Finite Group Databasebeta

← C22×#15688968 #26374447

Subgroups — C22×#15688968 #26374447

Order 12032.

5150 conjugacy classes of subgroups; only the 2363 normal subgroups are shown.

normal subgroups only

This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 2363 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×Dic47C213yesmaximal
2C2×#15688968C2124yesmaximal, direct product factor
3C22×C47⋊#95C213yesmaximal
4C22×#95×C47C211yesmaximal, characteristic
5C24×Dic47C2213yes—
6C24×Dic47C2211yescharacteristic
7C22×C4×Dic47C4148yescomplemented
8C22×C4×Dic47C22136yes—
9#15688968C22164yesdirect product factor
10C2×C47⋊#95C22136yes—
11C24×C4×C47C2213yes—
12C2×#95×C47C22112yes—
13C23×Dic47—212no—
14C23×Dic47—212no—
15C23×Dic47C2×C4124yes—
16C23×Dic47C2×C4124yes—
17C23×Dic47C23118yes—
18C23×Dic47C2316yes—
19C2×C4×Dic47C2×C41288yescomplemented
20C2×C4×Dic47C23148yes—
21C47⋊#95C23148yes—
22C25×C47C2311yescharacteristic
23C23×C4×C47—224no—
24C23×C4×C47C2×C4124yes—
25C23×C4×C47C23118yes—
26#95×C47C23116yes—
27C24×C47C22×C4112yes—
28C24×C47#41112yes—
29C24×C47#4114yes—
30C24×C47C2413yes—
31C22×C4×C47—296no—
32C22×C4×C47—272no—
33C22×C4×C47C22×C4172yes—
34C22×C4×C47C24112yes—
35C22×Dic47—296no—
36C22×Dic47—236no—
37C22×Dic47—236no—
38C22×Dic47C42164yes—
39C22×Dic47C22×C4172yes—
40C22×Dic47C22×C4172yes—
41C22×Dic47C24112yes—
42C22×Dic47C2414yes—
43C4×Dic47C22×C41192yescomplemented
44C23×C47C2×C42116yes—
45C23×C47#117148yes—
46C23×C47#117148yes—
47C23×C47C23×C4118yes—
48C23×C47C2×#41118yes—
49C23×C47C2×#4116yes—
50C23×C47C2511yescharacteristic
51C2×C4×C47—2144no—
52C2×C4×C47—224no—
53C2×C4×C47C23×C4124yes—
54C2×Dic47—2144no—
55C2×Dic47—212no—
56C2×Dic47—212no—
57C2×Dic47C2×C42196yes—
58C2×Dic47C23×C4124yes—
59C2×Dic47C23×C4124yes—
60C22×#376—471nomaximal, Sylow
61C22×C47#376164yescomplemented
62C22×C47C22×C42112yes—
63C22×C47C2×#117136yes—
64C22×C47C2×#117136yes—
65C22×C47C24×C413yes—
66C22×C47C22×#4113yes—
67C22×C47C22×#4111yescharacteristic
68C4×C47—224no—
69Dic47—224no—
70Dic47C22×C42116yes—
71C23×C42—473no—
72C2×#376—4724no—
73C22×#95—473no—
74C22×#95D4711yescharacteristic
75C2×C47C2×#376124yescomplemented
76C2×C47C23×C4211yescharacteristic
77C2×C47C22×#11713yes—
78C2×C47C22×#11713yes—
79C24×C4—471no—
80C24×C4—473no—
81C24×C4C2×D4713yes—
82C22×C42—4748no—
83C22×C42—4736no—
84#376—4764no—
85C2×#95—4736no—
86C2×#95C2×D47112yes—
87C47C22×#37611yescharacteristic, complemented, Sylow
88C25C22×D4711yescharacteristic
89C23×C4—224no—
90C23×C4—4724no—
91C23×C4—476no—
92C23×C4—4724no—
93C23×C4—4718no—
94C23×C4—9412no—
95C23×C4—9412no—
96C23×C4C4×D47124yes—
97C23×C4C22×D47118yes—
98C2×C42—47288no—
99C2×C42—4748no—
100#95—4748no—
101#95C22×D47116yes—
102C24C2×C4×D47112yes—
103C24#10625352112yes—
104C24#1062535414yes—
105C24C23×D4713yes—
106C22×C4—296no—
107C22×C4—272no—
108C22×C4—4764no—
109C22×C4—4772no—
110C22×C4—474no—
111C22×C4—4772no—
112C22×C4—4712no—
113C22×C4—9496no—
114C22×C4—9436no—
115C22×C4—9436no—
116C22×C4C2×C4×D47172yes—
117C22×C4C23×D47112yes—
118C42—47192no—
119C23C42×D47116yes—
120C23#13093980148yes—
121C23#13093982148yes—
122C23C22×C4×D47118yes—
123C23C2×#10625352118yes—
124C23C2×#1062535416yes—
125C23C24×D4711yescharacteristic
126C2×C4—2144no—
127C2×C4—224no—
128C2×C4—4796no—
129C2×C4—4724no—
130C2×C4—4724no—
131C2×C4—94144no—
132C2×C4—9412no—
133C2×C4—9412no—
134C2×C4C22×C4×D47124yes—
135C22#15688968164yesdirect product factor
136C22C2×C42×D47112yes—
137C22C2×#13093980136yes—
138C22C2×#13093982136yes—
139C22C23×C4×D4713yes—
140C22C22×#1062535213yes—
141C22C22×#1062535411yescharacteristic
142C4—224no—
143C4—4716no—
144C4—9424no—
145C2C2×#15688968124yesdirect product factor
146C2C22×C42×D4711yescharacteristic
147C2C22×#1309398013yes—
148C2C22×#1309398213yes—
subgroupG/H
centerC25C22×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC22×#95×C47C2
socle, prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC22×#95D47
hypocenterC47C22×#376
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#15688968C2direct (N × H)
7. C22×C4×Dic47C4semidirect
9. #15688968C22direct (N × H)
19. C2×C4×Dic47C2×C4semidirect
43. C4×Dic47C22×C4semidirect
61. C22×C47#376semidirect
75. C2×C47C2×#376semidirect
87. C47C22×#376semidirect
135. C22#15688968direct (N × H)
145. C2C2×#15688968direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Dic472
C2×#156889682
C22×C47⋊#952
C22×#95×C472
C22×#37647