Finite Group Databasebeta

← #21458058

Subgroups — #21458058

Order 7808.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840478C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic, complemented
3#16840110C211yesmaximal, characteristic, complemented
4#16840088C212yesmaximal, complemented
5#16840016C212yesmaximal, complemented
6#16839958C211yesmaximal, characteristic, complemented
7#16839897C212yesmaximal, complemented
8C4×#11758199C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic, complemented
10#16839765C212yesmaximal, complemented
11C61×#476C211yesmaximal, characteristic, complemented
12C22×D244—21no—
13C2×D4×D61C2212yes—
14C2×D488C2212yescomplemented
15C2×#11758199C2211yescharacteristic
16C2×#11758189C2212yescomplemented
17#14519774C2211yescharacteristic
18#14519766—22no—
19#14519752—21no—
20#14519752C2212yes—
21#14519752C2212yescomplemented
22#14519751—21no—
23#14519747—22no—
24C4×D244C2211yescharacteristic
25C4×D244C2211yescharacteristic, complemented
26#14519735—21no—
27#14519735C2212yescomplemented
28#14519710C2211yescharacteristic, complemented
29#14519699C2212yescomplemented
30#14519698C2211yescharacteristic
31#14519697C2211yescharacteristic, complemented
32#14519697C2212yescomplemented
33#14519697C2212yescomplemented
34#14519689C2212yescomplemented
35C4×#92418C2211yescharacteristic, complemented
36C4⋊Q8×C61C2211yescharacteristic, complemented
37C4×D4×C61C2211yescharacteristic
38#106×C61C2212yescomplemented
39C4⋊C8×C61C2211yescharacteristic, complemented
40#102×C61C2212yes—
41C23×D61—22no—
42C2×Q8×C61—21no—
43C2×D4×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C2×C22⋊D61—22no—
46D4×D61—24no—
47D4×D61—42no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244—22no—
51C2×D244—21no—
52C2×D244—44no—
53C2×D244D411yescharacteristic
54C2×D244C2312yes—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×C4×D61C2312yes—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C22⋊C4×C61—21no—
63C42×C61C2311yescharacteristic
64#11758199—22no—
65#11758198—22no—
66#11758198—21no—
67#11758198—22no—
68#11758198—22no—
69#11758198D412yes—
70C4⋊Dic61D411yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72C4×Dic61—22no—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75D488—42no—
76#11758189—42no—
77C23×C61—21no—
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—82no—
83C22×D61C2×D412yes—
84Q8×C61—81no—
85D4×C61—21no—
86D4×C61#4112yes—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—44no—
94C2×Dic61—21no—
95C2×Dic61C2×D412yes—
96D244—22no—
97D244—21no—
98D244—22no—
99D244—21no—
100D244—22no—
101D244—44no—
102D244—42no—
103D244—81no—
104D244—82no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—42no—
108C8×C61—22no—
109#92418—21no—
110#92418—21no—
111C22×C61—22no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61C22×D411yescharacteristic
115C2×D61—22no—
116C2×D61—22no—
117C2×D61—22no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—88no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—42no—
128C4×C61AGL(1,ℤ/8)12yes—
129C4×C61C2×#4111yescharacteristic
130C4×C61H(5,𝔽2)11yescharacteristic
131Dic61—22no—
132Dic61—41no—
133#3325—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61#54611yescharacteristic
136C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C61#57611yescharacteristic
138D61—42no—
139D61—81no—
140D61—82no—
141#555—611no—
142D42—611no—
143#486—611no—
144#482—612no—
145#476D6111yescharacteristic, complemented
146#469—612no—
147#459—611no—
148#447—612no—
149C4×D8—611no—
150#436—611no—
151#418—612no—
152C61#332511yescharacteristic, complemented, Sylow
153C22×D4—612no—
154C22×D4—1221no—
155C2×D8—611no—
156C2×D8—612no—
157C2×M16—612no—
158C4⋊Q8C2×D6111yescharacteristic, complemented
159#127—611no—
160#124—1222no—
161#121—612no—
162#121—612no—
163#121—1221no—
164#121—1221no—
165#120—1222no—
166C4×D4—611no—
167C4×D4—611no—
168C4×D4C2×D6111yescharacteristic
169#117—612no—
170#117—1221no—
171#107—611no—
172#106C2×D6112yescomplemented
173C4⋊C8C2×D6111yescharacteristic, complemented
174#102—611no—
175#102—612no—
176#102—612no—
177#102—611no—
178#102—612no—
179#102C2×D6112yes—
180C22⋊C8—612no—
181C4×C8—611no—
182C24—1222no—
183C2×Q8—21no—
184C2×D4—611no—
185C2×D4—612no—
186C2×D4—611no—
187C2×D4—1222no—
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—1224no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4—2444no—
194C2×D4—2442no—
195C2×D4C22×D6111yescharacteristic
196C22×C4—21no—
197C22×C4—612no—
198C22×C4—1221no—
199D8—1222no—
200D8—2442no—
201M16—2442no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8C22×D6112yes—
205C4⋊C4—21no—
206C4⋊C4—611no—
207C4⋊C4—611no—
208C4⋊C4C22×D6112yes—
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—612no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1222no—
215C22⋊C4—1221no—
216C42—1222no—
217C42C22×D6111yescharacteristic
218C23—21no—
219C23—612no—
220C23—1221no—
221C23—1222no—
222C23—4882no—
223C23—2444no—
224C23—2444no—
225Q8—81no—
226D4—21no—
227D4—1221no—
228D4—1222no—
229D4—1221no—
230D4—1222no—
231D4—1222no—
232D4—4881no—
233D4—4882no—
234D4—2444no—
235D4—2444no—
236D4—2442no—
237D4#1175822612yes—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—612no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—2442no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—22no—
250C8—1221no—
251C8—1221no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—1222no—
256C22—1222no—
257C22—1222no—
258C22—4888no—
259C22—2441no—
260C22—2442no—
261C22—2441no—
262C22—2442no—
263C22—2442no—
264C22—2441no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—41no—
268C4—42no—
269C4—1222no—
270C4—2441no—
271C4#1451980412yes—
272C4C2×#1175822611yescharacteristic
273C4#1451982311yescharacteristic
274C2—42no—
275C2—4882no—
276C2—4881no—
277C2—2442no—
278C2#1684040311yescharacteristic
279C2C2×#1451980411yescharacteristic
280C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840478C2semidirect
2. D4×D244C2semidirect
3. #16840110C2semidirect
4. #16840088C2semidirect
5. #16840016C2semidirect
6. #16839958C2semidirect
7. #16839897C2semidirect
8. C4×#11758199C2semidirect
9. #16839839C2semidirect
10. #16839765C2semidirect
11. C61×#476C2semidirect
14. C2×D488C22semidirect
16. C2×#11758189C22semidirect
21. #14519752C22semidirect
25. C4×D244C22semidirect
27. #14519735C22semidirect
28. #14519710C22semidirect
29. #14519699C22semidirect
31. #14519697C22semidirect
32. #14519697C22semidirect
33. #14519697C22semidirect
34. #14519689C22semidirect
35. C4×#92418C22semidirect
36. C4⋊Q8×C61C22semidirect
38. #106×C61C22semidirect
39. C4⋊C8×C61C22semidirect
145. #476D61semidirect
152. C61#3325semidirect
158. C4⋊Q8C2×D61semidirect
172. #106C2×D61semidirect
173. C4⋊C8C2×D61semidirect