Finite Group Databasebeta

← C2×#24915460 #35610522

Subgroups — C2×#24915460 #35610522

Order 21248.

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×#14581761C212yesmaximal, complemented
2#24915460C2116yesmaximal, direct product factor
3C2×#19127626C213yesmaximal, complemented
4C2×#19127617C216yesmaximal, complemented
5C2×#19127610C213yesmaximal, complemented
6C2×#379×C83C211yesmaximal, characteristic, complemented
7C23×D332C2211yescharacteristic, complemented
8C23×C22⋊D83C2216yes—
9C2×#14581761—216no—
10C2×#14581761C22116yescomplemented
11C22×C4⋊Dic83C2213yescomplemented
12C22×C22⋊Dic83C2216yes—
13C22×(C2×D83)⋊C4C2216yescomplemented
14#19127626C22124yescomplemented
15#19127617C22148yescomplemented
16#19127610C22124yescomplemented
17C2×C83⋊#95C2213yescomplemented
18C2×C83⋊#95C2213yescomplemented
19C26×C83C2211yescharacteristic
20C22×C22⋊C4×C83C2213yes—
21C22×C22⋊C4×C83C2213yes—
22#379×C83C2218yescomplemented
23C24×D83C2312yes—
24C22×D332—46no—
25C22×D332C2314yescomplemented
26C22×C22⋊D83—224no—
27C22×C22⋊D83—412no—
28C22×C22⋊D83—412no—
29C22×C22⋊D83C23124yes—
30C23×Dic83C2316yes—
31#14581761—264no—
32C2×C4⋊Dic83—46no—
33C2×C4⋊Dic83C23112yescomplemented
34C2×C22⋊Dic83—224no—
35C2×C22⋊Dic83C23124yes—
36C2×(C2×D83)⋊C4—412no—
37C2×(C2×D83)⋊C4C23124yescomplemented
38C83⋊#95C23112yescomplemented
39C83⋊#95C23112yescomplemented
40C25×C83—46no—
41C25×C83—46no—
42C25×C83D418yescomplemented
43C25×C83C2313yes—
44C25×C83C2314yes—
45C23×C4×C83C2313yes—
46C23×C4×C83C2311yescharacteristic
47C2×C22⋊C4×C83—46no—
48C2×C22⋊C4×C83—46no—
49C2×C22⋊C4×C83C23112yes—
50C2×C22⋊C4×C83C23112yes—
51C23×D83—24no—
52C23×D83—212no—
53C23×D83—212no—
54C23×D83C2414yes—
55C2×D332—412no—
56C2×D332—416no—
57C2×C22⋊D83—248no—
58C2×C22⋊D83—424no—
59C2×C22⋊D83—424no—
60C2×C22⋊D83—496no—
61C22×Dic83—212no—
62C22×Dic83—212no—
63C22×Dic83—212no—
64C22×Dic83C24112yes—
65C4⋊Dic83—412no—
66C22⋊Dic83—248no—
67(C2×D83)⋊C4—424no—
68C24×C83—212no—
69C24×C83—212no—
70C24×C83—26no—
71C24×C83—26no—
72C24×C83—448no—
73C24×C83—412no—
74C24×C83—412no—
75C24×C83—448no—
76C24×C83—416no—
77C24×C83C2×D4112yes—
78C24×C83C2×D4116yescomplemented
79C24×C83C2416yes—
80C24×C83C2411yescharacteristic
81C22×C4×C83—26no—
82C22×C4×C83—212no—
83C22×C4×C83—26no—
84C22×C4×C83C2412yes—
85C22×C4×C83C2416yes—
86C22⋊C4×C83—412no—
87C22⋊C4×C83—412no—
88C23×C83—224no—
89C23×C83—248no—
90C23×C83—26no—
91C23×C83—26no—
92C23×C83—212no—
93C23×C83—212no—
94C23×C83—448no—
95C23×C83—448no—
96C23×C83—416no—
97C23×C83—4128no—
98C23×C83—412no—
99C23×C83—424no—
100C23×C83—412no—
101C23×C83C22×D4112yes—
102C23×C83C22×D412yes—
103C23×C83H(5,𝔽2)16yes—
104C23×C83H(5,𝔽2)16yes—
105C23×C83C2511yescharacteristic
106C22×D83—24no—
107C22×D83—212no—
108C22×D83—212no—
109C22×D83—424no—
110C22×D83—424no—
111C22×D83—48no—
112C2×C4×C83—212no—
113C2×C4×C83—26no—
114C2×C4×C83—26no—
115C2×C4×C83—412no—
116C2×C4×C83—44no—
117C22⋊D83—496no—
118C2×Dic83—212no—
119C2×Dic83—212no—
120C2×Dic83—212no—
121C2×Dic83—424no—
122D332—416no—
123C22×C83—224no—
124C22×C83—212no—
125C22×C83—464no—
126C22×C83—412no—
127C22×C83—46no—
128C22×C83—46no—
129C22×C83—448no—
130C22×C83#534112yes—
131C22×C83#560112yes—
132C22×C83H(3,𝔽4)14yes—
133C22×C83C23×D411yescharacteristic
134C22×C83C2×H(5,𝔽2)13yes—
135C22×C83C2×H(5,𝔽2)13yes—
136C2×D83—412no—
137C2×D83—412no—
138C2×D83—44no—
139C2×D83—816no—
140C4×C83—46no—
141C4×C83—42no—
142Dic83—412no—
143C2×#2812—831nomaximal, Sylow
144C2×C83—412no—
145C2×C83#281218yescomplemented
146C2×C83C2×#53413yes—
147C2×C83C2×#56013yes—
148C2×C83C2×H(3,𝔽4)11yescharacteristic
149D83—84no—
150C22×#120—832no—
151#2812—8316no—
152C2×#397—833no—
153C2×#394—836no—
154C2×#392—833no—
155C2×#379D8311yescharacteristic, complemented
156C83C2×#281211yescharacteristic, complemented, Sylow
157C26C2×D8311yescharacteristic
158C23×D4—836no—
159C23×D4—831no—
160C2×#120—8316no—
161C2×#120—16616no—
162C22×C4⋊C4—833no—
163C22×C22⋊C4—836no—
164C22×C22⋊C4—836no—
165C22×C22⋊C4C2×D8313yes—
166C22×C22⋊C4C2×D8313yes—
167#397—8324no—
168#394—8348no—
169#392—8324no—
170#379C2×D8318yescomplemented
171C2×#95—833no—
172C2×#95—833no—
173C25—46no—
174C25—46no—
175C25—832no—
176C25D33218yescomplemented
177C25C22×D8313yes—
178C25C22×D8314yes—
179C22×D4—3326no—
180C22×D4—33212no—
181C22×D4—33212no—
182C22×D4—8324no—
183C22×D4—834no—
184C22×D4—16624no—
185C23×C4—836no—
186C23×C4C22×D8313yes—
187C23×C4C22×D8311yescharacteristic
188#120—16664no—
189C2×C4⋊C4—3326no—
190C2×C4⋊C4—8312no—
191C2×C22⋊C4—46no—
192C2×C22⋊C4—46no—
193C2×C22⋊C4—33212no—
194C2×C22⋊C4—8324no—
195C2×C22⋊C4—8324no—
196C2×C22⋊C4—16624no—
197C2×C22⋊C4C22×D83112yes—
198C2×C22⋊C4C22×D83112yes—
199#95—8312no—
200#95—8312no—
201C24—26no—
202C24—26no—
203C24—212no—
204C24—212no—
205C24—448no—
206C24—412no—
207C24—412no—
208C24—448no—
209C24—416no—
210C24—834no—
211C24—1664no—
212C24—16612no—
213C24—16612no—
214C24C2×D332112yes—
215C24C2×D332116yescomplemented
216C24C23×D8316yes—
217C24C23×D8311yescharacteristic
218C2×D4—33212no—
219C2×D4—33216no—
220C2×D4—33296no—
221C2×D4—33224no—
222C2×D4—33224no—
223C2×D4—16648no—
224C22×C4—212no—
225C22×C4—26no—
226C22×C4—26no—
227C22×C4—8312no—
228C22×C4—16612no—
229C22×C4—16612no—
230C22×C4—16612no—
231C22×C4C23×D8312yes—
232C22×C4C23×D8316yes—
233C4⋊C4—33212no—
234C22⋊C4—412no—
235C22⋊C4—412no—
236C22⋊C4—33224no—
237C22⋊C4—16648no—
238C23—248no—
239C23—224no—
240C23—26no—
241C23—26no—
242C23—212no—
243C23—212no—
244C23—448no—
245C23—4128no—
246C23—448no—
247C23—416no—
248C23—424no—
249C23—412no—
250C23—412no—
251C23—33224no—
252C23—3328no—
253C23—33224no—
254C23—1664no—
255C23—16612no—
256C23—16612no—
257C23C22×D332112yes—
258C23C22×D33212yes—
259C23#1458183716yes—
260C23#1458183716yes—
261C23C24×D8311yescharacteristic
262D4—33216no—
263D4—33296no—
264C2×C4—212no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—412no—
268C2×C4—44no—
269C2×C4—33224no—
270C2×C4—16612no—
271C2×C4—16612no—
272C2×C4—16612no—
273C22—224no—
274C22—212no—
275C22—464no—
276C22—448no—
277C22—412no—
278C22—46no—
279C22—46no—
280C22—33212no—
281C22—33212no—
282C22—3324no—
283C22—66416no—
284C22#19128263112yes—
285C22#19128440112yes—
286C22#1912844414yes—
287C22C23×D33211yescharacteristic
288C22C2×#1458183713yes—
289C22C2×#1458183713yes—
290C4—46no—
291C4—42no—
292C4—33212no—
293C2—412no—
294C2—6644no—
295C2#2491546018yesdirect product factor
296C2C2×#1912826313yes—
297C2C2×#1912844013yes—
298C2C2×#1912844411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#379×C83C2
socleC24×C83C24
hypercenterC2×#379D83
hypocenterC83C2×#2812
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#14581761C2semidirect
2. #24915460C2direct (N × H)
3. C2×#19127626C2semidirect
4. C2×#19127617C2semidirect
5. C2×#19127610C2semidirect
6. C2×#379×C83C2semidirect
7. C23×D332C22semidirect
10. C2×#14581761C22semidirect
11. C22×C4⋊Dic83C22semidirect
13. C22×(C2×D83)⋊C4C22semidirect
14. #19127626C22semidirect
15. #19127617C22semidirect
16. #19127610C22semidirect
17. C2×C83⋊#95C22semidirect
18. C2×C83⋊#95C22semidirect
22. #379×C83C22semidirect
25. C22×D332C23semidirect
33. C2×C4⋊Dic83C23semidirect
37. C2×(C2×D83)⋊C4C23semidirect
38. C83⋊#95C23semidirect
39. C83⋊#95C23semidirect
42. C25×C83D4semidirect
78. C24×C83C2×D4semidirect
145. C2×C83#2812semidirect
155. C2×#379D83semidirect
156. C83C2×#2812semidirect
170. #379C2×D83semidirect
176. C25D332semidirect
215. C24C2×D332semidirect
295. C2#24915460direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817612
#249154602
C2×#191276262
C2×#191276172
C2×#191276102
C2×#379×C832
C2×#281283