Finite Group Databasebeta

← #21449177

Subgroups — #21449177

Order 7808.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×Q8×D61C211yesmaximal, characteristic, complemented
2C2×#14519754C212yesmaximal, complemented
3C2×#14519737C211yesmaximal, characteristic
4#16839683C211yesmaximal, characteristic, complemented
5#16839681C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839666C212yesmaximal, complemented
8#16839638C212yesmaximal
9#16839636C212yesmaximal, complemented
10#16839621C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2212yes—
14C2×Q8×D61—24no—
15C2×Q8×D61—28no—
16C22×C22⋊D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C22×C4×D61C2212yes—
19C22×C4×D61C2211yescharacteristic
20#14519754—28no—
21#14519737—24no—
22C2×C4⋊Dic61C2212yes—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2212yes—
25C2×#11758196C2212yes—
26C2×C22⋊Dic61C2212yes—
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C22×Q8×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2212yes—
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C24×C61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C2×Q8×C61—22no—
42C2×Q8×C61—24no—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61Q814yescomplemented
50C22×Dic61—22no—
51C22×Dic61—24no—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2311yescharacteristic
57Q8×D61—232no—
58C2×C4×D61—24no—
59C2×C4×D61—24no—
60C2×C4×D61—24no—
61C2×C4×D61—24no—
62C2×C4×D61D414yes—
63C2×Dic122—22no—
64C2×Dic122—24no—
65C2×Dic122—24no—
66C2×Dic122—24no—
67C2×Dic122D418yescomplemented
68C22⋊C4×C61—22no—
69C22⋊C4×C61—24no—
70C22⋊Dic61—24no—
71#11758198—22no—
72#11758198—24no—
73C4⋊Dic61—24no—
74#11758196—22no—
75#11758196—24no—
76#11758196—24no—
77C4×Dic61—22no—
78C23×C61—22no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—22no—
82C23×C61C2×Q812yescomplemented
83C23×C61C2411yescharacteristic
84C22×D61—22no—
85C22×D61—22no—
86C22×D61C2×D412yes—
87C22×D61C2×Q812yes—
88C22×D61#4112yes—
89Q8×C61—28no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61C2×D412yes—
99C2×C4×C61C2×D414yes—
100C22⋊D61—28no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—44no—
111C2×Dic61C2×D414yes—
112C2×Dic61C2×D412yes—
113C2×Dic61C2×D414yes—
114C2×Dic61C2×Q812yescomplemented
115C4×D61—216no—
116C4×D61—28no—
117Dic122—28no—
118Dic122—216no—
119C22×C61—22no—
120C22×C61—24no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—42no—
124C22×C61C22×D411yescharacteristic
125C22×C61C22×D412yes—
126C22×C61C22×Q811yescharacteristic
127C22×C61C2×#4111yescharacteristic
128C22×C612−1+412yes—
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—24no—
132C2×D61—24no—
133C2×D61C22⋊Q814yescomplemented
134C4×C61—22no—
135C4×C61—24no—
136C4×C61—41no—
137C4×C61—42no—
138Dic61—24no—
139Dic61—22no—
140Dic61—41no—
141Dic61—42no—
142Dic61#12014yes—
143#2409—611nomaximal, Sylow
144C2×C61—42no—
145C2×C61C2×#12011yescharacteristic
146C2×C61C2×C22⋊Q811yescharacteristic
147C2×C61#53611yescharacteristic
148C2×C61#54812yes—
149C2×C61D4×Q812yes—
150D61—24no—
151C23×Q8—611no—
152C2×C22⋊Q8—612no—
153C2×C4×D4—611no—
154#395—611no—
155#395—611no—
156#393—611no—
157#393D6111yescharacteristic, complemented
158#391—612no—
159#386—612no—
160#385—612no—
161#380—611no—
162C61#240911yescharacteristic, complemented, Sylow
163C22×Q8—612no—
164C22×Q8—611no—
165C22×Q8—1224no—
166C22×Q8—1228no—
167C22×Q8C2×D6111yescharacteristic
168C22×D4—611no—
169C23×C4—611no—
170C23×C4—611no—
171C23×C4—612no—
172C22⋊Q8—1228no—
173C4×D4—1224no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4—612no—
177C2×C4⋊C4—612no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4C2×D6111yescharacteristic
182C2×C22⋊C4C2×D6112yes—
183C2×C42—611no—
184#95—611no—
185#95—612no—
186#95—612no—
187#95—612no—
188#95C2×D6111yescharacteristic
189#95C2×D6112yes—
190C24—611no—
191C24C22×D6111yescharacteristic
192C2×Q8—22no—
193C2×Q8—24no—
194C2×Q8—618no—
195C2×Q8—1224no—
196C2×Q8—1224no—
197C2×Q8—1224no—
198C2×Q8—12232no—
199C2×Q8—1222no—
200C2×D4—614no—
201C2×D4—1222no—
202C2×D4—1222no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—612no—
206C22×C4—614no—
207C22×C4—612no—
208C22×C4—611no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4—1224no—
212C22×C4—1222no—
213C22×C4—1224no—
214C22×C4—1224no—
215C22×C4C22×D6111yescharacteristic
216C22×C4C22×D6112yes—
217C22×C4C22×D6111yescharacteristic
218C22×C4C22×D6112yes—
219C4⋊C4—1224no—
220C4⋊C4—1224no—
221C4⋊C4—1222no—
222C4⋊C4—1224no—
223C22⋊C4—22no—
224C22⋊C4—24no—
225C22⋊C4—1222no—
226C22⋊C4—1224no—
227C22⋊C4—1224no—
228C42—1222no—
229C23—22no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—612no—
234C23—612no—
235C23—612no—
236C23—1222no—
237C23—1222no—
238C23Q8×D6112yescomplemented
239C23C23×D6111yescharacteristic
240Q8—28no—
241Q8—12216no—
242Q8—1228no—
243D4—1228no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—612no—
253C2×C4—614no—
254C2×C4—614no—
255C2×C4—612no—
256C2×C4—1228no—
257C2×C4—12216no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—2444no—
268C2×C4D4×D6112yes—
269C2×C4D4×D6114yes—
270C22—22no—
271C22—24no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—614no—
276C22—1222no—
277C22—1222no—
278C22—1224no—
279C22—1224no—
280C22C2×D4×D6111yescharacteristic
281C22C2×D4×D6112yes—
282C22C2×Q8×D6111yescharacteristic
283C22#41×D6111yescharacteristic
284C22#1451982412yes—
285C4—22no—
286C4—24no—
287C4—41no—
288C4—42no—
289C4—614no—
290C4—1224no—
291C4—1222no—
292C4—2441no—
293C4—2442no—
294C2—42no—
295C2—1224no—
296C2#120×D6111yescharacteristic
297C2C22⋊Q8×D6111yescharacteristic
298C2#1684033211yescharacteristic
299C2#1684042012yes—
300C2#1684042512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2409
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D61C2semidirect
2. C2×#14519754C2semidirect
4. #16839683C2semidirect
5. #16839681C2semidirect
6. #16839674C2semidirect
7. #16839666C2semidirect
9. #16839636C2semidirect
10. #16839621C2semidirect
11. C61×#393C2semidirect
49. C2×C22⋊D61Q8semidirect
67. C2×Dic122D4semidirect
82. C23×C61C2×Q8semidirect
114. C2×Dic61C2×Q8semidirect
133. C2×D61C22⋊Q8semidirect
157. #393D61semidirect
162. C61#2409semidirect
238. C23Q8×D61semidirect