Finite Group Databasebeta

← #17995096

Subgroups — #17995096

Order 4736.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#14558333C211yesmaximal, characteristic
2C4×#10596962C211yesmaximal, characteristic, complemented
3#14557551C211yesmaximal, characteristic, complemented
4C2×#11924464C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic, complemented
6#14557305C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596962C2211yescharacteristic
10#11924569—21no—
11#11924569C412yescomplemented
12#11924564—21no—
13#11924564C412yescomplemented
14#11924558—22no—
15C2×#10596934C2211yescharacteristic
16C4×Dic74—21no—
17C4×D148—21no—
18C4×C22⋊D37—22no—
19#11924495C2211yescharacteristic
20#11924493—21no—
21C42×D37—21no—
22#11924464—22no—
23#11924464—21no—
24#11924464—21no—
25#11924450—22no—
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38#10596962—21no—
39#10596962C2×C412yes—
40#10596962D412yes—
41C2×D148C2×C411yescharacteristic, complemented
42C2×D148D411yescharacteristic
43C2×C4×D37—21no—
44C2×C4×D37—22no—
45C2×C4×D37—21no—
46C2×Dic74C2×C411yescharacteristic, complemented
47C2×Dic74D411yescharacteristic
48M16×C37—21no—
49M16×C37C2×C412yescomplemented
50C2×C8×C37—21no—
51C4⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C42×C37—21no—
54C42×C37—21no—
55C42×C37D411yescharacteristic
56C42×C37D411yescharacteristic
57C22⋊Dic37D412yes—
58#10596938—22no—
59C4⋊Dic37—21no—
60#10596936—22no—
61C4×Dic37—22no—
62C4×Dic37—21no—
63#10596934—21no—
64#10596934—21no—
65C2×#64436—21no—
66Dic148—22no—
67D296—22no—
68#10596930—22no—
69#10596930—22no—
70C23×C37C2×D411yescharacteristic
71C22×D37—21no—
72C22×D37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37—42no—
76C2×C4×C37—41no—
77C2×C4×C37C22×C411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C22⋊D37—22no—
84C22⋊D37—22no—
85C22⋊D37—41no—
86C22⋊D37—41no—
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—22no—
90D148—21no—
91D148—21no—
92D148—21no—
93D148C22⋊C412yes—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—44no—
97C4×D37—41no—
98C4×D37—41no—
99Dic74—21no—
100Dic74—21no—
101Dic74—21no—
102Dic74C22⋊C412yes—
103C8×C37—22no—
104#64436—41no—
105C22×C37—41no—
106C22×C37C4×D411yescharacteristic
107C22×C37#12011yescharacteristic
108C22×C37#12111yescharacteristic
109C2×D37—22no—
110C2×D37—42no—
111C2×D37—41no—
112C2×D37—81no—
113C4×C37—22no—
114C4×C37—41no—
115C4×C37—81no—
116C4×C37C2×C22⋊C411yescharacteristic
117C4×C37C4×D411yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12311yescharacteristic
120Dic37—22no—
121Dic37—42no—
122Dic37—41no—
123#1906—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37—21no—
127C2×C37#38611yescharacteristic
128D37—42no—
129D37—81no—
130#575—371no—
131C4×#41—371no—
132#421—371no—
133C2×#104—371no—
134#410—371no—
135#344—371no—
136#339D3711yescharacteristic, complemented
137C37#190611yescharacteristic, complemented, Sylow
138C2×#41—371no—
139C2×#41—371no—
140#137—372no—
141#137—741no—
142AGL(1,ℤ/8)—372no—
143AGL(1,ℤ/8)—741no—
144#135—742no—
145C2×M16—371no—
146C2×M16C2×D3711yescharacteristic
147C4×Q8—741no—
148C4×D4—741no—
149C4×D4—742no—
150#117—371no—
151#117—741no—
152#117C2×D3711yescharacteristic
153C2×C42—741no—
154C2×C42C2×D3711yescharacteristic
155#104—742no—
156#104—741no—
157#104—741no—
158#99—742no—
159#41—372no—
160#41—372no—
161#41—741no—
162#41—741no—
163#41—741no—
164#41—741no—
165#41—741no—
166#41—741no—
167C2×Q8—371no—
168C2×Q8—371no—
169C2×D4—371no—
170C2×D4—371no—
171C2×D4—741no—
172C2×D4—741no—
173C22×C4—21no—
174C22×C4—742no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178Q16—742no—
179SD16—742no—
180SD16—742no—
181D8—742no—
182M16—21no—
183M16—741no—
184M16—741no—
185M16C4×D3712yescomplemented
186C2×C8—21no—
187C2×C8—741no—
188C4⋊C4—21no—
189C4⋊C4—742no—
190C4⋊C4—741no—
191C22⋊C4—21no—
192C22⋊C4—372no—
193C22⋊C4—742no—
194C42—21no—
195C42—21no—
196C42—742no—
197C42—741no—
198C42D14811yescharacteristic
199C42D14811yescharacteristic
200C23—741no—
201C23—741no—
202C23D4×D3711yescharacteristic
203Q8—372no—
204Q8—741no—
205Q8—741no—
206Q8—741no—
207D4—372no—
208D4—742no—
209D4—742no—
210D4—741no—
211D4—741no—
212D4—741no—
213D4—1481no—
214D4—1481no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—742no—
224C2×C4—1484no—
225C2×C4—1481no—
226C2×C4—1481no—
227C2×C4C2×C4×D3711yescharacteristic
228C2×C4C2×D14811yescharacteristic
229C2×C4#1059696211yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4D4×D3711yescharacteristic
232C2×C4#1059696611yescharacteristic
233C8—22no—
234C8—1481no—
235C22—41no—
236C22—2961no—
237C22—742no—
238C22—1482no—
239C22—1481no—
240C22#1192449811yescharacteristic
241C22#1192450611yescharacteristic
242C22#1192450911yescharacteristic
243C4—22no—
244C4—41no—
245C4—81no—
246C4—742no—
247C4—1482no—
248C4—1481no—
249C4C22⋊C4×D3711yescharacteristic
250C4C4×D14811yescharacteristic
251C4#1192451111yescharacteristic
252C4#1192452111yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—2961no—
257C2—1482no—
258C2#1455741111yescharacteristic
subgroupG/H
centerC4#11924511
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC2×C37#386
prime radical#14558333C2
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1906
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C4×#10596962C2semidirect
3. #14557551C2semidirect
4. C2×#11924464C2semidirect
5. #14557506C2semidirect
6. #14557305C2semidirect
7. C37×#339C2semidirect
11. #11924569C4semidirect
13. #11924564C4semidirect
41. C2×D148C2×C4semidirect
46. C2×Dic74C2×C4semidirect
49. M16×C37C2×C4semidirect
136. #339D37semidirect
137. C37#1906semidirect
185. M16C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
C4×#105969622
#145575512
C2×#119244642
#145575062
#145573052
C37×#3392
#190637