Finite Group Databasebeta

← #17996244

Subgroups — #17996244

Order 4736.

266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558098C211yesmaximal, characteristic
2#14557514C211yesmaximal, characteristic, complemented
3#14557505C211yesmaximal, characteristic, complemented
4#14557321C211yesmaximal, characteristic, complemented
5#14557320C211yesmaximal, characteristic, complemented
6#14557319C211yesmaximal, characteristic, complemented
7C37×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C2×#10596964C2211yescharacteristic
9C22×C22⋊D37C411yescharacteristic, complemented
10M16×D37—21no—
11#11924532—21no—
12#11924522—21no—
13#11924509—21no—
14#11924508—21no—
15#11924506C411yescharacteristic, complemented
16#11924505C411yescharacteristic, complemented
17#11924504C2211yescharacteristic
18#11924492—21no—
19#11924492C411yescharacteristic, complemented
20#11924454—21no—
21#11924453C2211yescharacteristic
22#11924451C2211yescharacteristic
23#11924450—21no—
24#120×C37C2211yescharacteristic
25#100×C37C2211yescharacteristic
26#99×C37C2211yescharacteristic
27C24×C37C2×C411yescharacteristic
28C23×D37C2×C411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—41no—
36C2×C22⋊D37—41no—
37C2×C22⋊D37C2×C411yescharacteristic
38C2×C22⋊D37D411yescharacteristic
39C22×Dic37C2×C411yescharacteristic
40C22×Dic37D411yescharacteristic
41#10596964—41no—
42#10596964—41no—
43C2×D148—21no—
44C2×C4×D37D411yescharacteristic
45C2×Dic74D411yescharacteristic
46M16×C37—21no—
47C22⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37C2×C411yescharacteristic
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52C22⋊Dic37C2×C411yescharacteristic
53#10596938—21no—
54#10596938—21no—
55#10596936—21no—
56#10596936—41no—
57C4×Dic37—21no—
58C4×Dic37—41no—
59#10596934—21no—
60#10596929—41no—
61C8×D37—41no—
62C23×C37—21no—
63C23×C37—41no—
64C23×C37—81no—
65C23×C37C22×C411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C22×D37—41no—
69C22×D37—81no—
70C22×D37C22⋊C411yescharacteristic
71D4×C37—41no—
72D4×C37—81no—
73C2×C4×C37—21no—
74C2×C4×C37—41no—
75C2×C4×C37C2×D411yescharacteristic
76C22⋊D37—41no—
77C22⋊D37—41no—
78C22⋊D37—42no—
79C22⋊D37—41no—
80C22⋊D37—41no—
81C22⋊D37—81no—
82C22⋊D37—81no—
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C2×Dic37C22⋊C411yescharacteristic
90C2×Dic37C22⋊C411yescharacteristic
91C2×Dic37C22⋊C411yescharacteristic
92D148—81no—
93C4×D37—21no—
94C4×D37—21no—
95Dic74—41no—
96C8×C37—41no—
97#64436—41no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37—41no—
101C22×C37—41no—
102C22×C37—41no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—82no—
106C22×C37C2×C22⋊C411yescharacteristic
107C2×D37—21no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—82no—
113C4×C37—21no—
114C4×C37—41no—
115C4×C37—81no—
116Dic37—21no—
117Dic37—21no—
118Dic37—41no—
119Dic37—81no—
120Dic37#9911yescharacteristic
121Dic37#9911yescharacteristic
122#2122—371nomaximal, Sylow
123C2×C37—21no—
124C2×C37—41no—
125C2×C37—41no—
126C2×C37—81no—
127C2×C37C2×#9911yescharacteristic
128D37—41no—
129D37—81no—
130#535—371no—
131#413—371no—
132#410—371no—
133AΣL(1,𝔽16)—371no—
134AΣL(1,𝔽16)—371no—
135AΣL(1,𝔽16)—371no—
136AΣL(1,𝔽16)D3711yescharacteristic, complemented
137C37#212211yescharacteristic, complemented, Sylow
138C2×#41—371no—
139C22×D4—371no—
140C2×M16—741no—
141#127—741no—
142#124—741no—
143#121—741no—
144#121—741no—
145#120—371no—
146#120—371no—
147#120—371no—
148#120C2×D3711yescharacteristic
149#117—371no—
150#117—741no—
151#101—741no—
152#100—371no—
153#100C2×D3711yescharacteristic
154#99—371no—
155#99—741no—
156#99C2×D3711yescharacteristic
157C24—371no—
158C24C4×D3711yescharacteristic
159#41—1481no—
160#41—1481no—
161C2×Q8—371no—
162C2×D4—21no—
163C2×D4—371no—
164C2×D4—371no—
165C2×D4—741no—
166C2×D4—741no—
167C2×D4—741no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—1481no—
171C2×D4—1481no—
172C2×D4C22×D3711yescharacteristic
173C22×C4—371no—
174C22×C4—371no—
175C22×C4—371no—
176M16—21no—
177M16—741no—
178M16—1481no—
179C2×C8—1481no—
180C4⋊C4—741no—
181C4⋊C4—1481no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—371no—
185C22⋊C4—741no—
186C22⋊C4—741no—
187C22⋊C4—741no—
188C22⋊C4—741no—
189C22⋊C4C4×D3711yescharacteristic
190C42—741no—
191C42—1481no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—371no—
196C23—2961no—
197C23—741no—
198C23—1481no—
199C23C2×C4×D3711yescharacteristic
200C23D4×D3711yescharacteristic
201Q8—1481no—
202D4—41no—
203D4—81no—
204D4—2961no—
205D4—2961no—
206D4—2961no—
207D4—1481no—
208D4—1481no—
209D4—1481no—
210D4—1481no—
211D4—1482no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—741no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—1481no—
225C2×C4D4×D3711yescharacteristic
226C8—41no—
227C8—1481no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—2962no—
237C22—741no—
238C22—1481no—
239C22—1481no—
240C22—1481no—
241C22—1481no—
242C22C22⋊C4×D3711yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—371no—
247C4—371no—
248C4—2961no—
249C4—741no—
250C4—741no—
251C4—1481no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—2961no—
257C2—1481no—
258C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×AΣL(1,𝔽16)C2
socleC2×C37C2×#99
prime radical#14558098C2
cosocleC2×D4×C37C23
hypercenterAΣL(1,𝔽16)D37
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #14557514C2semidirect
3. #14557505C2semidirect
4. #14557321C2semidirect
5. #14557320C2semidirect
6. #14557319C2semidirect
7. C37×AΣL(1,𝔽16)C2semidirect
9. C22×C22⋊D37C4semidirect
15. #11924506C4semidirect
16. #11924505C4semidirect
19. #11924492C4semidirect
136. AΣL(1,𝔽16)D37semidirect
137. C37#2122semidirect

Maximal subgroups

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

subgroupindex
#145580982
#145575142
#145575052
#145573212
#145573202
#145573192
C37×AΣL(1,𝔽16)2
#212237