Finite Group Databasebeta

← #17995769

Subgroups — #17995769

Order 4736.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#14558090C211yesmaximal, characteristic, complemented
2#14557549C211yesmaximal, characteristic
3C2×#11924464C211yesmaximal, characteristic
4#14557506C211yesmaximal, characteristic
5#14557304C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924536—21no—
11#11924528—21no—
12#11924515—22no—
13C4×Dic74—22no—
14#11924495C2211yescharacteristic
15#11924495C2211yescharacteristic
16#11924464—21no—
17#11924464—21no—
18#11924462—22no—
19#11924450—22no—
20C2×M16×C37C2211yescharacteristic
21#117×C37C2211yescharacteristic
22C2×C42×C37C2211yescharacteristic
23C22×C4×C37—21no—
24C22×C4×C37C2311yescharacteristic
25C2×C22⋊D37—21no—
26#10596962—21no—
27#10596962—21no—
28#10596962—21no—
29#10596962—21no—
30C2×D148Q811yescharacteristic, complemented
31C2×C4×D37—21no—
32C2×Dic74—22no—
33C2×Dic74Q811yescharacteristic, complemented
34M16×C37—21no—
35M16×C37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C22⋊C4×C37—21no—
39C42×C37—21no—
40C42×C37—21no—
41C42×C37D411yescharacteristic
42C42×C37D411yescharacteristic
43C22⋊Dic37—21no—
44C22⋊Dic37D412yes—
45C4⋊Dic37—22no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48#10596936—24no—
49C4×Dic37—21no—
50C4×Dic37D412yes—
51#10596934—21no—
52#10596934—21no—
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55C22×D37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—42no—
59C2×C4×C37—41no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×Q811yescharacteristic
63C2×C4×C37#4111yescharacteristic
64C2×C4×C37#4111yescharacteristic
65C2×C4×C37#4111yescharacteristic
66C22⋊D37—41no—
67C22⋊D37—41no—
68C2×Dic37—22no—
69C2×Dic37—22no—
70C2×Dic37—21no—
71D148—21no—
72D148—21no—
73C4×D37—41no—
74C4×D37—41no—
75Dic74—21no—
76Dic74—21no—
77Dic74—44no—
78C8×C37—41no—
79#64436—41no—
80C22×C37—41no—
81C22×C37#12011yescharacteristic
82C22×C37C22⋊Q811yescharacteristic
83C22×C37#12411yescharacteristic
84C2×D37—41no—
85C2×D37—81no—
86C4×C37—22no—
87C4×C37—41no—
88C4×C37—81no—
89C4×C37C22⋊Q811yescharacteristic
90C4×C37C22⋊Q811yescharacteristic
91C4×C37#12411yescharacteristic
92C4×C37#12411yescharacteristic
93Dic37—42no—
94Dic37—42no—
95Dic37—41no—
96#2031—371nomaximal, Sylow
97C2×C37—21no—
98C2×C37—21no—
99C2×C37—21no—
100C2×C37#39311yescharacteristic
101D37—81no—
102#533—371no—
103#421—371no—
104C2×#104—371no—
105#410—371no—
106#344—371no—
107#339D3711yescharacteristic, complemented
108H(3,ℤ/4)—371no—
109C37#203111yescharacteristic, complemented, Sylow
110C2×#41—371no—
111C2×M16—371no—
112C2×M16C2×D3711yescharacteristic
113C4⋊Q8—741no—
114#125—741no—
115C22⋊Q8—742no—
116C4×Q8—742no—
117#117—371no—
118#117—371no—
119#117C2×D3711yescharacteristic
120C2×C42C2×D3711yescharacteristic
121#104—742no—
122#104—741no—
123#104—741no—
124#99—742no—
125#41—741no—
126#41—741no—
127#41—741no—
128#41—741no—
129C2×Q8—371no—
130C2×Q8—742no—
131C2×D4—371no—
132C2×D4—741no—
133C22×C4—21no—
134C22×C4—741no—
135C22×C4C22×D3711yescharacteristic
136M16—21no—
137M16—21no—
138M16—741no—
139M16—741no—
140C2×C8—21no—
141C2×C8—741no—
142C4⋊C4—21no—
143C4⋊C4—744no—
144C4⋊C4—742no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C22⋊C4—21no—
148C22⋊C4—372no—
149C22⋊C4—741no—
150C42—21no—
151C42—21no—
152C42—372no—
153C42—741no—
154C42D14811yescharacteristic
155C42D14811yescharacteristic
156C23—741no—
157C23D4×D3711yescharacteristic
158Q8—741no—
159Q8—741no—
160Q8—1484no—
161D4—741no—
162D4—741no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—742no—
170C2×C4—742no—
171C2×C4—741no—
172C2×C4—1481no—
173C2×C4—1481no—
174C2×C4C2×D14811yescharacteristic
175C2×C4#1059696211yescharacteristic
176C2×C4#1059696211yescharacteristic
177C2×C4D4×D3711yescharacteristic
178C2×C4#1059696411yescharacteristic
179C2×C4Q8×D3711yescharacteristic
180C8—41no—
181C8—1481no—
182C22—41no—
183C22—2961no—
184C22—1481no—
185C22#1192450611yescharacteristic
186C22#1192451411yescharacteristic
187C22#1192452211yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—1482no—
192C4—1482no—
193C4—1481no—
194C4#1192451411yescharacteristic
195C4#1192451611yescharacteristic
196C4#1192452211yescharacteristic
197C4#1192452411yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—2961no—
202C2#1455744611yescharacteristic
subgroupG/H
centerC4#11924522
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC2×C37#393
prime radicalC2×#10596962C22
hypercenter#339D37
hypocenterC37#2031
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #14558090C2semidirect
5. #14557304C2semidirect
6. #14557289C2semidirect
7. C37×#339C2semidirect
30. C2×D148Q8semidirect
33. C2×Dic74Q8semidirect
107. #339D37semidirect
109. C37#2031semidirect

Maximal subgroups

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

subgroupindex
#145580902
#145575492
C2×#119244642
#145575062
#145573042
#145572892
C37×#3392
#203137