Finite Group Databasebeta

← #21451744

Subgroups — #21451744

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×#14519757C211yesmaximal, characteristic, complemented
2C2×#14519739C211yesmaximal, characteristic
3#16839691C212yesmaximal, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839679C212yesmaximal
7#16839675C211yesmaximal, characteristic, complemented
8#16839648C212yesmaximal, complemented
9#16839636C212yesmaximal, complemented
10#16839624C211yesmaximal, characteristic, complemented
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519757—24no—
17#14519739—24no—
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—22no—
51C2×C4×D61—22no—
52C2×C4×D61—42no—
53C2×C4×D61—42no—
54C2×C4×D61D414yes—
55C2×Dic122—22no—
56C2×Dic122—42no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—24no—
60#11758198—22no—
61#11758198—24no—
62#11758198—24no—
63#11758198—22no—
64#11758198—42no—
65#11758198—42no—
66C4⋊Dic61—24no—
67#11758196—42no—
68C4×Dic61—22no—
69C23×C61C2411yescharacteristic
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61C2×D412yes—
79C22×D61#4112yes—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C2×C4×C61#4112yes—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61C2×D412yes—
103D244—28no—
104C4×D61—44no—
105C4×D61—44no—
106Dic122—44no—
107C22×C61C22×D411yescharacteristic
108C22×C61C2×#4111yescharacteristic
109C22×C61C2×#4111yescharacteristic
110C22×C61H(5,𝔽2)12yes—
111C22×C612−1+412yes—
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—22no—
116C2×D61—24no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C4×C61—22no—
123C4×C61—22no—
124C4×C61—42no—
125C4×C61—41no—
126C4×C61—42no—
127Dic61—22no—
128Dic61—42no—
129Dic61—41no—
130Dic61—42no—
131#2638—611nomaximal, Sylow
132C2×C61#52511yescharacteristic
133C2×C61#53411yescharacteristic
134C2×C61#53611yescharacteristic
135C2×C61#53912yes—
136C2×C61#54212yes—
137D61—42no—
138D61—42no—
139C2×C22⋊Q8—611no—
140C2×C4×D4—611no—
141#398D6111yescharacteristic, complemented
142#397—611no—
143#397—612no—
144#395—611no—
145#394—612no—
146#393—611no—
147#387—612no—
148#385—612no—
149#381—611no—
150C61#263811yescharacteristic, complemented, Sylow
151C22×Q8—611no—
152C22×D4—611no—
153C23×C4—611no—
154C23×C4—611no—
155C22⋊Q8—1224no—
156C4×D4—1224no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4C2×D6111yescharacteristic
160C2×C4⋊C4C2×D6111yescharacteristic
161C2×C4⋊C4C2×D6112yes—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
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—
177C24—611no—
178C2×Q8—1222no—
179C2×Q8—2442no—
180C2×D4—1222no—
181C2×D4—1222no—
182C2×D4—1222no—
183C22×C4—611no—
184C22×C4—614no—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4—612no—
188C22×C4—1222no—
189C22×C4—2442no—
190C22×C4—2442no—
191C22×C4C22×D6112yes—
192C22×C4C22×D6112yes—
193C22×C4C22×D6111yescharacteristic
194C22×C4C22×D6111yescharacteristic
195C22×C4C22×D6111yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—24no—
199C4⋊C4—1224no—
200C4⋊C4—2442no—
201C22⋊C4—1222no—
202C22⋊C4—1224no—
203C22⋊C4—1224no—
204C22⋊C4—1222no—
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C42—1222no—
208C23—612no—
209C23—612no—
210C23—1221no—
211C23—1221no—
212C23—1221no—
213C23—1221no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23—1222no—
218C23C23×D6111yescharacteristic
219Q8—2444no—
220D4—1228no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—612no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—2444no—
243C2×C4—2444no—
244C2×C4D4×D6112yes—
245C2×C4#1175822412yes—
246C22—1222no—
247C22—1222no—
248C22—1222no—
249C22—1222no—
250C22—1224no—
251C22—2441no—
252C22—2441no—
253C22—2442no—
254C22—2442no—
255C22—2442no—
256C22C2×D4×D6111yescharacteristic
257C22#41×D6111yescharacteristic
258C22C2×#1175822411yescharacteristic
259C22#1451982312yes—
260C22#1451982512yes—
261C4—22no—
262C4—22no—
263C4—42no—
264C4—41no—
265C4—42no—
266C4—1222no—
267C4—2442no—
268C4—2441no—
269C4—2442no—
270C2—2442no—
271C2—2442no—
272C2#1684027211yescharacteristic
273C2#1684032311yescharacteristic
274C2#1684033711yescharacteristic
275C2#1684036012yes—
276C2#1684038512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
3. #16839691C2semidirect
4. #16839688C2semidirect
5. #16839682C2semidirect
7. #16839675C2semidirect
8. #16839648C2semidirect
9. #16839636C2semidirect
10. #16839624C2semidirect
11. C61×#398C2semidirect
141. #398D61semidirect
150. C61#2638semidirect