Finite Group Databasebeta

← C22×#19127611 #35570581

Subgroups — C22×#19127611 #35570581

Order 21248.

13646 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.

normal subgroups only

This group has 13646 conjugacy classes of subgroups — too many to draw. Only its 1539 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
1C24×D332C213yesmaximal, complemented
2C23×(C2×D83)⋊C4C213yesmaximal, complemented
3C2×#19127611C2124yesmaximal, direct product factor
4C22×#95×C83C211yesmaximal, characteristic, complemented
5C25×D83C2213yes—
6C23×D332—224no—
7C23×D332—248no—
8C23×D332C22136yescomplemented
9C24×Dic83C2211yescharacteristic
10C22×(C2×D83)⋊C4—224no—
11C22×(C2×D83)⋊C4C22136yescomplemented
12#19127611C22164yesdirect product factor
13C24×C4×C83C2213yes—
14C2×#95×C83C22112yescomplemented
15C24×D83—212no—
16C24×D83—224no—
17C24×D83—224no—
18C24×D83—212no—
19C24×D83D4124yescomplemented
20C24×D83C23118yes—
21C22×D332—2384no—
22C22×D332—2288no—
23C22×D332—2144no—
24C22×D332C23148yescomplemented
25C23×Dic83—212no—
26C23×Dic83C2316yes—
27C2×(C2×D83)⋊C4—2144no—
28C2×(C2×D83)⋊C4C23148yescomplemented
29C25×C83C2311yescharacteristic
30C23×C4×C83—224no—
31C23×C4×C83D4124yescomplemented
32C23×C4×C83C23118yes—
33#95×C83C23116yescomplemented
34C23×D83—2192no—
35C23×D83—296no—
36C23×D83—272no—
37C23×D83—272no—
38C23×D83—236no—
39C23×D83—236no—
40C23×D83—448no—
41C23×D83—496no—
42C23×D83—448no—
43C23×D83C2×D4172yescomplemented
44C23×D83C24112yes—
45C2×D332—21152no—
46C2×D332—2192no—
47C2×D332—296no—
48C22×Dic83—236no—
49C22×Dic83—416no—
50C22×Dic83C2414yes—
51(C2×D83)⋊C4—296no—
52C24×C83C2×D4112yes—
53C24×C83C2×D4112yes—
54C24×C83#4114yes—
55C24×C83C2413yes—
56C22×C4×C83—296no—
57C22×C4×C83—272no—
58C22×C4×C83C2×D4172yescomplemented
59C22×C4×C83C24112yes—
60C23×C83#120148yes—
61C23×C83#121148yes—
62C23×C83#127116yes—
63C23×C83C22×D4118yes—
64C23×C83C22×D4118yes—
65C23×C83C2×#4116yes—
66C23×C83C2511yescharacteristic
67C22×D83—2288no—
68C22×D83—2144no—
69C22×D83—212no—
70C22×D83—224no—
71C22×D83—224no—
72C22×D83—212no—
73C22×D83—472no—
74C22×D83—4144no—
75C22×D83—472no—
76C22×D83—4384no—
77C22×D83C22×D4124yescomplemented
78C2×C4×C83—2144no—
79C2×C4×C83—224no—
80C2×C4×C83C22×D4124yescomplemented
81C2×Dic83—212no—
82C2×Dic83—424no—
83D332—2384no—
84C22×C83#392164yescomplemented
85C22×C83C2×#120136yes—
86C22×C83C2×#121136yes—
87C22×C83C2×#127112yes—
88C22×C83C23×D413yes—
89C22×C83C23×D413yes—
90C22×C83C22×#4111yescharacteristic
91C2×D83—248no—
92C2×D83—224no—
93C2×D83—4288no—
94C2×D83—412no—
95C2×D83—424no—
96C2×D83—412no—
97C4×C83—224no—
98Dic83—44no—
99C22×#392—831nomaximal, Sylow
100C2×C83C2×#392124yescomplemented
101C2×C83C22×#12013yes—
102C2×C83C22×#12113yes—
103C2×C83C22×#12711yescharacteristic
104D83—424no—
105C24×D4—833no—
106C23×C22⋊C4—833no—
107C2×#392—8324no—
108C22×#95D8311yescharacteristic, complemented
109C83C22×#39211yescharacteristic, complemented, Sylow
110C26—833no—
111C23×D4—8336no—
112C23×D4—16648no—
113C23×D4—16624no—
114C24×C4—831no—
115C24×C4C2×D8313yes—
116C22×C22⋊C4—8336no—
117C22×C22⋊C4—16624no—
118#392—8364no—
119C2×#95C2×D83112yescomplemented
120C25—8324no—
121C25—8318no—
122C25—16624no—
123C25—16612no—
124C25—16624no—
125C25—16612no—
126C25C22×D8311yescharacteristic
127C22×D4—8348no—
128C22×D4—166288no—
129C22×D4—166384no—
130C22×D4—166144no—
131C23×C4—224no—
132C23×C4—836no—
133C23×C4—16612no—
134C23×C4D332124yescomplemented
135C23×C4C22×D83118yes—
136C2×C22⋊C4—8348no—
137C2×C22⋊C4—166144no—
138#95C22×D83116yescomplemented
139C24—33248no—
140C24—33296no—
141C24—33248no—
142C24—8372no—
143C24—8312no—
144C24—166192no—
145C24—16696no—
146C24—16672no—
147C24—16636no—
148C24—16672no—
149C24—16636no—
150C24D4×D83112yes—
151C24C2×D332112yes—
152C24#1305059114yes—
153C24C23×D8313yes—
154C2×D4—166192no—
155C2×D4—1661152no—
156C2×D4—16696no—
157C22×C4—296no—
158C22×C4—272no—
159C22×C4—33216no—
160C22×C4—834no—
161C22×C4—16636no—
162C22×C4C2×D332172yescomplemented
163C22×C4C23×D83112yes—
164C22⋊C4—16696no—
165C23—332384no—
166C23—33272no—
167C23—332144no—
168C23—33272no—
169C23—8324no—
170C23—166288no—
171C23—166144no—
172C23—16624no—
173C23—16612no—
174C23—16624no—
175C23—16612no—
176C23#14581762148yes—
177C23#14581767148yes—
178C23#14581789116yes—
179C23C2×D4×D83118yes—
180C23C22×D332118yes—
181C23C2×#1305059116yes—
182C23C24×D8311yescharacteristic
183D4—166384no—
184C2×C4—2144no—
185C2×C4—224no—
186C2×C4—33224no—
187C2×C4—16612no—
188C2×C4C22×D332124yescomplemented
189C22—332288no—
190C22—33212no—
191C22—33224no—
192C22—33212no—
193C22—16648no—
194C22—16624no—
195C22#19127611164yesdirect product factor
196C22C2×#14581762136yes—
197C22C2×#14581767136yes—
198C22C2×#14581789112yes—
199C22C22×D4×D8313yes—
200C22C23×D33213yes—
201C22C22×#1305059111yescharacteristic
202C4—224no—
203C4—3324no—
204C2—33224no—
205C2C2×#19127611124yesdirect product factor
206C2C22×#1458176213yes—
207C2C22×#1458176713yes—
208C2C22×#1458178911yescharacteristic
subgroupG/H
centerC25C22×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#95×C83C2
socleC25×C83C23
hypercenterC22×#95D83
hypocenterC83C22×#392
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C24×D332C2semidirect
2. C23×(C2×D83)⋊C4C2semidirect
3. C2×#19127611C2direct (N × H)
4. C22×#95×C83C2semidirect
8. C23×D332C22semidirect
11. C22×(C2×D83)⋊C4C22semidirect
12. #19127611C22direct (N × H)
14. C2×#95×C83C22semidirect
19. C24×D83D4semidirect
24. C22×D332C23semidirect
28. C2×(C2×D83)⋊C4C23semidirect
31. C23×C4×C83D4semidirect
33. #95×C83C23semidirect
43. C23×D83C2×D4semidirect
58. C22×C4×C83C2×D4semidirect
77. C22×D83C22×D4semidirect
80. C2×C4×C83C22×D4semidirect
84. C22×C83#392semidirect
100. C2×C83C2×#392semidirect
108. C22×#95D83semidirect
109. C83C22×#392semidirect
119. C2×#95C2×D83semidirect
134. C23×C4D332semidirect
138. #95C22×D83semidirect
162. C22×C4C2×D332semidirect
188. C2×C4C22×D332semidirect
195. C22#19127611direct (N × H)
205. C2C2×#19127611direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3322
C23×(C2×D83)⋊C42
C2×#191276112
C22×#95×C832
C22×#39283