Finite Group Databasebeta

← C22×#10625066 #15686620

Subgroups — C22×#10625066 #15686620

Order 2944.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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
1C23×D92C212yesmaximal, complemented
2C23×D92C211yesmaximal, characteristic, complemented
3C23×C4×D23C211yesmaximal, characteristic, complemented
4C2×#10625066C2124yesmaximal, direct product factor
5C22×(C2×D23)⋊C4C212yesmaximal, complemented
6C22×C4⋊C4×C23C211yesmaximal, characteristic, complemented
7C24×D23C2212yes—
8C24×D23C2211yescharacteristic
9C23×C4×C23C2212yes—
10C23×C4×C23C2211yescharacteristic
11C23×Dic23C2211yescharacteristic
12C22×D92—216no—
13C22×D92—28no—
14C22×D92C22124yescomplemented
15C22×D92C22112yescomplemented
16C22×C4×D23—28no—
17C22×C4×D23C22112yescomplemented
18C2×C4⋊C4×C23C22112yescomplemented
19C2×(C2×D23)⋊C4C22124yescomplemented
20#10625066C22164yesdirect product factor
21C24×C23C2311yescharacteristic
22C23×D23—24no—
23C23×D23—24no—
24C23×D23—28no—
25C23×D23—28no—
26C23×D23—28no—
27C23×D23D418yescomplemented
28C23×D23C23112yes—
29C23×D23C2316yes—
30C22×C4×C23—28no—
31C22×C4×C23D418yescomplemented
32C22×C4×C23C23112yes—
33C22×C4×C23C2316yes—
34C22×Dic23—24no—
35C22×Dic23C2316yes—
36C2×D92—296no—
37C2×D92—248no—
38C2×D92C23132yescomplemented
39C2×D92C23116yescomplemented
40C2×C4×D23—248no—
41C2×C4×D23C23116yescomplemented
42C4⋊C4×C23C23116yescomplemented
43(C2×D23)⋊C4C23132yescomplemented
44C23×C23C2×D414yes—
45C23×C23C2×D414yes—
46C23×C23#4114yes—
47C23×C23C2413yes—
48C22×D23—232no—
49C22×D23—212no—
50C22×D23—212no—
51C22×D23—224no—
52C22×D23—224no—
53C22×D23—224no—
54C22×D23—432no—
55C22×D23C2×D4124yescomplemented
56C22×D23C2418yes—
57C22×D23C2414yes—
58C2×C4×C23—224no—
59C2×C4×C23C2×D4124yescomplemented
60C2×C4×C23C2418yes—
61C2×C4×C23C2414yes—
62C2×Dic23—212no—
63C2×Dic23C2414yes—
64D92—264no—
65D92—232no—
66C4×D23—232no—
67C22×#121—231nomaximal, Sylow
68C22×C23#121116yescomplemented
69C22×C23C22×D416yes—
70C22×C23C22×D416yes—
71C22×C23C2×#4116yes—
72C22×C23C2511yescharacteristic
73C2×D23—248no—
74C2×D23—24no—
75C2×D23—24no—
76C2×D23—28no—
77C2×D23—28no—
78C2×D23—28no—
79C2×D23—448no—
80C2×D23C22×D418yescomplemented
81C4×C23—28no—
82C4×C23C22×D418yescomplemented
83Dic23—24no—
84C23×D4—232no—
85C23×D4—231no—
86C24×C4—231no—
87C2×#121—2324no—
88C22×C4⋊C4D2311yescharacteristic, complemented
89C22×C22⋊C4—232no—
90C2×C23C2×#121112yescomplemented
91C2×C23C23×D411yescharacteristic
92C2×C23C23×D411yescharacteristic
93C2×C23C22×#4111yescharacteristic
94D23—28no—
95D23—48no—
96C25—231no—
97C25—232no—
98C22×D4—2324no—
99C22×D4—2312no—
100C22×D4—4616no—
101C22×D4—468no—
102C23×C4—231no—
103C23×C4—2312no—
104C23×C4—468no—
105C23×C4C2×D2312yes—
106C23×C4C2×D2311yescharacteristic
107#121—2364no—
108C2×C4⋊C4C2×D23112yescomplemented
109C2×C22⋊C4—2324no—
110C23C22×#12111yescharacteristic, complemented, Sylow
111C24—238no—
112C24—236no—
113C24—2312no—
114C24—464no—
115C24—464no—
116C24—468no—
117C24—468no—
118C24—468no—
119C24C22×D2311yescharacteristic
120C2×D4—2332no—
121C2×D4—2316no—
122C2×D4—4696no—
123C2×D4—4648no—
124C22×C4—28no—
125C22×C4—236no—
126C22×C4—2316no—
127C22×C4—464no—
128C22×C4—4648no—
129C22×C4D9218yescomplemented
130C22×C4C22×D23112yes—
131C22×C4C22×D2316yes—
132C4⋊C4C22×D23116yescomplemented
133C22⋊C4—2332no—
134C23—2324no—
135C23—234no—
136C23—238no—
137C23—4632no—
138C23—4612no—
139C23—4612no—
140C23—4624no—
141C23—4624no—
142C23—4624no—
143C23—9232no—
144C23C2×D9214yes—
145C23D4×D2314yes—
146C23#6729214yes—
147C23C23×D2313yes—
148D4—4664no—
149D4—4632no—
150C2×C4—224no—
151C2×C4—234no—
152C2×C4—4612no—
153C2×C4—4632no—
154C2×C4C2×D92124yescomplemented
155C2×C4C23×D2318yes—
156C2×C4C23×D2314yes—
157C22—238no—
158C22—4648no—
159C22—464no—
160C22—464no—
161C22—468no—
162C22—468no—
163C22—468no—
164C22—9248no—
165C22#10625066116yesdirect product factor
166C22C22×D9216yes—
167C22C2×D4×D2316yes—
168C22C2×#6729216yes—
169C22C24×D2311yescharacteristic
170C4—28no—
171C4—464no—
172C4C22×D9218yescomplemented
173C2—468no—
174C2—928no—
175C2C2×#10625066112yesdirect product factor
176C2C22×D4×D2311yescharacteristic
177C2C23×D9211yescharacteristic
178C2C22×#6729211yescharacteristic
subgroupG/H
centerC24C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×C4⋊C4×C23C2
socleC24×C23C23
hypercenterC22×C4⋊C4D23
hypocenterC23C22×#121
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D92C2semidirect
2. C23×D92C2semidirect
3. C23×C4×D23C2semidirect
4. C2×#10625066C2direct (N × H)
5. C22×(C2×D23)⋊C4C2semidirect
6. C22×C4⋊C4×C23C2semidirect
14. C22×D92C22semidirect
15. C22×D92C22semidirect
17. C22×C4×D23C22semidirect
18. C2×C4⋊C4×C23C22semidirect
19. C2×(C2×D23)⋊C4C22semidirect
20. #10625066C22direct (N × H)
27. C23×D23D4semidirect
31. C22×C4×C23D4semidirect
38. C2×D92C23semidirect
39. C2×D92C23semidirect
41. C2×C4×D23C23semidirect
42. C4⋊C4×C23C23semidirect
43. (C2×D23)⋊C4C23semidirect
55. C22×D23C2×D4semidirect
59. C2×C4×C23C2×D4semidirect
68. C22×C23#121semidirect
80. C2×D23C22×D4semidirect
82. C4×C23C22×D4semidirect
88. C22×C4⋊C4D23semidirect
90. C2×C23C2×#121semidirect
108. C2×C4⋊C4C2×D23semidirect
110. C23C22×#121semidirect
129. C22×C4D92semidirect
132. C4⋊C4C22×D23semidirect
154. C2×C4C2×D92semidirect
165. C22#10625066direct (N × H)
172. C4C22×D92semidirect
175. C2C2×#10625066direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D922
C23×C4×D232
C2×#106250662
C22×(C2×D23)⋊C42
C22×C4⋊C4×C232
C22×#12123