Finite Group Databasebeta

← #17994971

Subgroups — #17994971

Order 4736.

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

normal subgroups only

This group has 370 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
1C2×#11924564C211yesmaximal, characteristic
2#14558014C211yesmaximal, characteristic, complemented
3C2×#11924462C211yesmaximal, characteristic, complemented
4#14557539C211yesmaximal, characteristic, complemented
5#14557434C211yesmaximal, characteristic, complemented
6#14557294C211yesmaximal, characteristic, complemented
7C37×#343C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924564—22no—
11#11924564C414yescomplemented
12C2×#10596930—21no—
13C2×D296—21no—
14#11924501—21no—
15#11924498—21no—
16C4×C22⋊D37—22no—
17#11924495C2211yescharacteristic
18#11924494—21no—
19C4⋊C4×D37—21no—
20C2×#10596938—22no—
21C2×C4×Dic37C2211yescharacteristic
22#11924462—22no—
23#11924458—21no—
24#11924458—21no—
25C2×M16×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28C23×D37—21no—
29C22×C4×C37D412yes—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962C2×C412yes—
36#10596962D412yes—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148C2×C412yescomplemented
43C2×D148D411yescharacteristic
44C2×C4×D37—21no—
45C2×C4×D37—22no—
46C2×Dic74D411yescharacteristic
47M16×C37—21no—
48M16×C37—21no—
49M16×C37—21no—
50M16×C37C2×C412yescomplemented
51C2×C8×C37—21no—
52C2×C8×C37—21no—
53C4⋊C4×C37—21no—
54C4⋊C4×C37—21no—
55C22⋊Dic37—21no—
56#10596938—22no—
57#10596938—44no—
58C4⋊Dic37D411yescharacteristic
59C4⋊Dic37D411yescharacteristic
60#10596936—22no—
61C4×Dic37—22no—
62C4×Dic37—21no—
63C4×Dic37—21no—
64C4×Dic37—21no—
65D296—24no—
66#10596930—24no—
67C23×C37C2×D411yescharacteristic
68C22×D37—21no—
69C22×D37—22no—
70C22×D37—42no—
71C22×D37—42no—
72C22×D37—41no—
73C22×D37—41no—
74C2×C4×C37—22no—
75C2×C4×C37—42no—
76C2×C4×C37C22×C411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C22⋊D37—22no—
83C22⋊D37—22no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90D148—22no—
91D148—22no—
92D148—21no—
93D148—41no—
94D148—41no—
95D148C22⋊C412yescomplemented
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—82no—
99Dic74—21no—
100Dic74C22⋊C412yescomplemented
101C8×C37—22no—
102C8×C37—41no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37C4×D411yescharacteristic
106C22×C37#12011yescharacteristic
107C22×C37#12111yescharacteristic
108C2×D37—22no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—44no—
112C2×D37—42no—
113C2×D37—82no—
114C2×D37—81no—
115C2×D37—81no—
116C4×C37—42no—
117C4×C37C2×C22⋊C411yescharacteristic
118C4×C37C4×D411yescharacteristic
119C4×C37#12111yescharacteristic
120C4×C37#12311yescharacteristic
121Dic37—22no—
122Dic37—42no—
123Dic37—41no—
124Dic37—41no—
125#1883—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37#38611yescharacteristic
129C2×C37#45311yescharacteristic
130C2×C37#45411yescharacteristic
131D37—42no—
132D37—82no—
133C2×AGL(1,ℤ/8)—371no—
134#520—371no—
135C2×#104—371no—
136#418—371no—
137#390—371no—
138#343D3711yescharacteristic, complemented
139#339—371no—
140C37#188311yescharacteristic, complemented, Sylow
141C2×#41—371no—
142C22×D4—371no—
143AGL(1,ℤ/8)—374no—
144AGL(1,ℤ/8)—742no—
145C2×SD16—741no—
146C2×D8—741no—
147C2×M16C2×D3711yescharacteristic
148C2×M16C2×D3711yescharacteristic
149C4×Q8—741no—
150C4×D4—741no—
151C4×D4—742no—
152#117—371no—
153#117—741no—
154C2×C4⋊C4—741no—
155C2×C4⋊C4C2×D3711yescharacteristic
156C2×C22⋊C4—742no—
157C2×C42—371no—
158#104—742no—
159#102—741no—
160#102—741no—
161C24—741no—
162#41—372no—
163#41—372no—
164#41—741no—
165#41—741no—
166C2×Q8—371no—
167C2×D4—372no—
168C2×D4—371no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4—741no—
175C22×C4—742no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4D14812yes—
179C22×C4C22×D3711yescharacteristic
180SD16—744no—
181D8—744no—
182M16—21no—
183M16—21no—
184M16—21no—
185M16C4×D3712yescomplemented
186C2×C8—21no—
187C2×C8—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—371no—
191C4⋊C4—371no—
192C4⋊C4—742no—
193C22⋊C4—742no—
194C22⋊C4—741no—
195C22⋊C4—1484no—
196C42—742no—
197C42—741no—
198C42—741no—
199C42—741no—
200C23—741no—
201C23—742no—
202C23—1482no—
203C23—1482no—
204C23—1481no—
205C23—1481no—
206C23C2×D14811yescharacteristic
207Q8—372no—
208Q8—741no—
209D4—372no—
210D4—742no—
211D4—742no—
212D4—742no—
213D4—742no—
214D4—741no—
215D4—1481no—
216D4—1481no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—2962no—
220C2×C4—741no—
221C2×C4—742no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4C2×C4×D3711yescharacteristic
229C2×C4#1059696211yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4D4×D3711yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4#1059696611yescharacteristic
234C8—22no—
235C8—41no—
236C22—21no—
237C22—21no—
238C22—2962no—
239C22—2961no—
240C22—2961no—
241C22—742no—
242C22—1484no—
243C22—1482no—
244C22—1481no—
245C22—1481no—
246C22C4×D14811yescharacteristic
247C22#1192450611yescharacteristic
248C22#1192451111yescharacteristic
249C4—42no—
250C4—742no—
251C4—1482no—
252C4—1481no—
253C4—1481no—
254C4C22⋊C4×D3711yescharacteristic
255C4#1192449811yescharacteristic
256C4#1192450911yescharacteristic
257C4#1192452111yescharacteristic
258C2—21no—
259C2—21no—
260C2—2962no—
261C2—1482no—
262C2#1455741111yescharacteristic
263C2#1455770311yescharacteristic
264C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#120
prime radicalC2×#11924564C2
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1883
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. #14558014C2semidirect
3. C2×#11924462C2semidirect
4. #14557539C2semidirect
5. #14557434C2semidirect
6. #14557294C2semidirect
7. C37×#343C2semidirect
11. #11924564C4semidirect
42. C2×D148C2×C4semidirect
50. M16×C37C2×C4semidirect
95. D148C22⋊C4semidirect
100. Dic74C22⋊C4semidirect
138. #343D37semidirect
140. C37#1883semidirect
185. M16C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
#145580142
C2×#119244622
#145575392
#145574342
#145572942
C37×#3432
#188337