Finite Group Databasebeta

← #21451172

Subgroups — #21451172

Order 7808.

564 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic61C211yesmaximal, characteristic, complemented
2C2×#14519737C211yesmaximal, characteristic
3#16839699C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic, complemented
5#16839673C211yesmaximal, characteristic, complemented
6#16839662C212yesmaximal
7#16839659C212yesmaximal, complemented
8#16839637C212yesmaximal, complemented
9#16839636C212yesmaximal, complemented
10#16839626C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15Q8×Dic61—24no—
16#14519737—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—24no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61Q814yescomplemented
48C22×Dic61—22no—
49C22×Dic61—42no—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2312yes—
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C2×C4×D61—22no—
56C2×C4×D61—42no—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—24no—
59C22⋊Dic61—42no—
60#11758198—22no—
61#11758198—24no—
62#11758198—42no—
63C4⋊Dic61—22no—
64C4⋊Dic61—24no—
65C4⋊Dic61—42no—
66#11758196—22no—
67#11758196—24no—
68#11758196—42no—
69C4×Dic61—24no—
70C4×Dic61D414yes—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61C2×Q812yes—
76C23×C61C2411yescharacteristic
77C22×D61—21no—
78C22×D61—22no—
79C22×D61—21no—
80C22×D61—22no—
81C22×D61C2×Q812yes—
82Q8×C61—28no—
83C2×C4×C61—22no—
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—22no—
91C2×C4×C61C2×D412yes—
92C2×C4×C61#4114yes—
93C22⋊D61—28no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—44no—
104C2×Dic61C2×D412yes—
105C2×Dic61C2×D412yes—
106C2×Dic61C2×Q812yes—
107C2×Dic61#4112yes—
108C4×D61—44no—
109C22×C61—22no—
110C22×C61—24no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61C22×D411yescharacteristic
115C22×C61C22×Q811yescharacteristic
116C22×C61C2×#4111yescharacteristic
117C22×C61C2×#4112yes—
118C22×C61H(5,𝔽2)12yes—
119C2×D61—22no—
120C2×D61—24no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C4×C61—22no—
125C4×C61—24no—
126C4×C61—41no—
127C4×C61—42no—
128Dic61—22no—
129Dic61—42no—
130Dic61—41no—
131Dic61—42no—
132Dic61C22⋊Q814yes—
133#2580—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61C2×C22⋊Q811yescharacteristic
136C2×C61#52511yescharacteristic
137C2×C61#53511yescharacteristic
138C2×C61#55412yes—
139C2×C61#55912yes—
140D61—42no—
141C2×C4×Q8—611no—
142C2×C4×D4—611no—
143#399—611no—
144#399—611no—
145#393—611no—
146#393D6111yescharacteristic, complemented
147#390—612no—
148#389—612no—
149#385—612no—
150#385—612no—
151#382—611no—
152C61#258011yescharacteristic, complemented, Sylow
153C22×Q8C2×D6111yescharacteristic
154C22×D4—611no—
155C23×C4—611no—
156C23×C4—611no—
157C4×Q8—1224no—
158C4×D4—1224no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—612no—
165C2×C22⋊C4—611no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4C2×D6112yes—
171C2×C42—611no—
172C2×C42—612no—
173#95—612no—
174#95—611no—
175#95—612no—
176#95C2×D6111yescharacteristic
177#95C2×D6112yes—
178C24—611no—
179C24C22×D6111yescharacteristic
180C2×Q8—22no—
181C2×Q8—24no—
182C2×D4—614no—
183C2×D4—1222no—
184C2×D4—1222no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—612no—
188C22×C4—611no—
189C22×C4—612no—
190C22×C4—1222no—
191C22×C4—1222no—
192C22×C4—2442no—
193C22×C4—2442no—
194C22×C4C22×D6112yes—
195C22×C4C22×D6111yescharacteristic
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6112yes—
198C4⋊C4—1224no—
199C4⋊C4—1222no—
200C4⋊C4—1224no—
201C4⋊C4—1222no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C22⋊C4—22no—
205C22⋊C4—24no—
206C22⋊C4—1222no—
207C22⋊C4—1224no—
208C22⋊C4—2442no—
209C22⋊C4—2442no—
210C42—614no—
211C42—1224no—
212C23—21no—
213C23—21no—
214C23—22no—
215C23—22no—
216C23—612no—
217C23—1221no—
218C23—1221no—
219C23—1222no—
220C23—1222no—
221C23Q8×D6112yes—
222C23C23×D6111yescharacteristic
223Q8—28no—
224D4—1228no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—612no—
234C2×C4—612no—
235C2×C4—612no—
236C2×C4—612no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—2444no—
247C2×C4—2444no—
248C2×C4D4×D6112yes—
249C2×C4#1175822414yes—
250C22—24no—
251C22—22no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—1224no—
256C22—1222no—
257C22—2442no—
258C22—2441no—
259C22—2441no—
260C22C2×D4×D6111yescharacteristic
261C22C2×Q8×D6111yescharacteristic
262C22#41×D6111yescharacteristic
263C22C2×#1175822412yes—
264C22#1451982312yes—
265C4—22no—
266C4—24no—
267C4—42no—
268C4—41no—
269C4—614no—
270C4—1222no—
271C4—2442no—
272C4—2442no—
273C4—2441no—
274C2—42no—
275C2—2442no—
276C2C22⋊Q8×D6111yescharacteristic
277C2#1684026811yescharacteristic
278C2#1684033011yescharacteristic
279C2#1684047012yes—
280C2#1684049412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2580
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic61C2semidirect
3. #16839699C2semidirect
4. #16839698C2semidirect
5. #16839673C2semidirect
7. #16839659C2semidirect
8. #16839637C2semidirect
9. #16839636C2semidirect
10. #16839626C2semidirect
11. C61×#393C2semidirect
47. C2×C22⋊D61Q8semidirect
146. #393D61semidirect
152. C61#2580semidirect