Finite Group Databasebeta

← #18003956

Subgroups — #18003956

Order 4736.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#11924581C211yesmaximal, characteristic, complemented
2#14558333C212yesmaximal, complemented
3#14558100C211yesmaximal, characteristic, complemented
4#14557713C214yesmaximal, complemented
5#14557703C214yesmaximal, complemented
6#14557549C212yesmaximal, complemented
7C2×#100×C37C211yesmaximal, characteristic, complemented
8#11924581—22no—
9#11924581—24no—
10#11924581C2214yes—
11C2×#10596962C2212yes—
12C2×#10596962C2211yescharacteristic, complemented
13C2×#10596964—22no—
14C22×C22⋊D37—22no—
15C2×D4×D37—22no—
16#11924569—22no—
17#11924569C2214yescomplemented
18#11924564—22no—
19#11924564C2214yescomplemented
20#11924558—24no—
21#11924532C2212yescomplemented
22#11924523C2212yescomplemented
23#11924507—22no—
24#11924505—22no—
25#11924495C2211yescharacteristic, complemented
26#11924462C2218yescomplemented
27C22×D4×C37C2211yescharacteristic
28C2×M16×C37C2212yescomplemented
29#100×C37C2214yescomplemented
30C24×C37D412yes—
31C23×D37—22no—
32C2×D4×C37—22no—
33C2×D4×C37—22no—
34C2×D4×C37D412yes—
35C2×D4×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—24no—
38C2×C22⋊D37—28no—
39C2×C22⋊D37—22no—
40C2×C22⋊D37—28no—
41C2×C22⋊D37—21no—
42C2×C22⋊D37—24no—
43C22×Dic37—22no—
44#10596964—28no—
45#10596964—28no—
46D4×D37—28no—
47D4×D37—28no—
48#10596962—22no—
49#10596962—22no—
50#10596962—22no—
51#10596962—22no—
52#10596962D414yescomplemented
53#10596962C2314yes—
54C2×D148D412yescomplemented
55C2×D148C2311yescharacteristic, complemented
56C2×C4×D37—22no—
57C2×C4×D37—21no—
58C2×Dic74D412yescomplemented
59C2×Dic74C2311yescharacteristic, complemented
60M16×C37—22no—
61M16×C37C2314yescomplemented
62C2×C8×C37—22no—
63C22⋊Dic37—21no—
64C22⋊Dic37—24no—
65C4⋊Dic37—21no—
66C4×Dic37C2312yescomplemented
67Dic148—24no—
68D296—24no—
69#10596930—24no—
70#10596930—24no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37—82no—
74C23×C37C2×D414yes—
75C23×C37C2×D411yescharacteristic
76C22×D37—22no—
77C22×D37—28no—
78C22×D37—21no—
79C22×D37—84no—
80D4×C37—24no—
81D4×C37—24no—
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D412yes—
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2411yescharacteristic
86C22⋊D37—216no—
87C22⋊D37—24no—
88C22⋊D37—24no—
89C22⋊D37—41no—
90C22⋊D37—41no—
91C22⋊D37—84no—
92C2×Dic37—28no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—21no—
96D148—22no—
97D148—22no—
98D148C2×D414yes—
99C4×D37—24no—
100C4×D37—24no—
101C4×D37—42no—
102Dic74—22no—
103Dic74—22no—
104Dic74C2×D414yes—
105C8×C37—24no—
106C22×C37—24no—
107C22×C37—41no—
108C22×C37—44no—
109C22×C37—44no—
110C22×C37—82no—
111C22×C37#12011yescharacteristic
112C22×C37#12011yescharacteristic
113C22×C37C22×D411yescharacteristic
114C2×D37—24no—
115C2×D37—44no—
116C2×D37—42no—
117C2×D37—41no—
118C2×D37—88no—
119C4×C37#12012yes—
120C4×C37C22×D412yes—
121Dic37—24no—
122Dic37—42no—
123Dic37—41no—
124#3019—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—44no—
129C2×C37C2×#12011yescharacteristic
130D37—44no—
131D37—81no—
132C2×H(5,𝔽2)—371no—
133#575—372no—
134#535—371no—
135#455—374no—
136#453—374no—
137#421—372no—
138C2×#100D3711yescharacteristic, complemented
139C37#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—374no—
141H(5,𝔽2)—744no—
142H(5,𝔽2)—742no—
143C2×#41—372no—
144C2×#41—371no—
145C2×#41—742no—
146C22×D4—742no—
147C22×D4—742no—
148C22×D4C2×D3711yescharacteristic
149#137—374no—
150#137—742no—
151AGL(1,ℤ/8)—374no—
152AGL(1,ℤ/8)—742no—
153#135—744no—
154C2×M16C2×D3712yescomplemented
155#127—372no—
156#124—372no—
157#121—742no—
158#120—742no—
159#117—371no—
160#104—378no—
161#100C2×D3714yescomplemented
162C24—742no—
163C24D14812yes—
164#41—374no—
165#41—374no—
166#41—748no—
167#41—748no—
168#41—742no—
169#41—742no—
170#41—742no—
171#41—742no—
172C2×Q8—372no—
173C2×Q8—371no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—372no—
177C2×D4—371no—
178C2×D4—748no—
179C2×D4—748no—
180C2×D4—744no—
181C2×D4—744no—
182C2×D4—748no—
183C2×D4—742no—
184C2×D4—748no—
185C2×D4—741no—
186C2×D4D14812yes—
187C2×D4C22×D3712yes—
188C22×C4—742no—
189C22×C4—742no—
190C22×C4—741no—
191C22×C4C22×D3711yescharacteristic
192Q16—744no—
193SD16—744no—
194SD16—744no—
195D8—744no—
196M16—22no—
197M16C22×D3714yescomplemented
198C2×C8—22no—
199C4⋊C4—741no—
200C22⋊C4—741no—
201C22⋊C4—744no—
202C42—372no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—2964no—
207C23—748no—
208C23—742no—
209C23—741no—
210C23C2×D14814yes—
211C23C2×D14811yescharacteristic
212Q8—374no—
213Q8—742no—
214Q8—742no—
215D4—24no—
216D4—24no—
217D4—374no—
218D4—2964no—
219D4—7416no—
220D4—744no—
221D4—744no—
222D4—742no—
223D4—742no—
224D4—1481no—
225D4—1481no—
226C2×C4—748no—
227C2×C4—742no—
228C2×C4—744no—
229C2×C4—744no—
230C2×C4—742no—
231C2×C4—741no—
232C2×C4—1482no—
233C2×C4C2×D14811yescharacteristic
234C2×C4D4×D3712yes—
235C2×C4D4×D3712yes—
236C2×C4C23×D3711yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—2968no—
244C22—744no—
245C22—1482no—
246C22—1484no—
247C22—1481no—
248C22#1192450611yescharacteristic
249C22#1192450611yescharacteristic
250C22C22×D14811yescharacteristic
251C4—744no—
252C4—1482no—
253C4—1481no—
254C4#1192450612yes—
255C4C2×D4×D3712yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—2961no—
261C2—1484no—
262C2C2×#1192450611yescharacteristic
subgroupG/H
centerC2C2×#11924506
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#100×C37C2
socleC2×C37C2×#120
hypercenterC2×#100D37
hypocenterC37#3019
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#11924581C2semidirect
2. #14558333C2semidirect
3. #14558100C2semidirect
4. #14557713C2semidirect
5. #14557703C2semidirect
6. #14557549C2semidirect
7. C2×#100×C37C2semidirect
12. C2×#10596962C22semidirect
17. #11924569C22semidirect
19. #11924564C22semidirect
21. #11924532C22semidirect
22. #11924523C22semidirect
25. #11924495C22semidirect
26. #11924462C22semidirect
28. C2×M16×C37C22semidirect
29. #100×C37C22semidirect
52. #10596962D4semidirect
54. C2×D148D4semidirect
55. C2×D148C23semidirect
58. C2×Dic74D4semidirect
59. C2×Dic74C23semidirect
61. M16×C37C23semidirect
66. C4×Dic37C23semidirect
138. C2×#100D37semidirect
139. C37#3019semidirect
154. C2×M16C2×D37semidirect
161. #100C2×D37semidirect
197. M16C22×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245812
#145583332
#145581002
#145577132
#145577032
#145575492
C2×#100×C372
#301937