Finite Group Databasebeta

← #2842×D83 #35610813

Subgroups — #2842×D83 #35610813

Order 21248.

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#24915728C214yesmaximal, complemented
2#24915727C213yesmaximal, complemented
3#24915726C218yesmaximal, complemented
4#399×D83C214yesmaximal, complemented
5#396×D83C218yesmaximal, complemented
6#379×D83C213yesmaximal
7C83×#2842C211yesmaximal, characteristic, complemented
8C25×D83C2211yescharacteristic
9C2×C4⋊C4×D83C22112yescomplemented
10C2×C22⋊C4×D83C22112yes—
11C2×C22⋊C4×D83C2216yes—
12#19127638C2214yescomplemented
13#19127637C22112yescomplemented
14#19127636C22112yescomplemented
15#19127625C2218yescomplemented
16#19127624C22124yescomplemented
17#19127623C22124yescomplemented
18#19127557C2213yes—
19#19127556C22112yes—
20#19127556C2216yes—
21#95×D83C2214yescomplemented
22#399×C83C2214yescomplemented
23#396×C83C2218yescomplemented
24#379×C83C2213yes—
25C24×D83—412no—
26C24×D83Q818yes—
27C24×D83C2312yes—
28C24×D83C2311yescharacteristic
29C24×D83C2312yes—
30C24×D83C2311yescharacteristic
31C22×C4×D83C23112yes—
32C2×C4⋊Dic83C23112yescomplemented
33C2×Dic83⋊C4C23124yescomplemented
34C4⋊C4×D83—424no—
35C2×C22⋊Dic83C23112yes—
36C2×C22⋊Dic83C2316yes—
37C2×(C2×D83)⋊C4C23124yes—
38C2×(C2×D83)⋊C4C23112yes—
39C22⋊C4×D83—424no—
40C22⋊C4×D83—412no—
41C83⋊#95C23112yescomplemented
42C25×C83C2311yescharacteristic
43C2×C4⋊C4×C83C23112yescomplemented
44C2×C22⋊C4×C83C23112yes—
45C2×C22⋊C4×C83C2316yes—
46#95×C83C2314yescomplemented
47C23×D83—224no—
48C23×D83—212no—
49C23×D83—448no—
50C23×D83—412no—
51C23×D83—46no—
52C23×D83—464no—
53C23×D83C2×Q818yes—
54C23×D83C2×Q814yes—
55C23×D83C2×Q818yes—
56C23×D83C2×Q814yes—
57C23×D83C2412yes—
58C23×D83C2411yescharacteristic
59C23×D83C2411yescharacteristic
60C22×Dic83C24112yes—
61C2×C4×D83—224no—
62C2×C4×D83—248no—
63C4⋊Dic83—412no—
64Dic83⋊C4—424no—
65C22⋊Dic83—46no—
66C22⋊Dic83—412no—
67(C2×D83)⋊C4—412no—
68(C2×D83)⋊C4—424no—
69C24×C83—46no—
70C24×C83C2×Q814yes—
71C24×C83C2412yes—
72C24×C83C2411yescharacteristic
73C22×C4×C83C24112yes—
74C4⋊C4×C83—412no—
75C22⋊C4×C83—412no—
76C22⋊C4×C83—46no—
77C23×C83—212no—
78C23×C83—26no—
79C23×C83—412no—
80C23×C83—416no—
81C23×C83C22×Q814yes—
82C23×C83C22×Q812yes—
83C23×C83C2511yescharacteristic
84C22×D83—26no—
85C22×D83—212no—
86C22×D83—248no—
87C22×D83—224no—
88C22×D83—424no—
89C22×D83—412no—
90C22×D83—432no—
91C22×D83—416no—
92C22×D83—4128no—
93C22×D83—432no—
94C22×D83—416no—
95C22×D83C22×Q814yes—
96C22×D83C22×Q812yes—
97C22×D83C22×Q812yes—
98C22×D83H(5,𝔽2)112yes—
99C2×C4×C83—224no—
100C2×C4×C83—212no—
101C2×Dic83—212no—
102C2×Dic83—224no—
103C4×D83—448no—
104C22×C83—212no—
105C22×C83—26no—
106C22×C83—416no—
107C22×C83—48no—
108C22×C83—44no—
109C22×C83C23×Q811yescharacteristic
110C22×C83C2×H(5,𝔽2)16yes—
111C2×D83—26no—
112C2×D83—212no—
113C2×D83—432no—
114C2×D83—416no—
115C2×D83—44no—
116C2×D83—48no—
117C2×D83—432no—
118C2×D83—416no—
119C2×D83#543112yes—
120C2×D83#560116yes—
121C4×C83—412no—
122Dic83—412no—
123C2×#2842—831nomaximal, Sylow
124C2×C83—44no—
125C2×C83—42no—
126C2×C83C2×#54313yes—
127C2×C83C2×#56014yes—
128D83—42no—
129D83—44no—
130D83#284218yesdirect product factor
131#2842—834no—
132#2842—838no—
133#2842—833no—
134#2842D8311yescharacteristic, direct product factor
135C2×#399—834no—
136C2×#396—838no—
137C2×#379—833no—
138C83C2×#284211yescharacteristic, complemented, Sylow
139C26—831no—
140C22×C4⋊C4—8312no—
141C22×C22⋊C4—8312no—
142C22×C22⋊C4—836no—
143#399—8312no—
144#399—8312no—
145#399—834no—
146#399C2×D8314yescomplemented
147#396—8324no—
148#396—8324no—
149#396—838no—
150#396C2×D8318yescomplemented
151#379—833no—
152#379—8312no—
153#379—836no—
154#379C2×D8313yes—
155C2×#95—834no—
156C25—33212no—
157C25—838no—
158C25—831no—
159C25—832no—
160C25—832no—
161C25—831no—
162C25C22×D8311yescharacteristic
163C23×C4—8312no—
164C2×C4⋊C4—33224no—
165C2×C4⋊C4—8324no—
166C2×C4⋊C4—8312no—
167C2×C4⋊C4C22×D83112yescomplemented
168C2×C22⋊C4—33224no—
169C2×C22⋊C4—33212no—
170C2×C22⋊C4—8312no—
171C2×C22⋊C4—836no—
172C2×C22⋊C4—8324no—
173C2×C22⋊C4—8312no—
174C2×C22⋊C4C22×D83112yes—
175C2×C22⋊C4C22×D8316yes—
176#95—8312no—
177#95C22×D8314yescomplemented
178C24—46no—
179C24—33212no—
180C24—3326no—
181C24—33264no—
182C24—33248no—
183C24—834no—
184C24—838no—
185C24—831no—
186C24—838no—
187C24—834no—
188C24—832no—
189C24—831no—
190C24—16624no—
191C24—16612no—
192C24Q8×D8314yes—
193C24C23×D8312yes—
194C24C23×D8311yescharacteristic
195C22×C4—8312no—
196C22×C4—16648no—
197C22×C4—16624no—
198C22×C4C23×D83112yes—
199C4⋊C4—412no—
200C4⋊C4—33224no—
201C4⋊C4—33212no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—33224no—
205C22⋊C4—33212no—
206C22⋊C4—33212no—
207C22⋊C4—3326no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—33224no—
213C23—33212no—
214C23—332128no—
215C23—33232no—
216C23—33216no—
217C23—33232no—
218C23—33216no—
219C23—832no—
220C23—8312no—
221C23—834no—
222C23—832no—
223C23—16648no—
224C23—16624no—
225C23—16612no—
226C23—1666no—
227C23C2×Q8×D8314yes—
228C23C2×Q8×D8312yes—
229C23C24×D8311yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—33248no—
233C2×C4—16612no—
234C2×C4—16624no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—33232no—
241C22—33216no—
242C22—33232no—
243C22—33216no—
244C22—3328no—
245C22—3324no—
246C22—8312no—
247C22—8316no—
248C22—16612no—
249C22—1666no—
250C22C22×Q8×D8311yescharacteristic
251C22H(5,𝔽2)×D8316yes—
252C4—412no—
253C4—33212no—
254C2—44no—
255C2—42no—
256C2—3324no—
257C2—3322no—
258C2—838no—
259C2#543×D8313yes—
260C2#560×D8314yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2842C2
prime radicalC25×D83C22
hypercenter#2842D83
hypocenterC83C2×#2842
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #24915728C2semidirect
2. #24915727C2semidirect
3. #24915726C2semidirect
4. #399×D83C2semidirect
5. #396×D83C2semidirect
7. C83×#2842C2semidirect
9. C2×C4⋊C4×D83C22semidirect
12. #19127638C22semidirect
13. #19127637C22semidirect
14. #19127636C22semidirect
15. #19127625C22semidirect
16. #19127624C22semidirect
17. #19127623C22semidirect
21. #95×D83C22semidirect
22. #399×C83C22semidirect
23. #396×C83C22semidirect
32. C2×C4⋊Dic83C23semidirect
33. C2×Dic83⋊C4C23semidirect
41. C83⋊#95C23semidirect
43. C2×C4⋊C4×C83C23semidirect
46. #95×C83C23semidirect
130. D83#2842direct (N × H)
134. #2842D83direct (N × H)
138. C83C2×#2842semidirect
146. #399C2×D83semidirect
150. #396C2×D83semidirect
167. C2×C4⋊C4C22×D83semidirect
177. #95C22×D83semidirect

Maximal subgroups

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

subgroupindex
#249157282
#249157272
#249157262
#399×D832
#396×D832
#379×D832
C83×#28422
C2×#284283