Finite Group Databasebeta

← #17995638

Subgroups — #17995638

Order 4736.

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

normal subgroups only

This group has 406 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×#11924561C212yesmaximal, complemented
2C2×#11924463C212yesmaximal, complemented
3#14557434C211yesmaximal, characteristic, complemented
4#14557302C211yesmaximal, characteristic, complemented
5C37×#537C211yesmaximal, characteristic, complemented
6C22×D148C2211yescharacteristic
7#11924561—24no—
8#11924561—24no—
9C2×#10596941—22no—
10C2×#10596939—22no—
11C2×#10596934C2212yes—
12C2×#10596938—22no—
13C2×C4×Dic37C2211yescharacteristic
14#11924463—24no—
15C2×#41×C37C2212yes—
16C22⋊Q8×C37—22no—
17#121×C37—22no—
18#121×C37—22no—
19C2×C4⋊C4×C37C2211yescharacteristic
20C23×D37—21no—
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×C37—22no—
28C2×D4×C37D412yes—
29C22×C4×C37—22no—
30C22×C4×C37D412yes—
31C22×C4×C37C2311yescharacteristic
32C22×Dic37—21no—
33C2×D148—22no—
34C2×D148—22no—
35C2×D148—21no—
36C2×D148D412yescomplemented
37C4⋊C4×C37—22no—
38C4⋊C4×C37—22no—
39C22⋊C4×C37—24no—
40#10596941—28no—
41#10596939—28no—
42#10596938—44no—
43C4×Dic37—22no—
44#10596934—22no—
45#10596934D414yescomplemented
46C2×#64436—22no—
47C23×C37—22no—
48C23×C37C2×D411yescharacteristic
49C22×D37—22no—
50C22×D37—42no—
51C22×D37—42no—
52C22×D37—41no—
53C22×D37—41no—
54Q8×C37—22no—
55Q8×C37—22no—
56D4×C37—22no—
57D4×C37—22no—
58D4×C37—42no—
59D4×C37—42no—
60D4×C37—82no—
61C2×C4×C37—22no—
62C2×C4×C37—22no—
63C2×C4×C37—42no—
64C2×C4×C37—42no—
65C2×C4×C37—42no—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D412yes—
68C2×C4×C37C2×D412yes—
69C2×C4×C37#4111yescharacteristic
70C2×Dic37—22no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73D148—24no—
74D148—42no—
75#64436—24no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—42no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37#12011yescharacteristic
82C22×C37#12111yescharacteristic
83C22×C37#12711yescharacteristic
84C2×D37—44no—
85C2×D37—42no—
86C2×D37—82no—
87C2×D37—81no—
88C2×D37—81no—
89C4×C37—42no—
90C4×C37—42no—
91C4×C37#12012yes—
92C4×C37#12112yes—
93Dic37—42no—
94#2006—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37—82no—
98C2×C37#39211yescharacteristic
99C2×C37#45311yescharacteristic
100C2×C37#45411yescharacteristic
101D37—82no—
102C2×AGL(1,ℤ/8)—372no—
103#537D3711yescharacteristic, complemented
104C2×#104—372no—
105#390—371no—
106#343—371no—
107C37#200611yescharacteristic, complemented, Sylow
108C2×#41C2×D3712yes—
109C22×D4—371no—
110AGL(1,ℤ/8)—744no—
111AGL(1,ℤ/8)—744no—
112C2×SD16—742no—
113C2×D8—742no—
114C2×M16—372no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D3711yescharacteristic
119C2×C22⋊C4—742no—
120C2×C42—371no—
121#104—744no—
122C24—741no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D3712yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—372no—
131C2×D4—742no—
132C2×D4—741no—
133C2×D4—742no—
134C2×D4C22⋊D3712yes—
135C22×C4—22no—
136C22×C4—741no—
137C22×C4C22⋊D3712yes—
138C22×C4C22×D3711yescharacteristic
139SD16—748no—
140D8—748no—
141M16—374no—
142M16—742no—
143C2×C8—742no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—1484no—
148C42—742no—
149C23—22no—
150C23—742no—
151C23—1482no—
152C23—1482no—
153C23—1481no—
154C23—1481no—
155C23C2×C22⋊D3711yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—744no—
164D4—1482no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—742no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3712yes—
175C2×C4#1059696411yescharacteristic
176C2×C4C2×C22⋊D3712yes—
177C8—744no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—2962no—
184C22—2961no—
185C22—2961no—
186C22—1484no—
187C22—1482no—
188C22#1192450511yescharacteristic
189C22#1192450711yescharacteristic
190C22#1192453211yescharacteristic
191C4—42no—
192C4—42no—
193C4—1482no—
194C4#1192450412yes—
195C4#1192450812yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2962no—
200C2#1455744111yescharacteristic
201C2#1455770111yescharacteristic
202C2#1455770611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#537C2
socleC22×C37#120
hypercenter#537D37
hypocenterC37#2006
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#11924561C2semidirect
2. C2×#11924463C2semidirect
3. #14557434C2semidirect
4. #14557302C2semidirect
5. C37×#537C2semidirect
36. C2×D148D4semidirect
45. #10596934D4semidirect
103. #537D37semidirect
107. C37#2006semidirect

Maximal subgroups

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

subgroupindex
C2×#119245612
C2×#119244632
#145574342
#145573022
C37×#5372
#200637