Finite Group Databasebeta

← C22×#14582809 #25262774

Subgroups — C22×#14582809 #25262774

Order 11008.

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×D172C213yesmaximal, complemented
2C23×(C2×D43)⋊C4C213yesmaximal, complemented
3C2×#14582809C2124yesmaximal, direct product factor
4C22×#95×C43C211yesmaximal, characteristic, complemented
5C25×D43C2213yes—
6C23×D172—248no—
7C23×D172—224no—
8C23×D172C22136yescomplemented
9C24×Dic43C2211yescharacteristic
10C22×(C2×D43)⋊C4—224no—
11C22×(C2×D43)⋊C4C22136yescomplemented
12#14582809C22164yesdirect product factor
13C24×C4×C43C2213yes—
14C2×#95×C43C22112yescomplemented
15C24×D43—212no—
16C24×D43—224no—
17C24×D43—224no—
18C24×D43—212no—
19C24×D43D4124yescomplemented
20C24×D43C23118yes—
21C22×D172—2384no—
22C22×D172—2288no—
23C22×D172—2144no—
24C22×D172C23148yescomplemented
25C23×Dic43—212no—
26C23×Dic43C2316yes—
27C2×(C2×D43)⋊C4—2144no—
28C2×(C2×D43)⋊C4C23148yescomplemented
29C25×C43C2311yescharacteristic
30C23×C4×C43—224no—
31C23×C4×C43D4124yescomplemented
32C23×C4×C43C23118yes—
33#95×C43C23116yescomplemented
34C24×C43C2×D4112yes—
35C24×C43C2×D4112yes—
36C24×C43#4114yes—
37C24×C43C2413yes—
38C23×D43—2192no—
39C23×D43—296no—
40C23×D43—236no—
41C23×D43—272no—
42C23×D43—272no—
43C23×D43—236no—
44C23×D43—448no—
45C23×D43—496no—
46C23×D43—448no—
47C23×D43C2×D4172yescomplemented
48C23×D43C24112yes—
49C22×C4×C43—296no—
50C22×C4×C43—272no—
51C22×C4×C43C2×D4172yescomplemented
52C22×C4×C43C24112yes—
53C22×Dic43—236no—
54C22×Dic43—416no—
55C22×Dic43C2414yes—
56C2×D172—21152no—
57C2×D172—296no—
58C2×D172—2192no—
59(C2×D43)⋊C4—296no—
60C23×C43#120148yes—
61C23×C43#121148yes—
62C23×C43#127116yes—
63C23×C43C22×D4118yes—
64C23×C43C22×D4118yes—
65C23×C43C2×#4116yes—
66C23×C43C2511yescharacteristic
67C22×D43—2288no—
68C22×D43—2144no—
69C22×D43—212no—
70C22×D43—224no—
71C22×D43—224no—
72C22×D43—212no—
73C22×D43—472no—
74C22×D43—4144no—
75C22×D43—472no—
76C22×D43—4384no—
77C22×D43C22×D4124yescomplemented
78C2×C4×C43—2144no—
79C2×C4×C43—224no—
80C2×C4×C43C22×D4124yescomplemented
81C2×Dic43—212no—
82C2×Dic43—424no—
83D172—2384no—
84C22×#392—431nomaximal, Sylow
85C22×C43#392164yescomplemented
86C22×C43C2×#120136yes—
87C22×C43C2×#121136yes—
88C22×C43C2×#127112yes—
89C22×C43C23×D413yes—
90C22×C43C23×D413yes—
91C22×C43C22×#4111yescharacteristic
92C2×D43—248no—
93C2×D43—224no—
94C2×D43—4288no—
95C2×D43—412no—
96C2×D43—424no—
97C2×D43—412no—
98C4×C43—224no—
99Dic43—44no—
100C24×D4—433no—
101C23×C22⋊C4—433no—
102C2×#392—4324no—
103C22×#95D4311yescharacteristic, complemented
104C2×C43C2×#392124yescomplemented
105C2×C43C22×#12013yes—
106C2×C43C22×#12113yes—
107C2×C43C22×#12711yescharacteristic
108D43—424no—
109C26—433no—
110C23×D4—4336no—
111C23×D4—8648no—
112C23×D4—8624no—
113C24×C4—431no—
114C24×C4C2×D4313yes—
115C22×C22⋊C4—4336no—
116C22×C22⋊C4—8624no—
117#392—4364no—
118C2×#95C2×D43112yescomplemented
119C43C22×#39211yescharacteristic, complemented, Sylow
120C25—4324no—
121C25—4318no—
122C25—8612no—
123C25—8624no—
124C25—8624no—
125C25—8612no—
126C25C22×D4311yescharacteristic
127C22×D4—4348no—
128C22×D4—86288no—
129C22×D4—86384no—
130C22×D4—86144no—
131C23×C4—224no—
132C23×C4—436no—
133C23×C4—8612no—
134C23×C4D172124yescomplemented
135C23×C4C22×D43118yes—
136C2×C22⋊C4—4348no—
137C2×C22⋊C4—86144no—
138#95C22×D43116yescomplemented
139C24—4372no—
140C24—4312no—
141C24—86192no—
142C24—8696no—
143C24—8672no—
144C24—8636no—
145C24—8672no—
146C24—8636no—
147C24—17248no—
148C24—17296no—
149C24—17248no—
150C24C2×D172112yes—
151C24D4×D43112yes—
152C24#1062190214yes—
153C24C23×D4313yes—
154C2×D4—86192no—
155C2×D4—861152no—
156C2×D4—8696no—
157C22×C4—296no—
158C22×C4—272no—
159C22×C4—434no—
160C22×C4—8636no—
161C22×C4—17216no—
162C22×C4C2×D172172yescomplemented
163C22×C4C23×D43112yes—
164C22⋊C4—8696no—
165C23—4324no—
166C23—86288no—
167C23—86144no—
168C23—8624no—
169C23—8612no—
170C23—8624no—
171C23—8612no—
172C23—172384no—
173C23—17272no—
174C23—172144no—
175C23—17272no—
176C23#13063295148yes—
177C23#13063300148yes—
178C23#13063322116yes—
179C23C2×D4×D43118yes—
180C23C22×D172118yes—
181C23C2×#1062190216yes—
182C23C24×D4311yescharacteristic
183D4—86384no—
184C2×C4—2144no—
185C2×C4—224no—
186C2×C4—8612no—
187C2×C4—17224no—
188C2×C4C22×D172124yescomplemented
189C22—8648no—
190C22—8624no—
191C22—172288no—
192C22—17212no—
193C22—17224no—
194C22—17212no—
195C22#14582809164yesdirect product factor
196C22C2×#13063295136yes—
197C22C2×#13063300136yes—
198C22C2×#13063322112yes—
199C22C22×D4×D4313yes—
200C22C23×D17213yes—
201C22C22×#1062190211yescharacteristic
202C4—224no—
203C4—1724no—
204C2—17224no—
205C2C2×#14582809124yesdirect product factor
206C2C22×#1306329513yes—
207C2C22×#1306330013yes—
208C2C22×#1306332211yescharacteristic
subgroupG/H
centerC25C22×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#95×C43C2
socleC25×C43C23
hypercenterC22×#95D43
hypocenterC43C22×#392
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C24×D172C2semidirect
2. C23×(C2×D43)⋊C4C2semidirect
3. C2×#14582809C2direct (N × H)
4. C22×#95×C43C2semidirect
8. C23×D172C22semidirect
11. C22×(C2×D43)⋊C4C22semidirect
12. #14582809C22direct (N × H)
14. C2×#95×C43C22semidirect
19. C24×D43D4semidirect
24. C22×D172C23semidirect
28. C2×(C2×D43)⋊C4C23semidirect
31. C23×C4×C43D4semidirect
33. #95×C43C23semidirect
47. C23×D43C2×D4semidirect
51. C22×C4×C43C2×D4semidirect
77. C22×D43C22×D4semidirect
80. C2×C4×C43C22×D4semidirect
85. C22×C43#392semidirect
103. C22×#95D43semidirect
104. C2×C43C2×#392semidirect
118. C2×#95C2×D43semidirect
119. C43C22×#392semidirect
134. C23×C4D172semidirect
138. #95C22×D43semidirect
162. C22×C4C2×D172semidirect
188. C2×C4C22×D172semidirect
195. C22#14582809direct (N × H)
205. C2C2×#14582809direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D1722
C23×(C2×D43)⋊C42
C2×#145828092
C22×#95×C432
C22×#39243