes—
218C2×C4C2×Dic12212yes—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#1451976814yes—
226C22C22×Dic12211yescharacteristic
227C22C2×#1175822411yescharacteristic
228C22C2×#1175822611yescharacteristic
229C22#1451982211yescharacteristic
230C22#1451982211yescharacteristic
231C22#1451982311yescharacteristic
232C22#1451982411yescharacteristic
233C4—22no—
234C4—22no—
235C4—42no—
236C4—42no—
237C4—2442no—
238C4—2442no—
239C4—2442no—
240C4—2442no—
241C2—24no—
242C2C2×#1451976811yescharacteristic
243C2#1684034911yescharacteristic
244C2#1684035211yescharacteristic
245C2#1684035711yescharacteristic
246C2#1684036111yescharacteristic
247C2#1684038811yescharacteristic
248C2#1684039011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2646
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839701C2semidirect
3. #16839695C2semidirect
4. #16839694C2semidirect
134. C61#2646semidirect