Finite Group Databasebeta

← C22×C4×D92 #15686569

Subgroups — C22×C4×D92 #15686569

Order 2944.

2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 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×D92C211yesmaximal, characteristic
2C23×C4×D23C212yesmaximal, complemented
3C2×C4×D92C2124yesmaximal, direct product factor
4C22×C4⋊Dic23C211yesmaximal, characteristic, complemented
5C22×(C2×D23)⋊C4C212yesmaximal, complemented
6C22×C42×C23C211yesmaximal, characteristic, complemented
7C24×D23C2212yes—
8C23×C4×C23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic
10C23×C4×C23C2211yescharacteristic
11C23×Dic23C2212yes—
12C22×D92C4116yesdirect product factor
13C22×D92C22112yes—
14C22×C4×D23—216no—
15C22×C4×D23C22124yescomplemented
16C2×C42×C23C22112yescomplemented
17C2×(C2×D23)⋊C4C22124yescomplemented
18C2×C4⋊Dic23C22112yescomplemented
19C4×D92C22164yesdirect product factor
20C24×C23C2311yescharacteristic
21C23×D23—28no—
22C23×D23—28no—
23C23×D23C2×C4116yescomplemented
24C23×D23C23112yes—
25C22×C4×C23—24no—
26C22×C4×C23C2×C418yescomplemented
27C22×C4×C23D418yescomplemented
28C22×C4×C23C2316yes—
29C22×C4×C23C2316yes—
30C22×C4×C23C2316yes—
31C22×Dic23—28no—
32C22×Dic23C23112yes—
33C2×D92C2×C4196yesdirect product factor
34C2×D92C23116yes—
35C2×C4×D23—296no—
36C2×C4×D23C23132yescomplemented
37C42×C23C23116yescomplemented
38(C2×D23)⋊C4C23132yescomplemented
39C4⋊Dic23C23116yescomplemented
40C23×C23C22×C414yes—
41C23×C23C2×D414yes—
42C23×C23#4114yes—
43C23×C23C2413yes—
44C22×D23—264no—
45C22×D23—224no—
46C22×D23—224no—
47C22×D23C22×C4148yescomplemented
48C22×D23C2418yes—
49C2×C4×C23—212no—
50C2×C4×C23C22×C4124yescomplemented
51C2×C4×C23C2×D4124yescomplemented
52C2×C4×C23C2414yes—
53C2×C4×C23C2414yes—
54C2×C4×C23C2414yes—
55C2×Dic23—224no—
56C2×Dic23C2418yes—
57D92C22×C4164yesdirect product factor
58C4×D23—264no—
59C22×C4×D4—231nomaximal, Sylow
60C22×C23C4×D4116yescomplemented
61C22×C23C23×C416yes—
62C22×C23C22×D416yes—
63C22×C23C2×#4116yes—
64C22×C23C2511yescharacteristic
65C2×D23—296no—
66C2×D23—28no—
67C2×D23—28no—
68C2×D23C23×C4116yescomplemented
69C4×C23—24no—
70C4×C23C23×C418yescomplemented
71C4×C23C22×D418yescomplemented
72Dic23—28no—
73C23×D4—231no—
74C24×C4—232no—
75C2×C4×D4—2324no—
76C22×C4⋊C4—231no—
77C22×C22⋊C4—232no—
78C22×C42D2311yescharacteristic, complemented
79C2×C23C2×C4×D4112yescomplemented
80C2×C23C24×C411yescharacteristic
81C2×C23C23×D411yescharacteristic
82C2×C23C22×#4111yescharacteristic
83D23—216no—
84C25—232no—
85C22×D4—2316no—
86C22×D4—2312no—
87C23×C4—232no—
88C23×C4—2324no—
89C23×C4—4616no—
90C23×C4C2×D2311yescharacteristic
91C23×C4C2×D2311yescharacteristic
92C23×C4C2×D2311yescharacteristic
93C4×D4—2364no—
94C2×C4⋊C4—2312no—
95C2×C22⋊C4—2324no—
96C2×C42C2×D23112yescomplemented
97C23C22×C4×D411yescharacteristic, complemented, Sylow
98C24—2316no—
99C24—2312no—
100C24—468no—
101C24—468no—
102C24C22×D2311yescharacteristic
103C2×D4—2396no—
104C2×D4—2316no—
105C22×C4—24no—
106C22×C4—2312no—
107C22×C4—2332no—
108C22×C4—468no—
109C22×C4—4696no—
110C22×C4C4×D2318yescomplemented
111C22×C4D9218yesdirect product factor
112C22×C4C22×D2316yes—
113C22×C4C22×D2316yes—
114C22×C4C22×D2316yes—
115C4⋊C4—2316no—
116C22⋊C4—2332no—
117C42C22×D23116yescomplemented
118C23—2348no—
119C23—238no—
120C23—4664no—
121C23—4624no—
122C23—4624no—
123C23C2×C4×D2314yes—
124C23C2×D9214yes—
125C23#6728814yes—
126C23C23×D2313yes—
127D4—2364no—
128C2×C4—212no—
129C2×C4—238no—
130C2×C4—4624no—
131C2×C4—4664no—
132C2×C4C2×C4×D23124yescomplemented
133C2×C4C2×D92124yesdirect product factor
134C2×C4C23×D2314yes—
135C2×C4C23×D2314yes—
136C2×C4C23×D2314yes—
137C22—2316no—
138C22—4696no—
139C22—468no—
140C22—468no—
141C22C4×D92116yesdirect product factor
142C22C22×C4×D2316yes—
143C22C22×D9216yes—
144C22C2×#6728816yes—
145C22C24×D2311yescharacteristic
146C4—24no—
147C4—468no—
148C4C22×C4×D2318yescomplemented
149C4C22×D9218yesdirect product factor
150C2—4616no—
151C2C2×C4×D92112yesdirect product factor
152C2C23×C4×D2311yescharacteristic
153C2C23×D9211yescharacteristic
154C2C22×#6728811yescharacteristic
subgroupG/H
centerC23×C4C2×D23
commutatorC2×C23C24×C4
FrattiniC22C24×D23
FittingC22×C42×C23C2
socleC24×C23C23
prime radicalC23×D92C2
cosocleC22×C23C25
hypercenterC22×C42D23
hypocenterC23C22×C4×D4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×D23C2semidirect
3. C2×C4×D92C2direct (N × H)
4. C22×C4⋊Dic23C2semidirect
5. C22×(C2×D23)⋊C4C2semidirect
6. C22×C42×C23C2semidirect
12. C22×D92C4direct (N × H)
15. C22×C4×D23C22semidirect
16. C2×C42×C23C22semidirect
17. C2×(C2×D23)⋊C4C22semidirect
18. C2×C4⋊Dic23C22semidirect
19. C4×D92C22direct (N × H)
23. C23×D23C2×C4semidirect
26. C22×C4×C23C2×C4semidirect
27. C22×C4×C23D4semidirect
33. C2×D92C2×C4direct (N × H)
36. C2×C4×D23C23semidirect
37. C42×C23C23semidirect
38. (C2×D23)⋊C4C23semidirect
39. C4⋊Dic23C23semidirect
47. C22×D23C22×C4semidirect
50. C2×C4×C23C22×C4semidirect
51. C2×C4×C23C2×D4semidirect
57. D92C22×C4direct (N × H)
60. C22×C23C4×D4semidirect
68. C2×D23C23×C4semidirect
70. C4×C23C23×C4semidirect
71. C4×C23C22×D4semidirect
78. C22×C42D23semidirect
79. C2×C23C2×C4×D4semidirect
96. C2×C42C2×D23semidirect
97. C23C22×C4×D4semidirect
110. C22×C4C4×D23semidirect
111. C22×C4D92direct (N × H)
117. C42C22×D23semidirect
132. C2×C4C2×C4×D23semidirect
133. C2×C4C2×D92direct (N × H)
141. C22C4×D92direct (N × H)
148. C4C22×C4×D23semidirect
149. C4C22×D92direct (N × H)
151. C2C2×C4×D92direct (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×C4×D922
C22×C4⋊Dic232
C22×(C2×D23)⋊C42
C22×C42×C232
C22×C4×D423