Finite Group Databasebeta

← #21451193

Subgroups — #21451193

Order 7808.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839693C211yesmaximal, characteristic, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839661C212yesmaximal, complemented
7#16839659C212yesmaximal, complemented
8#16839636C212yesmaximal
9#16839633C212yesmaximal
10#16839609C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519757—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C4⋊C4×D61—24no—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61—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—24no—
61#11758198Q818yescomplemented
62C4⋊Dic61—22no—
63C4⋊Dic61—24no—
64C4⋊Dic61—42no—
65#11758196—22no—
66#11758196—22no—
67#11758196—24no—
68#11758196—42no—
69C4×Dic61—42no—
70C23×C61C2411yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61C2×D412yes—
75C22×D61C2×Q814yes—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×Q814yes—
88C2×C4×C61#4112yes—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61C2×D412yes—
100C2×Dic61C2×Q814yes—
101C2×Dic61#4112yes—
102C4×D61—28no—
103C4×D61—44no—
104C4×D61—44no—
105Dic122—44no—
106C22×C61C22×D411yescharacteristic
107C22×C61C22×Q812yes—
108C22×C61C2×#4111yescharacteristic
109C22×C61C2×#4111yescharacteristic
110C22×C61H(5,𝔽2)12yes—
111C2×D61—22no—
112C2×D61—22no—
113C2×D61—24no—
114C2×D61—24no—
115C2×D61C4⋊Q814yes—
116C4×C61—22no—
117C4×C61—22no—
118C4×C61—24no—
119C4×C61—42no—
120C4×C61—41no—
121Dic61—22no—
122Dic61—22no—
123Dic61—24no—
124Dic61—42no—
125Dic61—41no—
126#2583—611nomaximal, Sylow
127C2×C61#52511yescharacteristic
128C2×C61C2×C4⋊Q811yescharacteristic
129C2×C61#53411yescharacteristic
130C2×C61#55412yes—
131C2×C61#55412yes—
132D61—24no—
133C2×C22⋊Q8—611no—
134C22×C4⋊C4—611no—
135#398—611no—
136#398D6111yescharacteristic, complemented
137#395—611no—
138#395—611no—
139#389—612no—
140#389—612no—
141#385—612no—
142#385—612no—
143C4×C22⋊C4—611no—
144C61#258311yescharacteristic, complemented, Sylow
145C22×Q8—611no—
146C23×C4—611no—
147C23×C4—611no—
148C23×C4—611no—
149C22⋊Q8—1224no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1224no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C4⋊C4C2×D6111yescharacteristic
160C2×C4⋊C4C2×D6112yes—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—612no—
163C2×C42—612no—
164#95—611no—
165#95—612no—
166#95—612no—
167#95—612no—
168#95C2×D6111yescharacteristic
169#95C2×D6112yes—
170C24—611no—
171C2×Q8—1222no—
172C2×Q8—2442no—
173C22×C4—612no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—614no—
177C22×C4—612no—
178C22×C4—611no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—2442no—
184C22×C4—2442no—
185C22×C4C22×D6112yes—
186C22×C4C22×D6111yescharacteristic
187C22×C4C22×D6111yescharacteristic
188C22×C4C22×D6111yescharacteristic
189C22×C4C22×D6112yes—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1224no—
196C4⋊C4—1224no—
197C4⋊C4—1222no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C22⋊C4—618no—
201C22⋊C4—1224no—
202C42—2442no—
203C23—612no—
204C23—614no—
205C23—1221no—
206C23—1221no—
207C23—1222no—
208C23C23×D6111yescharacteristic
209Q8—2444no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—612no—
221C2×C4—614no—
222C2×C4—612no—
223C2×C4—1228no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—2444no—
235C2×C4—2444no—
236C2×C4D4×D6112yes—
237C2×C4#1175822412yes—
238C2×C4Q8×D6114yes—
239C22—614no—
240C22—1224no—
241C22—1224no—
242C22—1222no—
243C22—1222no—
244C22C2×D4×D6111yescharacteristic
245C22C2×Q8×D6112yes—
246C22#41×D6111yescharacteristic
247C22C2×#1175822411yescharacteristic
248C22#1451982312yes—
249C4—24no—
250C4—22no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—1224no—
255C4—1222no—
256C4—1222no—
257C4—2441no—
258C4—2442no—
259C2—1224no—
260C2#1684027211yescharacteristic
261C2C4⋊Q8×D6111yescharacteristic
262C2#1684032311yescharacteristic
263C2#1684046812yes—
264C2#1684047012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2583
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #16839693C2semidirect
4. #16839683C2semidirect
5. #16839682C2semidirect
6. #16839661C2semidirect
7. #16839659C2semidirect
11. C61×#398C2semidirect
61. #11758198Q8semidirect
136. #398D61semidirect
144. C61#2583semidirect