Finite Group Databasebeta

← #17995700

Subgroups — #17995700

Order 4736.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558333C211yesmaximal, characteristic, complemented
2#14558331C212yesmaximal, complemented
3#14557499C212yesmaximal, complemented
4#14557291C211yesmaximal, characteristic, complemented
5C37×#408C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7#11924569—22no—
8#11924567—22no—
9#11924566—22no—
10#11924564—22no—
11#11924562—22no—
12#11924561—22no—
13#11924558—22no—
14#11924556—24no—
15C2×#10596934C2212yes—
16#11924448—24no—
17C2×#41×C37C2211yescharacteristic
18C2×M16×C37C2211yescharacteristic
19C22×C8×C37C2211yescharacteristic
20C22⋊C8×C37—22no—
21#41×C37—22no—
22#41×C37—22no—
23C2×Q8×C37D411yescharacteristic
24C2×D4×C37—21no—
25C2×D4×C37D411yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—22no—
29#10596962—22no—
30#10596962—22no—
31#10596962—22no—
32#10596962—22no—
33C2×D148D412yes—
34C2×C4×D37—22no—
35C2×Dic74D412yes—
36M16×C37—22no—
37C2×C8×C37—21no—
38C2×C8×C37—22no—
39C2×C8×C37D412yes—
40#10596942—24no—
41#10596941—24no—
42#10596940—24no—
43#10596939—24no—
44#10596934—22no—
45#10596934—22no—
46C2×#64436D414yes—
47Dic148—22no—
48D296—22no—
49#10596930—24no—
50C23×C37—21no—
51C23×C37#4111yescharacteristic
52C22×D37—22no—
53Q8×C37—22no—
54D4×C37—22no—
55D4×C37—42no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D412yes—
61C2×C4×C37C2×D412yes—
62C2×C4×C37C2×D411yescharacteristic
63C22⋊D37—42no—
64C22⋊D37—42no—
65C2×Dic37—22no—
66D148—22no—
67D148—22no—
68C4×D37—42no—
69C4×D37—42no—
70Dic74—22no—
71Dic74—22no—
72C8×C37—22no—
73C8×C37—41no—
74#64436—24no—
75C22×C37—41no—
76C22×C37—42no—
77C22×C37—41no—
78C22×C37#12112yes—
79C22×C37#12111yescharacteristic
80C2×D37—44no—
81C2×D37—42no—
82C4×C37—41no—
83C4×C37#12011yescharacteristic
84C4×C37#12012yes—
85C4×C37#12711yescharacteristic
86Dic37—42no—
87#2017—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37—21no—
90C2×C37—81no—
91C2×C37#39211yescharacteristic
92D37—82no—
93#575—372no—
94#575—371no—
95#408—372no—
96#408D3711yescharacteristic, complemented
97#338—371no—
98C37#201711yescharacteristic, complemented, Sylow
99C2×#41—372no—
100C2×#41C2×D3711yescharacteristic
101#137—742no—
102#137—742no—
103#137—742no—
104AGL(1,ℤ/8)—742no—
105AGL(1,ℤ/8)—742no—
106AGL(1,ℤ/8)—742no—
107#135—744no—
108#135—742no—
109C2×M16—372no—
110C2×M16C2×D3711yescharacteristic
111C22×C8C2×D3711yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—744no—
114#41—22no—
115#41—22no—
116#41—742no—
117#41—742no—
118#41—742no—
119#41—742no—
120C2×Q8—372no—
121C2×Q8D14811yescharacteristic
122C2×D4—21no—
123C2×D4—372no—
124C2×D4—742no—
125C2×D4D14811yescharacteristic
126C22×C4—21no—
127C22×C4—742no—
128C22×C4C22×D3711yescharacteristic
129Q16—742no—
130Q16—744no—
131SD16—744no—
132SD16—744no—
133SD16—744no—
134D8—742no—
135D8—744no—
136M16—22no—
137M16—742no—
138M16—742no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—374no—
142C2×C8C22⋊D3712yes—
143C23—21no—
144C23—742no—
145C23#1059696211yescharacteristic
146Q8—22no—
147Q8—742no—
148Q8—742no—
149D4—22no—
150D4—42no—
151D4—742no—
152D4—742no—
153D4—1482no—
154D4—1482no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—742no—
159C2×C4—1482no—
160C2×C4—1482no—
161C2×C4C2×D14811yescharacteristic
162C2×C4D4×D3712yes—
163C2×C4D4×D3712yes—
164C2×C4C2×C22⋊D3711yescharacteristic
165C8—22no—
166C8—41no—
167C8—744no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—1484no—
172C22—1482no—
173C22#1192450912yes—
174C22#1192451011yescharacteristic
175C4—41no—
176C4—1482no—
177C4#1192450411yescharacteristic
178C4#1192450612yes—
179C4#1192453211yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—2962no—
184C2#1455744211yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#408C2
socleC2×C37#392
hypercenter#408D37
hypocenterC37#2017
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14558333C2semidirect
2. #14558331C2semidirect
3. #14557499C2semidirect
4. #14557291C2semidirect
5. C37×#408C2semidirect
96. #408D37semidirect
98. C37#2017semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145583312
#145574992
#145572912
C37×#4082
#201737