Finite Group Databasebeta

← #21451579

Subgroups — #21451579

Order 7808.

612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519765C211yesmaximal, characteristic, complemented
2C2×#14519757C211yesmaximal, characteristic, complemented
3C2×#14519752C211yesmaximal, characteristic
4C2×#14519734C211yesmaximal, characteristic, complemented
5#16839684C214yesmaximal, complemented
6#16839679C214yesmaximal, complemented
7#16839667C211yesmaximal, characteristic, complemented
8#16839663C211yesmaximal, characteristic, complemented
9C61×#384C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×D244C2212yes—
13C22×C4×D61C2211yescharacteristic
14#14519765—24no—
15#14519757—24no—
16#14519752—24no—
17#14519734—24no—
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2214yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2214yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2214yes—
30C2×C42×C61C2211yescharacteristic
31C23×D61C2312yes—
32C23×D61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2311yescharacteristic
40C2×D244—24no—
41C2×D244—22no—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244—44no—
45C2×C4×D61—22no—
46C2×C4×D61—22no—
47C2×C4×D61D414yes—
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—44no—
54C42×C61D414yescomplemented
55#11758198—24no—
56#11758198—24no—
57#11758198—28no—
58#11758198—24no—
59#11758198—44no—
60C4⋊Dic61—24no—
61#11758196—24no—
62C4×Dic61—22no—
63C23×C61C2411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—24no—
72C22×D61—24no—
73C22×D61C2×D412yes—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—24no—
79C2×C4×C61—24no—
80C2×C4×C61C2×D414yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61#4112yes—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61C2×D412yes—
93D244—48no—
94D244—44no—
95C4×D61—28no—
96Dic122—44no—
97C22×C61C22×D411yescharacteristic
98C22×C61C22×D411yescharacteristic
99C22×C61C2×#4111yescharacteristic
100C22×C61H(5,𝔽2)12yes—
101C22×C612−1+412yes—
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—22no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—44no—
111C2×D61—44no—
112C4×C61—24no—
113C4×C61—42no—
114C4×C61—42no—
115C4×C61#12114yes—
116Dic61—22no—
117Dic61—42no—
118Dic61—42no—
119#2620—611nomaximal, Sylow
120C2×C61C2×#12111yescharacteristic
121C2×C61#53511yescharacteristic
122C2×C61#53611yescharacteristic
123C2×C61#53712yes—
124C2×C61#54212yes—
125D61—42no—
126D61—82no—
127C2×#124—611no—
128C2×C22⋊Q8—611no—
129C2×#121—611no—
130C2×#117—611no—
131#396—614no—
132#394—614no—
133#391—611no—
134#390—611no—
135#384D6111yescharacteristic, complemented
136C61#262011yescharacteristic, complemented, Sylow
137C22×Q8—611no—
138C22×D4—611no—
139C22×D4—612no—
140C23×C4—611no—
141#124—1224no—
142C22⋊Q8—1224no—
143#121—1224no—
144#117—1224no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C4⋊C4C2×D6114yes—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—614no—
154C2×C22⋊C4—614no—
155C2×C42—611no—
156C2×C42C2×D6111yescharacteristic
157#95—614no—
158C24—611no—
159C24—612no—
160C2×Q8—1222no—
161C2×Q8—1222no—
162C2×Q8—1222no—
163C2×D4—1224no—
164C2×D4—1222no—
165C2×D4—1222no—
166C2×D4—1222no—
167C2×D4—2444no—
168C22×C4—611no—
169C22×C4—614no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4C22×D6112yes—
175C22×C4C22×D6112yes—
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—44no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C22⋊C4—1224no—
184C22⋊C4—1224no—
185C22⋊C4—1224no—
186C22⋊C4—1228no—
187C22⋊C4—2444no—
188C42—1222no—
189C42D24414yescomplemented
190C23—612no—
191C23—1221no—
192C23—1221no—
193C23—1222no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23—1222no—
198C23—1224no—
199C23—1224no—
200C23C23×D6111yescharacteristic
201Q8—2444no—
202D4—2448no—
203D4—2444no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—612no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1228no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4C2×D24414yes—
221C2×C4C2×D24412yes—
222C2×C4D4×D6112yes—
223C2×C4#1175822612yes—
224C22—1222no—
225C22—1222no—
226C22—1222no—
227C22—2442no—
228C22—2442no—
229C22—2442no—
230C22—2444no—
231C22—2444no—
232C22—2442no—
233C22—2442no—
234C22C2×D4×D6111yescharacteristic
235C22C22×D24411yescharacteristic
236C22C2×#1175822611yescharacteristic
237C22#1451982212yes—
238C22#1451982512yes—
239C4—24no—
240C4—42no—
241C4—42no—
242C4—1222no—
243C4—2442no—
244C4—2442no—
245C4#1451975214yes—
246C2—4882no—
247C2—2442no—
248C2C2×#1451975211yescharacteristic
249C2#1684032511yescharacteristic
250C2#1684033711yescharacteristic
251C2#1684034312yes—
252C2#1684038612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#384C2
hypercenter#384D61
hypocenterC61#2620
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. C2×#14519757C2semidirect
4. C2×#14519734C2semidirect
5. #16839684C2semidirect
6. #16839679C2semidirect
7. #16839667C2semidirect
8. #16839663C2semidirect
9. C61×#384C2semidirect
54. C42×C61D4semidirect
135. #384D61semidirect
136. C61#2620semidirect
189. C42D244semidirect