Finite Group Databasebeta

← #17996239

Subgroups — #17996239

Order 4736.

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

normal subgroups only

This group has 280 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#14558093C211yesmaximal, characteristic
2#100×D37C211yesmaximal, characteristic, complemented
3#99×D37C211yesmaximal, characteristic, complemented
4#14557324C211yesmaximal, characteristic, complemented
5#14557322C211yesmaximal, characteristic, complemented
6#14557320C211yesmaximal, characteristic, complemented
7C37×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C411yescharacteristic, complemented
9C2×D4×D37C2211yescharacteristic
10M16×D37—21no—
11#11924520C411yescharacteristic, complemented
12#11924518—21no—
13#11924517C2211yescharacteristic
14#11924509—21no—
15#11924507—21no—
16#11924505C411yescharacteristic, complemented
17#11924504—21no—
18C22⋊C4×D37—21no—
19C22⋊C4×D37C411yescharacteristic, complemented
20#11924453C2211yescharacteristic
21#11924452—21no—
22#11924451C2211yescharacteristic
23#11924450—21no—
24#120×C37C2211yescharacteristic
25#100×C37C2211yescharacteristic
26#99×C37C2211yescharacteristic
27C24×C37C2×C411yescharacteristic, complemented
28C23×D37C2×C411yescharacteristic
29C23×D37D411yescharacteristic
30C2×D4×C37—21no—
31C2×D4×C37C2311yescharacteristic
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, complemented
40D4×D37—41no—
41D4×D37—41no—
42C2×D148D411yescharacteristic
43C2×C4×D37—21no—
44C2×C4×D37—41no—
45C2×C4×D37D411yescharacteristic
46M16×C37—21no—
47C22⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37C2×C411yescharacteristic, complemented
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52C22⋊Dic37—21no—
53C22⋊Dic37C2×C411yescharacteristic, complemented
54#10596938—21no—
55#10596938—21no—
56#10596938—41no—
57C4⋊Dic37—21no—
58#10596936—21no—
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—21no—
69C22×D37—21no—
70C22×D37—21no—
71C22×D37—81no—
72C22×D37—81no—
73C22×D37C22⋊C411yescharacteristic
74C22×D37C22⋊C411yescharacteristic
75C22×D37C22⋊C411yescharacteristic
76D4×C37—41no—
77D4×C37—81no—
78C2×C4×C37—21no—
79C2×C4×C37—41no—
80C2×C4×C37C2×D411yescharacteristic
81C22⋊D37—41no—
82C22⋊D37—41no—
83C22⋊D37—42no—
84C22⋊D37—41no—
85C22⋊D37—41no—
86C22⋊D37—81no—
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37C22⋊C411yescharacteristic
92D148—41no—
93C4×D37—21no—
94C4×D37—21no—
95C4×D37—81no—
96C4×D37—82no—
97C8×C37—41no—
98#64436—41no—
99C22×C37—21no—
100C22×C37—21no—
101C22×C37—41no—
102C22×C37—41no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37—82no—
107C22×C37C2×C22⋊C411yescharacteristic
108C2×D37—21no—
109C2×D37—21no—
110C2×D37—41no—
111C2×D37—42no—
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—81no—
115C2×D37—81no—
116C2×D37—81no—
117C2×D37#9911yescharacteristic
118C2×D37#9911yescharacteristic
119C4×C37—21no—
120C4×C37—41no—
121C4×C37—81no—
122Dic37—21no—
123Dic37—41no—
124Dic37—41no—
125Dic37—81no—
126#2121—371nomaximal, Sylow
127C2×C37—21no—
128C2×C37—41no—
129C2×C37—41no—
130C2×C37—81no—
131C2×C37C2×#9911yescharacteristic
132D37—21no—
133D37—21no—
134D37—41no—
135D37—41no—
136#534—371no—
137C2×#100—371no—
138C2×#99—371no—
139#352—371no—
140#352—371no—
141AΣL(1,𝔽16)—371no—
142AΣL(1,𝔽16)D3711yescharacteristic, complemented
143C37#212111yescharacteristic, complemented, Sylow
144C22×D4—371no—
145C22×D4—371no—
146C2×M16—741no—
147#123—371no—
148#123—371no—
149#123—741no—
150#121—741no—
151#121—741no—
152#120—371no—
153#120—741no—
154#120C2×D3711yescharacteristic
155C2×C22⋊C4—371no—
156C2×C22⋊C4—741no—
157#100—371no—
158#100—741no—
159#100C2×D3711yescharacteristic
160#99—371no—
161#99—741no—
162#99C2×D3711yescharacteristic
163C24—371no—
164C24—371no—
165C24C4×D3711yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—371no—
168C2×D4—371no—
169C2×D4—371no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—1481no—
174C2×D4—1481no—
175C2×D4—1481no—
176C2×D4—1481no—
177C2×D4C22×D3711yescharacteristic
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—741no—
181C22×C4—1481no—
182M16—21no—
183M16—741no—
184M16—1481no—
185C2×C8—1481no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—371no—
191C22⋊C4—741no—
192C22⋊C4—741no—
193C22⋊C4—741no—
194C22⋊C4—741no—
195C22⋊C4—741no—
196C22⋊C4—1481no—
197C22⋊C4C4×D3711yescharacteristic, complemented
198C23—21no—
199C23—41no—
200C23—81no—
201C23—371no—
202C23—371no—
203C23—371no—
204C23—2961no—
205C23—2961no—
206C23—741no—
207C23—741no—
208C23—741no—
209C23—741no—
210C23C2×C4×D3711yescharacteristic
211C23D4×D3711yescharacteristic
212D4—41no—
213D4—81no—
214D4—2961no—
215D4—1481no—
216D4—1481no—
217D4—1481no—
218D4—1481no—
219D4—1481no—
220D4—1482no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—371no—
224C2×C4—2961no—
225C2×C4—2962no—
226C2×C4—741no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—741no—
230C2×C4—1481no—
231C2×C4—1481no—
232C2×C4D4×D3711yescharacteristic
233C8—41no—
234C8—1481no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—82no—
243C22—371no—
244C22—371no—
245C22—2961no—
246C22—2961no—
247C22—2961no—
248C22—741no—
249C22—741no—
250C22—1481no—
251C22—1481no—
252C22—1481no—
253C22—1482no—
254C22C22⋊C4×D3711yescharacteristic
255C4—21no—
256C4—41no—
257C4—81no—
258C4—2961no—
259C4—741no—
260C4—1481no—
261C4—1481no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—81no—
266C2—741no—
267C2—741no—
268C2—1481no—
269C2—1481no—
270C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×AΣL(1,𝔽16)C2
socleC2×C37C2×#99
prime radical#14558093C2
cosocleC2×D4×C37C23
hypercenterAΣL(1,𝔽16)D37
hypocenterC37#2121
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. #100×D37C2semidirect
3. #99×D37C2semidirect
4. #14557324C2semidirect
5. #14557322C2semidirect
6. #14557320C2semidirect
7. C37×AΣL(1,𝔽16)C2semidirect
8. C22×C22⋊D37C4semidirect
11. #11924520C4semidirect
16. #11924505C4semidirect
19. C22⋊C4×D37C4semidirect
27. C24×C37C2×C4semidirect
39. C22×Dic37C2×C4semidirect
49. C22⋊C4×C37C2×C4semidirect
53. C22⋊Dic37C2×C4semidirect
142. AΣL(1,𝔽16)D37semidirect
143. C37#2121semidirect
165. C24C4×D37semidirect
197. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145580932
#100×D372
#99×D372
#145573242
#145573222
#145573202
C37×AΣL(1,𝔽16)2
#212137