Finite Group Databasebeta

← #18004274

Subgroups — #18004274

Order 4736.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924542C211yesmaximal, characteristic, complemented
3#14558114C211yesmaximal, characteristic, complemented
4#14558100C211yesmaximal, characteristic, complemented
5#14557785C212yesmaximal, complemented
6#14557778C212yesmaximal, complemented
7#14557768C212yesmaximal, complemented
8#14557761C212yesmaximal, complemented
9#14557573C211yesmaximal, characteristic, complemented
10#14557530C211yesmaximal, characteristic, complemented
11C2×#102×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14#11924562—24no—
15C2×#10596940C2212yes—
16C2×#10596939C2212yes—
17#11924542—24no—
18C2×#10596934C2211yescharacteristic
19C2×#10596929C2212yescomplemented
20C2×C8×D37C2212yescomplemented
21#11924532—21no—
22#11924523—21no—
23#11924516—21no—
24#11924516C2212yescomplemented
25#11924511—21no—
26#11924511C2212yescomplemented
27#11924510—22no—
28#11924507C2212yes—
29#11924507C2212yes—
30#11924505—22no—
31#11924495C2211yescharacteristic
32#11924469C2212yescomplemented
33#11924467C2212yescomplemented
34#11924461C2211yescharacteristic, complemented
35#11924461C2211yescharacteristic, complemented
36#11924458C2211yescharacteristic, complemented
37#11924458C2211yescharacteristic, complemented
38C22×D4×C37C2211yescharacteristic
39C22×C8×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41#102×C37C2212yes—
42#102×C37C2212yes—
43C24×C37—21no—
44C2×D4×C37—22no—
45C2×D4×C37—21no—
46C2×D4×C37—22no—
47C2×D4×C37C2312yes—
48C22×C4×C37—21no—
49C22×C4×C37C2311yescharacteristic
50C2×C22⋊D37—21no—
51C2×C22⋊D37—22no—
52C2×C22⋊D37—22no—
53C2×C22⋊D37D412yes—
54#10596962—22no—
55#10596962—22no—
56#10596962—22no—
57#10596962—22no—
58C2×D148—22no—
59C2×D148D411yescharacteristic
60C2×D148C2311yescharacteristic
61C2×C4×D37—21no—
62C2×C4×D37C2312yes—
63C2×Dic74D411yescharacteristic
64C2×Dic74C2311yescharacteristic
65C2×C8×C37—22no—
66C2×C8×C37C2311yescharacteristic
67C2×C8×C37C2311yescharacteristic
68C4⋊C4×C37—21no—
69C4⋊C4×C37C2312yes—
70C22⋊Dic37—21no—
71C22⋊Dic37—22no—
72C22⋊Dic37—22no—
73#10596940—24no—
74#10596939—24no—
75#10596938—22no—
76#10596938—22no—
77C4⋊Dic37—22no—
78C4⋊Dic37C2311yescharacteristic
79C4⋊Dic37C2311yescharacteristic
80C4×Dic37—21no—
81#10596934D414yescomplemented
82C2×#64436C2312yes—
83#10596929—24no—
84C8×D37—24no—
85C23×C37—22no—
86C23×C37—42no—
87C23×C37—81no—
88C23×C37—81no—
89C23×C37C2×D411yescharacteristic
90C22×D37—21no—
91C22×D37C2×D412yes—
92D4×C37—22no—
93D4×C37—22no—
94D4×C37—42no—
95C2×C4×C37—22no—
96C2×C4×C37—81no—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D412yes—
99C2×C4×C37#4112yes—
100C2×C4×C37C2411yescharacteristic
101C22⋊D37—24no—
102C22⋊D37—42no—
103C22⋊D37—82no—
104C22⋊D37—82no—
105C2×Dic37—21no—
106C2×Dic37—21no—
107C2×Dic37—21no—
108C2×Dic37C2×D412yes—
109D148—22no—
110D148—21no—
111D148—21no—
112D148—82no—
113C4×D37—22no—
114C4×D37—22no—
115C4×D37—42no—
116Dic74—22no—
117Dic74—21no—
118Dic74—21no—
119C8×C37—21no—
120C8×C37—21no—
121#64436C2×D414yes—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—42no—
125C22×C37—42no—
126C22×C37—42no—
127C22×C37—84no—
128C22×C37#12112yes—
129C22×C37C22×D411yescharacteristic
130C2×D37—22no—
131C2×D37—22no—
132C2×D37—22no—
133C2×D37—41no—
134C2×D37—41no—
135C2×D37—41no—
136C4×C37—42no—
137C4×C37#12112yes—
138C4×C37C22×D411yescharacteristic
139C4×C37C2×#4111yescharacteristic
140Dic37—22no—
141Dic37—41no—
142Dic37—41no—
143Dic37—41no—
144#3062—371nomaximal, Sylow
145C2×C37—22no—
146C2×C37—82no—
147C2×C37C2×#12111yescharacteristic
148C2×C37#57611yescharacteristic
149C2×C37#57711yescharacteristic
150D37—42no—
151D37—81no—
152C2×AGL(1,ℤ/8)—371no—
153C2×#131—371no—
154#537—371no—
155#535—371no—
156#469—372no—
157#468—372no—
158#466—372no—
159#465—372no—
160#428—371no—
161#416—371no—
162C2×#102D3711yescharacteristic, complemented
163C37#306211yescharacteristic, complemented, Sylow
164C2×#41—371no—
165C2×#41—371no—
166C22×D4C2×D3711yescharacteristic
167AGL(1,ℤ/8)—744no—
168C2×SD16—372no—
169C2×D8—372no—
170#131—744no—
171C2×M16—371no—
172C2×M16—372no—
173C22×C8—372no—
174C22×C8C2×D3711yescharacteristic
175#127—741no—
176#124—741no—
177C22⋊Q8—372no—
178C22⋊Q8—741no—
179#121—372no—
180#121—372no—
181#121—372no—
182#121—741no—
183#121—742no—
184#120—742no—
185#117—371no—
186C2×C4⋊C4C2×D3711yescharacteristic
187#107—372no—
188#106—372no—
189#103—371no—
190#103—371no—
191#102—371no—
192#102—371no—
193#102C2×D3712yes—
194#102C2×D3712yes—
195C24—21no—
196#41—742no—
197#41—742no—
198#41—742no—
199#41—742no—
200C2×Q8—371no—
201C2×Q8—371no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—372no—
206C2×D4—371no—
207C2×D4—371no—
208C2×D4—742no—
209C2×D4—742no—
210C2×D4—742no—
211C2×D4—741no—
212C2×D4C22×D3712yes—
213C22×C4—21no—
214C22×C4—372no—
215C22×C4—741no—
216C22×C4C22×D3711yescharacteristic
217SD16—744no—
218D8—744no—
219M16—374no—
220M16—744no—
221C2×C8—22no—
222C2×C8—372no—
223C2×C8—744no—
224C2×C8C22×D3711yescharacteristic
225C2×C8C22×D3711yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—371no—
228C4⋊C4—371no—
229C4⋊C4—742no—
230C4⋊C4C22×D3712yes—
231C22⋊C4—742no—
232C22⋊C4—742no—
233C22⋊C4—742no—
234C22⋊C4—742no—
235C22⋊C4—741no—
236C42—741no—
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—372no—
242C23—741no—
243C23D4×D3711yescharacteristic
244Q8—742no—
245Q8—741no—
246Q8—741no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—2962no—
251D4—2962no—
252D4—2962no—
253D4—744no—
254D4—742no—
255D4—741no—
256D4—741no—
257D4—1482no—
258C2×C4—22no—
259C2×C4—81no—
260C2×C4—372no—
261C2×C4—742no—
262C2×C4—742no—
263C2×C4—741no—
264C2×C4—741no—
265C2×C4—741no—
266C2×C4—1482no—
267C2×C4#1059696212yes—
268C2×C4D4×D3711yescharacteristic
269C2×C4D4×D3712yes—
270C2×C4C23×D3711yescharacteristic
271C8—21no—
272C8—21no—
273C8—374no—
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—84no—
280C22—742no—
281C22—742no—
282C22—742no—
283C22—1481no—
284C22—1481no—
285C22—1481no—
286C22#1192450912yes—
287C22C2×D4×D3711yescharacteristic
288C4—42no—
289C4—742no—
290C4—1481no—
291C4—1481no—
292C4—1481no—
293C4#1192450912yes—
294C4C2×D4×D3711yescharacteristic
295C4C2×#1059696211yescharacteristic
296C2—22no—
297C2—82no—
298C2—2961no—
299C2—1482no—
300C2C2×#1192450911yescharacteristic
301C2#1455833411yescharacteristic
302C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC22×C37C22×D4
hypercenterC2×#102D37
hypocenterC37#3062
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924542C2semidirect
3. #14558114C2semidirect
4. #14558100C2semidirect
5. #14557785C2semidirect
6. #14557778C2semidirect
7. #14557768C2semidirect
8. #14557761C2semidirect
9. #14557573C2semidirect
10. #14557530C2semidirect
11. C2×#102×C37C2semidirect
19. C2×#10596929C22semidirect
20. C2×C8×D37C22semidirect
24. #11924516C22semidirect
26. #11924511C22semidirect
32. #11924469C22semidirect
33. #11924467C22semidirect
34. #11924461C22semidirect
35. #11924461C22semidirect
36. #11924458C22semidirect
37. #11924458C22semidirect
81. #10596934D4semidirect
162. C2×#102D37semidirect
163. C37#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245422
#145581142
#145581002
#145577852
#145577782
#145577682
#145577612
#145575732
#145575302
C2×#102×C372
#306237