Finite Group Databasebeta

← #21451684

Subgroups — #21451684

Order 7808.

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

normal subgroups only

This group has 500 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×#14519764C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic, complemented
3#16839698C212yesmaximal, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839676C211yesmaximal, characteristic
7#16839674C212yesmaximal, complemented
8#16839656C212yesmaximal, complemented
9#16839655C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14#14519764—24no—
15#14519742—24no—
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C2×D4×C61—22no—
39C2×D4×C61—42no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C4⋊C4×C61—22no—
56C22⋊C4×C61—24no—
57C22⋊C4×C61—42no—
58C22⋊Dic61—24no—
59C22⋊Dic61—24no—
60C22⋊Dic61—24no—
61C22⋊Dic61—42no—
62C4⋊Dic61—42no—
63#11758196—22no—
64#11758196—22no—
65#11758196—42no—
66C4×Dic61—22no—
67C4×Dic61—22no—
68C4×Dic61D414yes—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61C2411yescharacteristic
77D4×C61—44no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
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×C61#4112yes—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61C2×D412yes—
102C2×Dic61C2×D412yes—
103C2×Dic61#4112yes—
104Dic122—28no—
105Dic122—44no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61C22×D411yescharacteristic
114C22×C61C2×#4111yescharacteristic
115C22×C61C2×#4111yescharacteristic
116C22×C61H(5,𝔽2)12yes—
117C22×C612−1+412yes—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—41no—
121C4×C61—42no—
122Dic61—22no—
123Dic61—22no—
124Dic61—22no—
125Dic61—42no—
126Dic61—41no—
127Dic61—42no—
128#2632—611nomaximal, Sylow
129C2×C61—82no—
130C2×C61#52511yescharacteristic
131C2×C61#53511yescharacteristic
132C2×C61#53611yescharacteristic
133C2×C61#54212yes—
134C2×C61#54212yes—
135C2×#124—611no—
136C2×C4×Q8—611no—
137#399—612no—
138#395—611no—
139#395—611no—
140#394—611no—
141#394D6111yescharacteristic
142#393—612no—
143#388—612no—
144#388—612no—
145#383—611no—
146C61#263211yescharacteristic, complemented, Sylow
147C22×Q8—611no—
148C22×Q8—611no—
149C22×D4C2×D6111yescharacteristic
150#124—1224no—
151C4×Q8—1224no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4C2×D6111yescharacteristic
157C2×C22⋊C4—612no—
158C2×C22⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4—612no—
161C2×C22⋊C4C2×D6112yes—
162C2×C22⋊C4C2×D6112yes—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42—611no—
166#95—612no—
167#95—612no—
168#95—611no—
169#95—612no—
170#95—612no—
171#95C2×D6111yescharacteristic
172C24C22×D6112yes—
173C2×Q8—1222no—
174C2×Q8—1222no—
175C2×Q8—1222no—
176C2×Q8—1222no—
177C2×Q8—2442no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—612no—
184C22×C4—612no—
185C22×C4—611no—
186C22×C4C22×D6112yes—
187C22×C4C22×D6111yescharacteristic
188C22×C4C22×D6111yescharacteristic
189C22×C4C22×D6111yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—1224no—
198C22⋊C4—1224no—
199C22⋊C4—1224no—
200C22⋊C4—2442no—
201C42—614no—
202C42—1222no—
203C42—1222no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23C23×D6111yescharacteristic
212Q8—1228no—
213Q8—2444no—
214D4—44no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—612no—
224C2×C4—612no—
225C2×C4—612no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4D4×D6112yes—
240C2×C4#1175822412yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D6111yescharacteristic
249C22#41×D6111yescharacteristic
250C22C2×#1175822411yescharacteristic
251C22#1451982212yes—
252C22#1451982412yes—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—1222no—
258C4—1222no—
259C4—1222no—
260C4—2441no—
261C4—2442no—
262C4—2442no—
263C2—82no—
264C2#1684027211yescharacteristic
265C2#1684032711yescharacteristic
266C2#1684033211yescharacteristic
267C2#1684037912yes—
268C2#1684038012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2632
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14519742C2semidirect
3. #16839698C2semidirect
4. #16839683C2semidirect
5. #16839682C2semidirect
7. #16839674C2semidirect
8. #16839656C2semidirect
9. #16839655C2semidirect
10. #16839629C2semidirect
146. C61#2632semidirect