Finite Group Databasebeta

← #17996236

Subgroups — #17996236

Order 4736.

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

normal subgroups only

This group has 264 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#14558041C211yesmaximal, characteristic
2#14557514C211yesmaximal, characteristic, complemented
3#14557505C211yesmaximal, characteristic, complemented
4#14557323C211yesmaximal, characteristic, complemented
5#14557321C211yesmaximal, characteristic, complemented
6#14557319C211yesmaximal, characteristic, complemented
7C37×#352C211yesmaximal, characteristic, complemented
8C2×#10596964C2211yescharacteristic
9C22×C4×D37C411yescharacteristic, complemented
10M16×D37—21no—
11#11924519C411yescharacteristic, complemented
12#11924514—21no—
13#11924509—21no—
14#11924506C411yescharacteristic, complemented
15#11924504C2211yescharacteristic
16#11924498—21no—
17#11924496—21no—
18#11924492—21no—
19#11924492C411yescharacteristic, complemented
20#11924454—21no—
21#11924453C2211yescharacteristic
22#11924451C2211yescharacteristic
23#11924450—21no—
24#123×C37C2211yescharacteristic
25#100×C37C2211yescharacteristic
26#99×C37C2211yescharacteristic
27C23×D37C2×C411yescharacteristic
28C2×D4×C37C2311yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31C2×C22⋊D37C2×C411yescharacteristic
32C2×C22⋊D37D411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37D411yescharacteristic
35#10596964—41no—
36#10596964—41no—
37C2×D148—21no—
38C2×C4×D37—21no—
39C2×C4×D37—21no—
40C2×C4×D37—41no—
41C2×C4×D37—41no—
42C2×C4×D37D411yescharacteristic
43C2×Dic74D411yescharacteristic
44M16×C37—21no—
45C4⋊C4×C37—21no—
46C22⋊C4×C37—21no—
47C22⋊C4×C37—21no—
48C22⋊C4×C37C2×C411yescharacteristic
49C22⋊Dic37—21no—
50C22⋊Dic37C2×C411yescharacteristic
51#10596938—21no—
52#10596938—21no—
53#10596938—21no—
54#10596936—21no—
55#10596936—21no—
56#10596936—41no—
57C4×Dic37—21no—
58C4×Dic37—41no—
59#10596934—21no—
60#10596929—41no—
61C8×D37—41no—
62C23×C37C22×C411yescharacteristic
63C23×C37C2×D411yescharacteristic
64C22×D37—21no—
65C22×D37—42no—
66C22×D37—41no—
67C22×D37C22⋊C411yescharacteristic
68D4×C37—41no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C2×D411yescharacteristic
74C22⋊D37—41no—
75C22⋊D37—41no—
76C22⋊D37—42no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—41no—
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37C22⋊C411yescharacteristic
85C2×Dic37C22⋊C411yescharacteristic
86D148—42no—
87C4×D37—21no—
88C4×D37—21no—
89C4×D37—42no—
90C4×D37—41no—
91C4×D37—41no—
92Dic74—41no—
93C8×C37—41no—
94#64436—41no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37C2×C22⋊C411yescharacteristic
100C2×D37—22no—
101C2×D37—21no—
102C2×D37—41no—
103C2×D37—42no—
104C2×D37—41no—
105C2×D37—41no—
106C2×D37—42no—
107C4×C37—21no—
108C4×C37—41no—
109C4×C37—41no—
110C4×C37—81no—
111Dic37—21no—
112Dic37—21no—
113Dic37—41no—
114Dic37—81no—
115Dic37#9911yescharacteristic
116Dic37#9911yescharacteristic
117#2120—371nomaximal, Sylow
118C2×C37—21no—
119C2×C37—41no—
120C2×C37—41no—
121C2×C37C2×#9911yescharacteristic
122D37—41no—
123D37—42no—
124#525—371no—
125#413—371no—
126#410—371no—
127#352—371no—
128#352D3711yescharacteristic, complemented
129AΣL(1,𝔽16)—371no—
130AΣL(1,𝔽16)—371no—
131C37#212011yescharacteristic, complemented, Sylow
132C2×#41—371no—
133C23×C4—371no—
134C2×M16—741no—
135#123—371no—
136#123C2×D3711yescharacteristic
137C22⋊Q8—741no—
138#121—741no—
139#120—371no—
140#120—371no—
141C4×D4—741no—
142C4×D4—741no—
143#117—371no—
144#117—741no—
145#101—741no—
146#100—371no—
147#100C2×D3711yescharacteristic
148#99—371no—
149#99—741no—
150#99C2×D3711yescharacteristic
151C24—371no—
152#41—1481no—
153#41—1481no—
154C2×Q8—371no—
155C2×D4—371no—
156C2×D4—371no—
157C2×D4—741no—
158C2×D4—741no—
159C2×D4C22×D3711yescharacteristic
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—741no—
164C22×C4—741no—
165C22×C4—1481no—
166C22×C4—1481no—
167C22×C4C4×D3711yescharacteristic
168M16—21no—
169M16—741no—
170M16—1481no—
171C2×C8—1481no—
172C4⋊C4—21no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C4⋊C4—1481no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—371no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4C4×D3711yescharacteristic
184C42—741no—
185C42—1481no—
186C23—371no—
187C23—741no—
188C23—1481no—
189C23—1482no—
190C23C2×C4×D3711yescharacteristic
191C23D4×D3711yescharacteristic
192Q8—1481no—
193D4—41no—
194D4—1482no—
195D4—1481no—
196D4—1481no—
197D4—1482no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—741no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4—1482no—
215C2×C4—1481no—
216C2×C4D4×D3711yescharacteristic
217C8—41no—
218C8—1481no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—742no—
224C22—741no—
225C22—1481no—
226C22—1481no—
227C22—1482no—
228C22—1482no—
229C22—1481no—
230C22C22⋊C4×D3711yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—371no—
236C4—371no—
237C4—2961no—
238C4—741no—
239C4—741no—
240C4—1481no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—1482no—
245C2—1481no—
246C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#352C2
socleC2×C37C2×#99
prime radical#14558041C2
cosocleC2×D4×C37C23
hypercenter#352D37
hypocenterC37#2120
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #14557514C2semidirect
3. #14557505C2semidirect
4. #14557323C2semidirect
5. #14557321C2semidirect
6. #14557319C2semidirect
7. C37×#352C2semidirect
9. C22×C4×D37C4semidirect
11. #11924519C4semidirect
14. #11924506C4semidirect
19. #11924492C4semidirect
128. #352D37semidirect
131. C37#2120semidirect

Maximal subgroups

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

subgroupindex
#145580412
#145575142
#145575052
#145573232
#145573212
#145573192
C37×#3522
#212037