Finite Group Databasebeta

← #17995614

Subgroups — #17995614

Order 4736.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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#14558102C211yesmaximal, characteristic, complemented
3C2×#11924533C211yesmaximal, characteristic, complemented
4C2×#11924464C211yesmaximal, characteristic, complemented
5#14557537C211yesmaximal, characteristic, complemented
6C2×#11924452C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148—22no—
10C22×D148C2211yescharacteristic
11C22×D148C2211yescharacteristic
12#11924564—22no—
13#11924564—22no—
14C2×#10596930—21no—
15C2×D296—21no—
16C2×#10596934C2211yescharacteristic
17#11924533—22no—
18#11924533—21no—
19#11924533—22no—
20#11924524—21no—
21#11924511—22no—
22#11924506—22no—
23#11924464—22no—
24#11924456—22no—
25#11924452—22no—
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29C23×D37—21no—
30C23×D37D412yes—
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148—28no—
43C2×D148—21no—
44C2×D148—21no—
45C2×D148—21no—
46C2×D148—21no—
47C2×D148—21no—
48C2×D148—21no—
49C2×D148—21no—
50C2×D148—24no—
51C2×D148—48no—
52C2×D148D411yescharacteristic, complemented
53C2×D148D412yescomplemented
54C2×C4×D37—21no—
55C2×Dic74D411yescharacteristic, complemented
56M16×C37—21no—
57M16×C37D412yescomplemented
58C2×C8×C37—21no—
59C4⋊C4×C37D412yescomplemented
60C22⋊C4×C37—21no—
61C42×C37—21no—
62C42×C37—21no—
63C42×C37D412yescomplemented
64#10596938—24no—
65#10596934—21no—
66#10596934—21no—
67C2×#64436—21no—
68D296—24no—
69#10596930—24no—
70C23×C37C2×D411yescharacteristic
71C22×D37—22no—
72C22×D37—21no—
73C22×D37—22no—
74C22×D37—22no—
75C22×D37—22no—
76C22×D37—44no—
77C22×D37—44no—
78C22×D37—41no—
79C22×D37—41no—
80C2×C4×C37—24no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37#4111yescharacteristic
89C22⋊D37—41no—
90C22⋊D37—41no—
91C2×Dic37—21no—
92D148—22no—
93D148—21no—
94D148—22no—
95D148—21no—
96D148—416no—
97D148—41no—
98D148—41no—
99D148—41no—
100D148—41no—
101D148—41no—
102D148—41no—
103D148—84no—
104C4×D37—41no—
105C4×D37—41no—
106Dic74—21no—
107Dic74—21no—
108C8×C37—22no—
109#64436—41no—
110C22×C37—22no—
111C22×C37#12011yescharacteristic
112C22×C37#12011yescharacteristic
113C22×C37#12111yescharacteristic
114C2×D37—44no—
115C2×D37—44no—
116C2×D37—41no—
117C2×D37—42no—
118C2×D37—42no—
119C2×D37—42no—
120C2×D37—44no—
121C2×D37—82no—
122C2×D37—82no—
123C2×D37—82no—
124C4×C37—24no—
125C4×C37—42no—
126C4×C37#12011yescharacteristic
127C4×C37#12111yescharacteristic
128C4×C37#12111yescharacteristic
129C4×C37#12711yescharacteristic
130Dic37—41no—
131#2002—371nomaximal, Sylow
132C2×C37—21no—
133C2×C37—21no—
134C2×C37#39211yescharacteristic
135C2×C37#45312yes—
136D37—81no—
137D37—82no—
138D37—82no—
139C2×AGL(1,ℤ/8)—371no—
140#535—371no—
141C2×#127—371no—
142C2×#104—371no—
143#418—371no—
144C2×#100—371no—
145#339D3711yescharacteristic, complemented
146C37#200211yescharacteristic, complemented, Sylow
147C2×#41—371no—
148C22×D4—371no—
149C22×D4—371no—
150C22×D4—742no—
151AGL(1,ℤ/8)—742no—
152AGL(1,ℤ/8)—742no—
153C2×SD16—741no—
154C2×D8—741no—
155C2×M16—371no—
156C2×M16C2×D3711yescharacteristic
157#127—742no—
158#127—741no—
159#127—742no—
160#124—741no—
161#121—742no—
162#120—742no—
163#117C2×D3711yescharacteristic
164C2×C42C2×D3711yescharacteristic
165#104—742no—
166#102—742no—
167#100—742no—
168C24—372no—
169C24—741no—
170#41—741no—
171#41—741no—
172#41—741no—
173#41—741no—
174C2×Q8—371no—
175C2×D4—371no—
176C2×D4—372no—
177C2×D4—744no—
178C2×D4—748no—
179C2×D4—741no—
180C2×D4—741no—
181C2×D4—741no—
182C2×D4—741no—
183C2×D4—741no—
184C2×D4—741no—
185C2×D4—741no—
186C2×D4—741no—
187C2×D4—741no—
188C2×D4—741no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—1488no—
192C22×C4—21no—
193C22×C4—741no—
194C22×C4C22×D3711yescharacteristic
195SD16—744no—
196D8—744no—
197M16—21no—
198M16—741no—
199M16—741no—
200M16D14812yescomplemented
201C2×C8—21no—
202C2×C8—741no—
203C4⋊C4D14812yescomplemented
204C22⋊C4—21no—
205C22⋊C4—744no—
206C42—21no—
207C42—21no—
208C42D14812yescomplemented
209C23—742no—
210C23—742no—
211C23—742no—
212C23—742no—
213C23—741no—
214C23—1484no—
215C23—1484no—
216C23—1481no—
217C23—1481no—
218C23D4×D3711yescharacteristic
219Q8—741no—
220Q8—741no—
221D4—2964no—
222D4—741no—
223D4—742no—
224D4—742no—
225D4—741no—
226D4—14816no—
227D4—1481no—
228D4—1481no—
229D4—1481no—
230D4—1481no—
231D4—1481no—
232D4—1481no—
233D4—1481no—
234D4—1481no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—741no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4C2×D14811yescharacteristic
242C2×C4C2×D14811yescharacteristic
243C2×C4C2×D14811yescharacteristic
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4#1059696611yescharacteristic
247C8—22no—
248C8—1481no—
249C22—22no—
250C22—2962no—
251C22—2962no—
252C22—2962no—
253C22—1484no—
254C22—1484no—
255C22—1481no—
256C22—1482no—
257C22—1482no—
258C22—1482no—
259C22—1484no—
260C22#1192450611yescharacteristic
261C22#1192450611yescharacteristic
262C22#1192451111yescharacteristic
263C4—24no—
264C4—42no—
265C4—1481no—
266C4#1192450611yescharacteristic
267C4#1192451111yescharacteristic
268C4#1192451111yescharacteristic
269C4#1192453311yescharacteristic
270C2—21no—
271C2—21no—
272C2—2962no—
273C2—2962no—
274C2—2961no—
275C2#1455744311yescharacteristic
276C2#1455770212yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
hypercenter#339D37
hypocenterC37#2002
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. #14558102C2semidirect
3. C2×#11924533C2semidirect
4. C2×#11924464C2semidirect
5. #14557537C2semidirect
6. C2×#11924452C2semidirect
7. C37×#339C2semidirect
52. C2×D148D4semidirect
53. C2×D148D4semidirect
55. C2×Dic74D4semidirect
57. M16×C37D4semidirect
59. C4⋊C4×C37D4semidirect
63. C42×C37D4semidirect
145. #339D37semidirect
146. C37#2002semidirect
200. M16D148semidirect
203. C4⋊C4D148semidirect
208. C42D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
#145581022
C2×#119245332
C2×#119244642
#145575372
C2×#119244522
C37×#3392
#200237