Finite Group Databasebeta

← #17993657

Subgroups — #17993657

Order 4736.

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

normal subgroups only

This group has 240 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#14558268C211yesmaximal, characteristic, complemented
2#14557910C211yesmaximal, characteristic
3#14557734C211yesmaximal, characteristic, complemented
4#14557733C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic, complemented
6#14557265C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×#10596941—21no—
10C2×D296—22no—
11#11924533C2211yescharacteristic
12#11924533C2211yescharacteristic
13#11924525—21no—
14#11924524—21no—
15#11924521—22no—
16C4×Dic74C2211yescharacteristic
17C4×D148—21no—
18#11924498—21no—
19C4⋊#64436C2211yescharacteristic
20#11924458—21no—
21#11924456—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148—21no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148D412yes—
32C2×C4×D37—22no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C42×C37—21no—
39C42×C37C2311yescharacteristic
40#10596941—42no—
41#10596938—22no—
42#10596938—22no—
43#10596938—22no—
44C4⋊Dic37D411yescharacteristic
45#10596936—21no—
46C4×Dic37—21no—
47C2×#64436—21no—
48D296—44no—
49#10596930—42no—
50C22×D37—22no—
51C22×D37—41no—
52Q8×C37—21no—
53Q8×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61D148—42no—
62D148—42no—
63D148—41no—
64D148—41no—
65D148—41no—
66D148—41no—
67D148—41no—
68D148—41no—
69D148—41no—
70D148—41no—
71C4×D37—82no—
72Dic74—21no—
73Dic74—21no—
74C8×C37—22no—
75C8×C37—41no—
76#64436—41no—
77C22×C37#12011yescharacteristic
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—42no—
81C2×D37—81no—
82C2×D37—81no—
83C2×D37—81no—
84C4×C37—21no—
85C4×C37—41no—
86C4×C37—41no—
87C4×C37#13511yescharacteristic
88C4×C37#13511yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91Dic37—41no—
92Dic37—41no—
93#1620—371nomaximal, Sylow
94C2×C37#44911yescharacteristic
95C2×C37#44911yescharacteristic
96C2×C37#45311yescharacteristic
97D37—82no—
98D37—161no—
99#559—371no—
100#493—371no—
101#460—371no—
102#460—371no—
103#331—371no—
104Q8⋊C8—371no—
105Q8⋊C8D3711yescharacteristic, complemented
106C37#162011yescharacteristic, complemented, Sylow
107C2×SD16—741no—
108C2×SD16—741no—
109C2×D8—742no—
110#127—371no—
111#127—371no—
112#124—741no—
113#124—741no—
114#123—742no—
115C4×Q8—371no—
116C4×Q8C2×D3711yescharacteristic
117C4×D4—741no—
118C4×D4—741no—
119C4⋊C8—371no—
120C4⋊C8C2×D3711yescharacteristic
121#102—741no—
122#102—741no—
123C4×C8C2×D3711yescharacteristic
124C2×Q8—371no—
125C2×Q8D14811yescharacteristic
126C2×D4—372no—
127C2×D4—741no—
128C2×D4—741no—
129C2×D4—741no—
130C2×D4—741no—
131C2×D4—741no—
132C22×C4—742no—
133SD16—1482no—
134SD16—1482no—
135D8—1484no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—741no—
139C4⋊C4—21no—
140C4⋊C4—371no—
141C4⋊C4—741no—
142C4⋊C4D14811yescharacteristic
143C22⋊C4—742no—
144C22⋊C4—742no—
145C22⋊C4—742no—
146C42—21no—
147C42—741no—
148C42C22×D3711yescharacteristic
149C23—742no—
150C23—1481no—
151Q8—21no—
152Q8—21no—
153Q8—741no—
154Q8—741no—
155D4—1482no—
156D4—1482no—
157D4—1481no—
158D4—1481no—
159D4—1481no—
160D4—1481no—
161D4—1481no—
162D4—1481no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—2962no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4C2×D14811yescharacteristic
171C2×C4D4×D3711yescharacteristic
172C2×C4D4×D3711yescharacteristic
173C8—22no—
174C8—41no—
175C8—1481no—
176C22—2961no—
177C22—2961no—
178C22—2961no—
179C22—1482no—
180C22—1482no—
181C22—1482no—
182C22#1192450611yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1481no—
187C4—1481no—
188C4#1192455811yescharacteristic
189C4#1192455911yescharacteristic
190C4#1192456311yescharacteristic
191C4#1192456411yescharacteristic
192C2—2962no—
193C2—5921no—
194C2#1455768011yescharacteristic
195C2#1455768111yescharacteristic
196C2#1455770211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#14557910C2
hypercenterQ8⋊C8D37
hypocenterC37#1620
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14558268C2semidirect
3. #14557734C2semidirect
4. #14557733C2semidirect
5. #14557276C2semidirect
6. #14557265C2semidirect
7. C37×Q8⋊C8C2semidirect
105. Q8⋊C8D37semidirect
106. C37#1620semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145579102
#145577342
#145577332
#145572762
#145572652
C37×Q8⋊C82
#162037