Finite Group Databasebeta

← #21454140

Subgroups — #21454140

Order 7808.

582 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519758C211yesmaximal, characteristic
2C22×C4×Dic61C211yesmaximal, characteristic, complemented
3#16839656C212yesmaximal, complemented
4#16839655C212yesmaximal, complemented
5#16839645C212yesmaximal, complemented
6#16839644C212yesmaximal, complemented
7#16839642C211yesmaximal, characteristic
8#16839637C211yesmaximal, characteristic, complemented
9#16839635C211yesmaximal, characteristic, complemented
10#16839623C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic
12C23×Dic61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14#14519758—24no—
15C2×C4⋊Dic61C2212yes—
16C2×#11758196C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×C4×Dic61—24no—
25C2×C4×Dic61C2212yes—
26C2×C4×Dic61C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C23×C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C24×C61C2311yescharacteristic
39C2×D4×C61—22no—
40C2×D4×C61—22no—
41C2×D4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—24no—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2312yes—
46C22×C4×C61C2312yes—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—22no—
50C22×Dic61—24no—
51C22×Dic61D414yes—
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2312yes—
58C22⋊C4×C61—22no—
59C22⋊C4×C61—24no—
60C22⋊Dic61—22no—
61C22⋊Dic61—22no—
62C22⋊Dic61—22no—
63C22⋊Dic61—22no—
64C22⋊Dic61—24no—
65C4⋊Dic61—24no—
66#11758196—24no—
67#11758196—22no—
68#11758196—22no—
69C4×Dic61—24no—
70C4×Dic61—24no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61C2×D412yes—
79C23×C61#4112yes—
80C23×C61#4112yes—
81C23×C61C2411yescharacteristic
82D4×C61—44no—
83C2×C4×C61—28no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61#4114yes—
93C2×Dic61—28no—
94C2×Dic61—28no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61C2×D412yes—
109C2×Dic61C2×D412yes—
110C2×Dic61#4114yes—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—24no—
114C22×C61—24no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61#12314yes—
121C22×C61C22×D411yescharacteristic
122C22×C61C2×#4112yes—
123C22×C61C2×#4111yescharacteristic
124C22×C61C2×#4112yes—
125C22×C61C2×#4111yescharacteristic
126C4×C61—24no—
127C4×C61—41no—
128C4×C61—42no—
129Dic61—22no—
130Dic61—22no—
131Dic61—24no—
132Dic61—41no—
133Dic61—41no—
134Dic61—42no—
135#2853—611nomaximal, Sylow
136C2×C61—24no—
137C2×C61—81no—
138C2×C61C2×#12311yescharacteristic
139C2×C61#52511yescharacteristic
140C2×C61#52511yescharacteristic
141C2×C61#52912yes—
142C2×C61#52912yes—
143C2×#123—611no—
144C22×C42—611no—
145#388—612no—
146#388—612no—
147#387—612no—
148#387—612no—
149#386—611no—
150#386D6111yescharacteristic
151#385—611no—
152#385—611no—
153#381—611no—
154C61#285311yescharacteristic, complemented, Sylow
155C22×D4C2×D6111yescharacteristic
156C23×C4—611no—
157C23×C4—611no—
158C23×C4C2×D6111yescharacteristic
159#123—1224no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—612no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—611no—
166C2×C22⋊C4—611no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4C2×D6112yes—
171C2×C42—612no—
172C2×C42—612no—
173C2×C42—1224no—
174#95—612no—
175#95—612no—
176#95—612no—
177#95—612no—
178#95—612no—
179#95C2×D6112yes—
180C24C22×D6111yescharacteristic
181C24C22×D6111yescharacteristic
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—614no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—612no—
191C22×C4—612no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—1224no—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4—1222no—
198C22×C4C22×D6112yes—
199C22×C4C22×D6111yescharacteristic
200C22×C4C22×D6112yes—
201C4⋊C4—1222no—
202C4⋊C4—1222no—
203C4⋊C4—1224no—
204C4⋊C4—1224no—
205C22⋊C4—22no—
206C22⋊C4—24no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1224no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C42—1224no—
213C42—1224no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—22no—
219C23—21no—
220C23—21no—
221C23#1175822212yes—
222C23D4×D6112yes—
223C23#1175822412yes—
224C23C23×D6111yescharacteristic
225D4—44no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—612no—
236C2×C4—612no—
237C2×C4—614no—
238C2×C4—1228no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1228no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4#1175822414yes—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22#1451975914yes—
264C22C2×D4×D6111yescharacteristic
265C22#41×D6112yes—
266C22C2×#1175822411yescharacteristic
267C22C2×#1175822412yes—
268C22C2×#1175822211yescharacteristic
269C4—24no—
270C4—41no—
271C4—42no—
272C4—1222no—
273C4—1222no—
274C4—1224no—
275C4—2441no—
276C4—2441no—
277C4—2442no—
278C2—24no—
279C2—81no—
280C2C2×#1451975911yescharacteristic
281C2#1684026811yescharacteristic
282C2#1684027011yescharacteristic
283C2#1684029212yes—
284C2#1684029312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2853
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic61C2semidirect
3. #16839656C2semidirect
4. #16839655C2semidirect
5. #16839645C2semidirect
6. #16839644C2semidirect
8. #16839637C2semidirect
9. #16839635C2semidirect
10. #16839623C2semidirect
154. C61#2853semidirect