Finite Group Databasebeta

← #21448882

Subgroups — #21448882

Order 7808.

832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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×#14519773C211yesmaximal, characteristic
2C2×C4×C22⋊D61C212yesmaximal, complemented
3C2×#14519737C212yesmaximal, complemented
4#16839662C212yesmaximal, complemented
5#16839662C212yesmaximal, complemented
6#16839642C211yesmaximal, characteristic, complemented
7#16839640C212yesmaximal, complemented
8#16839613C212yesmaximal, complemented
9C61×#386C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2212yes—
15#14519773C418yescomplemented
16C4×C22⋊D61—28no—
17#14519737—28no—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2211yescharacteristic
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×C4×Dic61C2212yes—
26C2×C4×Dic61C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29C22×D4×C61C2211yescharacteristic
30C23×C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2212yes—
32C2×C22⋊C4×C61C2211yescharacteristic
33#95×C61C2212yes—
34C24×C61C2311yescharacteristic
35C24×C61C2311yescharacteristic
36C23×D61C2312yes—
37C2×D4×C61—41no—
38C2×D4×C61—41no—
39C2×D4×C61C2×C414yescomplemented
40C22×C4×C61—24no—
41C22×C4×C61—41no—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61C2×C418yescomplemented
50C2×C22⋊D61C2×C418yescomplemented
51C22×Dic61—24no—
52C22×Dic61—41no—
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C2×D244—41no—
57C2×D244—41no—
58C2×D244C2×C414yescomplemented
59C2×C4×D61—24no—
60C2×C4×D61—24no—
61C2×C4×D61—42no—
62C22⋊C4×C61—24no—
63C22⋊C4×C61—41no—
64C22⋊Dic61—24no—
65C22⋊Dic61—41no—
66#11758198—24no—
67#11758198—24no—
68#11758198—42no—
69#11758196—24no—
70#11758196D418yescomplemented
71C4×Dic61—24no—
72C4×Dic61—24no—
73C4×Dic61C2×C414yescomplemented
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61C22×C412yes—
83C23×C61C22×C412yes—
84C23×C61C2411yescharacteristic
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61C22×C414yes—
92D4×C61—44no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—44no—
101C2×C4×C61C22×C412yes—
102C2×C4×C61C2×D414yes—
103C22⋊D61—216no—
104C22⋊D61—216no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—44no—
111C2×Dic61C22×C414yes—
112C2×Dic61C2×D414yes—
113C2×Dic61C2×D414yes—
114C2×Dic61#4114yes—
115D244—44no—
116C4×D61—48no—
117C22×C61—24no—
118C22×C61—24no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61C23×C411yescharacteristic
128C22×C61C22×D412yes—
129C22×C61C2×#4112yes—
130C22×C61H(5,𝔽2)11yescharacteristic
131C22×C61H(5,𝔽2)11yescharacteristic
132C2×D61—24no—
133C2×D61—24no—
134C2×D61—24no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—24no—
141C4×C61—42no—
142Dic61—24no—
143Dic61—42no—
144Dic61C4×D418yescomplemented
145#2366—611nomaximal, Sylow
146C2×C61—42no—
147C2×C61—42no—
148C2×C61C2×C4×D412yes—
149C2×C61#51811yescharacteristic
150C2×C61D4211yescharacteristic
151C2×C61#55012yes—
152C2×C61#55911yescharacteristic
153D61—44no—
154C2×#127—611no—
155C2×C4×D4—612no—
156C2×C4×D4—612no—
157#390—612no—
158#390—612no—
159#386—611no—
160#386—612no—
161#386D6111yescharacteristic, complemented
162C4×C4⋊C4—612no—
163C61#236611yescharacteristic, complemented, Sylow
164C22×D4—612no—
165C22×D4—612no—
166C22×D4—611no—
167C22×D4C2×D6111yescharacteristic
168C23×C4—611no—
169C23×C4—612no—
170C23×C4C2×D6111yescharacteristic
171#127—618no—
172C4×D4—1228no—
173C4×D4—1228no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4C2×D6112yes—
182C2×C22⋊C4C2×D6111yescharacteristic
183C2×C42—611no—
184C2×C42—612no—
185C2×C42—612no—
186#95—612no—
187#95C2×D6112yes—
188C24—612no—
189C24C22×D6111yescharacteristic
190C24C22×D6111yescharacteristic
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—618no—
194C2×D4—618no—
195C2×D4—614no—
196C2×D4—1224no—
197C2×D4—1224no—
198C2×D4—1224no—
199C2×D4—1224no—
200C2×D4—2441no—
201C2×D4—2441no—
202C2×D4C4×D6114yescomplemented
203C22×C4—24no—
204C22×C4—41no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—612no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4—2442no—
212C22×C4—2441no—
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6112yes—
216C4⋊C4—618no—
217C4⋊C4—1224no—
218C22⋊C4—24no—
219C22⋊C4—41no—
220C22⋊C4—1224no—
221C22⋊C4—1224no—
222C22⋊C4—1224no—
223C22⋊C4—2442no—
224C22⋊C4—2441no—
225C42—614no—
226C42—1224no—
227C42—1224no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—614no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23C2×C4×D6112yes—
244C23C2×C4×D6112yes—
245C23C23×D6111yescharacteristic
246D4—44no—
247D4—12216no—
248D4—12216no—
249D4—2444no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—614no—
259C2×C4—614no—
260C2×C4—614no—
261C2×C4—614no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—2448no—
268C2×C4—2444no—
269C2×C4C2×C4×D6112yes—
270C2×C4D4×D6114yes—
271C22—24no—
272C22—24no—
273C22—22no—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—1224no—
282C22—1224no—
283C22—1224no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22C22×C4×D6111yescharacteristic
289C22C2×D4×D6112yes—
290C22#41×D6112yes—
291C22#1451982211yescharacteristic
292C22#1451982211yescharacteristic
293C4—22no—
294C4—24no—
295C4—42no—
296C4—618no—
297C4—1224no—
298C4—2442no—
299C2—42no—
300C2—42no—
301C2—2444no—
302C2C4×D4×D6112yes—
303C2#1684023511yescharacteristic
304C2#1684039411yescharacteristic
305C2#1684043012yes—
306C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#386C2
socleC23×C61C24
hypercenter#386D61
hypocenterC61#2366
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D61C2semidirect
3. C2×#14519737C2semidirect
4. #16839662C2semidirect
5. #16839662C2semidirect
6. #16839642C2semidirect
7. #16839640C2semidirect
8. #16839613C2semidirect
9. C61×#386C2semidirect
15. #14519773C4semidirect
39. C2×D4×C61C2×C4semidirect
49. C2×C22⋊D61C2×C4semidirect
50. C2×C22⋊D61C2×C4semidirect
58. C2×D244C2×C4semidirect
70. #11758196D4semidirect
73. C4×Dic61C2×C4semidirect
144. Dic61C4×D4semidirect
161. #386D61semidirect
163. C61#2366semidirect
202. C2×D4C4×D61semidirect