Finite Group Databasebeta

← #21456833

Subgroups — #21456833

Order 7808.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#127×D61C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840127C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16839960C212yesmaximal, complemented
7#16839955C212yesmaximal, complemented
8#16839911C212yesmaximal, complemented
9#16839894C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2212yes—
15C2×#11758201C2212yescomplemented
16C2×#11758199C2212yescomplemented
17#14519774C2211yescharacteristic
18#14519773—21no—
19#14519773—21no—
20#14519773C2212yes—
21#14519770—21no—
22#14519769C2211yescharacteristic, complemented
23#14519759—21no—
24#14519753C2211yescharacteristic
25#14519748C2211yescharacteristic
26Q8×Dic61C2211yescharacteristic, complemented
27D4×Dic61C2211yescharacteristic, complemented
28#14519737—21no—
29#14519733—21no—
30C42×D61C2211yescharacteristic
31#14519706C2212yescomplemented
32#14519699C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519698C2212yescomplemented
36#14519689C2212yes—
37#14519688C2211yescharacteristic, complemented
38C2×SD16×C61C2212yescomplemented
39C2×D8×C61C2212yescomplemented
40#127×C61C2211yescharacteristic
41#124×C61C2211yescharacteristic, complemented
42#97×C61C2211yescharacteristic, complemented
43C23×D61—22no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61C2312yes—
48C2×D4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C22×Dic61—21no—
54D4×D61—42no—
55D4×D61—42no—
56D4×D61—44no—
57D4×D61—44no—
58C2×D244—21no—
59C2×D244—21no—
60C2×D244C2312yes—
61C2×C4×D61D411yescharacteristic
62C2×C4×D61D411yescharacteristic
63C2×C4×D61C2311yescharacteristic
64SD16×C61—42no—
65D8×C61—42no—
66C2×C8×C61C2312yes—
67C22⋊C4×C61—21no—
68C22⋊C4×C61—21no—
69C42×C61C2311yescharacteristic
70C22⋊Dic61—21no—
71C22⋊Dic61—21no—
72#11758201—42no—
73#11758199—42no—
74#11758198—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61C2311yescharacteristic
77C4⋊Dic61C2311yescharacteristic
78#11758196—21no—
79#11758196—21no—
80#11758196—21no—
81C4×Dic61—21no—
82C4×Dic61D411yescharacteristic
83C4×Dic61D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85C2×#92418C2312yes—
86C23×C61—21no—
87C23×C61—22no—
88C22×D61—22no—
89C22×D61—44no—
90C22×D61—44no—
91C22×D61—44no—
92C22×D61C2×D411yescharacteristic
93Q8×C61—22no—
94D4×C61—22no—
95D4×C61—22no—
96D4×C61—22no—
97D4×C61—42no—
98D4×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—44no—
104C22⋊D61—44no—
105C22⋊D61—42no—
106C22⋊D61—44no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—42no—
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113D244—22no—
114D244—22no—
115D244—42no—
116D244—42no—
117C4×D61—22no—
118C4×D61—22no—
119C4×D61—22no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—42no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—41no—
128C22×C61C22×D411yescharacteristic
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—88no—
135C2×D61AGL(1,ℤ/8)12yes—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61H(5,𝔽2)12yes—
140Dic61—21no—
141Dic61—21no—
142Dic61—41no—
143Dic61—41no—
144Dic61AGL(1,ℤ/8)12yes—
145#3217—611nomaximal, Sylow
146C2×C61—82no—
147C2×C61—81no—
148C2×C61#53511yescharacteristic
149C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
151D61—22no—
152D61—82no—
153C2×#127—611no—
154#529—611no—
155#496—611no—
156#496D6111yescharacteristic, complemented
157#490—611no—
158#490—611no—
159#460—612no—
160#459—612no—
161#450—612no—
162#447—612no—
163#432—611no—
164C61#321711yescharacteristic, complemented, Sylow
165C22×D4—612no—
166C22×D4—1221no—
167C22×D4—1221no—
168C2×SD16—612no—
169C2×SD16C2×D6112yescomplemented
170C2×D8—612no—
171C2×D8C2×D6112yescomplemented
172#127—612no—
173#127—611no—
174#127—1221no—
175#127—1221no—
176#127C2×D6111yescharacteristic
177#126—1221no—
178#125—611no—
179#124C2×D6111yescharacteristic, complemented
180#123—1221no—
181C22⋊Q8—611no—
182#121—611no—
183C4×Q8—611no—
184C4×D4—611no—
185C4×D4—1221no—
186#117—1221no—
187C2×C42—611no—
188C4⋊C8—612no—
189#102—612no—
190#102—612no—
191#102—612no—
192#102—612no—
193C22⋊C8—612no—
194#97—611no—
195#97C2×D6111yescharacteristic, complemented
196C24—1222no—
197C2×Q8C22×D6111yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—612no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—1222no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4—2442no—
208C2×D4—2442no—
209C2×D4—2444no—
210C2×D4—2444no—
211C2×D4C22×D6112yes—
212C2×D4C22×D6111yescharacteristic
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217SD16—42no—
218SD16—2442no—
219D8—42no—
220D8—2442no—
221C2×C8—612no—
222C2×C8C22×D6112yes—
223C4⋊C4—611no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42—1221no—
238C42C22×D6111yescharacteristic
239C23—21no—
240C23—22no—
241C23—611no—
242C23—1222no—
243C23—2444no—
244C23—2444no—
245C23—2444no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—1222no—
253D4—1222no—
254D4—2442no—
255D4—2442no—
256D4—2444no—
257D4—2444no—
258D4—2444no—
259D4—2442no—
260C2×C4—21no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—2442no—
270C2×C4D4×D6111yescharacteristic
271C2×C4D4×D6111yescharacteristic
272C2×C4C23×D6111yescharacteristic
273C8—22no—
274C8—1222no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—612no—
282C22—1221no—
283C22—1221no—
284C22—4888no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22C2×D4×D6111yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—612no—
293C4—1221no—
294C4—1221no—
295C4—2441no—
296C4—2441no—
297C4#1451982212yes—
298C2—82no—
299C2—81no—
300C2—1222no—
301C2—4882no—
302C2#1684032511yescharacteristic
303C2AGL(1,ℤ/8)×D6111yescharacteristic
304C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D61C2semidirect
2. #16840291C2semidirect
3. #16840152C2semidirect
4. #16840127C2semidirect
5. #16840126C2semidirect
6. #16839960C2semidirect
7. #16839955C2semidirect
8. #16839911C2semidirect
9. #16839894C2semidirect
10. #16839817C2semidirect
11. C61×#496C2semidirect
15. C2×#11758201C22semidirect
16. C2×#11758199C22semidirect
22. #14519769C22semidirect
26. Q8×Dic61C22semidirect
27. D4×Dic61C22semidirect
31. #14519706C22semidirect
32. #14519699C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519698C22semidirect
37. #14519688C22semidirect
38. C2×SD16×C61C22semidirect
39. C2×D8×C61C22semidirect
41. #124×C61C22semidirect
42. #97×C61C22semidirect
156. #496D61semidirect
164. C61#3217semidirect
169. C2×SD16C2×D61semidirect
171. C2×D8C2×D61semidirect
179. #124C2×D61semidirect
195. #97C2×D61semidirect