Finite Group Databasebeta

← D61×#2842 #29886422

Subgroups — D61×#2842 #29886422

Order 15616.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 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#21454084C214yesmaximal, complemented
2#21454083C213yesmaximal, complemented
3#21454082C218yesmaximal, complemented
4#399×D61C214yesmaximal, complemented
5#396×D61C218yesmaximal, complemented
6#379×D61C213yesmaximal
7C61×#2842C211yesmaximal, characteristic, complemented
8C25×D61C2211yescharacteristic
9C2×C4⋊C4×D61C22112yescomplemented
10C2×C22⋊C4×D61C22112yes—
11C2×C22⋊C4×D61C2216yes—
12#16839699C2214yescomplemented
13#16839698C22112yescomplemented
14#16839697C22112yescomplemented
15#16839686C2218yescomplemented
16#16839685C22124yescomplemented
17#16839684C22124yescomplemented
18#16839618C2213yes—
19#16839617C22112yes—
20#16839617C2216yes—
21#95×D61C2214yescomplemented
22C61×#399C2214yescomplemented
23C61×#396C2218yescomplemented
24C61×#379C2213yes—
25C24×D61—412no—
26C24×D61Q818yes—
27C24×D61C2312yes—
28C24×D61C2311yescharacteristic
29C24×D61C2312yes—
30C24×D61C2311yescharacteristic
31C22×C4×D61C23112yes—
32C2×C4⋊Dic61C23112yescomplemented
33C2×#11758196C23124yescomplemented
34C4⋊C4×D61—424no—
35C2×C22⋊Dic61C23112yes—
36C2×C22⋊Dic61C2316yes—
37C2×#11758198C23124yes—
38C2×#11758198C23112yes—
39C22⋊C4×D61—424no—
40C22⋊C4×D61—412no—
41#14519684C23112yescomplemented
42C25×C61C2311yescharacteristic
43C2×C4⋊C4×C61C23112yescomplemented
44C2×C22⋊C4×C61C23112yes—
45C2×C22⋊C4×C61C2316yes—
46#95×C61C2314yescomplemented
47C24×C61—46no—
48C24×C61C2×Q814yes—
49C24×C61C2412yes—
50C24×C61C2411yescharacteristic
51C23×D61—224no—
52C23×D61—212no—
53C23×D61—448no—
54C23×D61—412no—
55C23×D61—46no—
56C23×D61—464no—
57C23×D61C2×Q818yes—
58C23×D61C2×Q814yes—
59C23×D61C2×Q818yes—
60C23×D61C2×Q814yes—
61C23×D61C2412yes—
62C23×D61C2411yescharacteristic
63C23×D61C2411yescharacteristic
64C22×C4×C61C24112yes—
65C22×Dic61C24112yes—
66C2×C4×D61—224no—
67C2×C4×D61—248no—
68C4⋊C4×C61—412no—
69C22⋊C4×C61—412no—
70C22⋊C4×C61—46no—
71C22⋊Dic61—46no—
72C22⋊Dic61—412no—
73#11758198—412no—
74#11758198—424no—
75C4⋊Dic61—412no—
76#11758196—424no—
77C23×C61—26no—
78C23×C61—212no—
79C23×C61—412no—
80C23×C61—416no—
81C23×C61C22×Q814yes—
82C23×C61C22×Q812yes—
83C23×C61C2511yescharacteristic
84C22×D61—26no—
85C22×D61—212no—
86C22×D61—248no—
87C22×D61—224no—
88C22×D61—424no—
89C22×D61—412no—
90C22×D61—432no—
91C22×D61—416no—
92C22×D61—4128no—
93C22×D61—432no—
94C22×D61—416no—
95C22×D61C22×Q814yes—
96C22×D61C22×Q812yes—
97C22×D61C22×Q812yes—
98C22×D61H(5,𝔽2)112yes—
99C2×C4×C61—224no—
100C2×C4×C61—212no—
101C2×Dic61—212no—
102C2×Dic61—224no—
103C4×D61—448no—
104C2×#2842—611nomaximal, Sylow
105C22×C61—26no—
106C22×C61—212no—
107C22×C61—416no—
108C22×C61—44no—
109C22×C61—48no—
110C22×C61C23×Q811yescharacteristic
111C22×C61C2×H(5,𝔽2)16yes—
112C2×D61—26no—
113C2×D61—212no—
114C2×D61—432no—
115C2×D61—416no—
116C2×D61—44no—
117C2×D61—48no—
118C2×D61—432no—
119C2×D61—416no—
120C2×D61#543112yes—
121C2×D61#560116yes—
122C4×C61—412no—
123Dic61—412no—
124#2842—614no—
125#2842—618no—
126#2842—613no—
127#2842D6111yescharacteristic, direct product factor
128C2×#399—614no—
129C2×#396—618no—
130C2×#379—613no—
131C2×C61—42no—
132C2×C61—44no—
133C2×C61C2×#54313yes—
134C2×C61C2×#56014yes—
135D61—42no—
136D61—44no—
137D61#284218yesdirect product factor
138C26—611no—
139C22×C4⋊C4—6112no—
140C22×C22⋊C4—6112no—
141C22×C22⋊C4—616no—
142#399—6112no—
143#399—6112no—
144#399—614no—
145#399C2×D6114yescomplemented
146#396—6124no—
147#396—6124no—
148#396—618no—
149#396C2×D6118yescomplemented
150#379—613no—
151#379—6112no—
152#379—616no—
153#379C2×D6113yes—
154C2×#95—614no—
155C61C2×#284211yescharacteristic, complemented, Sylow
156C25—612no—
157C25—611no—
158C25—618no—
159C25—611no—
160C25—612no—
161C25—24412no—
162C25C22×D6111yescharacteristic
163C23×C4—6112no—
164C2×C4⋊C4—6124no—
165C2×C4⋊C4—6112no—
166C2×C4⋊C4—24424no—
167C2×C4⋊C4C22×D61112yescomplemented
168C2×C22⋊C4—6112no—
169C2×C22⋊C4—616no—
170C2×C22⋊C4—6124no—
171C2×C22⋊C4—6112no—
172C2×C22⋊C4—24424no—
173C2×C22⋊C4—24412no—
174C2×C22⋊C4C22×D61112yes—
175C2×C22⋊C4C22×D6116yes—
176#95—6112no—
177#95C22×D6114yescomplemented
178C24—46no—
179C24—611no—
180C24—618no—
181C24—614no—
182C24—612no—
183C24—611no—
184C24—614no—
185C24—618no—
186C24—12224no—
187C24—12212no—
188C24—24412no—
189C24—2446no—
190C24—24448no—
191C24—24464no—
192C24Q8×D6114yes—
193C24C23×D6112yes—
194C24C23×D6111yescharacteristic
195C22×C4—6112no—
196C22×C4—12248no—
197C22×C4—12224no—
198C22×C4C23×D61112yes—
199C4⋊C4—412no—
200C4⋊C4—24424no—
201C4⋊C4—24412no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—24424no—
205C22⋊C4—24412no—
206C22⋊C4—24412no—
207C22⋊C4—2446no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—612no—
213C23—6112no—
214C23—614no—
215C23—612no—
216C23—12248no—
217C23—12224no—
218C23—12212no—
219C23—1226no—
220C23—24424no—
221C23—24412no—
222C23—24432no—
223C23—24416no—
224C23—244128no—
225C23—24432no—
226C23—24416no—
227C23C2×Q8×D6114yes—
228C23C2×Q8×D6112yes—
229C23C24×D6111yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—12212no—
233C2×C4—12224no—
234C2×C4—24448no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—6112no—
241C22—6116no—
242C22—12212no—
243C22—1226no—
244C22—24432no—
245C22—24416no—
246C22—24432no—
247C22—24416no—
248C22—2448no—
249C22—2444no—
250C22C22×Q8×D6111yescharacteristic
251C22H(5,𝔽2)×D6116yes—
252C4—412no—
253C4—24412no—
254C2—44no—
255C2—42no—
256C2—618no—
257C2—2444no—
258C2—2442no—
259C2#543×D6113yes—
260C2#560×D6114yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2842C2
prime radicalC25×D61C22
hypercenter#2842D61
hypocenterC61C2×#2842
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #21454084C2semidirect
2. #21454083C2semidirect
3. #21454082C2semidirect
4. #399×D61C2semidirect
5. #396×D61C2semidirect
7. C61×#2842C2semidirect
9. C2×C4⋊C4×D61C22semidirect
12. #16839699C22semidirect
13. #16839698C22semidirect
14. #16839697C22semidirect
15. #16839686C22semidirect
16. #16839685C22semidirect
17. #16839684C22semidirect
21. #95×D61C22semidirect
22. C61×#399C22semidirect
23. C61×#396C22semidirect
32. C2×C4⋊Dic61C23semidirect
33. C2×#11758196C23semidirect
41. #14519684C23semidirect
43. C2×C4⋊C4×C61C23semidirect
46. #95×C61C23semidirect
127. #2842D61direct (N × H)
137. D61#2842direct (N × H)
145. #399C2×D61semidirect
149. #396C2×D61semidirect
155. C61C2×#2842semidirect
167. C2×C4⋊C4C22×D61semidirect
177. #95C22×D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214540842
#214540832
#214540822
#399×D612
#396×D612
#379×D612
C61×#28422
C2×#284261