Finite Group Databasebeta

← #17995613

Subgroups — #17995613

Order 4736.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924564C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic, complemented
3C2×#11924532C211yesmaximal, characteristic, complemented
4C2×#11924462C211yesmaximal, characteristic, complemented
5#14557539C211yesmaximal, characteristic, complemented
6#14557294C211yesmaximal, characteristic, complemented
7C2×#100×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10C22×C22⋊D37—22no—
11#11924564—22no—
12#11924564—22no—
13C2×#10596930—21no—
14C2×D296—21no—
15#11924532—22no—
16#11924532—21no—
17#11924532—22no—
18#11924523—21no—
19#11924507—22no—
20#11924505—22no—
21#11924495C2211yescharacteristic
22C2×C4×Dic37C2211yescharacteristic
23#11924462—22no—
24#11924458—22no—
25C22×D4×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×M16×C37C2211yescharacteristic
28#100×C37—22no—
29C24×C37D412yes—
30C23×D37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—21no—
36C2×D4×C37—21no—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—28no—
39C2×C22⋊D37—21no—
40C2×C22⋊D37—24no—
41C2×C22⋊D37—48no—
42C22×Dic37—21no—
43#10596962—21no—
44#10596962—21no—
45#10596962—21no—
46#10596962—21no—
47C2×D148—21no—
48C2×D148—21no—
49C2×D148—21no—
50C2×D148—21no—
51C2×D148—21no—
52C2×D148D411yescharacteristic, complemented
53C2×D148D412yescomplemented
54C2×C4×D37—21no—
55C2×Dic74D411yescharacteristic, complemented
56M16×C37—21no—
57M16×C37—21no—
58M16×C37—21no—
59M16×C37D412yescomplemented
60C2×C8×C37—21no—
61C2×C8×C37—21no—
62C22⋊Dic37—24no—
63C22⋊Dic37—21no—
64C4⋊Dic37D412yescomplemented
65C4×Dic37—21no—
66C4×Dic37—21no—
67C4×Dic37D412yescomplemented
68D296—24no—
69#10596930—24no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37—44no—
74C23×C37C2×D411yescharacteristic
75C22×D37—21no—
76C22×D37—22no—
77C22×D37—44no—
78C22×D37—41no—
79C22×D37—41no—
80D4×C37—41no—
81D4×C37—41no—
82D4×C37—41no—
83D4×C37—41no—
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37#4111yescharacteristic
90C22⋊D37—416no—
91C22⋊D37—41no—
92C22⋊D37—41no—
93C22⋊D37—84no—
94C2×Dic37—24no—
95C2×Dic37—22no—
96C2×Dic37—22no—
97C2×Dic37—21no—
98D148—22no—
99D148—21no—
100D148—22no—
101D148—21no—
102D148—41no—
103D148—41no—
104C4×D37—41no—
105C4×D37—41no—
106Dic74—21no—
107Dic74—21no—
108C8×C37—22no—
109C8×C37—41no—
110C22×C37—22no—
111C22×C37—44no—
112C22×C37—42no—
113C22×C37—44no—
114C22×C37—82no—
115C22×C37#12011yescharacteristic
116C22×C37#12011yescharacteristic
117C22×C37#12111yescharacteristic
118C2×D37—44no—
119C2×D37—41no—
120C2×D37—42no—
121C2×D37—42no—
122C2×D37—82no—
123C2×D37—82no—
124C4×C37#12011yescharacteristic
125C4×C37#12111yescharacteristic
126C4×C37#12111yescharacteristic
127C4×C37#12711yescharacteristic
128Dic37—24no—
129Dic37—41no—
130Dic37—42no—
131#2002—371nomaximal, Sylow
132C2×C37—21no—
133C2×C37—21no—
134C2×C37—82no—
135C2×C37#39211yescharacteristic
136C2×C37#45312yes—
137D37—81no—
138D37—82no—
139C2×AGL(1,ℤ/8)—371no—
140#535—371no—
141C2×#127—371no—
142C2×#104—371no—
143#418—371no—
144C2×#100D3711yescharacteristic, complemented
145#339—371no—
146C37#200211yescharacteristic, complemented, Sylow
147C2×#41—371no—
148C22×D4—371no—
149C22×D4—742no—
150C22×D4C2×D3711yescharacteristic
151AGL(1,ℤ/8)—742no—
152AGL(1,ℤ/8)—742no—
153C2×SD16—741no—
154C2×D8—741no—
155C2×M16C2×D3711yescharacteristic
156C2×M16C2×D3711yescharacteristic
157#127—742no—
158#127—742no—
159#127—741no—
160#124—741no—
161#121—742no—
162#120—742no—
163#117—371no—
164C2×C42—371no—
165#104—742no—
166#102—742no—
167#100—22no—
168C24—741no—
169C24D14812yes—
170#41—741no—
171#41—741no—
172#41—741no—
173#41—741no—
174C2×Q8—371no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—371no—
182C2×D4—372no—
183C2×D4—744no—
184C2×D4—748no—
185C2×D4—741no—
186C2×D4—741no—
187C2×D4—741no—
188C2×D4—741no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—1488no—
192C22×C4—741no—
193C22×C4—741no—
194C22×C4C22×D3711yescharacteristic
195SD16—744no—
196D8—744no—
197M16—21no—
198M16—21no—
199M16—21no—
200M16C22⋊D3712yescomplemented
201C2×C8—21no—
202C2×C8—21no—
203C4⋊C4—372no—
204C22⋊C4—744no—
205C22⋊C4—741no—
206C42—372no—
207C42—741no—
208C42—741no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—44no—
213C23—742no—
214C23—741no—
215C23—1484no—
216C23—1481no—
217C23—1481no—
218C23C2×D14811yescharacteristic
219Q8—741no—
220Q8—741no—
221D4—41no—
222D4—41no—
223D4—41no—
224D4—41no—
225D4—2964no—
226D4—741no—
227D4—742no—
228D4—742no—
229D4—741no—
230D4—14816no—
231D4—1481no—
232D4—1481no—
233D4—1481no—
234D4—1481no—
235C2×C4—744no—
236C2×C4—742no—
237C2×C4—742no—
238C2×C4—741no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4#1059696211yescharacteristic
242C2×C4D4×D3711yescharacteristic
243C2×C4D4×D3711yescharacteristic
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4C2×C22⋊D3711yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—2962no—
255C22—2962no—
256C22—1484no—
257C22—1481no—
258C22—1482no—
259C22—1482no—
260C22#1192450611yescharacteristic
261C22#1192450611yescharacteristic
262C22#1192451011yescharacteristic
263C4—744no—
264C4—1481no—
265C4—1482no—
266C4#1192450411yescharacteristic
267C4#1192450911yescharacteristic
268C4#1192450911yescharacteristic
269C4#1192453211yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—2962no—
274C2—2961no—
275C2#1455744211yescharacteristic
276C2#1455770312yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#100×C37C2
socleC22×C37#120
hypercenterC2×#100D37
hypocenterC37#2002
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. #14558100C2semidirect
3. C2×#11924532C2semidirect
4. C2×#11924462C2semidirect
5. #14557539C2semidirect
6. #14557294C2semidirect
7. C2×#100×C37C2semidirect
52. C2×D148D4semidirect
53. C2×D148D4semidirect
55. C2×Dic74D4semidirect
59. M16×C37D4semidirect
64. C4⋊Dic37D4semidirect
67. C4×Dic37D4semidirect
144. C2×#100D37semidirect
146. C37#2002semidirect
200. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
#145581002
C2×#119245322
C2×#119244622
#145575392
#145572942
C2×#100×C372
#200237