Finite Group Databasebeta

← #17995699

Subgroups — #17995699

Order 4736.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#14558331C212yesmaximal, complemented
2#14557501C211yesmaximal, characteristic, complemented
3#14557500C212yesmaximal, complemented
4#14557291C211yesmaximal, characteristic, complemented
5C37×#575C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7#11924567—22no—
8#11924566—22no—
9#11924562—22no—
10#11924561—22no—
11#11924556—24no—
12C2×#10596934C2212yes—
13C22×#64436C2211yescharacteristic
14C22⋊#64436—24no—
15#11924448—22no—
16C2×#41×C37C2212yes—
17#137×C37—22no—
18AGL(1,ℤ/8)×C37—22no—
19#135×C37—22no—
20C2×M16×C37C2211yescharacteristic
21#41×C37—22no—
22#41×C37—22no—
23#41×C37—22no—
24#41×C37—22no—
25C2×Q8×C37D412yes—
26C2×D4×C37—22no—
27C2×D4×C37D412yes—
28C22×C4×C37—22no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31#10596962—22no—
32#10596962—22no—
33C2×D148D411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74D411yescharacteristic
36Q16×C37—22no—
37SD16×C37—24no—
38D8×C37—22no—
39M16×C37—22no—
40C2×C8×C37D412yes—
41#10596942—24no—
42#10596941—24no—
43#10596940—24no—
44#10596939—24no—
45#10596934—22no—
46#10596934—22no—
47C2×#64436—21no—
48C2×#64436—22no—
49C2×#64436D414yes—
50C23×C37—22no—
51C23×C37#4111yescharacteristic
52C22×D37—21no—
53Q8×C37—22no—
54Q8×C37—22no—
55D4×C37—22no—
56D4×C37—22no—
57D4×C37—42no—
58D4×C37—42no—
59C2×C4×C37—22no—
60C2×C4×C37—42no—
61C2×C4×C37—42no—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D412yes—
64C2×C4×C37C2×D412yes—
65C2×C4×C37C2×D411yescharacteristic
66C22⋊D37—42no—
67C2×Dic37—21no—
68D148—22no—
69C4×D37—41no—
70C4×D37—41no—
71Dic74—22no—
72C8×C37—22no—
73#64436—24no—
74#64436—41no—
75C22×C37—41no—
76C22×C37—44no—
77C22×C37—42no—
78C22×C37#12111yescharacteristic
79C22×C37#12112yes—
80C2×D37—42no—
81C2×D37—41no—
82C4×C37—42no—
83C4×C37#12012yes—
84C4×C37#12011yescharacteristic
85C4×C37#12711yescharacteristic
86Dic37—41no—
87#2017—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—22no—
90C2×C37—82no—
91C2×C37#39211yescharacteristic
92D37—81no—
93#575—372no—
94#575D3711yescharacteristic, complemented
95#408—372no—
96#408—371no—
97#338—371no—
98C37#201711yescharacteristic, complemented, Sylow
99C2×#41—371no—
100C2×#41C2×D3712yes—
101#137—22no—
102#137—742no—
103#137—742no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—742no—
106AGL(1,ℤ/8)—742no—
107#135—22no—
108#135—744no—
109C2×M16—372no—
110C2×M16C2×D3711yescharacteristic
111C22×C8—371no—
112C22⋊C8—744no—
113C22⋊C8—742no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—742no—
119#41—742no—
120C2×Q8—371no—
121C2×Q8C22⋊D3712yes—
122C2×D4—22no—
123C2×D4—371no—
124C2×D4—741no—
125C2×D4C22⋊D3712yes—
126C22×C4—22no—
127C22×C4—741no—
128C22×C4C22×D3711yescharacteristic
129Q16—22no—
130Q16—744no—
131SD16—24no—
132SD16—744no—
133SD16—744no—
134D8—22no—
135D8—744no—
136M16—22no—
137M16—742no—
138M16—742no—
139C2×C8—374no—
140C2×C8—742no—
141C2×C8—741no—
142C2×C8C22⋊D3712yes—
143C23—22no—
144C23—741no—
145C23#1059696411yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—742no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—742no—
154D4—1482no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—741no—
159C2×C4—1481no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C2×C4D4×D3712yes—
163C2×C4C2×C22⋊D3712yes—
164C2×C4C2×C22⋊D3711yescharacteristic
165C8—22no—
166C8—744no—
167C8—1481no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—1482no—
172C22—1481no—
173C22#1192450711yescharacteristic
174C22#1192450812yes—
175C4—42no—
176C4—1481no—
177C4#1192450412yes—
178C4#1192450511yescharacteristic
179C4#1192453211yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—2961no—
184C2#1455744111yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#575C2
socleC2×C37#392
hypercenter#575D37
hypocenterC37#2017
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14557501C2semidirect
3. #14557500C2semidirect
4. #14557291C2semidirect
5. C37×#575C2semidirect
94. #575D37semidirect
98. C37#2017semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145575012
#145575002
#145572912
C37×#5752
#201737