Finite Group Databasebeta

← #21450731

Subgroups — #21450731

Order 7808.

788 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14519750C212yesmaximal, complemented
2C2×#14519749C212yesmaximal, complemented
3C2×#14519737C212yesmaximal, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839678C212yesmaximal, complemented
6#16839631C211yesmaximal, characteristic, complemented
7#16839621C212yesmaximal, complemented
8#16839620C212yesmaximal, complemented
9C61×#394C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C23×Dic61C2212yes—
14C22×C4×D61C2212yes—
15#14519750—28no—
16#14519749—28no—
17#14519737—28no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29C22×D4×C61C2211yescharacteristic
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2212yes—
32C2×C22⋊C4×C61C2212yes—
33#95×C61C2211yescharacteristic
34C24×C61C2312yes—
35C23×D61C2312yes—
36C2×D4×C61—24no—
37C2×D4×C61—41no—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—42no—
47C2×C22⋊D61D418yescomplemented
48C22×Dic61—24no—
49C22×Dic61—24no—
50C22×Dic61—24no—
51C22×Dic61C2312yes—
52C22×Dic61C2312yes—
53C22×Dic61C2312yes—
54C2×D244—24no—
55C2×D244—41no—
56C2×C4×D61—24no—
57C2×C4×D61—24no—
58C2×C4×D61—24no—
59C4⋊C4×C61—41no—
60C22⋊C4×C61—24no—
61C22⋊C4×C61—24no—
62C22⋊Dic61—24no—
63#11758198—24no—
64#11758198—24no—
65#11758198—24no—
66C4⋊Dic61—41no—
67#11758196—24no—
68#11758196—24no—
69#11758196—24no—
70C4×Dic61D414yescomplemented
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61C2×D414yes—
78C23×C61C2411yescharacteristic
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61C2×D414yes—
86D4×C61—44no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61C2×D412yes—
97C22⋊D61—216no—
98C22⋊D61—48no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—48no—
106C2×Dic61C2×D414yes—
107C2×Dic61C2×D414yes—
108C2×Dic61#4114yes—
109D244—44no—
110C4×D61—48no—
111C22×C61—24no—
112C22×C61—24no—
113C22×C61—24no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61C22×D411yescharacteristic
119C22×C61C22×D412yes—
120C22×C61C2×#4112yes—
121C22×C61H(5,𝔽2)11yescharacteristic
122C22×C612−1+411yescharacteristic
123C2×D61—24no—
124C2×D61—24no—
125C2×D61—24no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—42no—
130C4×C61—22no—
131C4×C61—42no—
132C4×C61—41no—
133C4×C61—41no—
134Dic61—42no—
135Dic61—42no—
136Dic61#12118yescomplemented
137#2537—611nomaximal, Sylow
138C2×C61—44no—
139C2×C61C2×#12112yes—
140C2×C61#53711yescharacteristic
141C2×C61D4211yescharacteristic
142C2×C61#54712yes—
143C2×C61#55511yescharacteristic
144D61—44no—
145C2×#121—612no—
146C2×#121—612no—
147C2×C4×D4—612no—
148#394—611no—
149#394—612no—
150#394D6111yescharacteristic, complemented
151#384—611no—
152#380—612no—
153#380—612no—
154C61#253711yescharacteristic, complemented, Sylow
155C22×D4—612no—
156C22×D4—612no—
157C22×D4—611no—
158C22×D4C2×D6111yescharacteristic
159C23×C4—612no—
160C23×C4—612no—
161#121—1228no—
162#121—1228no—
163C4×D4—1228no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4C2×D6111yescharacteristic
169C2×C22⋊C4—612no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4C2×D6112yes—
174C2×C22⋊C4C2×D6112yes—
175C2×C42—611no—
176#95—611no—
177#95—612no—
178#95C2×D6111yescharacteristic
179C24—612no—
180C24C22×D6112yes—
181C2×D4—24no—
182C2×D4—41no—
183C2×D4—618no—
184C2×D4—1224no—
185C2×D4—1224no—
186C2×D4—1224no—
187C2×D4—1224no—
188C2×D4—1224no—
189C2×D4—2441no—
190C2×D4—2442no—
191C22×C4—612no—
192C22×C4—612no—
193C22×C4—612no—
194C22×C4—1224no—
195C22×C4—1224no—
196C22×C4—1224no—
197C22×C4—1224no—
198C22×C4—1224no—
199C22×C4—1224no—
200C22×C4C22×D6112yes—
201C22×C4C22×D6111yescharacteristic
202C22×C4C22×D6111yescharacteristic
203C22×C4C22×D6111yescharacteristic
204C4⋊C4—41no—
205C4⋊C4—1224no—
206C4⋊C4—1224no—
207C4⋊C4—1224no—
208C4⋊C4—2441no—
209C22⋊C4—24no—
210C22⋊C4—24no—
211C22⋊C4—1224no—
212C22⋊C4—1224no—
213C22⋊C4—1224no—
214C22⋊C4—1224no—
215C42—614no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—614no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23—1222no—
229C23D4×D6114yes—
230C23C23×D6111yescharacteristic
231D4—44no—
232D4—12216no—
233D4—2444no—
234D4—2448no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—614no—
245C2×C4—614no—
246C2×C4—614no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—2448no—
254C2×C4—2448no—
255C2×C4D4×D6112yes—
256C22—24no—
257C22—24no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—1224no—
264C22—1224no—
265C22—1224no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22—2442no—
270C22C2×D4×D6111yescharacteristic
271C22C2×D4×D6112yes—
272C22#41×D6112yes—
273C22#1451982211yescharacteristic
274C22#1451982411yescharacteristic
275C4—22no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—618no—
280C4—2442no—
281C4—2442no—
282C2—44no—
283C2—2444no—
284C2#121×D6112yes—
285C2#1684033911yescharacteristic
286C2#1684039411yescharacteristic
287C2#1684041012yes—
288C2#1684047411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2537
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519750C2semidirect
2. C2×#14519749C2semidirect
3. C2×#14519737C2semidirect
4. #16839679C2semidirect
5. #16839678C2semidirect
6. #16839631C2semidirect
7. #16839621C2semidirect
8. #16839620C2semidirect
9. C61×#394C2semidirect
47. C2×C22⋊D61D4semidirect
70. C4×Dic61D4semidirect
136. Dic61#121semidirect
150. #394D61semidirect
154. C61#2537semidirect