Finite Group Databasebeta

← C2×#20246669 #26382544

Subgroups — C2×#20246669 #26382544

Order 12032.

5150 conjugacy classes of subgroups; only the 939 normal subgroups are shown.

normal subgroups only

This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 939 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
1C22×C4×D188C216yesmaximal, complemented
2#20246669C2116yesmaximal, direct product factor
3C2×#15689060C214yesmaximal, complemented
4C2×#15689033C214yesmaximal, complemented
5C2×C47×#376C211yesmaximal, characteristic, complemented
6C23×D188C2216yes—
7C23×C4×D47C2214yes—
8C2×C4×D188—248no—
9C2×C4×D188C22148yescomplemented
10C22×C4⋊Dic47C2216yes—
11C22×(C2×D47)⋊C4C22112yes—
12#15689060C22132yescomplemented
13#15689033C22132yescomplemented
14C22×C42×C47C2213yes—
15C47×#376C2218yescomplemented
16C2×#95×C47C2214yes—
17C24×D47C2314yes—
18C22×D188—248no—
19C22×D188—224no—
20C22×D188C23124yes—
21C23×Dic47C2314yes—
22C22×C4×D47—248no—
23C22×C4×D47C23116yes—
24C4×D188—2192no—
25C2×C4⋊Dic47—224no—
26C2×C4⋊Dic47C23124yes—
27C2×(C2×D47)⋊C4—248no—
28C2×(C2×D47)⋊C4C23148yes—
29C23×C4×C47C2316yes—
30C23×C4×C47C2311yescharacteristic
31C2×C42×C47D4124yescomplemented
32C2×C42×C47C23112yes—
33#95×C47C23116yes—
34C24×C47C2411yescharacteristic
35C23×D47—224no—
36C23×D47—224no—
37C23×D47#41116yes—
38C23×D47C2418yes—
39C22×C4×C47—224no—
40C22×C4×C47C2×D4124yes—
41C22×C4×C47C2×D4112yes—
42C22×C4×C47C24112yes—
43C22×C4×C47C2412yes—
44C22×Dic47—224no—
45C22×Dic47C2418yes—
46C2×D188—2192no—
47C2×D188—296no—
48C2×D188—248no—
49C2×C4×D47—296no—
50C2×C4×D47—464no—
51C42×C47C2×D4148yescomplemented
52(C2×D47)⋊C4—296no—
53C4⋊Dic47—248no—
54C23×C47C22×D416yes—
55C23×C47C2×#4118yes—
56C23×C47C2511yescharacteristic
57C22×D47—296no—
58C22×D47—224no—
59C22×D47—224no—
60C22×D47—448no—
61C22×D47—416no—
62C22×D47C2×#41116yes—
63C2×C4×C47—248no—
64C2×C4×C47—224no—
65C2×C4×C47#127116yes—
66C2×C4×C47C22×D4124yes—
67C2×C4×C47C22×D4112yes—
68C2×Dic47—224no—
69C2×Dic47—416no—
70D188—2192no—
71C4×D47—464no—
72C2×#2397—471nomaximal, Sylow
73C22×C47#525124yes—
74C22×C47C2×#12714yes—
75C22×C47C23×D413yes—
76C22×C47C22×#4114yes—
77C2×D47—248no—
78C2×D47—464no—
79C2×D47—424no—
80C2×D47—48no—
81C4×C47—224no—
82C4×C47C2×#12718yes—
83Dic47—48no—
84C22×C4×D4—476no—
85#2397—4716no—
86C2×#399—474no—
87C2×#392—474no—
88C2×#376D4711yescharacteristic, complemented
89C2×C47#239718yescomplemented
90C2×C47C2×#52516yes—
91C2×C47C22×#12711yescharacteristic
92D47—416no—
93C23×D4—476no—
94C24×C4—474no—
95C2×C4×D4—4748no—
96C2×C4×D4—9448no—
97C22×C4⋊C4—476no—
98C22×C22⋊C4—4712no—
99C22×C42C2×D4713yes—
100#399—4732no—
101#392—4732no—
102#376C2×D4718yescomplemented
103C2×#95C2×D4714yes—
104C47C2×#239711yescharacteristic, complemented, Sylow
105C25—474no—
106C22×D4—4724no—
107C22×D4—9448no—
108C22×D4—9424no—
109C23×C4—474no—
110C23×C4—4716no—
111C23×C4—9448no—
112C23×C4C22×D4716yes—
113C23×C4C22×D4711yescharacteristic
114C4×D4—94192no—
115C2×C4⋊C4—4724no—
116C2×C4⋊C4—9424no—
117C2×C22⋊C4—4748no—
118C2×C22⋊C4—9448no—
119C2×C42D188124yescomplemented
120C2×C42C22×D47112yes—
121#95C22×D47116yes—
122C24—4716no—
123C24—478no—
124C24—9424no—
125C24—9424no—
126C24C23×D4711yescharacteristic
127C2×D4—9496no—
128C2×D4—94192no—
129C2×D4—9448no—
130C22×C4—224no—
131C22×C4—478no—
132C22×C4—9424no—
133C22×C4—9496no—
134C22×C4—18864no—
135C22×C4C2×D188124yes—
136C22×C4C2×D188112yes—
137C22×C4C23×D47112yes—
138C22×C4C23×D4712yes—
139C4⋊C4—9448no—
140C22⋊C4—9496no—
141C42C2×D188148yescomplemented
142C23—4716no—
143C23—9496no—
144C23—9424no—
145C23—9424no—
146C23—18848no—
147C23—18816no—
148C23C22×D18816yes—
149C23#41×D4718yes—
150C23C24×D4711yescharacteristic
151D4—94192no—
152C2×C4—248no—
153C2×C4—224no—
154C2×C4—9424no—
155C2×C4—18816no—
156C2×C4—18864no—
157C2×C4#13094021116yes—
158C2×C4C22×D188124yes—
159C2×C4C22×D188112yes—
160C22—9448no—
161C22—18824no—
162C22—18864no—
163C22—1888no—
164C22#15689635124yes—
165C22C2×#1309402114yes—
166C22C23×D18813yes—
167C22C2×#41×D4714yes—
168C4—224no—
169C4—1888no—
170C4C2×#1309402118yes—
171C2—18816no—
172C2#2024666918yesdirect product factor
173C2C2×#1568963516yes—
174C2C22×#1309402111yescharacteristic
subgroupG/H
centerC23×C4C22×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#376C2
socleC24×C47C24
hypercenterC2×#376D47
hypocenterC47C2×#2397
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. C22×C4×D188C2semidirect
2. #20246669C2direct (N × H)
3. C2×#15689060C2semidirect
4. C2×#15689033C2semidirect
5. C2×C47×#376C2semidirect
9. C2×C4×D188C22semidirect
12. #15689060C22semidirect
13. #15689033C22semidirect
15. C47×#376C22semidirect
31. C2×C42×C47D4semidirect
51. C42×C47C2×D4semidirect
88. C2×#376D47semidirect
89. C2×C47#2397semidirect
102. #376C2×D47semidirect
104. C47C2×#2397semidirect
119. C2×C42D188semidirect
141. C42C2×D188semidirect
172. C2#20246669direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D1882
#202466692
C2×#156890602
C2×#156890332
C2×C47×#3762
C2×#239747