Finite Group Databasebeta

← #21456836

Subgroups — #21456836

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
1#127×D61C211yesmaximal, characteristic, complemented
2#16840294C211yesmaximal, characteristic, complemented
3#16840150C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16839963C211yesmaximal, characteristic, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839914C212yesmaximal, complemented
9#16839894C212yesmaximal, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2212yes—
15C2×#11758190C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×#11758199C2212yescomplemented
18#14519774C2211yescharacteristic
19#14519773—21no—
20#14519773—21no—
21#14519773C2212yes—
22#14519770—21no—
23#14519768C2211yescharacteristic, complemented
24#14519764C2211yescharacteristic, complemented
25#14519759—21no—
26#14519757C2211yescharacteristic
27#14519748C2211yescharacteristic
28C4×Dic122C2211yescharacteristic, complemented
29C4×C22⋊D61—21no—
30#14519736—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic, complemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yes—
37#14519687C2212yescomplemented
38C2×D8×C61C2212yescomplemented
39#127×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic, complemented
41C4⋊C8×C61C2211yescharacteristic, complemented
42#102×C61C2212yescomplemented
43C23×D61—22no—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53D4×D61—42no—
54D4×D61—42no—
55D4×D61—44no—
56D4×D61—44no—
57C2×D244—21no—
58C2×D244—21no—
59C2×D244C2312yes—
60C2×C4×D61D411yescharacteristic
61C2×C4×D61D411yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×Dic122C2311yescharacteristic
64D8×C61—42no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—21no—
72#11758200—42no—
73#11758199—42no—
74#11758198—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2311yescharacteristic
78#11758196—21no—
79#11758196—21no—
80C4×Dic61—21no—
81C4×Dic61D411yescharacteristic
82C4×Dic61D411yescharacteristic
83C4×Dic61C2311yescharacteristic
84C2×#92418C2312yes—
85#11758190—42no—
86C23×C61—21no—
87C23×C61—22no—
88C22×D61—22no—
89C22×D61—44no—
90C22×D61—44no—
91C22×D61—44no—
92C22×D61C2×D411yescharacteristic
93D4×C61—21no—
94D4×C61—22no—
95D4×C61—21no—
96D4×C61—22no—
97D4×C61—42no—
98D4×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61—42no—
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—44no—
105C22⋊D61—44no—
106C22⋊D61—44no—
107C22⋊D61—42no—
108C2×Dic61—21no—
109C2×Dic61—21no—
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—21no—
120C4×D61—21no—
121Dic122—21no—
122Dic122—21no—
123C8×C61—22no—
124#92418—22no—
125C22×C61—42no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61C22×D411yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—88no—
138C2×D61AGL(1,ℤ/8)12yes—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61AGL(1,ℤ/8)12yes—
142C4×C61H(5,𝔽2)11yescharacteristic
143C4×C61H(5,𝔽2)11yescharacteristic
144Dic61—21no—
145Dic61—21no—
146Dic61—21no—
147Dic61—41no—
148Dic61—41no—
149#3217—611nomaximal, Sylow
150C2×C61—82no—
151C2×C61—81no—
152C2×C61#53511yescharacteristic
153C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
155D61—22no—
156D61—82no—
157C2×#127—611no—
158#529—611no—
159#496—612no—
160#490—612no—
161#460—611no—
162#460—611no—
163#459—611no—
164#459D6111yescharacteristic, complemented
165#450—612no—
166#447—612no—
167#432—611no—
168C61#321711yescharacteristic, complemented, Sylow
169C22×D4—612no—
170C22×D4—1221no—
171C22×D4—1221no—
172C2×SD16—612no—
173C2×SD16—612no—
174C2×D8—612no—
175C2×D8C2×D6112yescomplemented
176#127—612no—
177#127—611no—
178#127—1221no—
179#127—1221no—
180#127C2×D6111yescharacteristic
181#126—1221no—
182#125—611no—
183#124—611no—
184#123—1221no—
185C22⋊Q8—611no—
186#121—611no—
187C4×Q8—611no—
188C4×D4—1221no—
189C4×D4C2×D6111yescharacteristic, complemented
190#117—1221no—
191C2×C42—611no—
192C4⋊C8—611no—
193C4⋊C8C2×D6111yescharacteristic, complemented
194#102—612no—
195#102—612no—
196#102—612no—
197#102C2×D6112yescomplemented
198C22⋊C8—612no—
199#97—612no—
200C24—1222no—
201C2×Q8—611no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—612no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1221no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2444no—
214C2×D4—2444no—
215C2×D4C22×D6112yes—
216C2×D4C22×D6111yescharacteristic
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221SD16—2442no—
222SD16—2442no—
223D8—42no—
224D8—2442no—
225C2×C8—612no—
226C2×C8C22×D6112yes—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C4⋊C4C22×D6111yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—1221no—
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C42—611no—
239C42—611no—
240C42—611no—
241C42—1221no—
242C42C22×D6111yescharacteristic
243C23—21no—
244C23—22no—
245C23—611no—
246C23—1222no—
247C23—2444no—
248C23—2444no—
249C23—2444no—
250Q8—1221no—
251Q8—1221no—
252D4—21no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—1222no—
259D4—1222no—
260D4—2442no—
261D4—2444no—
262D4—2444no—
263D4—2444no—
264D4—2442no—
265D4—2442no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1222no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4D4×D6111yescharacteristic
278C2×C4D4×D6111yescharacteristic
279C2×C4C23×D6111yescharacteristic
280C8—22no—
281C8—1222no—
282C22—42no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—612no—
289C22—1221no—
290C22—1221no—
291C22—4888no—
292C22—2442no—
293C22—2442no—
294C22—2442no—
295C22C2×D4×D6111yescharacteristic
296C4—21no—
297C4—41no—
298C4—1221no—
299C4—1221no—
300C4—1221no—
301C4—2441no—
302C4—2441no—
303C4#1451980112yes—
304C4#1451982211yescharacteristic
305C4#1451982311yescharacteristic
306C2—82no—
307C2—81no—
308C2—1222no—
309C2—4882no—
310C2#1684032811yescharacteristic
311C2AGL(1,ℤ/8)×D6111yescharacteristic
312C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #127×D61C2semidirect
2. #16840294C2semidirect
3. #16840150C2semidirect
4. #16840125C2semidirect
5. #16839963C2semidirect
6. #16839959C2semidirect
7. #16839957C2semidirect
8. #16839914C2semidirect
9. #16839894C2semidirect
10. #16839818C2semidirect
11. C61×#459C2semidirect
15. C2×#11758190C22semidirect
16. C2×#11758200C22semidirect
17. C2×#11758199C22semidirect
23. #14519768C22semidirect
24. #14519764C22semidirect
28. C4×Dic122C22semidirect
32. C4⋊#92418C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
37. #14519687C22semidirect
38. C2×D8×C61C22semidirect
40. C4×D4×C61C22semidirect
41. C4⋊C8×C61C22semidirect
42. #102×C61C22semidirect
164. #459D61semidirect
168. C61#3217semidirect
175. C2×D8C2×D61semidirect
189. C4×D4C2×D61semidirect
193. C4⋊C8C2×D61semidirect
197. #102C2×D61semidirect