Finite Group Databasebeta

← #17995041

Subgroups — #17995041

Order 4736.

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

normal subgroups only

This group has 358 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#14558040C211yesmaximal, characteristic
2C2×#11924493C211yesmaximal, characteristic, complemented
3C2×#11924463C211yesmaximal, characteristic, complemented
4#14557496C211yesmaximal, characteristic, complemented
5#14557294C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924517—21no—
11#11924512C412yescomplemented
12#11924507C412yescomplemented
13#11924504—21no—
14C4×C22⋊D37—22no—
15#11924495C2211yescharacteristic
16#11924493—22no—
17#11924493—22no—
18C2×#10596936—21no—
19C2×#10596938—21no—
20C2×C4×Dic37C2211yescharacteristic
21#11924463—22no—
22#11924448—22no—
23C2×#41×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26#104×C37—22no—
27C23×D37D411yescharacteristic
28#41×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31#41×C37—21no—
32C2×Q8×C37C2×C411yescharacteristic
33C2×D4×C37—21no—
34C2×D4×C37C2×C411yescharacteristic
35C22×C4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—22no—
39C22×Dic37—21no—
40C22×Dic37D411yescharacteristic
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×C4×D37—21no—
44C2×C4×D37—21no—
45C2×C4×D37C2×C412yes—
46C2×C4×D37D412yes—
47M16×C37—21no—
48M16×C37—21no—
49C2×C8×C37—21no—
50C42×C37—21no—
51C42×C37D412yescomplemented
52C22⋊Dic37—21no—
53C22⋊Dic37—22no—
54#10596938—24no—
55#10596938—22no—
56C4⋊Dic37C2×C412yes—
57#10596936—24no—
58#10596936—22no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C4×Dic37D412yescomplemented
62#10596934—21no—
63#10596934—21no—
64C2×#64436—21no—
65C23×C37—21no—
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C22×D37—21no—
69C22×D37—42no—
70C22×D37C22⋊C412yes—
71Q8×C37—21no—
72Q8×C37—21no—
73D4×C37—21no—
74D4×C37—21no—
75D4×C37—41no—
76D4×C37—41no—
77C2×C4×C37—21no—
78C2×C4×C37—22no—
79C2×C4×C37—42no—
80C2×C4×C37—41no—
81C2×C4×C37—41no—
82C2×C4×C37C22×C411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37#4111yescharacteristic
87C2×C4×C37#4111yescharacteristic
88C22⋊D37—44no—
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37—42no—
94C2×Dic37C22⋊C412yes—
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—22no—
99C8×C37—41no—
100#64436—41no—
101C22×C37—22no—
102C22×C37—41no—
103C22×C37—42no—
104C22×C37C2×C22⋊C411yescharacteristic
105C22×C37#12011yescharacteristic
106C22×C37#12311yescharacteristic
107C2×D37—22no—
108C2×D37—22no—
109C2×D37—22no—
110C2×D37—42no—
111C2×D37—42no—
112C4×C37—42no—
113C4×C37—41no—
114C4×C37C4×D411yescharacteristic
115C4×C37C4×D411yescharacteristic
116C4×C37#12111yescharacteristic
117C4×C37#12111yescharacteristic
118Dic37—22no—
119Dic37—42no—
120Dic37—42no—
121#1897—371nomaximal, Sylow
122C2×C37—21no—
123C2×C37—21no—
124C2×C37—81no—
125C2×C37#38611yescharacteristic
126C2×C37#42112yes—
127D37—42no—
128#525—371no—
129C2×#117—371no—
130C2×#104—371no—
131C2×#104D3711yescharacteristic, complemented
132#407—371no—
133#339—371no—
134#339—371no—
135C37#189711yescharacteristic, complemented, Sylow
136C2×#41C2×D3711yescharacteristic
137C23×C4—371no—
138C2×M16—371no—
139C2×M16C2×D3711yescharacteristic
140#123—741no—
141C22⋊Q8—372no—
142#121—372no—
143#120—741no—
144C4×D4—742no—
145#117—371no—
146#117—742no—
147#117—742no—
148C2×C4⋊C4—741no—
149C2×C22⋊C4—741no—
150C2×C42—371no—
151C2×C42C2×D3711yescharacteristic
152#104—22no—
153#104—742no—
154C22⋊C8—742no—
155C24—371no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D3711yescharacteristic
161C2×D4—21no—
162C2×D4—742no—
163C2×D4C4×D3711yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—371no—
167C22×C4—372no—
168C22×C4—372no—
169C22×C4—741no—
170C22×C4—741no—
171C22×C4—741no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4C22×D3711yescharacteristic
175M16—21no—
176M16—21no—
177M16—741no—
178M16—741no—
179C2×C8—21no—
180C2×C8—741no—
181C4⋊C4—372no—
182C4⋊C4—742no—
183C4⋊C4—744no—
184C22⋊C4—742no—
185C22⋊C4—744no—
186C22⋊C4—742no—
187C22⋊C4—741no—
188C42—21no—
189C42—372no—
190C42—741no—
191C42—741no—
192C42C22⋊D3712yescomplemented
193C23—21no—
194C23—372no—
195C23—741no—
196C23—741no—
197C23—1482no—
198C23D4×D3711yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—1484no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—372no—
212C2×C4—741no—
213C2×C4—741no—
214C2×C4—742no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—742no—
219C2×C4—742no—
220C2×C4—1482no—
221C2×C4C2×C4×D3711yescharacteristic
222C2×C4#1059696211yescharacteristic
223C2×C4D4×D3711yescharacteristic
224C2×C4D4×D3711yescharacteristic
225C2×C4#1059696411yescharacteristic
226C2×C4C2×C22⋊D3711yescharacteristic
227C8—41no—
228C8—1481no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—742no—
233C22—742no—
234C22—742no—
235C22—1482no—
236C22—1482no—
237C22C22⋊C4×D3711yescharacteristic
238C22#1192450411yescharacteristic
239C22#1192451811yescharacteristic
240C4—42no—
241C4—41no—
242C4—742no—
243C4—1482no—
244C4—1482no—
245C4#1192449611yescharacteristic
246C4C4×C22⋊D3711yescharacteristic
247C4#1192450711yescharacteristic
248C4#1192450911yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—1482no—
253C2#1455740911yescharacteristic
254C2#1455754812yes—
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558040C2
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1897
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11924493C2semidirect
3. C2×#11924463C2semidirect
4. #14557496C2semidirect
5. #14557294C2semidirect
6. #14557293C2semidirect
7. C2×#104×C37C2semidirect
11. #11924512C4semidirect
12. #11924507C4semidirect
51. C42×C37D4semidirect
61. C4×Dic37D4semidirect
131. C2×#104D37semidirect
135. C37#1897semidirect
192. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580402
C2×#119244932
C2×#119244632
#145574962
#145572942
#145572932
C2×#104×C372
#189737