Finite Group Databasebeta

← #21451446

Subgroups — #21451446

Order 7808.

582 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×D244C211yesmaximal, characteristic, complemented
3#16839694C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic
7#16839664C212yesmaximal, complemented
8#16839653C212yesmaximal, complemented
9#16839640C212yesmaximal, complemented
10#16839636C212yesmaximal, complemented
11C61×#376C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×D244C2212yes—
14C22×C4×D61C2212yes—
15#14519771—24no—
16C4×D244—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758198C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C42×C61C2212yes—
33C2×C42×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
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—24no—
49C2×D244—22no—
50C2×D244—24no—
51C2×D244—24no—
52C2×D244—42no—
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—42no—
56C42×C61—24no—
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—
66C4⋊Dic61—22no—
67C4⋊Dic61—42no—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71C23×C61C2411yescharacteristic
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—21no—
82C22×D61—21no—
83C22×D61#4114yes—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
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—21no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107D244—28no—
108D244—48no—
109C4×D61—48no—
110C22×C61C22×D411yescharacteristic
111C22×C61C2×#4112yes—
112C22×C61C2×#4112yes—
113C22×C61H(5,𝔽2)11yescharacteristic
114C22×C61H(5,𝔽2)11yescharacteristic
115C2×D61—24no—
116C2×D61—24no—
117C2×D61—24no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—42no—
126C2×D61—42no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—24no—
131C4×C61—42no—
132Dic61—41no—
133Dic61—41no—
134Dic61—42no—
135Dic61—41no—
136#2603—611nomaximal, Sylow
137C2×C61#52511yescharacteristic
138C2×C61#53211yescharacteristic
139C2×C61#53511yescharacteristic
140C2×C61#55112yes—
141C2×C61#55312yes—
142D61—44no—
143D61—81no—
144C2×#126—611no—
145C2×C4×D4—611no—
146#398—611no—
147#397—611no—
148#394—611no—
149#392—611no—
150#390—612no—
151#388—612no—
152#386—612no—
153#385—612no—
154#376D6111yescharacteristic, complemented
155C61#260311yescharacteristic, complemented, Sylow
156C22×D4—611no—
157C22×D4—612no—
158C23×C4—612no—
159#126—1224no—
160C4×D4—1224no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C42C2×D6112yes—
175C2×C42C2×D6111yescharacteristic
176#95—612no—
177#95—612no—
178#95C2×D6112yes—
179#95C2×D6111yescharacteristic
180#95C2×D6111yescharacteristic
181C24—612no—
182C24—611no—
183C2×D4—1224no—
184C2×D4—1224no—
185C2×D4—1222no—
186C2×D4—1224no—
187C2×D4—2442no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—612no—
191C22×C4—611no—
192C22×C4—1224no—
193C22×C4—2442no—
194C22×C4—2442no—
195C22×C4C22×D6112yes—
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6111yescharacteristic
199C22×C4C22×D6112yes—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1222no—
203C4⋊C4—1222no—
204C4⋊C4—2442no—
205C22⋊C4—1224no—
206C22⋊C4—1224no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—1224no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C42—24no—
214C42D24414yescomplemented
215C23—614no—
216C23—1222no—
217C23—1222no—
218C23—1222no—
219C23—1222no—
220C23—1222no—
221C23—1222no—
222C23—1221no—
223C23—1222no—
224C23—1222no—
225C23—1221no—
226C23—1221no—
227C23C23×D6111yescharacteristic
228D4—1228no—
229D4—2448no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2448no—
250C2×C4C2×D24412yes—
251C2×C4C2×D24412yes—
252C2×C4C2×D24412yes—
253C2×C4#1175822214yes—
254C22—1224no—
255C22—1224no—
256C22—1224no—
257C22—2442no—
258C22—2441no—
259C22—2441no—
260C22—2441no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22C22×D24411yescharacteristic
267C22#41×D6112yes—
268C22C2×#1175822212yes—
269C22#1451982311yescharacteristic
270C22#1451982311yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—24no—
275C4—42no—
276C4—2441no—
277C4—2441no—
278C4—2441no—
279C4—2442no—
280C2—4881no—
281C2—2444no—
282C2#1684027411yescharacteristic
283C2#1684031211yescharacteristic
284C2#1684033111yescharacteristic
285C2#1684043612yes—
286C2#1684045612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#376C2
hypercenter#376D61
hypocenterC61#2603
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
1. C2×#14519771C2semidirect
2. C2×C4×D244C2semidirect
3. #16839694C2semidirect
4. #16839689C2semidirect
5. #16839680C2semidirect
7. #16839664C2semidirect
8. #16839653C2semidirect
9. #16839640C2semidirect
10. #16839636C2semidirect
11. C61×#376C2semidirect
57. C42×C61D4semidirect
154. #376D61semidirect
155. C61#2603semidirect
214. C42D244semidirect