Finite Group Databasebeta

← #17996550

Subgroups — #17996550

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#14558335C211yesmaximal, characteristic, complemented
2C2×#11924477C211yesmaximal, characteristic, complemented
3#14557800C211yesmaximal, characteristic, complemented
4#14557347C211yesmaximal, characteristic, complemented
5#14557340C211yesmaximal, characteristic, complemented
6#14557318C211yesmaximal, characteristic, complemented
7C37×#509C211yesmaximal, characteristic, complemented
8#11924582—21no—
9#11924563—22no—
10#11924562—21no—
11#11924561—21no—
12#11924559—21no—
13C2×D296C2211yescharacteristic
14D8×D37—21no—
15#11924542C2211yescharacteristic
16#11924477—22no—
17C2×#10596925C2211yescharacteristic, complemented
18#11924472C2211yescharacteristic, complemented
19#11924453—21no—
20#135×C37C2211yescharacteristic
21C2×D8×C37C2211yescharacteristic, complemented
22SD32×C37—21no—
23D16×C37—21no—
24M32×C37C2211yescharacteristic, complemented
25#41×C37—21no—
26C2×D4×C37—21no—
27#10596966—22no—
28D4×D37—22no—
29D4×D37—42no—
30#10596962—41no—
31#10596962D411yescharacteristic
32C2×D148—21no—
33C2×D148—41no—
34Q16×C37D411yescharacteristic
35SD16×C37—21no—
36D8×C37—21no—
37D8×C37—21no—
38D8×C37D411yescharacteristic
39C2×C8×C37C2311yescharacteristic
40#10596941—22no—
41#10596940—41no—
42#10596939—22no—
43#10596939—41no—
44#10596934—21no—
45#10596934D411yescharacteristic
46D296—21no—
47D296D412yes—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C23×C37—41no—
53C22×D37—42no—
54C22×D37—41no—
55Q8×C37—21no—
56D4×C37—21no—
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—21no—
63C22⋊D37—42no—
64D148—22no—
65D148—42no—
66D148—41no—
67D148D811yescharacteristic
68C4×D37—21no—
69C4×D37—42no—
70Dic74D811yescharacteristic
71C8×C37C2×D411yescharacteristic
72C8×C37C2×D411yescharacteristic
73#64436—21no—
74#64436—41no—
75C22×C37—41no—
76C22×C37—81no—
77C22×C37—161no—
78C22×C37AGL(1,ℤ/8)11yescharacteristic
79C2×D37—21no—
80C2×D37—42no—
81C2×D37—162no—
82C2×D37—161no—
83C4×C37—41no—
84C4×C37#12011yescharacteristic
85C4×C37C2×D811yescharacteristic
86Dic37—21no—
87#2192—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—81no—
90C2×C37—161no—
91C2×C37#44711yescharacteristic
92D37—41no—
93D37—82no—
94#576—371no—
95#509D3711yescharacteristic, complemented
96C2×D16—371no—
97#472—371no—
98#361—371no—
99#359—371no—
100#350—371no—
101C37#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—741no—
103AGL(1,ℤ/8)—741no—
104AGL(1,ℤ/8)—742no—
105AGL(1,ℤ/8)—741no—
106#135—741no—
107#135C2×D3711yescharacteristic
108C2×D8—371no—
109C2×D8—741no—
110C2×D8C2×D3711yescharacteristic, complemented
111#131—371no—
112SD32—21no—
113D16—21no—
114D16—742no—
115M32C2×D3711yescharacteristic, complemented
116C2×C16—371no—
117#108—371no—
118#100—741no—
119#41—21no—
120#41—371no—
121#41—742no—
122#41—1481no—
123C2×D4—21no—
124C2×D4—742no—
125C2×D4—741no—
126C2×D4—1481no—
127C2×D4—1482no—
128Q16C22⋊D3711yescharacteristic
129SD16—21no—
130SD16—742no—
131SD16—1481no—
132D8—21no—
133D8—21no—
134D8—372no—
135D8—742no—
136D8—741no—
137D8—1481no—
138D8C22⋊D3711yescharacteristic
139M16—371no—
140M16—741no—
141M16—741no—
142C2×C8—741no—
143C2×C8C22×D3711yescharacteristic
144C16—21no—
145C16—741no—
146C23—41no—
147C23—1482no—
148C23—1481no—
149Q8—21no—
150Q8—371no—
151D4—21no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—371no—
156D4—741no—
157D4—742no—
158D4—1482no—
159D4—1482no—
160D4—1481no—
161C2×C4—41no—
162C2×C4—741no—
163C2×C4—1482no—
164C2×C4D4×D3711yescharacteristic
165C8—741no—
166C8—1481no—
167C8D4×D3711yescharacteristic
168C8C2×C22⋊D3711yescharacteristic
169C22—41no—
170C22—81no—
171C22—161no—
172C22—741no—
173C22—5921no—
174C22—5922no—
175C22—1482no—
176C22#1192456011yescharacteristic
177C4—41no—
178C4—741no—
179C4#1192450411yescharacteristic
180C4D8×D3711yescharacteristic
181C2—21no—
182C2—81no—
183C2—161no—
184C2—2962no—
185C2—1481no—
186C2#1455766511yescharacteristic
subgroupG/H
centerC2#14557665
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#509C2
socleC2×C37#447
hypercenter#509D37
hypocenterC37#2192
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14558335C2semidirect
2. C2×#11924477C2semidirect
3. #14557800C2semidirect
4. #14557347C2semidirect
5. #14557340C2semidirect
6. #14557318C2semidirect
7. C37×#509C2semidirect
17. C2×#10596925C22semidirect
18. #11924472C22semidirect
21. C2×D8×C37C22semidirect
24. M32×C37C22semidirect
95. #509D37semidirect
101. C37#2192semidirect
110. C2×D8C2×D37semidirect
115. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583352
C2×#119244772
#145578002
#145573472
#145573402
#145573182
C37×#5092
#219237