Finite Group Databasebeta

← #17995640

Subgroups — #17995640

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×#11924564C212yesmaximal, complemented
2#14558114C211yesmaximal, characteristic, complemented
3C2×#11924462C212yesmaximal, complemented
4#14557434C211yesmaximal, characteristic, complemented
5C37×#343C211yesmaximal, characteristic, complemented
6C2×#10596962C2212yes—
7C22×D148C2211yescharacteristic
8#11924564—24no—
9#11924564—24no—
10C2×#10596930—22no—
11C2×D296—22no—
12#11924516—22no—
13#11924511—22no—
14#11924510—22no—
15C2×#10596938—22no—
16C2×C4×Dic37C2211yescharacteristic
17#11924462—24no—
18C2×M16×C37C2212yes—
19C2×C4⋊C4×C37C2211yescharacteristic
20C23×D37—21no—
21C22×C4×C37D412yes—
22C22×C4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C22×Dic37—21no—
25#10596962—22no—
26#10596962—22no—
27#10596962—22no—
28#10596962—22no—
29C2×D148—22no—
30C2×D148—22no—
31C2×D148—21no—
32C2×D148—22no—
33C2×D148D412yes—
34C2×D148D412yescomplemented
35C2×C4×D37—22no—
36C2×Dic74D412yes—
37M16×C37—22no—
38M16×C37D414yescomplemented
39C2×C8×C37—22no—
40C4⋊C4×C37—22no—
41#10596938—24no—
42#10596938—44no—
43C4⋊Dic37—22no—
44C4×Dic37—22no—
45D296—28no—
46#10596930—28no—
47C23×C37C2×D411yescharacteristic
48C22×D37—22no—
49C22×D37—22no—
50C22×D37—42no—
51C22×D37—42no—
52C22×D37—41no—
53C22×D37—41no—
54C2×C4×C37—22no—
55C2×C4×C37—42no—
56C2×C4×C37C2×D412yes—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D412yes—
59C2×C4×C37#4111yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—42no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66D148—24no—
67D148—22no—
68D148—22no—
69D148—42no—
70D148—82no—
71C4×D37—42no—
72C4×D37—42no—
73Dic74—22no—
74Dic74—22no—
75C8×C37—24no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37#12011yescharacteristic
79C22×C37#12111yescharacteristic
80C22×C37#12711yescharacteristic
81C2×D37—44no—
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37—42no—
86C2×D37—82no—
87C2×D37—81no—
88C2×D37—81no—
89C4×C37—42no—
90C4×C37#12012yes—
91C4×C37#12112yes—
92Dic37—42no—
93Dic37—42no—
94#2006—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37#39211yescharacteristic
98C2×C37#45311yescharacteristic
99C2×C37#45411yescharacteristic
100D37—82no—
101D37—82no—
102C2×AGL(1,ℤ/8)—372no—
103#537—371no—
104C2×#104—372no—
105#390—371no—
106#343D3711yescharacteristic, complemented
107C37#200611yescharacteristic, complemented, Sylow
108C2×#41—372no—
109C22×D4—371no—
110AGL(1,ℤ/8)—744no—
111AGL(1,ℤ/8)—744no—
112C2×SD16—742no—
113C2×D8—742no—
114C2×M16C2×D3712yes—
115C22⋊Q8—742no—
116#121—742no—
117#121—742no—
118C2×C4⋊C4C2×D3711yescharacteristic
119C2×C22⋊C4—742no—
120C2×C42—371no—
121#104—744no—
122C24—741no—
123#41—742no—
124#41—742no—
125#41—742no—
126#41—742no—
127C2×Q8—372no—
128C2×D4—372no—
129C2×D4—372no—
130C2×D4—742no—
131C2×D4—742no—
132C2×D4—742no—
133C2×D4—742no—
134C2×D4—741no—
135C22×C4—741no—
136C22×C4—742no—
137C22×C4D14812yes—
138C22×C4C22×D3711yescharacteristic
139SD16—748no—
140D8—748no—
141M16—22no—
142M16D14814yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—742no—
146C22⋊C4—744no—
147C22⋊C4—1484no—
148C42—742no—
149C23—742no—
150C23—742no—
151C23—1482no—
152C23—1482no—
153C23—1481no—
154C23—1481no—
155C23C2×D14811yescharacteristic
156Q8—742no—
157Q8—742no—
158D4—2962no—
159D4—742no—
160D4—744no—
161D4—742no—
162D4—1482no—
163D4—1482no—
164D4—1482no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—742no—
168C2×C4—742no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4C2×D14812yes—
174C2×C4D4×D3711yescharacteristic
175C2×C4D4×D3712yes—
176C2×C4#1059696611yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—2962no—
181C22—2961no—
182C22—2961no—
183C22—1484no—
184C22—1482no—
185C22—1482no—
186C22—1482no—
187C22—1482no—
188C22#1192450611yescharacteristic
189C22#1192451111yescharacteristic
190C22#1192453311yescharacteristic
191C4—42no—
192C4—1482no—
193C4—1482no—
194C4#1192450612yes—
195C4#1192451112yes—
196C2—21no—
197C2—21no—
198C2—2962no—
199C2—2962no—
200C2#1455744311yescharacteristic
201C2#1455770311yescharacteristic
202C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
hypercenter#343D37
hypocenterC37#2006
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×#11924564C2semidirect
2. #14558114C2semidirect
3. C2×#11924462C2semidirect
4. #14557434C2semidirect
5. C37×#343C2semidirect
34. C2×D148D4semidirect
38. M16×C37D4semidirect
106. #343D37semidirect
107. C37#2006semidirect
142. M16D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
#145581142
C2×#119244622
#145574342
C37×#3432
#200637