Finite Group Databasebeta

← #17993530

Subgroups — #17993530

Order 4736.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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, complemented
2#14557667C212yesmaximal, complemented
3#14557266C212yesmaximal, complemented
4#14557259C211yesmaximal, characteristic, complemented
5C37×#394C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7C2×#10596939—22no—
8#11924516—22no—
9#11924511—22no—
10#11924510—21no—
11#11924510C2212yes—
12#11924457—22no—
13C22⋊#64436C2212yes—
14C22×D4×C37C2211yescharacteristic
15C2×C4⋊C4×C37C2211yescharacteristic
16C2×C22⋊C4×C37—21no—
17C2×C22⋊C4×C37—21no—
18#95×C37C2211yescharacteristic
19C24×C37—21no—
20C2×D4×C37—22no—
21C2×D4×C37—42no—
22C22×C4×C37—21no—
23C22×C4×C37D411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C2×C22⋊D37—22no—
27#10596962—42no—
28#10596962—42no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148D412yes—
32C2×C4×D37—22no—
33C2×Dic74—21no—
34C4⋊C4×C37—22no—
35C22⋊C4×C37—42no—
36C22⋊C4×C37—42no—
37#10596939—44no—
38#10596938—22no—
39#10596938—22no—
40C4⋊Dic37—21no—
41C4⋊Dic37D412yes—
42C2×#64436—22no—
43C23×C37—22no—
44C23×C37—41no—
45C23×C37—41no—
46C23×C37—41no—
47C23×C37—41no—
48C23×C37—41no—
49C23×C37—41no—
50C23×C37C2×D411yescharacteristic
51C22×D37—22no—
52D4×C37—24no—
53D4×C37—42no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37D812yescomplemented
63C2×C4×C37C2×D412yes—
64C22⋊D37—42no—
65C22⋊D37—42no—
66C2×Dic37—22no—
67D148—42no—
68D148—42no—
69D148—81no—
70C4×D37—44no—
71Dic74—42no—
72#64436—42no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37—81no—
79C22×C37—81no—
80C22×C37—81no—
81C22×C37—81no—
82C22×C37#12011yescharacteristic
83C22×C37C2×D811yescharacteristic
84C22×C37AGL(1,ℤ/8)11yescharacteristic
85C2×D37—42no—
86C2×D37—42no—
87C2×D37—42no—
88C4×C37—22no—
89C4×C37—22no—
90C4×C37—41no—
91C4×C37—81no—
92Dic37—42no—
93#1598—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—21no—
96C2×C37—82no—
97C2×C37#44711yescharacteristic
98C2×C37#45411yescharacteristic
99C2×C37B(4,𝔽2)11yescharacteristic
100D37—82no—
101#537—371no—
102#447—372no—
103#394D3711yescharacteristic, complemented
104#327—372no—
105#324—371no—
106C37#159811yescharacteristic, complemented, Sylow
107C2×#41—741no—
108C22×D4C2×D3711yescharacteristic
109C2×D8—742no—
110C22⋊Q8—742no—
111#121—372no—
112#121—742no—
113#121—741no—
114C2×C4⋊C4C2×D3711yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—742no—
118C22⋊C8—372no—
119#95C2×D3711yescharacteristic
120C24—21no—
121#41—1482no—
122#41—1482no—
123C2×Q8—741no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—372no—
127C2×D4—741no—
128C2×D4—741no—
129C2×D4—742no—
130C22×C4—21no—
131C22×C4—742no—
132C22×C4C22⋊D3711yescharacteristic
133C22×C4C22⋊D3711yescharacteristic
134C22×C4C22×D3711yescharacteristic
135D8—1484no—
136C2×C8—742no—
137C4⋊C4—22no—
138C4⋊C4—372no—
139C4⋊C4—741no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—742no—
152C23C2×C22⋊D3711yescharacteristic
153Q8—1482no—
154D4—24no—
155D4—42no—
156D4—2961no—
157D4—1482no—
158D4—1482no—
159D4—1482no—
160D4—1482no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—742no—
170C2×C4—1484no—
171C2×C4#1059693912yescomplemented
172C2×C4D4×D3712yes—
173C8—1482no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—1482no—
184C22—1482no—
185C22—1482no—
186C22#1192450411yescharacteristic
187C22C2×#1059693911yescharacteristic
188C22#1192456111yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—1482no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—2962no—
198C2#1455766611yescharacteristic
199C2#1455770511yescharacteristic
200C2#1455771911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#394C2
socleC22×C37#120
hypercenter#394D37
hypocenterC37#1598
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #14558114C2semidirect
2. #14557667C2semidirect
3. #14557266C2semidirect
4. #14557259C2semidirect
5. C37×#394C2semidirect
62. C2×C4×C37D8semidirect
103. #394D37semidirect
106. C37#1598semidirect
171. C2×C4#10596939semidirect

Maximal subgroups

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

subgroupindex
#145581142
#145576672
#145572662
#145572592
C37×#3942
#159837