Finite Group Databasebeta

← #21451956

Subgroups — #21451956

Order 7808.

534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519771C211yesmaximal, characteristic, complemented
2C2×#14519765C211yesmaximal, characteristic, complemented
3#16839684C212yesmaximal, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839679C212yesmaximal, complemented
7#16839675C211yesmaximal, characteristic, complemented
8#16839672C211yesmaximal, characteristic
9#16839664C212yesmaximal, complemented
10#16839653C212yesmaximal, complemented
11C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×D244C2212yes—
15#14519771—24no—
16#14519765—24no—
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2212yes—
33C2×C42×C61C2212yes—
34C2×C42×C61C2211yescharacteristic
35#95×C61C2211yescharacteristic
36#95×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C23×D61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×D244—22no—
49C2×D244—24no—
50C2×D244—42no—
51C2×D244—42no—
52C2×D244—42no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C4⋊C4×C61—24no—
56C42×C61—42no—
57C42×C61D414yescomplemented
58#11758198—24no—
59#11758198—24no—
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63#11758198—24no—
64#11758198—42no—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—42no—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71C23×C61C2411yescharacteristic
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D412yes—
96C2×C4×C61#4114yes—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107D244—44no—
108D244—48no—
109Dic122—44no—
110C22×C61C22×D411yescharacteristic
111C22×C61C2×#4112yes—
112C22×C61H(5,𝔽2)11yescharacteristic
113C22×C61H(5,𝔽2)12yes—
114C22×C612−1+411yescharacteristic
115C2×D61—41no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—24no—
131C4×C61—42no—
132Dic61—41no—
133Dic61—42no—
134Dic61—41no—
135Dic61—41no—
136#2662—611nomaximal, Sylow
137C2×C61#53211yescharacteristic
138C2×C61#53511yescharacteristic
139C2×C61#53711yescharacteristic
140C2×C61#53812yes—
141C2×C61#54212yes—
142D61—82no—
143D61—81no—
144C2×#126—611no—
145C2×#124—611no—
146#396—612no—
147#395—611no—
148#394—612no—
149#394—611no—
150#393—611no—
151#392—611no—
152#390—612no—
153#388—612no—
154C4×C4⋊C4D6111yescharacteristic, complemented
155C61#266211yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4—611no—
158C22×D4—612no—
159#126—1224no—
160#124—1224no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4C2×D6112yes—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C42C2×D6112yes—
176C2×C42C2×D6111yescharacteristic
177#95—612no—
178#95—612no—
179#95C2×D6111yescharacteristic
180#95C2×D6111yescharacteristic
181C24—611no—
182C24—612no—
183C2×Q8—1222no—
184C2×Q8—2442no—
185C2×D4—1222no—
186C2×D4—1224no—
187C2×D4—2442no—
188C2×D4—2442no—
189C2×D4—2442no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—612no—
193C22×C4—611no—
194C22×C4C22×D6112yes—
195C22×C4C22×D6111yescharacteristic
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6112yes—
199C4⋊C4—24no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1222no—
203C4⋊C4—2442no—
204C22⋊C4—1224no—
205C22⋊C4—1224no—
206C22⋊C4—1222no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1224no—
210C22⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C42—42no—
214C42D24414yescomplemented
215C23—1221no—
216C23—1222no—
217C23—1222no—
218C23—1222no—
219C23—1222no—
220C23—1222no—
221C23—1221no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1221no—
226C23—1222no—
227C23C23×D6111yescharacteristic
228Q8—2444no—
229D4—2444no—
230D4—2448no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4C2×D24412yes—
251C2×C4C2×D24412yes—
252C2×C4C2×D24412yes—
253C2×C4#1175822214yes—
254C22—2441no—
255C22—2442no—
256C22—2442no—
257C22—2441no—
258C22—2441no—
259C22—2442no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22C22×D24411yescharacteristic
267C22C2×#1175822212yes—
268C22#1451982211yescharacteristic
269C22#1451982312yes—
270C22#1451982511yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—24no—
275C4—42no—
276C4—2441no—
277C4—2441no—
278C4—2442no—
279C4—2441no—
280C2—4882no—
281C2—4881no—
282C2#1684031211yescharacteristic
283C2#1684033111yescharacteristic
284C2#1684034311yescharacteristic
285C2#1684034512yes—
286C2#1684038412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C4⋊C4×C61C2
hypercenterC4×C4⋊C4D61
hypocenterC61#2662
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519771C2semidirect
2. C2×#14519765C2semidirect
3. #16839684C2semidirect
4. #16839683C2semidirect
5. #16839680C2semidirect
6. #16839679C2semidirect
7. #16839675C2semidirect
9. #16839664C2semidirect
10. #16839653C2semidirect
11. C4×C4⋊C4×C61C2semidirect
57. C42×C61D4semidirect
154. C4×C4⋊C4D61semidirect
155. C61#2662semidirect
214. C42D244semidirect