Finite Group Databasebeta

← #17995645

Subgroups — #17995645

Order 4736.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#11924569C212yesmaximal, complemented
2#14558114C211yesmaximal, characteristic
3C2×#11924462C212yesmaximal, complemented
4#14557438C211yesmaximal, characteristic, complemented
5C37×#343C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7C22×Dic74C2211yescharacteristic
8#11924569—24no—
9#11924569—24no—
10C2×Dic148—22no—
11C2×#10596930—22no—
12#11924516—22no—
13#11924511—22no—
14#11924510—22no—
15C2×C4×Dic37C2211yescharacteristic
16#11924462—24no—
17#11924443—22no—
18C2×M16×C37C2212yes—
19C2×C4⋊C4×C37C2211yescharacteristic
20C22×C4×C37D412yes—
21C22×C4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24C22×Dic37—21no—
25#10596962—22no—
26#10596962—22no—
27#10596962—22no—
28#10596962—22no—
29C2×D148—22no—
30C2×D148D412yes—
31C2×C4×D37—22no—
32C2×Dic74—22no—
33C2×Dic74—22no—
34C2×Dic74—21no—
35C2×Dic74D412yes—
36C2×Dic74D412yescomplemented
37M16×C37—22no—
38M16×C37D414yescomplemented
39C2×C8×C37—22no—
40C4⋊C4×C37—22no—
41#10596938—24no—
42C4⋊Dic37—22no—
43C4×Dic37—22no—
44Dic148—28no—
45#10596930—28no—
46C23×C37C2×D411yescharacteristic
47C22×D37—22no—
48C2×C4×C37—22no—
49C2×C4×C37—42no—
50C2×C4×C37C2×D412yes—
51C2×C4×C37C2×D411yescharacteristic
52C2×C4×C37C2×D412yes—
53C2×C4×C37#4111yescharacteristic
54C22⋊D37—42no—
55C22⋊D37—42no—
56C2×Dic37—22no—
57C2×Dic37—22no—
58C2×Dic37—22no—
59C2×Dic37—41no—
60C2×Dic37—41no—
61C2×Dic37—41no—
62C2×Dic37—41no—
63D148—22no—
64D148—22no—
65D148—82no—
66C4×D37—42no—
67C4×D37—42no—
68Dic74—24no—
69Dic74—22no—
70Dic74—22no—
71Dic74—42no—
72C8×C37—24no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37#12011yescharacteristic
76C22×C37#12111yescharacteristic
77C22×C37#12711yescharacteristic
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—42no—
81C4×C37—42no—
82C4×C37#12012yes—
83C4×C37#12112yes—
84Dic37—42no—
85Dic37—42no—
86Dic37—42no—
87#2007—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—21no—
90C2×C37#39211yescharacteristic
91C2×C37#45511yescharacteristic
92C2×C37#45611yescharacteristic
93D37—82no—
94C2×#137—372no—
95#537—371no—
96C2×#104—372no—
97#391—371no—
98#343D3711yescharacteristic, complemented
99C37#200711yescharacteristic, complemented, Sylow
100C2×#41—372no—
101C22×Q8—371no—
102#137—744no—
103#137—744no—
104C2×Q16—742no—
105C2×SD16—742no—
106C2×M16C2×D3712yes—
107C22⋊Q8—742no—
108#121—742no—
109#121—742no—
110C2×C4⋊C4C2×D3711yescharacteristic
111C2×C42—371no—
112#104—744no—
113#95—742no—
114#41—742no—
115#41—742no—
116#41—742no—
117#41—742no—
118C2×Q8—372no—
119C2×Q8—372no—
120C2×Q8—741no—
121C2×Q8—742no—
122C2×Q8—742no—
123C2×D4—372no—
124C2×D4—742no—
125C2×D4—742no—
126C22×C4—741no—
127C22×C4—741no—
128C22×C4—742no—
129C22×C4D14812yes—
130C22×C4C22×D3711yescharacteristic
131Q16—748no—
132SD16—748no—
133M16—22no—
134M16D14814yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—742no—
138C22⋊C4—744no—
139C42—742no—
140C23—742no—
141C23C2×D14811yescharacteristic
142Q8—744no—
143Q8—742no—
144Q8—742no—
145Q8—1482no—
146D4—2962no—
147D4—742no—
148D4—742no—
149D4—1482no—
150D4—1482no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—742no—
154C2×C4—742no—
155C2×C4—742no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4—1482no—
161C2×C4—1482no—
162C2×C4C2×D14812yes—
163C2×C4D4×D3711yescharacteristic
164C2×C4D4×D3712yes—
165C2×C4#1059696611yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—1482no—
170C22—1482no—
171C22—1482no—
172C22#1192450611yescharacteristic
173C22#1192451111yescharacteristic
174C22#1192453311yescharacteristic
175C4—42no—
176C4—1482no—
177C4—1482no—
178C4—1482no—
179C4#1192450612yes—
180C4#1192451112yes—
181C2—21no—
182C2—21no—
183C2—2962no—
184C2#1455744311yescharacteristic
185C2#1455771311yescharacteristic
186C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
prime radical#14558114C2
hypercenter#343D37
hypocenterC37#2007
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
3. C2×#11924462C2semidirect
4. #14557438C2semidirect
5. C37×#343C2semidirect
36. C2×Dic74D4semidirect
38. M16×C37D4semidirect
98. #343D37semidirect
99. C37#2007semidirect
134. M16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145581142
C2×#119244622
#145574382
C37×#3432
#200737