Finite Group Databasebeta

← #17996584

Subgroups — #17996584

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#14558214C211yesmaximal, characteristic, complemented
2#14557723C211yesmaximal, characteristic, complemented
3#14557711C211yesmaximal, characteristic, complemented
4#14557327C211yesmaximal, characteristic, complemented
5#14557322C211yesmaximal, characteristic, complemented
6#14557320C211yesmaximal, characteristic, complemented
7C37×B(4,𝔽2)C211yesmaximal, characteristic
8#11924566—21no—
9#11924529—21no—
10#11924523C2211yescharacteristic
11#11924517—21no—
12#11924517—21no—
13#11924517C2211yescharacteristic
14#11924513—21no—
15D4×Dic37—21no—
16#11924492—21no—
17C2×C22⋊Dic37—21no—
18#11924463—21no—
19#11924453C2211yescharacteristic
20#11924451—21no—
21#11924451C2211yescharacteristic
22H(5,𝔽2)×C37C2211yescharacteristic
23#120×C37—21no—
24#120×C37C2211yescharacteristic
25#99×C37—21no—
26#99×C37C2211yescharacteristic
27C24×C37D411yescharacteristic
28#41×C37—21no—
29#41×C37—41no—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—41no—
34C2×D4×C37—41no—
35C2×D4×C37C2311yescharacteristic
36C22×Dic37—21no—
37C22×Dic37—21no—
38C22×Dic37D411yescharacteristic, complemented
39C2×Dic74D411yescharacteristic, complemented
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—41no—
43C22⋊C4×C37D411yescharacteristic
44C22⋊Dic37—21no—
45C22⋊Dic37—21no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49C22⋊Dic37—21no—
50C22⋊Dic37—41no—
51C22⋊Dic37D411yescharacteristic, complemented
52#10596942—41no—
53#10596940—41no—
54C4⋊Dic37—21no—
55#10596936—21no—
56#10596936—21no—
57#10596936—21no—
58#10596936—41no—
59C4×Dic37—21no—
60C4×Dic37D411yescharacteristic, complemented
61#10596934—21no—
62C23×C37—21no—
63C23×C37—21no—
64C23×C37—21no—
65C23×C37—41no—
66C23×C37—42no—
67C23×C37C2×D411yescharacteristic
68C23×C37C2×D411yescharacteristic
69Q8×C37—21no—
70D4×C37—21no—
71D4×C37—41no—
72D4×C37—42no—
73D4×C37—41no—
74D4×C37—41no—
75D4×C37—41no—
76D4×C37—82no—
77C2×C4×C37—21no—
78C2×C4×C37—21no—
79C2×C4×C37—21no—
80C2×C4×C37—41no—
81C2×C4×C37—41no—
82C2×C4×C37C2×D411yescharacteristic
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—42no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37—81no—
91Dic74—41no—
92#64436—41no—
93C22×C37—22no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—42no—
100C22×C37—41no—
101C22×C37—41no—
102C22×C37—81no—
103C22×C37—81no—
104C22×C37—81no—
105C22×C37#12011yescharacteristic
106C4×C37—21no—
107C4×C37—41no—
108C4×C37—41no—
109C4×C37—81no—
110Dic37—41no—
111Dic37—41no—
112Dic37—41no—
113Dic37—41no—
114Dic37—81no—
115#2197—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—41no—
118C2×C37—41no—
119C2×C37—42no—
120C2×C37—81no—
121C2×C37B(4,𝔽2)11yescharacteristic
122#551—371no—
123#458—371no—
124B(4,𝔽2)D3711yescharacteristic
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—371no—
135#123—741no—
136#123—741no—
137C22⋊Q8—741no—
138#120—21no—
139#120C2×D3711yescharacteristic
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
149C24C22⋊D3711yescharacteristic
150#41—21no—
151#41—41no—
152C2×Q8—371no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4C22×D3711yescharacteristic
159C22×C4—371no—
160C22×C4—741no—
161C22×C4—741no—
162Q16—1481no—
163SD16—1481no—
164M16—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C4⋊C4—741no—
168C4⋊C4—741no—
169C4⋊C4—1481no—
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
182C42—371no—
183C42—741no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23D4×D3711yescharacteristic
190C23C2×C22⋊D3711yescharacteristic
191Q8—21no—
192Q8—1481no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—42no—
198D4—41no—
199D4—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2961no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1481no—
211C2×C4—1482no—
212C2×C4—1481no—
213C2×C4D4×D3711yescharacteristic
214C8—1481no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22—81no—
227C22#1192450411yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—2961no—
233C4—1481no—
234C4—1481no—
235C4—1481no—
236C4—1481no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—81no—
242C2#1455771911yescharacteristic
subgroupG/H
centerC2#14557719
commutator, cosocleC2×D4×C37C23
FrattiniC2×D4C22×D37
Fitting, prime radicalC37×B(4,𝔽2)C2
socleC2×C37B(4,𝔽2)
hypercenterB(4,𝔽2)D37
hypocenterC37#2197
LCSG ▷ C2×D4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14558214C2semidirect
2. #14557723C2semidirect
3. #14557711C2semidirect
4. #14557327C2semidirect
5. #14557322C2semidirect
6. #14557320C2semidirect
38. C22×Dic37D4semidirect
39. C2×Dic74D4semidirect
51. C22⋊Dic37D4semidirect
60. C4×Dic37D4semidirect
129. C37#2197semidirect

Maximal subgroups

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

subgroupindex
#145582142
#145577232
#145577112
#145573272
#145573222
#145573202
C37×B(4,𝔽2)2
#219737