Finite Group Databasebeta

← C23×#14519846 #30625239

Subgroups — C23×#14519846 #30625239

Order 15616.

3614 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.

normal subgroups only

This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 1464 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×C4⋊#6923C212yesmaximal
2C22×#14519846C2128yesmaximal, direct product factor
3C23×C8×D61C211yesmaximal, characteristic
4C24×#6923—22no—
5C22×C4⋊#6923—214no—
6C22×C4⋊#6923C22128yes—
7C2×#14519846C221112yesdirect product factor
8C23×C4×D61C2211yescharacteristic
9C23×#92418C411yescharacteristic, complemented
10C22×C8×D61C4114yescomplemented
11C22×C8×D61C22114yes—
12C23×C8×C61C411yescharacteristic, complemented
13C23×#6923—228no—
14C23×#6923—416no—
15C2×C4⋊#6923—284no—
16C2×C4⋊#6923C23156yes—
17#14519846C23164yesdirect product factor
18C24×D61D411yescharacteristic
19C23×Dic61Q811yescharacteristic
20C22×C4×D61C2×C417yes—
21C22×C4×D61D417yes—
22C22×C4×D61Q817yes—
23C22×C4×D61C2317yes—
24C22×#92418C2×C4114yescomplemented
25C2×C8×D61C2×C4184yescomplemented
26C2×C8×D61C23128yes—
27C23×C4×C61C2×C411yescharacteristic
28C22×C8×C61C2×C4114yescomplemented
29C24×C61C4⋊C411yescharacteristic
30C23×D61C4⋊C417yes—
31C23×D61D818yes—
32C23×D61Q1618yes—
33C23×D61C2×D417yes—
34C22×#6923—256no—
35C22×#6923—4112no—
36C22×C4×C61C4⋊C417yes—
37C22×C4×C61C22×C417yes—
38C22×Dic61C4⋊C417yes—
39C22×Dic61C2×Q817yes—
40C2×C4×D61C4⋊C4142yes—
41C2×C4×D61C22×C4121yes—
42C2×C4×D61C2×D4121yes—
43C2×C4×D61C2×Q8121yes—
44C2×C4×D61C2417yes—
45C4⋊#6923—256no—
46C4⋊#6923C24116yes—
47C2×C8×C61C22×C4128yescomplemented
48C2×#92418C22×C4128yescomplemented
49C8×D61C22×C4156yescomplemented
50C8×D61C2418yes—
51C23×C61#10718yescomplemented
52C23×C61C2×C4⋊C417yes—
53C22×D61#107156yescomplemented
54C22×D61C2×C4⋊C4121yes—
55C22×D61C2×D8128yes—
56C22×D61C2×Q16128yes—
57C22×D61C22×D417yes—
58C2×#6923—216no—
59C2×#6923—4112no—
60C2×C4×C61C2×C4⋊C4121yes—
61C2×C4×C61C23×C417yes—
62C2×Dic61C2×C4⋊C4121yes—
63C2×Dic61C22×Q817yes—
64C4×D61C2×C4⋊C4142yes—
65C4×D61C23×C417yes—
66C4×D61C22×D417yes—
67C4×D61C22×Q817yes—
68C4×D61C2511yescharacteristic
69C8×C61C23×C418yescomplemented
70#92418C23×C418yescomplemented
71C23×#107—611nomaximal, Sylow
72C22×C61C2×#107128yescomplemented
73C22×C61C22×C4⋊C417yes—
74C2×D61C2×#107184yescomplemented
75C2×D61C22×C4⋊C417yes—
76C2×D61C22×D8114yes—
77C2×D61C22×Q16114yes—
78C2×D61C23×D411yescharacteristic
79#6923—416no—
80C4×C61C22×C4⋊C417yes—
81C4×C61C24×C411yescharacteristic
82Dic61C22×C4⋊C417yes—
83Dic61C23×Q811yescharacteristic
84C24×C8—611no—
85C23×C4⋊C4—612no—
86C22×#107—6128no—
87C2×C61C22×#107114yescomplemented
88C2×C61C23×C4⋊C411yescharacteristic
89D61C22×#107114yescomplemented
90D61C23×D811yescharacteristic
91D61C23×Q1611yescharacteristic
92C24×C4—611no—
93C24×C4—1222no—
94C23×C8—611no—
95C23×C8—6114no—
96C23×C8—6114no—
97C23×C8#692311yescharacteristic, complemented
98C22×C4⋊C4—6128no—
99C22×C4⋊C4—12214no—
100C2×#107—61112no—
101C61C23×#10711yescharacteristic, complemented, Sylow
102C25—611no—
103C23×C4—611no—
104C23×C4—617no—
105C23×C4—617no—
106C23×C4—617no—
107C23×C4—617no—
108C23×C4—12228no—
109C23×C4—24416no—
110C23×C4C2×#692311yescharacteristic
111C22×C8—6114no—
112C22×C8—6128no—
113C22×C8—6184no—
114C22×C8C2×#6923114yescomplemented
115C2×C4⋊C4—6156no—
116C2×C4⋊C4—12284no—
117#107—6164no—
118C24—618no—
119C24—618no—
120C24—617no—
121C24—617no—
122C24C4⋊#692311yescharacteristic
123C22×C4—617no—
124C22×C4—617no—
125C22×C4—6121no—
126C22×C4—6142no—
127C22×C4—6121no—
128C22×C4—617no—
129C22×C4—6121no—
130C22×C4—12256no—
131C22×C4—244112no—
132C22×C4C4⋊#692317yes—
133C22×C4C22×#692317yes—
134C2×C8—6128no—
135C2×C8—618no—
136C2×C8—6156no—
137C2×C8C22×#6923128yescomplemented
138C4⋊C4—6116no—
139C4⋊C4—12256no—
140C23—6156no—
141C23—6128no—
142C23—6128no—
143C23—6121no—
144C23—617no—
145C23#1451984618yesdirect product factor
146C23C2×C4⋊#692317yes—
147C2×C4—6121no—
148C2×C4—617no—
149C2×C4—6142no—
150C2×C4—617no—
151C2×C4—617no—
152C2×C4—617no—
153C2×C4—611no—
154C2×C4—12216no—
155C2×C4—244112no—
156C2×C4C2×C4⋊#6923121yes—
157C2×C4C23×#692317yes—
158C8—618no—
159C8C23×#692318yescomplemented
160C22—611no—
161C22—617no—
162C22—6114no—
163C22—6114no—
164C22—6184no—
165C22C2×#14519846128yesdirect product factor
166C22C22×C4⋊#692317yes—
167C4—617no—
168C4—611no—
169C4—24416no—
170C4C22×C4⋊#692317yes—
171C4C24×#692311yescharacteristic
172C2—611no—
173C2—6114no—
174C2—611no—
175C2C22×#14519846114yesdirect product factor
176C2C23×C4⋊#692311yescharacteristic
subgroupG/H
centerC24C4⋊#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC23×C8×C61C4
socleC24×C61C4⋊C4
prime radicalC24×D61D4
cosocleC4×D61C25
hypercenterC23×C8#6923
hypocenterC61C23×#107
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. C22×#14519846C2direct (N × H)
7. C2×#14519846C22direct (N × H)
9. C23×#92418C4semidirect
10. C22×C8×D61C4semidirect
12. C23×C8×C61C4semidirect
17. #14519846C23direct (N × H)
24. C22×#92418C2×C4semidirect
25. C2×C8×D61C2×C4semidirect
28. C22×C8×C61C2×C4semidirect
47. C2×C8×C61C22×C4semidirect
48. C2×#92418C22×C4semidirect
49. C8×D61C22×C4semidirect
51. C23×C61#107semidirect
53. C22×D61#107semidirect
69. C8×C61C23×C4semidirect
70. #92418C23×C4semidirect
72. C22×C61C2×#107semidirect
74. C2×D61C2×#107semidirect
87. C2×C61C22×#107semidirect
89. D61C22×#107semidirect
97. C23×C8#6923semidirect
101. C61C23×#107semidirect
114. C22×C8C2×#6923semidirect
137. C2×C8C22×#6923semidirect
145. C23#14519846direct (N × H)
159. C8C23×#6923semidirect
165. C22C2×#14519846direct (N × H)
175. C2C22×#14519846direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊#69232
C22×#145198462
C23×C8×D612
C23×#10761