Finite Group Databasebeta

← #17995821

Subgroups — #17995821

Order 4736.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#14558114C211yesmaximal, characteristic
2C2×#11924462C212yesmaximal, complemented
3#14557535C212yesmaximal, complemented
4#14557402C211yesmaximal, characteristic, complemented
5C37×#343C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7#11924516—22no—
8#11924511—22no—
9#11924510—22no—
10C2×C4⋊Dic37C2211yescharacteristic
11C2×#10596936—22no—
12C2×C4×Dic37C2211yescharacteristic
13#11924462—24no—
14#11924461—22no—
15#11924458—22no—
16C2×M16×C37C2212yes—
17C2×C4⋊C4×C37C2211yescharacteristic
18C22×C4×C37D412yes—
19C22×C4×C37C2311yescharacteristic
20C2×C22⋊D37—22no—
21C22×Dic37—21no—
22C22×Dic37—21no—
23#10596962—22no—
24#10596962—22no—
25#10596962—22no—
26#10596962—22no—
27C2×D148—22no—
28C2×D148D412yes—
29C2×C4×D37—22no—
30C2×Dic74D412yes—
31M16×C37—22no—
32M16×C37—22no—
33C2×C8×C37—22no—
34C4⋊C4×C37—22no—
35#10596938—24no—
36C4⋊Dic37—22no—
37C4⋊Dic37—22no—
38#10596936—44no—
39C4×Dic37—21no—
40C4×Dic37D412yescomplemented
41C23×C37C2×D411yescharacteristic
42C22×D37—22no—
43C2×C4×C37—22no—
44C2×C4×C37—42no—
45C2×C4×C37C2×D411yescharacteristic
46C2×C4×C37C2×D412yes—
47C2×C4×C37#4112yes—
48C2×C4×C37#4111yescharacteristic
49C22⋊D37—42no—
50C22⋊D37—42no—
51C2×Dic37—22no—
52C2×Dic37—22no—
53C2×Dic37—22no—
54C2×Dic37—22no—
55C2×Dic37—42no—
56C2×Dic37—41no—
57D148—22no—
58D148—22no—
59D148—82no—
60C4×D37—42no—
61C4×D37—42no—
62Dic74—22no—
63Dic74—22no—
64C8×C37—42no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37#12011yescharacteristic
68C22×C37#12111yescharacteristic
69C22×C37#12411yescharacteristic
70C2×D37—42no—
71C2×D37—42no—
72C2×D37—42no—
73C4×C37—42no—
74C4×C37#12112yes—
75C4×C37#12312yes—
76Dic37—24no—
77Dic37—42no—
78Dic37—81no—
79#2039—371nomaximal, Sylow
80C2×C37—21no—
81C2×C37—21no—
82C2×C37#39411yescharacteristic
83C2×C37#45311yescharacteristic
84C2×C37#45611yescharacteristic
85D37—82no—
86#537—371no—
87C2×#104—372no—
88#417—372no—
89#384—371no—
90#343D3711yescharacteristic, complemented
91C37#203911yescharacteristic, complemented, Sylow
92C2×#41—372no—
93C2×M16C2×D3712yes—
94C22⋊Q8—742no—
95#121—742no—
96#121—742no—
97C2×C4⋊C4—371no—
98C2×C4⋊C4—742no—
99C2×C4⋊C4C2×D3711yescharacteristic
100C2×C42—371no—
101#104—744no—
102#103—742no—
103#102—742no—
104#41—742no—
105#41—742no—
106#41—742no—
107#41—742no—
108C2×Q8—372no—
109C2×D4—372no—
110C2×D4—742no—
111C2×D4—742no—
112C22×C4—741no—
113C22×C4—742no—
114C22×C4—741no—
115C22×C4D14812yes—
116C22×C4C22×D3711yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—742no—
122C4⋊C4—742no—
123C4⋊C4—1484no—
124C22⋊C4—744no—
125C42—372no—
126C42—741no—
127C23—742no—
128C23C2×D14811yescharacteristic
129Q8—742no—
130Q8—742no—
131D4—2962no—
132D4—742no—
133D4—742no—
134D4—1482no—
135D4—1482no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—742no—
139C2×C4—742no—
140C2×C4—742no—
141C2×C4—742no—
142C2×C4—1482no—
143C2×C4—1481no—
144C2×C4—1482no—
145C2×C4—1482no—
146C2×C4#1059696212yes—
147C2×C4D4×D3711yescharacteristic
148C2×C4D4×D3712yes—
149C2×C4#1059696611yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—1482no—
154C22—1482no—
155C22—1482no—
156C22#1192450611yescharacteristic
157C22#1192451111yescharacteristic
158C22#1192452411yescharacteristic
159C4—42no—
160C4—2961no—
161C4—744no—
162C4—1482no—
163C4#1192450912yes—
164C4#1192452112yes—
165C2—21no—
166C2—21no—
167C2—2962no—
168C2#1455745111yescharacteristic
169C2#1455770311yescharacteristic
170C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
prime radical#14558114C2
hypercenter#343D37
hypocenterC37#2039
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
2. C2×#11924462C2semidirect
3. #14557535C2semidirect
4. #14557402C2semidirect
5. C37×#343C2semidirect
40. C4×Dic37D4semidirect
90. #343D37semidirect
91. C37#2039semidirect

Maximal subgroups

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

subgroupindex
#145581142
C2×#119244622
#145575352
#145574022
C37×#3432
#203937