Finite Group Databasebeta

← C22×#19151508 #36720605

Subgroups — C22×#19151508 #36720605

Order 22784.

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×D356C213yesmaximal, complemented
2C23×#13083551C213yesmaximal, complemented
3C2×#19151508C2124yesmaximal, direct product factor
4C22×#95×C89C211yesmaximal, characteristic, complemented
5C25×D89C2213yes—
6C23×D356—224no—
7C23×D356—248no—
8C23×D356C22136yescomplemented
9C24×Dic89C2211yescharacteristic
10C22×#13083551—224no—
11C22×#13083551C22136yescomplemented
12#19151508C22164yesdirect product factor
13C24×C4×C89C2213yes—
14C2×#95×C89C22112yescomplemented
15C24×D89—224no—
16C24×D89—224no—
17C24×D89—212no—
18C24×D89—212no—
19C24×D89D4124yescomplemented
20C24×D89C23118yes—
21C22×D356—2384no—
22C22×D356—2288no—
23C22×D356—2144no—
24C22×D356C23148yescomplemented
25C23×Dic89—212no—
26C23×Dic89C2316yes—
27C2×#13083551—2144no—
28C2×#13083551C23148yescomplemented
29C25×C89C2311yescharacteristic
30C23×C4×C89—224no—
31C23×C4×C89D4124yescomplemented
32C23×C4×C89C23118yes—
33#95×C89C23116yescomplemented
34C23×D89—2192no—
35C23×D89—296no—
36C23×D89—272no—
37C23×D89—272no—
38C23×D89—236no—
39C23×D89—236no—
40C23×D89—448no—
41C23×D89—496no—
42C23×D89—448no—
43C23×D89C2×D4172yescomplemented
44C23×D89C24112yes—
45C2×D356—21152no—
46C2×D356—2192no—
47C2×D356—296no—
48C22×Dic89—236no—
49C22×Dic89—416no—
50C22×Dic89C2414yes—
51#13083551—296no—
52C24×C89C2×D4112yes—
53C24×C89C2×D4112yes—
54C24×C89#4114yes—
55C24×C89C2413yes—
56C22×C4×C89—296no—
57C22×C4×C89—272no—
58C22×C4×C89C2×D4172yescomplemented
59C22×C4×C89C24112yes—
60C23×C89#120148yes—
61C23×C89#121148yes—
62C23×C89#127116yes—
63C23×C89C22×D4118yes—
64C23×C89C22×D4118yes—
65C23×C89C2×#4116yes—
66C23×C89C2511yescharacteristic
67C22×D89—2288no—
68C22×D89—2144no—
69C22×D89—212no—
70C22×D89—224no—
71C22×D89—224no—
72C22×D89—212no—
73C22×D89—472no—
74C22×D89—4144no—
75C22×D89—472no—
76C22×D89—4384no—
77C22×D89C22×D4124yescomplemented
78C2×C4×C89—2144no—
79C2×C4×C89—224no—
80C2×C4×C89C22×D4124yescomplemented
81C2×Dic89—212no—
82C2×Dic89—424no—
83D356—2384no—
84C22×C89#392164yescomplemented
85C22×C89C2×#120136yes—
86C22×C89C2×#121136yes—
87C22×C89C2×#127112yes—
88C22×C89C23×D413yes—
89C22×C89C23×D413yes—
90C22×C89C22×#4111yescharacteristic
91C2×D89—248no—
92C2×D89—224no—
93C2×D89—4288no—
94C2×D89—412no—
95C2×D89—424no—
96C2×D89—412no—
97C4×C89—224no—
98Dic89—44no—
99C22×#392—891nomaximal, Sylow
100C2×C89C2×#392124yescomplemented
101C2×C89C22×#12013yes—
102C2×C89C22×#12113yes—
103C2×C89C22×#12711yescharacteristic
104D89—424no—
105C24×D4—893no—
106C23×C22⋊C4—893no—
107C2×#392—8924no—
108C22×#95D8911yescharacteristic, complemented
109C89C22×#39211yescharacteristic, complemented, Sylow
110C26—893no—
111C23×D4—8936no—
112C23×D4—17848no—
113C23×D4—17824no—
114C24×C4—891no—
115C24×C4C2×D8913yes—
116C22×C22⋊C4—8936no—
117C22×C22⋊C4—17824no—
118#392—8964no—
119C2×#95C2×D89112yescomplemented
120C25—8924no—
121C25—8918no—
122C25—17824no—
123C25—17812no—
124C25—17824no—
125C25—17812no—
126C25C22×D8911yescharacteristic
127C22×D4—8948no—
128C22×D4—178288no—
129C22×D4—178384no—
130C22×D4—178144no—
131C23×C4—224no—
132C23×C4—896no—
133C23×C4—17812no—
134C23×C4D356124yescomplemented
135C23×C4C22×D89118yes—
136C2×C22⋊C4—8948no—
137C2×C22⋊C4—178144no—
138#95C22×D89116yescomplemented
139C24—8972no—
140C24—8912no—
141C24—35648no—
142C24—35696no—
143C24—35648no—
144C24—178192no—
145C24—17896no—
146C24—17872no—
147C24—17836no—
148C24—17872no—
149C24—17836no—
150C24D4×D89112yes—
151C24C2×D356112yes—
152C24#1308357514yes—
153C24C23×D8913yes—
154C2×D4—178192no—
155C2×D4—1781152no—
156C2×D4—17896no—
157C22×C4—296no—
158C22×C4—272no—
159C22×C4—894no—
160C22×C4—35616no—
161C22×C4—17836no—
162C22×C4C2×D356172yescomplemented
163C22×C4C23×D89112yes—
164C22⋊C4—17896no—
165C23—8924no—
166C23—35672no—
167C23—356384no—
168C23—35672no—
169C23—356144no—
170C23—17824no—
171C23—17812no—
172C23—17824no—
173C23—17812no—
174C23—178288no—
175C23—178144no—
176C23#15667982148yes—
177C23#15667987148yes—
178C23#15668009116yes—
179C23C2×D4×D89118yes—
180C23C22×D356118yes—
181C23C2×#1308357516yes—
182C23C24×D8911yescharacteristic
183D4—178384no—
184C2×C4—224no—
185C2×C4—2144no—
186C2×C4—35624no—
187C2×C4—17812no—
188C2×C4C22×D356124yescomplemented
189C22—356288no—
190C22—35612no—
191C22—35624no—
192C22—35612no—
193C22—17848no—
194C22—17824no—
195C22#19151508164yesdirect product factor
196C22C2×#15667982136yes—
197C22C2×#15667987136yes—
198C22C2×#15668009112yes—
199C22C22×D4×D8913yes—
200C22C23×D35613yes—
201C22C22×#1308357511yescharacteristic
202C4—224no—
203C4—3564no—
204C2—35624no—
205C2C2×#19151508124yesdirect product factor
206C2C22×#1566798213yes—
207C2C22×#1566798713yes—
208C2C22×#1566800911yescharacteristic
subgroupG/H
centerC25C22×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC22×#95×C89C2
socleC25×C89C23
hypercenterC22×#95D89
hypocenterC89C22×#392
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C24×D356C2semidirect
2. C23×#13083551C2semidirect
3. C2×#19151508C2direct (N × H)
4. C22×#95×C89C2semidirect
8. C23×D356C22semidirect
11. C22×#13083551C22semidirect
12. #19151508C22direct (N × H)
14. C2×#95×C89C22semidirect
19. C24×D89D4semidirect
24. C22×D356C23semidirect
28. C2×#13083551C23semidirect
31. C23×C4×C89D4semidirect
33. #95×C89C23semidirect
43. C23×D89C2×D4semidirect
58. C22×C4×C89C2×D4semidirect
77. C22×D89C22×D4semidirect
80. C2×C4×C89C22×D4semidirect
84. C22×C89#392semidirect
100. C2×C89C2×#392semidirect
108. C22×#95D89semidirect
109. C89C22×#392semidirect
119. C2×#95C2×D89semidirect
134. C23×C4D356semidirect
138. #95C22×D89semidirect
162. C22×C4C2×D356semidirect
188. C2×C4C22×D356semidirect
195. C22#19151508direct (N × H)
205. C2C2×#19151508direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D3562
C23×#130835512
C2×#191515082
C22×#95×C892
C22×#39289