Finite Group Databasebeta

← C2×#21453816 #29886131

Subgroups — C2×#21453816 #29886131

Order 15616.

4438 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 4438 conjugacy classes of subgroups — too many to draw. Only its 667 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
1C22×#14519746C212yesmaximal, complemented
2#21453816C2116yesmaximal, direct product factor
3C2×#16839687C213yesmaximal, complemented
4C2×#16839678C216yesmaximal, complemented
5C2×#16839671C213yesmaximal, complemented
6C2×C61×#379C211yesmaximal, characteristic, complemented
7C23×D244C2211yescharacteristic, complemented
8C23×C22⋊D61C2216yes—
9C2×#14519746—216no—
10C2×#14519746C22116yescomplemented
11C22×C4⋊Dic61C2213yescomplemented
12C22×C22⋊Dic61C2216yes—
13C22×#11758198C2216yescomplemented
14#16839687C22124yescomplemented
15#16839678C22148yescomplemented
16#16839671C22124yescomplemented
17C2×#14519684C2213yescomplemented
18C2×#14519684C2213yescomplemented
19C26×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2213yes—
21C22×C22⋊C4×C61C2213yes—
22C61×#379C2218yescomplemented
23C24×D61C2312yes—
24C22×D244—46no—
25C22×D244C2314yescomplemented
26C22×C22⋊D61—224no—
27C22×C22⋊D61—412no—
28C22×C22⋊D61—412no—
29C22×C22⋊D61C23124yes—
30C23×Dic61C2316yes—
31#14519746—264no—
32C2×C4⋊Dic61—46no—
33C2×C4⋊Dic61C23112yescomplemented
34C2×C22⋊Dic61—224no—
35C2×C22⋊Dic61C23124yes—
36C2×#11758198—412no—
37C2×#11758198C23124yescomplemented
38#14519684C23112yescomplemented
39#14519684C23112yescomplemented
40C25×C61—46no—
41C25×C61—46no—
42C25×C61D418yescomplemented
43C25×C61C2313yes—
44C25×C61C2314yes—
45C23×C4×C61C2313yes—
46C23×C4×C61C2311yescharacteristic
47C2×C22⋊C4×C61—46no—
48C2×C22⋊C4×C61—46no—
49C2×C22⋊C4×C61C23112yes—
50C2×C22⋊C4×C61C23112yes—
51C24×C61—212no—
52C24×C61—212no—
53C24×C61—26no—
54C24×C61—26no—
55C24×C61—448no—
56C24×C61—412no—
57C24×C61—412no—
58C24×C61—448no—
59C24×C61—416no—
60C24×C61C2×D4112yes—
61C24×C61C2×D4116yescomplemented
62C24×C61C2416yes—
63C24×C61C2411yescharacteristic
64C23×D61—24no—
65C23×D61—212no—
66C23×D61—212no—
67C23×D61C2414yes—
68C22×C4×C61—26no—
69C22×C4×C61—212no—
70C22×C4×C61—26no—
71C22×C4×C61C2412yes—
72C22×C4×C61C2416yes—
73C2×C22⋊D61—248no—
74C2×C22⋊D61—424no—
75C2×C22⋊D61—424no—
76C2×C22⋊D61—496no—
77C22×Dic61—212no—
78C22×Dic61—212no—
79C22×Dic61—212no—
80C22×Dic61C24112yes—
81C2×D244—412no—
82C2×D244—416no—
83C22⋊C4×C61—412no—
84C22⋊C4×C61—412no—
85C22⋊Dic61—248no—
86#11758198—424no—
87C4⋊Dic61—412no—
88C23×C61—248no—
89C23×C61—224no—
90C23×C61—26no—
91C23×C61—26no—
92C23×C61—212no—
93C23×C61—212no—
94C23×C61—448no—
95C23×C61—448no—
96C23×C61—416no—
97C23×C61—4128no—
98C23×C61—412no—
99C23×C61—424no—
100C23×C61—412no—
101C23×C61C22×D4112yes—
102C23×C61C22×D412yes—
103C23×C61H(5,𝔽2)16yes—
104C23×C61H(5,𝔽2)16yes—
105C23×C61C2511yescharacteristic
106C22×D61—24no—
107C22×D61—212no—
108C22×D61—212no—
109C22×D61—424no—
110C22×D61—424no—
111C22×D61—48no—
112C2×C4×C61—26no—
113C2×C4×C61—212no—
114C2×C4×C61—26no—
115C2×C4×C61—412no—
116C2×C4×C61—44no—
117C22⋊D61—496no—
118C2×Dic61—212no—
119C2×Dic61—212no—
120C2×Dic61—212no—
121C2×Dic61—424no—
122D244—416no—
123C2×#2812—611nomaximal, Sylow
124C22×C61—224no—
125C22×C61—212no—
126C22×C61—464no—
127C22×C61—412no—
128C22×C61—46no—
129C22×C61—46no—
130C22×C61—448no—
131C22×C61#534112yes—
132C22×C61#560112yes—
133C22×C61H(3,𝔽4)14yes—
134C22×C61C23×D411yescharacteristic
135C22×C61C2×H(5,𝔽2)13yes—
136C22×C61C2×H(5,𝔽2)13yes—
137C2×D61—412no—
138C2×D61—412no—
139C2×D61—44no—
140C2×D61—816no—
141C4×C61—46no—
142C4×C61—42no—
143Dic61—412no—
144C22×#120—612no—
145#2812—6116no—
146C2×#397—613no—
147C2×#394—616no—
148C2×#392—613no—
149C2×#379D6111yescharacteristic, complemented
150C2×C61—412no—
151C2×C61#281218yescomplemented
152C2×C61C2×#53413yes—
153C2×C61C2×#56013yes—
154C2×C61C2×H(3,𝔽4)11yescharacteristic
155D61—84no—
156C26C2×D6111yescharacteristic
157C23×D4—616no—
158C23×D4—611no—
159C2×#120—6116no—
160C2×#120—12216no—
161C22×C4⋊C4—613no—
162C22×C22⋊C4—616no—
163C22×C22⋊C4—616no—
164C22×C22⋊C4C2×D6113yes—
165C22×C22⋊C4C2×D6113yes—
166#397—6124no—
167#394—6148no—
168#392—6124no—
169#379C2×D6118yescomplemented
170C2×#95—613no—
171C2×#95—613no—
172C61C2×#281211yescharacteristic, complemented, Sylow
173C25—46no—
174C25—46no—
175C25—612no—
176C25D24418yescomplemented
177C25C22×D6113yes—
178C25C22×D6114yes—
179C22×D4—6124no—
180C22×D4—614no—
181C22×D4—12224no—
182C22×D4—2446no—
183C22×D4—24412no—
184C22×D4—24412no—
185C23×C4—616no—
186C23×C4C22×D6113yes—
187C23×C4C22×D6111yescharacteristic
188#120—12264no—
189C2×C4⋊C4—6112no—
190C2×C4⋊C4—2446no—
191C2×C22⋊C4—46no—
192C2×C22⋊C4—46no—
193C2×C22⋊C4—6124no—
194C2×C22⋊C4—6124no—
195C2×C22⋊C4—12224no—
196C2×C22⋊C4—24412no—
197C2×C22⋊C4C22×D61112yes—
198C2×C22⋊C4C22×D61112yes—
199#95—6112no—
200#95—6112no—
201C24—26no—
202C24—26no—
203C24—212no—
204C24—212no—
205C24—448no—
206C24—412no—
207C24—412no—
208C24—448no—
209C24—416no—
210C24—614no—
211C24—1224no—
212C24—12212no—
213C24—12212no—
214C24C2×D244112yes—
215C24C2×D244116yescomplemented
216C24C23×D6116yes—
217C24C23×D6111yescharacteristic
218C2×D4—12248no—
219C2×D4—24412no—
220C2×D4—24416no—
221C2×D4—24424no—
222C2×D4—24424no—
223C2×D4—24496no—
224C22×C4—212no—
225C22×C4—26no—
226C22×C4—26no—
227C22×C4—6112no—
228C22×C4—12212no—
229C22×C4—12212no—
230C22×C4—12212no—
231C22×C4C23×D6112yes—
232C22×C4C23×D6116yes—
233C4⋊C4—24412no—
234C22⋊C4—412no—
235C22⋊C4—412no—
236C22⋊C4—12248no—
237C22⋊C4—24424no—
238C23—248no—
239C23—224no—
240C23—26no—
241C23—26no—
242C23—212no—
243C23—212no—
244C23—448no—
245C23—448no—
246C23—416no—
247C23—4128no—
248C23—424no—
249C23—412no—
250C23—412no—
251C23—1224no—
252C23—12212no—
253C23—12212no—
254C23—24424no—
255C23—2448no—
256C23—24424no—
257C23C22×D244112yes—
258C23C22×D24412yes—
259C23#1451982216yes—
260C23#1451982216yes—
261C23C24×D6111yescharacteristic
262D4—24416no—
263D4—24496no—
264C2×C4—212no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—412no—
268C2×C4—44no—
269C2×C4—12212no—
270C2×C4—12212no—
271C2×C4—12212no—
272C2×C4—24424no—
273C22—224no—
274C22—212no—
275C22—464no—
276C22—412no—
277C22—46no—
278C22—46no—
279C22—448no—
280C22—48816no—
281C22—24412no—
282C22—24412no—
283C22—2444no—
284C22#16840324112yes—
285C22#16840501112yes—
286C22#1684050514yes—
287C22C23×D24411yescharacteristic
288C22C2×#1451982213yes—
289C22C2×#1451982213yes—
290C4—46no—
291C4—42no—
292C4—24412no—
293C2—412no—
294C2—4884no—
295C2#2145381618yesdirect product factor
296C2C2×#1684032413yes—
297C2C2×#1684050113yes—
298C2C2×#1684050511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#379C2
socleC24×C61C24
hypercenterC2×#379D61
hypocenterC61C2×#2812
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#14519746C2semidirect
2. #21453816C2direct (N × H)
3. C2×#16839687C2semidirect
4. C2×#16839678C2semidirect
5. C2×#16839671C2semidirect
6. C2×C61×#379C2semidirect
7. C23×D244C22semidirect
10. C2×#14519746C22semidirect
11. C22×C4⋊Dic61C22semidirect
13. C22×#11758198C22semidirect
14. #16839687C22semidirect
15. #16839678C22semidirect
16. #16839671C22semidirect
17. C2×#14519684C22semidirect
18. C2×#14519684C22semidirect
22. C61×#379C22semidirect
25. C22×D244C23semidirect
33. C2×C4⋊Dic61C23semidirect
37. C2×#11758198C23semidirect
38. #14519684C23semidirect
39. #14519684C23semidirect
42. C25×C61D4semidirect
61. C24×C61C2×D4semidirect
149. C2×#379D61semidirect
151. C2×C61#2812semidirect
169. #379C2×D61semidirect
172. C61C2×#2812semidirect
176. C25D244semidirect
215. C24C2×D244semidirect
295. C2#21453816direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197462
#214538162
C2×#168396872
C2×#168396782
C2×#168396712
C2×C61×#3792
C2×#281261