Finite Group Databasebeta

← C22×#17988497 #33252161

Subgroups — C22×#17988497 #33252161

Order 18688.

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×D292C213yesmaximal, complemented
2C23×#11924005C213yesmaximal, complemented
3C2×#17988497C2124yesmaximal, direct product factor
4C22×#95×C73C211yesmaximal, characteristic, complemented
5C25×D73C2213yes—
6C23×D292—248no—
7C23×D292—224no—
8C23×D292C22136yescomplemented
9C24×Dic73C2211yescharacteristic
10C22×#11924005—224no—
11C22×#11924005C22136yescomplemented
12#17988497C22164yesdirect product factor
13C24×C4×C73C2213yes—
14C2×#95×C73C22112yescomplemented
15C24×D73—224no—
16C24×D73—224no—
17C24×D73—212no—
18C24×D73—212no—
19C24×D73D4124yescomplemented
20C24×D73C23118yes—
21C22×D292—2384no—
22C22×D292—2288no—
23C22×D292—2144no—
24C22×D292C23148yescomplemented
25C23×Dic73—212no—
26C23×Dic73C2316yes—
27C2×#11924005—2144no—
28C2×#11924005C23148yescomplemented
29C25×C73C2311yescharacteristic
30C23×C4×C73—224no—
31C23×C4×C73D4124yescomplemented
32C23×C4×C73C23118yes—
33#95×C73C23116yescomplemented
34C23×D73—2192no—
35C23×D73—296no—
36C23×D73—236no—
37C23×D73—272no—
38C23×D73—272no—
39C23×D73—236no—
40C23×D73—448no—
41C23×D73—496no—
42C23×D73—448no—
43C23×D73C2×D4172yescomplemented
44C23×D73C24112yes—
45C2×D292—21152no—
46C2×D292—2192no—
47C2×D292—296no—
48C22×Dic73—236no—
49C22×Dic73—416no—
50C22×Dic73C2414yes—
51#11924005—296no—
52C24×C73C2×D4112yes—
53C24×C73C2×D4112yes—
54C24×C73#4114yes—
55C24×C73C2413yes—
56C22×C4×C73—296no—
57C22×C4×C73—272no—
58C22×C4×C73C2×D4172yescomplemented
59C22×C4×C73C24112yes—
60C23×C73#120148yes—
61C23×C73#121148yes—
62C23×C73#127116yes—
63C23×C73C22×D4118yes—
64C23×C73C22×D4118yes—
65C23×C73C2×#4116yes—
66C23×C73C2511yescharacteristic
67C22×D73—2288no—
68C22×D73—2144no—
69C22×D73—212no—
70C22×D73—224no—
71C22×D73—224no—
72C22×D73—212no—
73C22×D73—472no—
74C22×D73—4144no—
75C22×D73—472no—
76C22×D73—4384no—
77C22×D73C22×D4124yescomplemented
78C2×C4×C73—2144no—
79C2×C4×C73—224no—
80C2×C4×C73C22×D4124yescomplemented
81C2×Dic73—212no—
82C2×Dic73—424no—
83D292—2384no—
84C22×C73#392164yescomplemented
85C22×C73C2×#120136yes—
86C22×C73C2×#121136yes—
87C22×C73C2×#127112yes—
88C22×C73C23×D413yes—
89C22×C73C23×D413yes—
90C22×C73C22×#4111yescharacteristic
91C2×D73—248no—
92C2×D73—224no—
93C2×D73—4288no—
94C2×D73—412no—
95C2×D73—424no—
96C2×D73—412no—
97C4×C73—224no—
98Dic73—44no—
99C22×#392—731nomaximal, Sylow
100C2×C73C2×#392124yescomplemented
101C2×C73C22×#12013yes—
102C2×C73C22×#12113yes—
103C2×C73C22×#12711yescharacteristic
104D73—424no—
105C24×D4—733no—
106C23×C22⋊C4—733no—
107C2×#392—7324no—
108C22×#95D7311yescharacteristic, complemented
109C73C22×#39211yescharacteristic, complemented, Sylow
110C26—733no—
111C23×D4—7336no—
112C23×D4—14648no—
113C23×D4—14624no—
114C24×C4—731no—
115C24×C4C2×D7313yes—
116C22×C22⋊C4—7336no—
117C22×C22⋊C4—14624no—
118#392—7364no—
119C2×#95C2×D73112yescomplemented
120C25—7324no—
121C25—7318no—
122C25—14624no—
123C25—14612no—
124C25—14624no—
125C25—14612no—
126C25C22×D7311yescharacteristic
127C22×D4—7348no—
128C22×D4—146288no—
129C22×D4—146384no—
130C22×D4—146144no—
131C23×C4—224no—
132C23×C4—736no—
133C23×C4—14612no—
134C23×C4D292124yescomplemented
135C23×C4C22×D73118yes—
136C2×C22⋊C4—7348no—
137C2×C22⋊C4—146144no—
138#95C22×D73116yescomplemented
139C24—29248no—
140C24—29296no—
141C24—29248no—
142C24—7372no—
143C24—7312no—
144C24—146192no—
145C24—14696no—
146C24—14672no—
147C24—14636no—
148C24—14672no—
149C24—14636no—
150C24D4×D73112yes—
151C24C2×D292112yes—
152C24#1192402914yes—
153C24C23×D7313yes—
154C2×D4—146192no—
155C2×D4—1461152no—
156C2×D4—14696no—
157C22×C4—296no—
158C22×C4—272no—
159C22×C4—29216no—
160C22×C4—734no—
161C22×C4—14636no—
162C22×C4C2×D292172yescomplemented
163C22×C4C23×D73112yes—
164C22⋊C4—14696no—
165C23—29272no—
166C23—292384no—
167C23—29272no—
168C23—292144no—
169C23—7324no—
170C23—14624no—
171C23—14612no—
172C23—14624no—
173C23—14612no—
174C23—146288no—
175C23—146144no—
176C23#14556561148yes—
177C23#14556566148yes—
178C23#14556588116yes—
179C23C2×D4×D73118yes—
180C23C22×D292118yes—
181C23C2×#1192402916yes—
182C23C24×D7311yescharacteristic
183D4—146384no—
184C2×C4—224no—
185C2×C4—2144no—
186C2×C4—29224no—
187C2×C4—14612no—
188C2×C4C22×D292124yescomplemented
189C22—292288no—
190C22—29212no—
191C22—29224no—
192C22—29212no—
193C22—14648no—
194C22—14624no—
195C22#17988497164yesdirect product factor
196C22C2×#14556561136yes—
197C22C2×#14556566136yes—
198C22C2×#14556588112yes—
199C22C22×D4×D7313yes—
200C22C23×D29213yes—
201C22C22×#1192402911yescharacteristic
202C4—224no—
203C4—2924no—
204C2—29224no—
205C2C2×#17988497124yesdirect product factor
206C2C22×#1455656113yes—
207C2C22×#1455656613yes—
208C2C22×#1455658811yescharacteristic
subgroupG/H
centerC25C22×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC22×#95×C73C2
socleC25×C73C23
hypercenterC22×#95D73
hypocenterC73C22×#392
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C24×D292C2semidirect
2. C23×#11924005C2semidirect
3. C2×#17988497C2direct (N × H)
4. C22×#95×C73C2semidirect
8. C23×D292C22semidirect
11. C22×#11924005C22semidirect
12. #17988497C22direct (N × H)
14. C2×#95×C73C22semidirect
19. C24×D73D4semidirect
24. C22×D292C23semidirect
28. C2×#11924005C23semidirect
31. C23×C4×C73D4semidirect
33. #95×C73C23semidirect
43. C23×D73C2×D4semidirect
58. C22×C4×C73C2×D4semidirect
77. C22×D73C22×D4semidirect
80. C2×C4×C73C22×D4semidirect
84. C22×C73#392semidirect
100. C2×C73C2×#392semidirect
108. C22×#95D73semidirect
109. C73C22×#392semidirect
119. C2×#95C2×D73semidirect
134. C23×C4D292semidirect
138. #95C22×D73semidirect
162. C22×C4C2×D292semidirect
188. C2×C4C22×D292semidirect
195. C22#17988497direct (N × H)
205. C2C2×#17988497direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D2922
C23×#119240052
C2×#179884972
C22×#95×C732
C22×#39273