Finite Group Databasebeta

← #17993762

Subgroups — #17993762

Order 4736.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558198C211yesmaximal, characteristic
2#14557885C211yesmaximal, characteristic, complemented
3#14557829C211yesmaximal, characteristic, complemented
4#14557824C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic
7C37×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9#11924536C2211yescharacteristic
10#11924535—21no—
11#11924514—22no—
12#11924512—21no—
13C4×Dic74C2211yescharacteristic
14C4×D148C2211yescharacteristic
15#11924498—21no—
16#11924470—21no—
17#11924468—21no—
18#11924461—21no—
19#11924459—22no—
20#11924458—21no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26Q8×D37—42no—
27Q8×D37—42no—
28C2×D148D411yescharacteristic
29C2×C4×D37—22no—
30C2×C4×D37—21no—
31C2×Dic74—22no—
32C2×Dic74—21no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D412yes—
38C42×C37C2311yescharacteristic
39#10596938—22no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D411yescharacteristic
45#10596936—22no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C22×D37—21no—
50Q8×C37—41no—
51Q8×C37—41no—
52C2×C4×C37—22no—
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—41no—
60D148—21no—
61D148Q1612yes—
62C4×D37—44no—
63C4×D37—41no—
64C4×D37—41no—
65Dic74—21no—
66Dic74—44no—
67Dic74—42no—
68Dic74SD1612yes—
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—22no—
74C2×D37—41no—
75C2×D37—41no—
76C4×C37—21no—
77C4×C37—42no—
78C4×C37C2×SD1611yescharacteristic
79C4×C37C2×Q1611yescharacteristic
80C4×C37AGL(1,ℤ/8)11yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—22no—
83Dic37—41no—
84Dic37—41no—
85Dic37—81no—
86#1637—371nomaximal, Sylow
87C2×C37#45011yescharacteristic
88C2×C37#45111yescharacteristic
89C2×C37#45411yescharacteristic
90D37—42no—
91D4×Q8—371no—
92#487—371no—
93#477—371no—
94#476—371no—
95#332D3711yescharacteristic, complemented
96Q8⋊C8—371no—
97D4⋊C8—371no—
98C37#163711yescharacteristic, complemented, Sylow
99C22×Q8—741no—
100C4⋊Q8—371no—
101C4⋊Q8—741no—
102C4⋊Q8C2×D3711yescharacteristic
103C22⋊Q8—741no—
104C22⋊Q8—742no—
105C4×Q8—371no—
106C4×D4—371no—
107C4×D4—741no—
108#107—741no—
109#106—741no—
110C4⋊C8C2×D3711yescharacteristic
111C4⋊C8C2×D3711yescharacteristic
112#103—741no—
113#103—742no—
114#102—741no—
115C4×C8—371no—
116C2×Q8—21no—
117C2×Q8—371no—
118C2×Q8—742no—
119C2×Q8—741no—
120C2×Q8—1482no—
121C2×Q8—1482no—
122C2×D4—371no—
123C22×C4—742no—
124C22×C4—741no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—741no—
128C4⋊C4—21no—
129C4⋊C4—371no—
130C4⋊C4—371no—
131C4⋊C4—742no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4D14812yes—
136C22⋊C4—742no—
137C22⋊C4—741no—
138C42—741no—
139C42C22×D3711yescharacteristic
140C23—741no—
141Q8—41no—
142Q8—41no—
143Q8—372no—
144Q8—741no—
145Q8—1482no—
146Q8—1484no—
147D4—372no—
148D4—741no—
149C2×C4—22no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—741no—
153C2×C4—1484no—
154C2×C4—1481no—
155C2×C4—1481no—
156C2×C4—1481no—
157C2×C4C2×D14811yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C2×C4D4×D3711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1481no—
163C22—742no—
164C22—1481no—
165C22—1481no—
166C22#1192450611yescharacteristic
167C4—21no—
168C4—42no—
169C4—2961no—
170C4—742no—
171C4—1481no—
172C4—1481no—
173C4SD16×D3711yescharacteristic
174C4Q16×D3711yescharacteristic
175C4#1192456011yescharacteristic
176C4#1192456511yescharacteristic
177C2—1482no—
178C2#1455768511yescharacteristic
179C2#1455769011yescharacteristic
180C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#332D37
hypocenterC37#1637
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14557885C2semidirect
3. #14557829C2semidirect
5. #14557263C2semidirect
7. C37×#332C2semidirect
95. #332D37semidirect
98. C37#1637semidirect

Maximal subgroups

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

subgroupindex
#145581982
#145578852
#145578292
#145578242
#145572632
#145572602
C37×#3322
#163737