Finite Group Databasebeta

← #21458051

Subgroups — #21458051

Order 7808.

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

normal subgroups only

This group has 448 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#16840482C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic
3#16840109C211yesmaximal, characteristic, complemented
4#16840087C212yesmaximal, complemented
5#16840043C211yesmaximal, characteristic, complemented
6#16840008C212yesmaximal, complemented
7#16839963C211yesmaximal, characteristic, complemented
8#16839915C212yesmaximal, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839768C212yesmaximal, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C2×D4×D61—21no—
14C2×#11758190C2211yescharacteristic
15C2×#11758190C2212yescomplemented
16#14519777C2211yescharacteristic, complemented
17#14519774C2211yescharacteristic
18#14519770—22no—
19#14519764—21no—
20#14519756C2212yescomplemented
21#14519752—21no—
22#14519751C2212yes—
23#14519747—22no—
24C4×Dic122C2211yescharacteristic, complemented
25#14519742—21no—
26C4×D244C2211yescharacteristic
27#14519736C2212yescomplemented
28#14519711C2212yescomplemented
29#14519709C2211yescharacteristic, complemented
30#14519702C2211yescharacteristic, complemented
31#14519699C2211yescharacteristic
32#14519699C2212yes—
33#14519699C2212yescomplemented
34#14519699C2212yescomplemented
35#14519699C2212yescomplemented
36C2×M16×C61C2212yescomplemented
37C4×D4×C61C2211yescharacteristic
38C4⋊C8×C61C2211yescharacteristic, complemented
39C22⋊C8×C61C2212yescomplemented
40C4×C8×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×D4×C61D411yescharacteristic
43C22×C4×C61C2312yes—
44C2×C22⋊D61—22no—
45D4×D61—44no—
46C2×D244—24no—
47C2×D244—21no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244—42no—
51C2×D244C2312yes—
52C2×D244C2311yescharacteristic
53C2×C4×D61—21no—
54C2×Dic122—21no—
55C2×Dic122C2311yescharacteristic
56M16×C61—42no—
57C2×C8×C61C2311yescharacteristic
58C2×C8×C61C2311yescharacteristic
59C2×C8×C61C2312yes—
60C4⋊C4×C61D411yescharacteristic
61C22⋊C4×C61D412yes—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65#11758198—21no—
66#11758198—22no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72#11758196—21no—
73C4×Dic61—22no—
74C4×Dic61—21no—
75#11758190—22no—
76#11758190—42no—
77C23×C61C2×D412yes—
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—82no—
83D4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—44no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95D244—22no—
96D244—21no—
97D244—22no—
98D244—44no—
99D244—42no—
100D244—81no—
101D244#4112yes—
102C4×D61—42no—
103Dic122—21no—
104Dic122—21no—
105Dic122—42no—
106C8×C61—21no—
107C8×C61—22no—
108C8×C61—21no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61C22×D411yescharacteristic
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—41no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—88no—
120C4×C61—22no—
121C4×C61—21no—
122C4×C61AGL(1,ℤ/8)12yes—
123C4×C61C2×#4111yescharacteristic
124C4×C61H(5,𝔽2)11yescharacteristic
125Dic61—41no—
126Dic61—42no—
127Dic61—41no—
128Dic61—41no—
129#3324—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61#54611yescharacteristic
132C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C61#57711yescharacteristic
134D61—42no—
135D61—82no—
136#556—611no—
137D42—611no—
138#486—611no—
139#482—612no—
140#474—611no—
141#468—612no—
142#460—611no—
143#450—612no—
144C4×SD16—611no—
145#436D6111yescharacteristic, complemented
146#418—612no—
147C61#332411yescharacteristic, complemented, Sylow
148C22×D4—612no—
149C22×D4—1221no—
150C2×SD16—611no—
151C2×SD16—612no—
152C2×M16C2×D6112yescomplemented
153C4⋊Q8—611no—
154#127—611no—
155#126—1222no—
156#124—1221no—
157C22⋊Q8—612no—
158#121—612no—
159#121—1221no—
160#120—1222no—
161C4×Q8—611no—
162C4×Q8—1221no—
163C4×D4—611no—
164C4×D4C2×D6111yescharacteristic
165#117—612no—
166#107—612no—
167#106—611no—
168C4⋊C8C2×D6111yescharacteristic, complemented
169#103—611no—
170#102—611no—
171#102—612no—
172#102—612no—
173#102—612no—
174#102—612no—
175C22⋊C8C2×D6112yescomplemented
176C4×C8C2×D6111yescharacteristic, complemented
177C24—1222no—
178C2×Q8—611no—
179C2×Q8—1221no—
180C2×D4—611no—
181C2×D4—612no—
182C2×D4—1224no—
183C2×D4—1222no—
184C2×D4—1221no—
185C2×D4—1222no—
186C2×D4—1221no—
187C2×D4—2442no—
188C2×D4—2444no—
189C2×D4D24411yescharacteristic
190C22×C4—1221no—
191C22×C4C22×D6112yes—
192SD16—1222no—
193SD16—2442no—
194M16—42no—
195C2×C8C22×D6111yescharacteristic
196C2×C8C22×D6111yescharacteristic
197C2×C8C22×D6112yes—
198C4⋊C4—611no—
199C4⋊C4—612no—
200C4⋊C4—611no—
201C4⋊C4—1221no—
202C4⋊C4—1222no—
203C4⋊C4—1221no—
204C4⋊C4D24411yescharacteristic
205C22⋊C4—1222no—
206C22⋊C4—1222no—
207C22⋊C4—1221no—
208C22⋊C4—1222no—
209C22⋊C4D24412yes—
210C42—1222no—
211C42—1221no—
212C42C22×D6111yescharacteristic
213C23—1221no—
214C23—1222no—
215C23—4882no—
216C23—2444no—
217C23—2444no—
218C23C2×D24412yes—
219Q8—1221no—
220Q8—1221no—
221Q8—2442no—
222D4—22no—
223D4—612no—
224D4—1222no—
225D4—1221no—
226D4—1222no—
227D4—4881no—
228D4—2444no—
229D4—2444no—
230D4—2442no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—2442no—
238C2×C4C2×D24412yes—
239C2×C4C2×D24411yescharacteristic
240C2×C4C2×D24411yescharacteristic
241C2×C4C23×D6111yescharacteristic
242C8—21no—
243C8—21no—
244C8—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—1222no—
249C22—4888no—
250C22—2442no—
251C22—2442no—
252C22—2442no—
253C22—2441no—
254C22—2441no—
255C22C22×D24411yescharacteristic
256C4—21no—
257C4—22no—
258C4—2441no—
259C4—2442no—
260C4—2441no—
261C4—2441no—
262C4#1451980512yes—
263C4#41×D6111yescharacteristic
264C4#1451982211yescharacteristic
265C2—42no—
266C2—4882no—
267C2—2442no—
268C2#1684040711yescharacteristic
269C2C2×#1451980511yescharacteristic
270C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16840482C2semidirect
3. #16840109C2semidirect
4. #16840087C2semidirect
5. #16840043C2semidirect
6. #16840008C2semidirect
7. #16839963C2semidirect
8. #16839915C2semidirect
9. C4×#11758190C2semidirect
10. #16839768C2semidirect
11. C61×#436C2semidirect
15. C2×#11758190C22semidirect
16. #14519777C22semidirect
20. #14519756C22semidirect
24. C4×Dic122C22semidirect
27. #14519736C22semidirect
28. #14519711C22semidirect
29. #14519709C22semidirect
30. #14519702C22semidirect
33. #14519699C22semidirect
34. #14519699C22semidirect
35. #14519699C22semidirect
36. C2×M16×C61C22semidirect
38. C4⋊C8×C61C22semidirect
39. C22⋊C8×C61C22semidirect
40. C4×C8×C61C22semidirect
145. #436D61semidirect
147. C61#3324semidirect
152. C2×M16C2×D61semidirect
168. C4⋊C8C2×D61semidirect
175. C22⋊C8C2×D61semidirect
176. C4×C8C2×D61semidirect