Finite Group Databasebeta

← #17996583

Subgroups — #17996583

Order 4736.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#14558211C211yesmaximal, characteristic, complemented
2#14557720C211yesmaximal, characteristic
3#14557711C211yesmaximal, characteristic, complemented
4#14557327C211yesmaximal, characteristic, complemented
5#14557323C211yesmaximal, characteristic, complemented
6#14557319C211yesmaximal, characteristic, complemented
7C37×#458C211yesmaximal, characteristic, complemented
8#11924566—21no—
9#11924529—21no—
10#11924523C2211yescharacteristic
11#11924518—21no—
12#11924514—21no—
13#11924504—21no—
14#11924504C2211yescharacteristic
15C4×C22⋊D37—21no—
16#11924494—21no—
17C22⋊C4×D37—21no—
18#11924463—21no—
19#11924453C2211yescharacteristic
20#11924451—21no—
21#11924451C2211yescharacteristic
22H(5,𝔽2)×C37C2211yescharacteristic
23#123×C37—21no—
24#123×C37C2211yescharacteristic
25#99×C37—21no—
26#99×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28#41×C37—21no—
29#41×C37—41no—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—41no—
33C2×D4×C37C2311yescharacteristic
34C22×C4×C37D411yescharacteristic, complemented
35C2×C22⋊D37—21no—
36C2×C22⋊D37—41no—
37C2×C4×D37—21no—
38C2×C4×D37—21no—
39C2×Dic74D411yescharacteristic, complemented
40C4⋊C4×C37—21no—
41C4⋊C4×C37—41no—
42C22⋊C4×C37—21no—
43C22⋊C4×C37—21no—
44C22⋊C4×C37—41no—
45C22⋊C4×C37D411yescharacteristic, complemented
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49C22⋊Dic37D411yescharacteristic
50#10596942—41no—
51#10596940—41no—
52#10596938—21no—
53#10596938—21no—
54#10596938—21no—
55#10596938—41no—
56C4⋊Dic37—21no—
57#10596936—21no—
58#10596936—21no—
59C4×Dic37—21no—
60C4×Dic37D411yescharacteristic, complemented
61#10596934—21no—
62C23×C37—21no—
63C23×C37—21no—
64C23×C37C2×D411yescharacteristic
65C23×C37C2×D411yescharacteristic
66C22×D37—21no—
67C22×D37—42no—
68C22×D37—41no—
69Q8×C37—21no—
70D4×C37—21no—
71D4×C37—41no—
72D4×C37—41no—
73D4×C37—41no—
74D4×C37—41no—
75C2×C4×C37—21no—
76C2×C4×C37—21no—
77C2×C4×C37—21no—
78C2×C4×C37—21no—
79C2×C4×C37—41no—
80C2×C4×C37—41no—
81C2×C4×C37—41no—
82C2×C4×C37C2×D411yescharacteristic
83C22⋊D37—42no—
84C22⋊D37—82no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—41no—
89C4×D37—42no—
90C4×D37—81no—
91Dic74—41no—
92#64436—41no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—81no—
99C22×C37—81no—
100C22×C37#12011yescharacteristic
101C2×D37—22no—
102C2×D37—41no—
103C2×D37—41no—
104C2×D37—42no—
105C2×D37—81no—
106C4×C37—21no—
107C4×C37—41no—
108C4×C37—41no—
109C4×C37—41no—
110C4×C37—81no—
111Dic37—41no—
112Dic37—41no—
113Dic37—41no—
114Dic37—81no—
115#2197—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—41no—
118C2×C37—41no—
119C2×C37—81no—
120C2×C37B(4,𝔽2)11yescharacteristic
121D37—42no—
122#551—371no—
123#458D3711yescharacteristic, complemented
124B(4,𝔽2)—371no—
125#455—371no—
126#354—371no—
127#352—371no—
128AΣL(1,𝔽16)—371no—
129C37#219711yescharacteristic, complemented, Sylow
130H(5,𝔽2)C2×D3711yescharacteristic
131#137—741no—
132#126—741no—
133#124—371no—
134#123—21no—
135#123—741no—
136#123C2×D3711yescharacteristic
137C22⋊Q8—741no—
138#120—371no—
139#120—741no—
140C4×D4—741no—
141#117—741no—
142C2×C22⋊C4—741no—
143#104—741no—
144#100—371no—
145#99—21no—
146#99—371no—
147#99—741no—
148#99C2×D3711yescharacteristic
149C24—371no—
150#41—21no—
151#41—41no—
152C2×Q8—371no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—741no—
157C2×D4—1481no—
158C2×D4C22×D3711yescharacteristic
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22⋊D3711yescharacteristic, complemented
162Q16—1481no—
163SD16—1481no—
164M16—741no—
165C4⋊C4—21no—
166C4⋊C4—41no—
167C4⋊C4—741no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—41no—
173C22⋊C4—371no—
174C22⋊C4—741no—
175C22⋊C4—741no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—1481no—
181C22⋊C4C22⋊D3711yescharacteristic, complemented
182C42—371no—
183C42—741no—
184C23—21no—
185C23—21no—
186C23—741no—
187C23—1481no—
188C23—1482no—
189C23D4×D3711yescharacteristic
190C23C2×C22⋊D3711yescharacteristic
191Q8—21no—
192Q8—1481no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—2962no—
199D4—1482no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—2961no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—1482no—
212C2×C4—1481no—
213C2×C4D4×D3711yescharacteristic
214C8—1481no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22—2961no—
223C22—742no—
224C22—1481no—
225C22—1482no—
226C22—1481no—
227C22#1192450411yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—2961no—
234C4—1481no—
235C4—1481no—
236C4—1481no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—81no—
241C2—1482no—
242C2#1455771911yescharacteristic
subgroupG/H
centerC2#14557719
commutator, cosocleC2×D4×C37C23
FrattiniC2×D4C22×D37
FittingC37×#458C2
socleC2×C37B(4,𝔽2)
prime radical#14557720C2
hypercenter#458D37
hypocenterC37#2197
LCSG ▷ C2×D4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #14558211C2semidirect
3. #14557711C2semidirect
4. #14557327C2semidirect
5. #14557323C2semidirect
6. #14557319C2semidirect
7. C37×#458C2semidirect
34. C22×C4×C37D4semidirect
39. C2×Dic74D4semidirect
45. C22⋊C4×C37D4semidirect
60. C4×Dic37D4semidirect
123. #458D37semidirect
129. C37#2197semidirect
161. C22×C4C22⋊D37semidirect
181. C22⋊C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145582112
#145577202
#145577112
#145573272
#145573232
#145573192
C37×#4582
#219737