Finite Group Databasebeta

← #21451742

Subgroups — #21451742

Order 7808.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14519753C211yesmaximal, characteristic, complemented
2C2×#14519737C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic, complemented
4#16839691C212yesmaximal, complemented
5#16839687C211yesmaximal, characteristic, complemented
6#16839681C211yesmaximal, characteristic, complemented
7#16839678C212yesmaximal
8#16839645C212yesmaximal, complemented
9#16839634C212yesmaximal, complemented
10#16839624C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519753—24no—
16#14519737—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—42no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C22×Dic61—22no—
49C22×Dic61—42no—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2312yes—
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C2×C4×D61—42no—
56C2×C4×D61D414yes—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—42no—
59C22⋊Dic61—24no—
60#11758198—22no—
61#11758198—24no—
62#11758198—42no—
63C4⋊Dic61—22no—
64C4⋊Dic61—24no—
65#11758196—22no—
66#11758196—24no—
67#11758196—42no—
68C4×Dic61—22no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61#4112yes—
74C23×C61C2411yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61C2×D412yes—
80Q8×C61—44no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61C2×D412yes—
91C22⋊D61—28no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—44no—
104C2×Dic61C2×D412yes—
105C2×Dic61#4112yes—
106C4×D61—44no—
107C22×C61—22no—
108C22×C61—24no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61C22×D411yescharacteristic
113C22×C61C2×#4111yescharacteristic
114C22×C61C2×#4111yescharacteristic
115C22×C61H(5,𝔽2)12yes—
116C22×C612−1+412yes—
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—42no—
121C2×D61—42no—
122C4×C61—22no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61—42no—
126Dic61—22no—
127Dic61—22no—
128Dic61—42no—
129Dic61—41no—
130Dic61—42no—
131#2638—611nomaximal, Sylow
132C2×C61—42no—
133C2×C61#52511yescharacteristic
134C2×C61#53411yescharacteristic
135C2×C61#53611yescharacteristic
136C2×C61#53912yes—
137C2×C61#54212yes—
138D61—42no—
139C2×C22⋊Q8—611no—
140C2×C4×D4—611no—
141#398—611no—
142#397—611no—
143#397—612no—
144#395—611no—
145#394—612no—
146#393D6111yescharacteristic, complemented
147#387—612no—
148#385—612no—
149#381—611no—
150C61#263811yescharacteristic, complemented, Sylow
151C22×Q8C2×D6111yescharacteristic
152C22×D4—611no—
153C23×C4—611no—
154C23×C4—611no—
155C22⋊Q8—1224no—
156C4×D4—1224no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—612no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4C2×D6111yescharacteristic
167C2×C22⋊C4C2×D6112yes—
168C2×C42—611no—
169#95—612no—
170#95—611no—
171#95—612no—
172#95—612no—
173#95—612no—
174#95C2×D6111yescharacteristic
175#95C2×D6112yes—
176C24—611no—
177C24C22×D6111yescharacteristic
178C2×Q8—22no—
179C2×Q8—42no—
180C2×D4—1222no—
181C2×D4—1222no—
182C2×D4—1222no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—614no—
186C22×C4—612no—
187C22×C4—612no—
188C22×C4—611no—
189C22×C4—1222no—
190C22×C4—2442no—
191C22×C4—2442no—
192C22×C4C22×D6111yescharacteristic
193C22×C4C22×D6112yes—
194C22×C4C22×D6112yes—
195C22×C4C22×D6111yescharacteristic
196C4⋊C4—1224no—
197C4⋊C4—1224no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C22⋊C4—22no—
202C22⋊C4—42no—
203C22⋊C4—1222no—
204C22⋊C4—1224no—
205C22⋊C4—1224no—
206C22⋊C4—2442no—
207C42—1222no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—612no—
213C23—1221no—
214C23—1221no—
215C23—1222no—
216C23—1222no—
217C23#1175822612yes—
218C23C23×D6111yescharacteristic
219Q8—44no—
220D4—1228no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—612no—
231C2×C4—612no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1221no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—2444no—
244C2×C4—2444no—
245C2×C4D4×D6112yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—1222no—
252C22—1222no—
253C22—1222no—
254C22—2442no—
255C22—2442no—
256C22C2×D4×D6111yescharacteristic
257C22#41×D6111yescharacteristic
258C22C2×#1175822611yescharacteristic
259C22#1451982212yes—
260C22#1451982412yes—
261C4—22no—
262C4—42no—
263C4—41no—
264C4—42no—
265C4—1222no—
266C4—1222no—
267C4—2442no—
268C4—2441no—
269C4—2442no—
270C2—42no—
271C2—2442no—
272C2#1684027511yescharacteristic
273C2#1684032211yescharacteristic
274C2#1684033211yescharacteristic
275C2#1684036112yes—
276C2#1684037612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14519753C2semidirect
3. #16839694C2semidirect
4. #16839691C2semidirect
5. #16839687C2semidirect
6. #16839681C2semidirect
8. #16839645C2semidirect
9. #16839634C2semidirect
10. #16839624C2semidirect
11. C61×#393C2semidirect
146. #393D61semidirect
150. C61#2638semidirect