Finite Group Databasebeta

← #21449179

Subgroups — #21449179

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×#14519755C212yesmaximal, complemented
3C2×#14519739C211yesmaximal, characteristic
4#16839682C211yesmaximal, characteristic, complemented
5#16839675C211yesmaximal, characteristic, complemented
6#16839673C211yesmaximal, characteristic, complemented
7#16839666C212yesmaximal, complemented
8#16839640C212yesmaximal
9#16839633C212yesmaximal, complemented
10#16839621C211yesmaximal, characteristic, complemented
11C61×#395C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2212yes—
14C2×Q8×D61—24no—
15C2×Q8×D61—28no—
16C22×D244C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2212yes—
19C22×C4×D61C2211yescharacteristic
20#14519755—28no—
21#14519739—24no—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C22×Q8×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C4⋊C4×C61C2212yes—
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C23×D61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C2×Q8×C61—22no—
42C2×Q8×C61—24no—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52Q8×D61—232no—
53C2×D244—22no—
54C2×D244—22no—
55C2×D244Q814yescomplemented
56C2×C4×D61—24no—
57C2×C4×D61—24no—
58C2×C4×D61—24no—
59C2×C4×D61—24no—
60C2×C4×D61—22no—
61C2×C4×D61—24no—
62C2×C4×D61D414yes—
63C2×Dic122—22no—
64C2×Dic122—24no—
65C2×Dic122—24no—
66C2×Dic122—24no—
67C2×Dic122D418yescomplemented
68C4⋊C4×C61—22no—
69C4⋊C4×C61—24no—
70#11758198—22no—
71#11758198—24no—
72#11758198—22no—
73#11758198—24no—
74#11758198—24no—
75#11758196—24no—
76#11758196—24no—
77C4×Dic61—22no—
78C23×C61C2411yescharacteristic
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—22no—
85C22×D61C2×D412yes—
86C22×D61C2×Q812yes—
87C22×D61C2×Q812yescomplemented
88C22×D61#4112yes—
89Q8×C61—28no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2×D414yes—
102C2×C4×C61C2×Q812yescomplemented
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61C2×D414yes—
111C2×Dic61C2×D412yes—
112C2×Dic61C2×D414yes—
113D244—28no—
114C4×D61—216no—
115C4×D61—28no—
116C4×D61—44no—
117Dic122—28no—
118Dic122—216no—
119C22×C61C22×D411yescharacteristic
120C22×C61C22×D412yes—
121C22×C61C22×Q811yescharacteristic
122C22×C61C2×#4111yescharacteristic
123C22×C612−1+412yes—
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—24no—
127C2×D61—24no—
128C2×D61—22no—
129C2×D61—24no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—42no—
133C2×D61C22⋊Q814yescomplemented
134C4×C61—22no—
135C4×C61—24no—
136C4×C61—22no—
137C4×C61—41no—
138C4×C61—42no—
139Dic61—24no—
140Dic61—41no—
141Dic61—42no—
142Dic61#12014yes—
143#2409—611nomaximal, Sylow
144C2×C61C2×#12011yescharacteristic
145C2×C61C2×C22⋊Q811yescharacteristic
146C2×C61#53611yescharacteristic
147C2×C61#54812yes—
148C2×C61D4×Q812yes—
149D61—24no—
150D61—42no—
151C23×Q8—611no—
152C2×C22⋊Q8—612no—
153C2×C4×D4—611no—
154#395—611no—
155#395D6111yescharacteristic, complemented
156#393—611no—
157#393—611no—
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—612no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4C2×D6111yescharacteristic
177C2×C4⋊C4C2×D6112yes—
178C2×C22⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C42—611no—
184#95—611no—
185#95—612no—
186#95—612no—
187#95—612no—
188#95C2×D6111yescharacteristic
189#95C2×D6112yes—
190C24—611no—
191C24—611no—
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—612no—
205C22×C4—614no—
206C22×C4—611no—
207C22×C4—612no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1222no—
211C22×C4—1224no—
212C22×C4—1224no—
213C22×C4—1224no—
214C22×C4C22×D6112yes—
215C22×C4C22×D6111yescharacteristic
216C22×C4C22×D6111yescharacteristic
217C22×C4C22×D6112yes—
218C22×C4C22×D6111yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—24no—
221C4⋊C4—1224no—
222C4⋊C4—1224no—
223C22⋊C4—1224no—
224C22⋊C4—1222no—
225C22⋊C4—1224no—
226C22⋊C4—1222no—
227C22⋊C4—1224no—
228C42—1222no—
229C23—612no—
230C23—612no—
231C23—612no—
232C23—612no—
233C23—1222no—
234C23—1222no—
235C23—1222no—
236C23—1221no—
237C23—1221no—
238C23—1222no—
239C23C23×D6111yescharacteristic
240Q8—28no—
241Q8—12216no—
242Q8—1228no—
243D4—1228no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—612no—
255C2×C4—614no—
256C2×C4—614no—
257C2×C4—1228no—
258C2×C4—12216no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—2444no—
267C2×C4D4×D6112yes—
268C2×C4D4×D6114yes—
269C2×C4Q8×D6112yescomplemented
270C22—614no—
271C22—1222no—
272C22—1222no—
273C22—1224no—
274C22—1224no—
275C22—1222no—
276C22—1224no—
277C22—2441no—
278C22—2441no—
279C22—2442no—
280C22C2×D4×D6111yescharacteristic
281C22C2×D4×D6112yes—
282C22C2×Q8×D6111yescharacteristic
283C22#41×D6111yescharacteristic
284C22#1451982512yes—
285C4—22no—
286C4—24no—
287C4—22no—
288C4—41no—
289C4—42no—
290C4—614no—
291C4—1224no—
292C4—2441no—
293C4—2442no—
294C2—1224no—
295C2—2442no—
296C2#120×D6111yescharacteristic
297C2C22⋊Q8×D6111yescharacteristic
298C2#1684033711yescharacteristic
299C2#1684042212yes—
300C2#1684042712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2409
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D61C2semidirect
2. C2×#14519755C2semidirect
4. #16839682C2semidirect
5. #16839675C2semidirect
6. #16839673C2semidirect
7. #16839666C2semidirect
9. #16839633C2semidirect
10. #16839621C2semidirect
11. C61×#395C2semidirect
55. C2×D244Q8semidirect
67. C2×Dic122D4semidirect
87. C22×D61C2×Q8semidirect
102. C2×C4×C61C2×Q8semidirect
133. C2×D61C22⋊Q8semidirect
155. #395D61semidirect
162. C61#2409semidirect
269. C2×C4Q8×D61semidirect