Finite Group Databasebeta

← #17996556

Subgroups — #17996556

Order 4736.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#14558334C211yesmaximal, characteristic, complemented
2#14557971C211yesmaximal, characteristic, complemented
3C2×#11924477C211yesmaximal, characteristic, complemented
4#14557804C211yesmaximal, characteristic, complemented
5#14557339C211yesmaximal, characteristic, complemented
6#14557318C211yesmaximal, characteristic, complemented
7C37×#361C211yesmaximal, characteristic, complemented
8#11924581—21no—
9#11924564—21no—
10#11924562—21no—
11#11924560—22no—
12#11924558C2211yescharacteristic
13#11924555—21no—
14C2×D296C2211yescharacteristic, complemented
15D8×D37—21no—
16#11924542C2211yescharacteristic
17#11924481—21no—
18D592—21no—
19#11924477—22no—
20C2×#10596925C2211yescharacteristic, complemented
21#11924452—21no—
22C2×D8×C37C2211yescharacteristic
23M32×C37C2211yescharacteristic, complemented
24#108×C37C2211yescharacteristic, complemented
25C2×D4×C37—21no—
26C2×C22⋊D37—42no—
27#10596964—22no—
28#10596964—41no—
29D4×D37—22no—
30D4×D37—41no—
31#10596962—21no—
32#10596962D411yescharacteristic
33C2×D148—21no—
34D8×C37—21no—
35D8×C37D412yes—
36M16×C37—21no—
37C2×C8×C37C2311yescharacteristic
38#10596940—22no—
39#10596939—22no—
40#10596934D411yescharacteristic
41Dic148D411yescharacteristic
42D296—21no—
43D296—21no—
44D296—41no—
45D296D411yescharacteristic
46#10596930—21no—
47#10596930—41no—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C23×C37—41no—
53C22×D37—42no—
54C22×D37—41no—
55D4×C37—22no—
56D4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C22⋊D37—21no—
59C22⋊D37—42no—
60C22⋊D37—42no—
61C22⋊D37—41no—
62C2×Dic37—42no—
63D148—21no—
64D148—41no—
65D148—41no—
66D148D811yescharacteristic
67C4×D37—21no—
68C4×D37—41no—
69Dic74—21no—
70Dic74D811yescharacteristic
71C8×C37—41no—
72C8×C37C2×D411yescharacteristic
73C8×C37C2×D411yescharacteristic
74#64436—21no—
75C22×C37—42no—
76C22×C37—161no—
77C22×C37AGL(1,ℤ/8)11yescharacteristic
78C2×D37—21no—
79C2×D37—41no—
80C2×D37—81no—
81C2×D37—162no—
82C2×D37—161no—
83C4×C37#12011yescharacteristic
84C4×C37C2×D811yescharacteristic
85Dic37—21no—
86Dic37—41no—
87#2192—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—82no—
90C2×C37#44711yescharacteristic
91D37—41no—
92D37—81no—
93D37—161no—
94#576—371no—
95#509—371no—
96C2×D16—371no—
97#472—371no—
98#361D3711yescharacteristic, complemented
99#359—371no—
100#350—371no—
101C37#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—741no—
103AGL(1,ℤ/8)—741no—
104AGL(1,ℤ/8)—741no—
105AGL(1,ℤ/8)—742no—
106#135—371no—
107#135—741no—
108C2×D8—371no—
109C2×D8—741no—
110C2×D8C2×D3711yescharacteristic
111#131—371no—
112SD32—741no—
113D16—741no—
114D16—742no—
115M32C2×D3711yescharacteristic, complemented
116C2×C16—371no—
117#108C2×D3711yescharacteristic, complemented
118#100—741no—
119#41—371no—
120#41—742no—
121#41—741no—
122#41—1481no—
123C2×D4—21no—
124C2×D4—742no—
125C2×D4—741no—
126C2×D4—1481no—
127C2×D4—1482no—
128Q16—371no—
129SD16—742no—
130SD16—741no—
131SD16—1481no—
132D8—21no—
133D8—371no—
134D8—742no—
135D8—741no—
136D8—741no—
137D8—1481no—
138D8D14812yes—
139M16—21no—
140M16—371no—
141M16—741no—
142C2×C8—741no—
143C2×C8C22×D3711yescharacteristic
144C16—21no—
145C16—741no—
146C23—41no—
147C23—1482no—
148C23—1481no—
149Q8—371no—
150Q8—741no—
151D4—22no—
152D4—41no—
153D4—371no—
154D4—741no—
155D4—741no—
156D4—1482no—
157D4—1482no—
158D4—1481no—
159D4—1481no—
160D4—1481no—
161C2×C4—741no—
162C2×C4—1482no—
163C2×C4—1481no—
164C2×C4D4×D3711yescharacteristic
165C8—41no—
166C8—741no—
167C8C2×D14811yescharacteristic
168C8D4×D3711yescharacteristic
169C22—42no—
170C22—161no—
171C22—2961no—
172C22—741no—
173C22—5921no—
174C22—5922no—
175C22—1481no—
176C22#1192456311yescharacteristic
177C4—741no—
178C4—1481no—
179C4#1192450611yescharacteristic
180C4D8×D3711yescharacteristic
181C2—21no—
182C2—82no—
183C2—2961no—
184C2—5921no—
185C2—1481no—
186C2#1455766811yescharacteristic
subgroupG/H
centerC2#14557668
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#361C2
socleC2×C37#447
hypercenter#361D37
hypocenterC37#2192
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #14558334C2semidirect
2. #14557971C2semidirect
3. C2×#11924477C2semidirect
4. #14557804C2semidirect
5. #14557339C2semidirect
6. #14557318C2semidirect
7. C37×#361C2semidirect
14. C2×D296C22semidirect
20. C2×#10596925C22semidirect
23. M32×C37C22semidirect
24. #108×C37C22semidirect
98. #361D37semidirect
101. C37#2192semidirect
115. M32C2×D37semidirect
117. #108C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583342
#145579712
C2×#119244772
#145578042
#145573392
#145573182
C37×#3612
#219237