Finite Group Databasebeta

← #21455814

Subgroups — #21455814

Order 7808.

492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#16840307C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3#16840076C211yesmaximal, characteristic, complemented
4#16840073C211yesmaximal, characteristic, complemented
5#16840040C212yesmaximal, complemented
6#16839955C212yesmaximal, complemented
7#16839896C211yesmaximal, characteristic, complemented
8D8×Dic61C212yesmaximal, complemented
9#16839842C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C23×Dic61—21no—
14C2×#11758199C2212yes—
15#14519776C2211yescharacteristic, complemented
16#14519773C2211yescharacteristic, complemented
17#14519763—21no—
18#14519751C2211yescharacteristic
19#14519749—21no—
20D4×Dic61—21no—
21D4×Dic61—21no—
22D4×Dic61C2212yes—
23D4×Dic61C2212yes—
24D4×Dic61C2211yescharacteristic, complemented
25#14519739C2211yescharacteristic, complemented
26#14519737—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519711C2212yescomplemented
31#14519710C2212yescomplemented
32#14519706C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yes—
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×D8×C61C2212yes—
40#121×C61C2211yescharacteristic
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C2×D4×C61—24no—
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C2×D4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C2×C22⋊D61—21no—
53C22×Dic61—21no—
54C22×Dic61—22no—
55C22×Dic61—22no—
56C22×Dic61—21no—
57C22×Dic61—44no—
58C22×Dic61D411yescharacteristic
59C22×Dic61D411yescharacteristic
60#11758224—44no—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×Dic122—21no—
64D8×C61—24no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—22no—
69C22⋊Dic61—22no—
70C22⋊Dic61—21no—
71#11758199—24no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2312yes—
77#11758196—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83C23×C61—24no—
84C23×C61—22no—
85C23×C61—21no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61C2×D411yescharacteristic
89C22×D61—21no—
90D4×C61—24no—
91D4×C61—22no—
92D4×C61—22no—
93D4×C61—42no—
94D4×C61#4114yescomplemented
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C22⋊D61—42no—
101C22⋊D61—42no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—44no—
108C2×Dic61—44no—
109C2×Dic61D814yescomplemented
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113C2×Dic61C2×D411yescharacteristic
114D244—22no—
115C4×D61—42no—
116Dic122—42no—
117C8×C61—22no—
118#92418—22no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—24no—
122C22×C61—48no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61C2×D812yes—
129C22×C61C22×D411yescharacteristic
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61C2×#4112yes—
136Dic61—21no—
137Dic61—21no—
138Dic61—41no—
139Dic61—42no—
140Dic61C2×D812yes—
141Dic61C2×D812yes—
142#3100—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—44no—
145C2×C61—81no—
146C2×C61#52511yescharacteristic
147C2×C61C22×D811yescharacteristic
148C2×C61#57511yescharacteristic
149D61—81no—
150#532—611no—
151C2×C4×D4—611no—
152#480—611no—
153#480—611no—
154#474—612no—
155#459—612no—
156#447—611no—
157#447D6111yescharacteristic, complemented
158C4×D8—612no—
159C4×D8—612no—
160#431—611no—
161C61#310011yescharacteristic, complemented, Sylow
162C2×#41—1221no—
163C22×D4C2×D6111yescharacteristic
164C23×C4—1221no—
165C2×D8—612no—
166C2×D8C2×D6112yes—
167C4⋊Q8—611no—
168#127—611no—
169#124—1221no—
170#121—611no—
171#121—1221no—
172#121C2×D6111yescharacteristic
173C4×D4—612no—
174C4×D4—612no—
175C4×D4—611no—
176C4×D4—611no—
177C4×D4—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—611no—
181C2×C22⋊C4—1221no—
182C2×C42—611no—
183#107—612no—
184#107—612no—
185C4⋊C8—612no—
186#102—612no—
187#102—612no—
188#102—612no—
189#102C2×D6112yes—
190C22⋊C8—611no—
191C22⋊C8C2×D6111yescharacteristic
192C4×C8—612no—
193C24—21no—
194#41—2444no—
195C2×Q8—1221no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—611no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4C22×D6111yescharacteristic
204C2×D4C22×D6112yes—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—2444no—
213C22×C4C22×D6111yescharacteristic
214D8—24no—
215D8—1224no—
216C2×C8—612no—
217C2×C8C22×D6112yes—
218C4⋊C4—612no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4C22×D6111yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—1221no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—611no—
233C23—24no—
234C23—22no—
235C23—21no—
236C23—42no—
237C23—42no—
238C23—1221no—
239C23D4×D6111yescharacteristic
240Q8—2442no—
241D4—24no—
242D4—22no—
243D4—22no—
244D4—42no—
245D4—1222no—
246D4—2442no—
247D4—2442no—
248D4—2442no—
249D4#1175822414yescomplemented
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—614no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—1222no—
258C2×C4—1221no—
259C2×C4—2442no—
260C2×C4—2444no—
261C2×C4—2444no—
262C2×C4—2442no—
263C2×C4—2441no—
264C2×C4—2442no—
265C2×C4D4×D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—21no—
270C22—21no—
271C22—24no—
272C22—48no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22D8×D6112yes—
282C22C2×D4×D6111yescharacteristic
283C4—21no—
284C4—41no—
285C4—612no—
286C4—612no—
287C4—1221no—
288C4—1221no—
289C4—2442no—
290C4—2441no—
291C4C2×#1175822412yes—
292C2—22no—
293C2—44no—
294C2—81no—
295C2—4881no—
296C2#1684026811yescharacteristic
297C2C2×D8×D6111yescharacteristic
298C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3100
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840307C2semidirect
2. C2×D4×Dic61C2semidirect
3. #16840076C2semidirect
4. #16840073C2semidirect
5. #16840040C2semidirect
6. #16839955C2semidirect
7. #16839896C2semidirect
8. D8×Dic61C2semidirect
9. #16839842C2semidirect
10. #16839812C2semidirect
11. C61×#447C2semidirect
15. #14519776C22semidirect
16. #14519773C22semidirect
24. D4×Dic61C22semidirect
25. #14519739C22semidirect
30. #14519711C22semidirect
31. #14519710C22semidirect
32. #14519706C22semidirect
33. #14519699C22semidirect
35. #14519698C22semidirect
37. C8×Dic61C22semidirect
94. D4×C61#41semidirect
109. C2×Dic61D8semidirect
157. #447D61semidirect
161. C61#3100semidirect
249. D4#11758224semidirect