Finite Group Databasebeta

← C22×#11745255 #16832662

Subgroups — C22×#11745255 #16832662

Order 3712.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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×D116C211yesmaximal, characteristic
2C23×C4×D29C212yesmaximal, complemented
3C2×#11745255C2124yesmaximal, direct product factor
4C22×#90781C212yesmaximal, complemented
5C22×C4×Dic29C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C29C211yesmaximal, characteristic, complemented
7C24×D29C2212yes—
8C23×C4×C29C2212yes—
9C23×C4×C29C2211yescharacteristic
10C23×Dic29C2211yescharacteristic
11C23×Dic29C2211yescharacteristic
12C22×D116C4116yescomplemented
13C22×D116C22112yes—
14C22×C4×D29—216no—
15C22×C4×D29C22124yescomplemented
16C2×C4⋊C4×C29C22112yescomplemented
17C2×#90781C22124yescomplemented
18C2×C4×Dic29C22112yescomplemented
19#11745255C22164yesdirect product factor
20C24×C29C2311yescharacteristic
21C23×D29—28no—
22C23×D29—28no—
23C23×D29C2×C4116yescomplemented
24C23×D29C23112yes—
25C22×C4×C29—28no—
26C22×C4×C29C2×C418yescomplemented
27C22×C4×C29C23112yes—
28C22×C4×C29C2316yes—
29C22×Dic29—24no—
30C22×Dic29D418yescomplemented
31C22×Dic29C2316yes—
32C22×Dic29C2316yes—
33C2×D116C2×C4196yescomplemented
34C2×D116C23116yes—
35C2×C4×D29—296no—
36C2×C4×D29C23132yescomplemented
37C4⋊C4×C29C23116yescomplemented
38#90781C23132yescomplemented
39C4×Dic29C23116yescomplemented
40C23×C29C22×C414yes—
41C23×C29C2×D414yes—
42C23×C29#4114yes—
43C23×C29C2413yes—
44C22×D29—264no—
45C22×D29—224no—
46C22×D29—224no—
47C22×D29C22×C4148yescomplemented
48C22×D29C2418yes—
49C2×C4×C29—224no—
50C2×C4×C29C22×C4124yescomplemented
51C2×C4×C29C2418yes—
52C2×C4×C29C2414yes—
53C2×Dic29—212no—
54C2×Dic29C2×D4124yescomplemented
55C2×Dic29C2414yes—
56C2×Dic29C2414yes—
57D116C22×C4164yescomplemented
58C4×D29—264no—
59C22×C4×D4—291nomaximal, Sylow
60C22×C29C4×D4116yescomplemented
61C22×C29C23×C416yes—
62C22×C29C22×D416yes—
63C22×C29C2×#4116yes—
64C22×C29C2511yescharacteristic
65C2×D29—296no—
66C2×D29—28no—
67C2×D29—28no—
68C2×D29C23×C4116yescomplemented
69C4×C29—28no—
70C4×C29C23×C418yescomplemented
71Dic29—24no—
72Dic29C22×D418yescomplemented
73C23×D4—291no—
74C24×C4—292no—
75C2×C4×D4—2924no—
76C22×C4⋊C4D2911yescharacteristic, complemented
77C22×C22⋊C4—292no—
78C22×C42—291no—
79C2×C29C2×C4×D4112yescomplemented
80C2×C29C24×C411yescharacteristic
81C2×C29C23×D411yescharacteristic
82C2×C29C22×#4111yescharacteristic
83D29—216no—
84C25—292no—
85C22×D4—2916no—
86C22×D4—2912no—
87C23×C4—291no—
88C23×C4—291no—
89C23×C4—2924no—
90C23×C4—5816no—
91C23×C4C2×D2912yes—
92C23×C4C2×D2911yescharacteristic
93C4×D4—2964no—
94C2×C4⋊C4C2×D29112yescomplemented
95C2×C22⋊C4—2924no—
96C2×C42—2912no—
97C29C22×C4×D411yescharacteristic, complemented, Sylow
98C24—2916no—
99C24—2912no—
100C24—588no—
101C24—588no—
102C24C22×D2911yescharacteristic
103C2×D4—2996no—
104C2×D4—2916no—
105C22×C4—28no—
106C22×C4—298no—
107C22×C4—296no—
108C22×C4—296no—
109C22×C4—2932no—
110C22×C4—5896no—
111C22×C4—584no—
112C22×C4C4×D2918yescomplemented
113C22×C4C22×D29112yes—
114C22×C4C22×D2916yes—
115C4⋊C4C22×D29116yescomplemented
116C22⋊C4—2932no—
117C42—2916no—
118C23—2948no—
119C23—298no—
120C23—5824no—
121C23—5824no—
122C23—5864no—
123C23C2×C4×D2914yes—
124C23D4×D2914yes—
125C23#9080914yes—
126C23C23×D2913yes—
127D4—2964no—
128C2×C4—224no—
129C2×C4—2924no—
130C2×C4—294no—
131C2×C4—294no—
132C2×C4—5864no—
133C2×C4—5812no—
134C2×C4C2×C4×D29124yescomplemented
135C2×C4C23×D2918yes—
136C2×C4C23×D2914yes—
137C22—2916no—
138C22—5896no—
139C22—588no—
140C22—588no—
141C22#11745255116yesdirect product factor
142C22C22×C4×D2916yes—
143C22C2×D4×D2916yes—
144C22C2×#9080916yes—
145C22C24×D2911yescharacteristic
146C4—28no—
147C4—298no—
148C4—584no—
149C4C22×C4×D2918yescomplemented
150C2—5816no—
151C2C2×#11745255112yesdirect product factor
152C2C23×C4×D2911yescharacteristic
153C2C22×D4×D2911yescharacteristic
154C2C22×#9080911yescharacteristic
subgroupG/H
centerC24C22×D29
commutatorC2×C29C24×C4
FrattiniC22C24×D29
FittingC22×C4⋊C4×C29C2
socleC24×C29C23
prime radicalC23×D116C2
cosocleC22×C29C25
hypercenterC22×C4⋊C4D29
hypocenterC29C22×C4×D4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D29C2semidirect
3. C2×#11745255C2direct (N × H)
4. C22×#90781C2semidirect
5. C22×C4×Dic29C2semidirect
6. C22×C4⋊C4×C29C2semidirect
12. C22×D116C4semidirect
15. C22×C4×D29C22semidirect
16. C2×C4⋊C4×C29C22semidirect
17. C2×#90781C22semidirect
18. C2×C4×Dic29C22semidirect
19. #11745255C22direct (N × H)
23. C23×D29C2×C4semidirect
26. C22×C4×C29C2×C4semidirect
30. C22×Dic29D4semidirect
33. C2×D116C2×C4semidirect
36. C2×C4×D29C23semidirect
37. C4⋊C4×C29C23semidirect
38. #90781C23semidirect
39. C4×Dic29C23semidirect
47. C22×D29C22×C4semidirect
50. C2×C4×C29C22×C4semidirect
54. C2×Dic29C2×D4semidirect
57. D116C22×C4semidirect
60. C22×C29C4×D4semidirect
68. C2×D29C23×C4semidirect
70. C4×C29C23×C4semidirect
72. Dic29C22×D4semidirect
76. C22×C4⋊C4D29semidirect
79. C2×C29C2×C4×D4semidirect
94. C2×C4⋊C4C2×D29semidirect
97. C29C22×C4×D4semidirect
112. C22×C4C4×D29semidirect
115. C4⋊C4C22×D29semidirect
134. C2×C4C2×C4×D29semidirect
141. C22#11745255direct (N × H)
149. C4C22×C4×D29semidirect
151. C2C2×#11745255direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D1162
C23×C4×D292
C2×#117452552
C22×#907812
C22×C4×Dic292
C22×C4⋊C4×C292
C22×C4×D429