Finite Group Databasebeta

← #21458047

Subgroups — #21458047

Order 7808.

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

normal subgroups only

This group has 448 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#16840486C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic
3#16840110C211yesmaximal, characteristic, complemented
4#16840089C212yesmaximal, complemented
5#16840009C212yesmaximal, complemented
6#16839963C211yesmaximal, characteristic, complemented
7#16839914C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic, complemented
10#16839765C212yesmaximal, complemented
11C61×#474C211yesmaximal, characteristic, complemented
12C22×D244—21no—
13C2×D4×D61C2212yes—
14C2×#11758190C2212yescomplemented
15C2×#11758200C2211yescharacteristic
16C2×#11758189C2212yescomplemented
17#14519774C2211yescharacteristic
18#14519772—22no—
19#14519766—21no—
20#14519757C2212yescomplemented
21#14519752C2212yes—
22#14519751—21no—
23#14519747—22no—
24Q8×Dic61—21no—
25C4×Dic122C2211yescharacteristic, complemented
26C4×D244C2211yescharacteristic
27#14519735C2212yescomplemented
28#14519708C2211yescharacteristic, complemented
29#14519700C2211yescharacteristic, complemented
30#14519699C2212yescomplemented
31#14519698C2211yescharacteristic
32#14519697C2212yescomplemented
33#14519697C2212yescomplemented
34#14519689C2212yescomplemented
35C4×#92418C2211yescharacteristic, complemented
36C4⋊Q8×C61C2211yescharacteristic, complemented
37C4×D4×C61C2211yescharacteristic
38#107×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—21no—
51C2×D244—44no—
52C2×D244D411yescharacteristic
53C2×D244C2312yes—
54C2×C4×D61C2312yes—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C22⋊C4×C61—21no—
61C42×C61C2311yescharacteristic
62#11758200—22no—
63#11758198—22no—
64#11758198—22no—
65#11758198—22no—
66#11758198D412yes—
67C4⋊Dic61—22no—
68C4⋊Dic61D411yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71C4×Dic61—21no—
72C4×Dic61—22no—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75#11758190—42no—
76#11758189—42no—
77C23×C61—21no—
78C22×D61—22no—
79C22×D61—44no—
80C22×D61—44no—
81C22×D61—82no—
82C22×D61C2×D412yes—
83Q8×C61—42no—
84D4×C61—21no—
85D4×C61#4112yes—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—44no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61C2×D412yes—
96D244—22no—
97D244—22no—
98D244—22no—
99D244—44no—
100D244—42no—
101D244—81no—
102C4×D61—22no—
103C4×D61—22no—
104Dic122—21no—
105Dic122—21no—
106C8×C61—22no—
107#92418—21no—
108#92418—21no—
109C22×C61—22no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61C22×D411yescharacteristic
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—22no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—88no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61AGL(1,ℤ/8)12yes—
124C4×C61C2×#4111yescharacteristic
125C4×C61H(5,𝔽2)11yescharacteristic
126Dic61—22no—
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#474D6111yescharacteristic, complemented
141#468—612no—
142#460—611no—
143#450—612no—
144C4×SD16—611no—
145#436—611no—
146#418—612no—
147C61#332411yescharacteristic, complemented, Sylow
148C22×D4—612no—
149C22×D4—1221no—
150C2×SD16—611no—
151C2×SD16—612no—
152C2×M16—612no—
153C4⋊Q8C2×D6111yescharacteristic, complemented
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#107C2×D6112yescomplemented
167#106—611no—
168C4⋊C8C2×D6111yescharacteristic, complemented
169#103—611no—
170#102—611no—
171#102—612no—
172#102—612no—
173#102—612no—
174#102C2×D6112yes—
175C22⋊C8—612no—
176C4×C8—611no—
177C24—1222no—
178C2×Q8—21no—
179C2×Q8—611no—
180C2×D4—611no—
181C2×D4—612no—
182C2×D4—1222no—
183C2×D4—1222no—
184C2×D4—1224no—
185C2×D4—1221no—
186C2×D4—1221no—
187C2×D4—2444no—
188C2×D4—2442no—
189C2×D4C22×D6111yescharacteristic
190C22×C4—21no—
191C22×C4—612no—
192SD16—1222no—
193SD16—2442no—
194M16—2442no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8C22×D6112yes—
198C4⋊C4—21no—
199C4⋊C4—611no—
200C4⋊C4—611no—
201C4⋊C4—1222no—
202C4⋊C4—1221no—
203C4⋊C4C22×D6112yes—
204C4⋊C4C22×D6111yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—612no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C42—1222no—
211C42—1221no—
212C42C22×D6111yescharacteristic
213C23—21no—
214C23—612no—
215C23—1222no—
216C23—4882no—
217C23—2444no—
218C23—2444no—
219Q8—42no—
220Q8—1221no—
221Q8—1221no—
222D4—21no—
223D4—1222no—
224D4—1222no—
225D4—1222no—
226D4—4881no—
227D4—2444no—
228D4—2444no—
229D4—2442no—
230D4#1175822612yes—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—612no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4D4×D6111yescharacteristic
240C2×C4D4×D6111yescharacteristic
241C2×C4C23×D6111yescharacteristic
242C8—22no—
243C8—1221no—
244C8—1221no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—1222no—
249C22—1222no—
250C22—1222no—
251C22—4888no—
252C22—2442no—
253C22—2442no—
254C22—2442no—
255C22C2×D4×D6111yescharacteristic
256C4—21no—
257C4—41no—
258C4—42no—
259C4—1222no—
260C4—2441no—
261C4—2441no—
262C4#1451980112yes—
263C4C2×#1175822611yescharacteristic
264C4#1451982311yescharacteristic
265C2—42no—
266C2—4882no—
267C2—2442no—
268C2#1684040311yescharacteristic
269C2C2×#1451980111yescharacteristic
270C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840486C2semidirect
3. #16840110C2semidirect
4. #16840089C2semidirect
5. #16840009C2semidirect
6. #16839963C2semidirect
7. #16839914C2semidirect
8. C4×#11758200C2semidirect
9. #16839839C2semidirect
10. #16839765C2semidirect
11. C61×#474C2semidirect
14. C2×#11758190C22semidirect
16. C2×#11758189C22semidirect
20. #14519757C22semidirect
25. C4×Dic122C22semidirect
27. #14519735C22semidirect
28. #14519708C22semidirect
29. #14519700C22semidirect
30. #14519699C22semidirect
32. #14519697C22semidirect
33. #14519697C22semidirect
34. #14519689C22semidirect
35. C4×#92418C22semidirect
36. C4⋊Q8×C61C22semidirect
38. #107×C61C22semidirect
39. C4⋊C8×C61C22semidirect
140. #474D61semidirect
147. C61#3324semidirect
153. C4⋊Q8C2×D61semidirect
166. #107C2×D61semidirect
168. C4⋊C8C2×D61semidirect