Finite Group Databasebeta

← #21456840

Subgroups — #21456840

Order 7808.

490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14519773C211yesmaximal, characteristic, complemented
2#16840298C211yesmaximal, characteristic, complemented
3#16840148C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16839960C212yesmaximal, complemented
6#16839956C212yesmaximal, complemented
7#16839912C211yesmaximal, characteristic, complemented
8#16839898C211yesmaximal, characteristic, complemented
9#16839896C211yesmaximal, characteristic, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61—21no—
14C22×C22⋊D61—21no—
15C2×#11758201C2212yescomplemented
16C2×D488C2212yescomplemented
17C2×#11758199C2212yescomplemented
18#14519773—21no—
19#14519773—21no—
20#14519773C2212yes—
21#14519773C2212yes—
22#14519772—21no—
23#14519768C2211yescharacteristic, complemented
24#14519766C2211yescharacteristic, complemented
25#14519761—21no—
26#14519751C2211yescharacteristic
27Q8×Dic61C2211yescharacteristic, complemented
28#14519739C2211yescharacteristic, complemented
29#14519737—21no—
30#14519735—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yescomplemented
38C22×D4×C61C2211yescharacteristic
39C2×SD16×C61C2212yescomplemented
40C22⋊Q8×C61C2211yescharacteristic
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61—21no—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—44no—
56C2×C22⋊D61—44no—
57C22×Dic61D411yescharacteristic
58C22×Dic61D411yescharacteristic
59C2×D244—21no—
60C2×D244—42no—
61C2×D244C2312yes—
62C2×D244C2311yescharacteristic
63C2×C4×D61—21no—
64SD16×C61—42no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61—21no—
67C4⋊C4×C61C2311yescharacteristic
68C22⋊C4×C61—21no—
69#11758201—42no—
70#11758199—42no—
71#11758198—21no—
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2311yescharacteristic
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61D411yescharacteristic
81C4×Dic61D411yescharacteristic
82C4×Dic61C2311yescharacteristic
83C4×Dic61C2311yescharacteristic
84C2×#92418C2312yes—
85D488—42no—
86C23×C61—22no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61C2×D411yescharacteristic
91C22×D61—21no—
92C22×D61—22no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96Q8×C61—22no—
97D4×C61—22no—
98D4×C61—22no—
99D4×C61—42no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2411yescharacteristic
105C22⋊D61—44no—
106C22⋊D61—44no—
107C22⋊D61—44no—
108C22⋊D61—42no—
109C22⋊D61—44no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—21no—
113C2×Dic61C2×D411yescharacteristic
114C2×Dic61C2×D411yescharacteristic
115C2×Dic61C2×D411yescharacteristic
116C2×Dic61C2×D411yescharacteristic
117D244—22no—
118D244—22no—
119D244—22no—
120D244—42no—
121C4×D61—42no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—84no—
130C22×C61AGL(1,ℤ/8)12yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—41no—
138C2×D61—84no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61H(5,𝔽2)12yes—
143Dic61—21no—
144Dic61—21no—
145Dic61—21no—
146Dic61—41no—
147Dic61AGL(1,ℤ/8)12yes—
148#3217—611nomaximal, Sylow
149C2×C61—22no—
150C2×C61—82no—
151C2×C61#53511yescharacteristic
152C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
154D61—81no—
155D61—82no—
156C2×#127—611no—
157#529—611no—
158#496—612no—
159#490—612no—
160#460—612no—
161#459—612no—
162#450—611no—
163#450D6111yescharacteristic, complemented
164#447—611no—
165#447—611no—
166#432—611no—
167C61#321711yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C22×D4—1221no—
170C22×D4—1221no—
171C22×D4C2×D6111yescharacteristic
172C2×SD16—612no—
173C2×SD16C2×D6112yescomplemented
174C2×D8—612no—
175C2×D8—612no—
176#127—612no—
177#127—612no—
178#127—1221no—
179#127—1221no—
180#126—1221no—
181#125—611no—
182#124—611no—
183#123—1221no—
184C22⋊Q8C2×D6111yescharacteristic
185#121—611no—
186C4×Q8—611no—
187C4×D4—611no—
188C4×D4—1221no—
189#117—1221no—
190C2×C42—611no—
191C4⋊C8—612no—
192#102—612no—
193#102—612no—
194#102—612no—
195#102C2×D6112yescomplemented
196C22⋊C8—611no—
197C22⋊C8C2×D6111yescharacteristic
198#97—612no—
199C24—21no—
200C24—1221no—
201C2×Q8C22×D6111yescharacteristic
202C2×D4—21no—
203C2×D4—42no—
204C2×D4—612no—
205C2×D4—611no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1221no—
211C2×D4—1221no—
212C2×D4—2442no—
213C2×D4—2444no—
214C2×D4—2444no—
215C2×D4C22×D6112yes—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1221no—
219C22×C4C22×D6111yescharacteristic
220SD16—42no—
221SD16—2442no—
222D8—2442no—
223D8—2442no—
224C2×C8—612no—
225C2×C8C22×D6112yes—
226C4⋊C4—21no—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4C22×D6111yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—1221no—
234C22⋊C4—1221no—
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C42—611no—
238C42—611no—
239C42—611no—
240C42—611no—
241C42—1221no—
242C23—22no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—1221no—
247C23—1222no—
248C23—2442no—
249C23—2442no—
250C23—2442no—
251C23D4×D6111yescharacteristic
252Q8—22no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—1222no—
257D4—1222no—
258D4—1222no—
259D4—2442no—
260D4—2444no—
261D4—2444no—
262D4—2444no—
263D4—2444no—
264D4—2442no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1221no—
275C2×C4—2442no—
276C2×C4D4×D6111yescharacteristic
277C2×C4C23×D6111yescharacteristic
278C8—22no—
279C8—1222no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—4884no—
287C22—2441no—
288C22—2442no—
289C22—2442no—
290C22—2441no—
291C22—2442no—
292C22—2441no—
293C22#1451980412yes—
294C22C2×D4×D6111yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—612no—
299C4—1221no—
300C4—1221no—
301C4—1221no—
302C4—2441no—
303C4#1451982212yes—
304C2—22no—
305C2—82no—
306C2—4882no—
307C2—4881no—
308C2#1684032711yescharacteristic
309C2AGL(1,ℤ/8)×D6111yescharacteristic
310C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. #16840298C2semidirect
3. #16840148C2semidirect
4. #16840125C2semidirect
5. #16839960C2semidirect
6. #16839956C2semidirect
7. #16839912C2semidirect
8. #16839898C2semidirect
9. #16839896C2semidirect
10. #16839816C2semidirect
11. C61×#450C2semidirect
15. C2×#11758201C22semidirect
16. C2×D488C22semidirect
17. C2×#11758199C22semidirect
23. #14519768C22semidirect
24. #14519766C22semidirect
27. Q8×Dic61C22semidirect
28. #14519739C22semidirect
32. #14519706C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
37. #14519687C22semidirect
39. C2×SD16×C61C22semidirect
41. #102×C61C22semidirect
163. #450D61semidirect
167. C61#3217semidirect
173. C2×SD16C2×D61semidirect
195. #102C2×D61semidirect