Finite Group Databasebeta

← #21457635

Subgroups — #21457635

Order 7808.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840417C211yesmaximal, characteristic, complemented
2#16840397C211yesmaximal, characteristic, complemented
3#16840108C211yesmaximal, characteristic, complemented
4#16840074C212yesmaximal, complemented
5#16840043C211yesmaximal, characteristic, complemented
6#16839995C212yesmaximal, complemented
7#16839894C212yesmaximal, complemented
8C4×#11758199C211yesmaximal, characteristic, complemented
9#16839827C211yesmaximal, characteristic, complemented
10#102×D61C212yesmaximal, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2212yes—
15C2×#11758199C2211yescharacteristic
16C2×C8×D61C2212yescomplemented
17#14519777C2211yescharacteristic, complemented
18#14519759—22no—
19#14519756—21no—
20#14519748—21no—
21#14519748C2212yes—
22#14519748C2212yescomplemented
23#14519745—22no—
24C4×D244C2211yescharacteristic
25C4×D244C2211yescharacteristic
26C4⋊C4×D61C2212yescomplemented
27#14519711C2212yescomplemented
28#14519710C2211yescharacteristic, complemented
29#14519699C2212yes—
30#14519698C2211yescharacteristic, complemented
31#14519698C2212yescomplemented
32#14519698C2212yescomplemented
33#14519697C2211yescharacteristic
34#14519689C2212yescomplemented
35C4×#92418C2211yescharacteristic, complemented
36C2×D8×C61C2212yescomplemented
37#127×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic, complemented
39C4⋊C8×C61C2211yescharacteristic, complemented
40#102×C61C2212yescomplemented
41C23×D61—22no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50D4×D61—24no—
51D4×D61—42no—
52D4×D61—44no—
53#11758222—44no—
54C2×D244D411yescharacteristic
55C2×D244C2311yescharacteristic
56C2×C4×D61—22no—
57C2×C4×D61—21no—
58C2×C4×D61C2312yes—
59C2×Dic122—21no—
60D8×C61—42no—
61C2×C8×C61C2312yes—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67#11758199—22no—
68#11758198—21no—
69#11758198D412yes—
70C4⋊Dic61—21no—
71C4⋊Dic61D411yescharacteristic
72C4⋊Dic61C2312yes—
73C4⋊Dic61C2311yescharacteristic
74#11758196—22no—
75C2×#92418C2311yescharacteristic
76C2×#92418C2311yescharacteristic
77C8×D61—42no—
78C23×C61—21no—
79C23×C61—22no—
80C22×D61—21no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61—82no—
84C22×D61C2×D412yes—
85D4×C61—21no—
86D4×C61—22no—
87D4×C61—21no—
88D4×C61—22no—
89D4×C61—42no—
90D4×C61—81no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—44no—
97C22⋊D61—44no—
98C22⋊D61—44no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61C2×D412yes—
102D244—21no—
103D244D814yescomplemented
104D244#4112yescomplemented
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—44no—
108C4×D61—42no—
109Dic122—42no—
110C8×C61—22no—
111#92418—21no—
112#92418—21no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—41no—
119C22×C61C22×D411yescharacteristic
120C2×D61—22no—
121C2×D61—22no—
122C2×D61—22no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—88no—
126C2×D61C2×D814yes—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61C2×D812yes—
130C4×C61C2×#4111yescharacteristic
131C4×C61H(5,𝔽2)11yescharacteristic
132Dic61—22no—
133Dic61—42no—
134Dic61—41no—
135#3294—611nomaximal, Sylow
136C2×C61—82no—
137C2×C61—81no—
138C2×C61#54611yescharacteristic
139C2×C61C22×D811yescharacteristic
140C2×C61#57711yescharacteristic
141D61—24no—
142D61—42no—
143#547—611no—
144D42—611no—
145#486—611no—
146#480—612no—
147#474—611no—
148#466—612no—
149#459D6111yescharacteristic, complemented
150#447—612no—
151C4×D8—611no—
152C8×D4—611no—
153C2×#102—612no—
154C61#329411yescharacteristic, complemented, Sylow
155C2×#41—1221no—
156C22×D4—612no—
157C22×D4—1221no—
158C2×D8—611no—
159C2×D8C2×D6112yescomplemented
160C22×C8—612no—
161C4⋊Q8—611no—
162#127C2×D6111yescharacteristic
163#123—1222no—
164C22⋊Q8—1221no—
165#121—612no—
166#121—612no—
167#121—1221no—
168#120—1222no—
169C4×D4—611no—
170C4×D4—611no—
171C4×D4C2×D6111yescharacteristic, complemented
172C2×C4⋊C4—612no—
173#107—612no—
174#107—611no—
175C4⋊C8C2×D6111yescharacteristic, complemented
176#102—612no—
177#102—611no—
178#102—612no—
179#102—612no—
180#102—611no—
181#102C2×D6112yescomplemented
182C22⋊C8—612no—
183C4×C8—611no—
184C24—1222no—
185#41—2444no—
186C2×Q8—1221no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—611no—
190C2×D4—611no—
191C2×D4—1222no—
192C2×D4—1224no—
193C2×D4—1222no—
194C2×D4—1222no—
195C2×D4—2442no—
196C2×D4—2444no—
197C2×D4C22×D6112yes—
198C2×D4C22×D6111yescharacteristic
199C22×C4—21no—
200C22×C4—612no—
201C22×C4—1222no—
202C22×C4—1221no—
203D8—42no—
204D8—1222no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—2442no—
208C2×C8C22×D6112yes—
209C4⋊C4—611no—
210C4⋊C4—612no—
211C4⋊C4—611no—
212C4⋊C4—1222no—
213C4⋊C4—1221no—
214C4⋊C4C22×D6111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—612no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C22⋊C4—1221no—
220C42C22×D6111yescharacteristic
221C23—21no—
222C23—22no—
223C23—612no—
224C23—1221no—
225C23—4882no—
226C23—2444no—
227C23—2444no—
228Q8—2442no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—612no—
236D4—614no—
237D4—1221no—
238D4—2444no—
239D4—2444no—
240D4—2444no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—612no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1222no—
248C2×C4—2444no—
249C2×C4—2442no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—1221no—
255C8—1221no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—614no—
263C22—1222no—
264C22—1222no—
265C22—1222no—
266C22—4888no—
267C22—2441no—
268C22—2441no—
269C22C2×D4×D6111yescharacteristic
270C4—21no—
271C4—41no—
272C4—1222no—
273C4—2441no—
274C4—2442no—
275C4D8×D6112yes—
276C4#41×D6111yescharacteristic
277C4#1451982211yescharacteristic
278C2—82no—
279C2—81no—
280C2—1224no—
281C2—2442no—
282C2#1684040911yescharacteristic
283C2C2×D8×D6111yescharacteristic
284C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3294
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. #16840417C2semidirect
2. #16840397C2semidirect
3. #16840108C2semidirect
4. #16840074C2semidirect
5. #16840043C2semidirect
6. #16839995C2semidirect
7. #16839894C2semidirect
8. C4×#11758199C2semidirect
9. #16839827C2semidirect
10. #102×D61C2semidirect
11. C61×#459C2semidirect
16. C2×C8×D61C22semidirect
17. #14519777C22semidirect
22. #14519748C22semidirect
26. C4⋊C4×D61C22semidirect
27. #14519711C22semidirect
28. #14519710C22semidirect
30. #14519698C22semidirect
31. #14519698C22semidirect
32. #14519698C22semidirect
34. #14519689C22semidirect
35. C4×#92418C22semidirect
36. C2×D8×C61C22semidirect
38. C4×D4×C61C22semidirect
39. C4⋊C8×C61C22semidirect
40. #102×C61C22semidirect
103. D244D8semidirect
104. D244#41semidirect
149. #459D61semidirect
154. C61#3294semidirect
159. C2×D8C2×D61semidirect
171. C4×D4C2×D61semidirect
175. C4⋊C8C2×D61semidirect
181. #102C2×D61semidirect