Finite Group Databasebeta

← #17994830

Subgroups — #17994830

Order 4736.

286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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#14558013C211yesmaximal, characteristic
2#14557576C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic
4#14557535C211yesmaximal, characteristic
5#14557399C211yesmaximal, characteristic, complemented
6#14557301C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10C4×Dic74—21no—
11C4×D148—21no—
12#11924496—22no—
13#11924494—21no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×C4⋊Dic37C2211yescharacteristic
16C4⋊C4×D37—21no—
17#11924469—21no—
18#11924467—21no—
19#11924464C414yescomplemented
20#11924461—21no—
21#11924458—21no—
22#11924443—22no—
23C2×M16×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—21no—
29C22×Dic37—21no—
30C22×Dic37D412yes—
31#10596962—21no—
32#10596962—21no—
33#10596962C2×C412yes—
34#10596962Q812yes—
35C2×D148D411yescharacteristic
36C2×C4×D37—21no—
37C2×C4×D37—22no—
38C2×Dic74D411yescharacteristic
39M16×C37—21no—
40M16×C37—21no—
41C2×C8×C37—21no—
42C4⋊C4×C37D411yescharacteristic
43C4⋊C4×C37D411yescharacteristic
44C22⋊C4×C37—21no—
45C42×C37—21no—
46C42×C37—21no—
47C42×C37C2×C412yescomplemented
48#10596938—22no—
49C4⋊Dic37—21no—
50C4⋊Dic37—21no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53#10596936—22no—
54C4×Dic37—22no—
55#10596934—21no—
56#10596934C2×C412yescomplemented
57C2×#64436—21no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60C2×C4×C37—22no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C22×C411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×Q811yescharacteristic
69C2×C4×C37#4111yescharacteristic
70C2×C4×C37#4111yescharacteristic
71C22⋊D37—22no—
72C22⋊D37—22no—
73C2×Dic37—21no—
74C2×Dic37—22no—
75C2×Dic37—42no—
76C2×Dic37—42no—
77C2×Dic37—41no—
78D148—21no—
79D148C4⋊C412yes—
80C4×D37—22no—
81C4×D37—22no—
82C4×D37—82no—
83Dic74—21no—
84Dic74C4⋊C412yes—
85C8×C37—41no—
86#64436—22no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37C4×D411yescharacteristic
90C22×C37#12011yescharacteristic
91C22×C37C22⋊Q811yescharacteristic
92C2×D37—22no—
93C2×D37—41no—
94C2×D37—41no—
95C4×C37—42no—
96C4×C37—41no—
97C4×C37—41no—
98C4×C37C2×C4⋊C411yescharacteristic
99C4×C37C4×D411yescharacteristic
100C4×C37C22⋊Q811yescharacteristic
101C4×C37#12311yescharacteristic
102Dic37—22no—
103Dic37—42no—
104Dic37—81no—
105#1860—371nomaximal, Sylow
106C2×C37—21no—
107C2×C37—21no—
108C2×C37#38511yescharacteristic
109C2×C37#45411yescharacteristic
110C2×C37#45511yescharacteristic
111D37—42no—
112#520—371no—
113#428—371no—
114C2×#104—371no—
115#417—371no—
116#382—371no—
117#343—371no—
118#339D3711yescharacteristic, complemented
119C37#186011yescharacteristic, complemented, Sylow
120C2×#41—371no—
121C2×M16—371no—
122C2×M16C2×D3711yescharacteristic
123C4×Q8—741no—
124C4×D4—741no—
125C4×D4—742no—
126#117—741no—
127#117C2×D3711yescharacteristic
128C2×C4⋊C4—371no—
129C2×C4⋊C4—371no—
130C2×C4⋊C4—741no—
131C2×C42C2×D3711yescharacteristic
132#107—741no—
133#106—741no—
134#104—374no—
135#103—741no—
136#102—741no—
137#95—742no—
138#41—372no—
139#41—372no—
140#41—741no—
141#41—741no—
142C2×Q8—371no—
143C2×D4—371no—
144C2×D4—741no—
145C22×C4—21no—
146C22×C4—372no—
147C22×C4—742no—
148C22×C4—741no—
149C22×C4—741no—
150C22×C4C22×D3711yescharacteristic
151M16—21no—
152M16—21no—
153M16—372no—
154M16—741no—
155C2×C8—21no—
156C2×C8—741no—
157C4⋊C4—742no—
158C4⋊C4—741no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4D14811yescharacteristic
163C4⋊C4D14811yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—742no—
166C42—21no—
167C42—21no—
168C42—742no—
169C42C4×D3712yescomplemented
170C23—741no—
171C23D4×D3711yescharacteristic
172Q8—372no—
173Q8—741no—
174D4—372no—
175D4—742no—
176D4—742no—
177D4—741no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2962no—
184C2×C4—741no—
185C2×C4—742no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—1482no—
189C2×C4—1481no—
190C2×C4—1482no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4C2×D14811yescharacteristic
193C2×C4#1059696211yescharacteristic
194C2×C4D4×D3711yescharacteristic
195C2×C4#1059696411yescharacteristic
196C2×C4Q8×D3711yescharacteristic
197C8—41no—
198C8—742no—
199C22—21no—
200C22—21no—
201C22—742no—
202C22—1481no—
203C22—1481no—
204C22#1192449611yescharacteristic
205C22#1192450611yescharacteristic
206C22#1192451411yescharacteristic
207C4—42no—
208C4—41no—
209C4—41no—
210C4—2961no—
211C4—742no—
212C4—1482no—
213C4C4⋊C4×D3711yescharacteristic
214C4C4×D14811yescharacteristic
215C4#1192451611yescharacteristic
216C4#1192451811yescharacteristic
217C2—21no—
218C2—21no—
219C2—1482no—
220C2#1455740711yescharacteristic
221C2#1455770711yescharacteristic
222C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1860
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14557576C2semidirect
5. #14557399C2semidirect
6. #14557301C2semidirect
7. C37×#339C2semidirect
19. #11924464C4semidirect
47. C42×C37C2×C4semidirect
56. #10596934C2×C4semidirect
118. #339D37semidirect
119. C37#1860semidirect
169. C42C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145580132
#145575762
C2×#119244642
#145575352
#145573992
#145573012
C37×#3392
#186037