Finite Group Databasebeta

← #17995044

Subgroups — #17995044

Order 4736.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#14558044C211yesmaximal, characteristic
2C2×#11924464C212yesmaximal, complemented
3#14557497C211yesmaximal, characteristic, complemented
4#14557293C212yesmaximal, complemented
5C2×#117×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7C2×#10596934C2212yes—
8#11924519—21no—
9#11924515C412yescomplemented
10#11924510C412yescomplemented
11#11924505—21no—
12C4×C22⋊D37—22no—
13#11924495C2211yescharacteristic
14#11924464—24no—
15C22⋊#64436—22no—
16C23×C4×C37C2211yescharacteristic
17#117×C37—24no—
18C2×C4⋊C4×C37—21no—
19C2×C22⋊C4×C37—21no—
20C2×C42×C37C2212yes—
21C24×C37D411yescharacteristic
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37—22no—
25C22×C4×C37C2×C412yes—
26C22×C4×C37D412yes—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—22no—
30C2×C22⋊D37—21no—
31#10596962—22no—
32#10596962—22no—
33C2×D148C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74C2×C411yescharacteristic
36C4⋊C4×C37—24no—
37C22⋊C4×C37—24no—
38C42×C37—22no—
39C42×C37D414yescomplemented
40C22⋊Dic37—22no—
41C22⋊Dic37—21no—
42#10596938—22no—
43C4⋊Dic37C2×C412yes—
44#10596936—22no—
45C4×Dic37—21no—
46#10596934—22no—
47#10596934—22no—
48C2×#64436—22no—
49C23×C37—21no—
50C23×C37—21no—
51C23×C37—42no—
52C23×C37C22⋊C412yes—
53C23×C37C2×D411yescharacteristic
54C22×D37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—24no—
58C2×C4×C37—24no—
59C2×C4×C37—24no—
60C2×C4×C37—44no—
61C2×C4×C37C22⋊C412yes—
62C2×C4×C37C22×C411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D412yes—
65C2×C4×C37#4112yes—
66C22⋊D37—44no—
67C22⋊D37—41no—
68C22⋊D37—41no—
69C2×Dic37—22no—
70C2×Dic37—21no—
71D148—22no—
72C4×D37—42no—
73Dic74—22no—
74#64436—42no—
75C22×C37—22no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37C2×C22⋊C411yescharacteristic
82C22×C37#12011yescharacteristic
83C22×C37#12311yescharacteristic
84C2×D37—41no—
85C2×D37—42no—
86C4×C37—22no—
87C4×C37—44no—
88C4×C37C4×D412yes—
89C4×C37#12112yes—
90Dic37—41no—
91Dic37—42no—
92#1897—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—21no—
95C2×C37—42no—
96C2×C37#38611yescharacteristic
97C2×C37#42112yes—
98D37—81no—
99#525—371no—
100C2×#117D3711yescharacteristic, complemented
101C2×#104—372no—
102#407—371no—
103#339—372no—
104C37#189711yescharacteristic, complemented, Sylow
105C2×#41—371no—
106C23×C4C2×D3711yescharacteristic
107C2×M16—372no—
108#123—741no—
109C22⋊Q8—372no—
110#121—372no—
111#120—741no—
112C4×D4—742no—
113#117—24no—
114#117—371no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D3712yes—
118#104—744no—
119C22⋊C8—742no—
120C24C22⋊D3711yescharacteristic
121#41—742no—
122#41—742no—
123C2×Q8—371no—
124C2×D4—371no—
125C2×D4—742no—
126C2×D4—741no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—741no—
131C22×C4C4×D3712yes—
132C22×C4D14812yes—
133C22×C4C22⋊D3711yescharacteristic
134C22×C4C22×D3711yescharacteristic
135M16—742no—
136M16—742no—
137C2×C8—742no—
138C4⋊C4—24no—
139C4⋊C4—372no—
140C4⋊C4—742no—
141C22⋊C4—24no—
142C22⋊C4—742no—
143C22⋊C4—741no—
144C22⋊C4—742no—
145C42—22no—
146C42—741no—
147C42C22⋊D3714yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—741no—
152C23#1059693812yes—
153C23C2×C22⋊D3711yescharacteristic
154Q8—742no—
155D4—742no—
156D4—1484no—
157D4—1481no—
158D4—1481no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—742no—
166C2×C4—741no—
167C2×C4—1482no—
168C2×C4#1059693812yes—
169C2×C4C2×C4×D3711yescharacteristic
170C2×C4C2×D14811yescharacteristic
171C2×C4#1059696212yes—
172C2×C4C2×C22⋊D3712yes—
173C8—1482no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1482no—
181C22—1481no—
182C22C2×#1059693811yescharacteristic
183C22#1192450511yescharacteristic
184C22#1192451911yescharacteristic
185C4—22no—
186C4—44no—
187C4—1482no—
188C4—1481no—
189C4C4×C22⋊D3712yes—
190C4#1192451012yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—2961no—
195C2#1455741211yescharacteristic
196C2#1455755112yes—
subgroupG/H
centerC2×C4C2×D148
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#117×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenterC2×#117D37
hypocenterC37#1897
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11924464C2semidirect
3. #14557497C2semidirect
4. #14557293C2semidirect
5. C2×#117×C37C2semidirect
9. #11924515C4semidirect
10. #11924510C4semidirect
39. C42×C37D4semidirect
100. C2×#117D37semidirect
104. C37#1897semidirect
147. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580442
C2×#119244642
#145574972
#145572932
C2×#117×C372
#189737