Finite Group Databasebeta

← #18004140

Subgroups — #18004140

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×#11924558C211yesmaximal, characteristic, complemented
3#14558100C211yesmaximal, characteristic, complemented
4#14558014C211yesmaximal, characteristic, complemented
5#14557754C212yesmaximal, complemented
6#14557747C212yesmaximal, complemented
7#14557732C212yesmaximal, complemented
8#14557727C212yesmaximal, complemented
9#14557559C211yesmaximal, characteristic, complemented
10#14557532C211yesmaximal, characteristic, complemented
11C2×#102×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14#11924562—24no—
15#11924558—24no—
16C2×Dic148C2211yescharacteristic, complemented
17C2×#10596930C2211yescharacteristic, complemented
18C2×#10596930C2211yescharacteristic, complemented
19C2×#10596940C2212yes—
20C2×D296C2211yescharacteristic, complemented
21C2×#10596939C2212yes—
22C2×#10596934C2211yescharacteristic
23#11924532C2212yes—
24#11924523C2212yes—
25#11924507—21no—
26#11924507—21no—
27#11924505—22no—
28#11924501C2212yescomplemented
29#11924498C2212yescomplemented
30C4×C22⋊D37—22no—
31#11924495C2211yescharacteristic
32#11924494—21no—
33C4⋊C4×D37—21no—
34#11924465C2212yescomplemented
35#11924465C2212yescomplemented
36#11924459C2212yescomplemented
37#11924456C2212yescomplemented
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—21no—
52C2×C22⋊D37—22no—
53C2×C22⋊D37—22no—
54#10596962—22no—
55#10596962—22no—
56#10596962—22no—
57#10596962D414yescomplemented
58C2×D148C2311yescharacteristic
59C2×D148C2311yescharacteristic
60C2×C4×D37—21no—
61C2×C4×D37—21no—
62C2×C4×D37—22no—
63C2×Dic74C2311yescharacteristic
64C2×Dic74C2311yescharacteristic
65C2×C8×C37—22no—
66C2×C8×C37C2311yescharacteristic
67C2×C8×C37C2311yescharacteristic
68C4⋊C4×C37—21no—
69C4⋊C4×C37C2312yes—
70C22⋊Dic37—22no—
71C22⋊Dic37—22no—
72C22⋊Dic37D412yes—
73#10596940—24no—
74#10596939—24no—
75#10596938—22no—
76C4⋊Dic37D411yescharacteristic
77C4⋊Dic37D411yescharacteristic
78#10596936—22no—
79C4×Dic37—22no—
80C4×Dic37C2312yes—
81#10596934—22no—
82C2×#64436C2312yes—
83Dic148—22no—
84D296—22no—
85#10596930—22no—
86#10596930—22no—
87C23×C37—22no—
88C23×C37—42no—
89C23×C37—81no—
90C23×C37—81no—
91C23×C37C2×D411yescharacteristic
92C22×D37—21no—
93C22×D37—21no—
94D4×C37—22no—
95D4×C37—22no—
96D4×C37—42no—
97C2×C4×C37—22no—
98C2×C4×C37—81no—
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D412yes—
101C2×C4×C37#4112yes—
102C2×C4×C37C2411yescharacteristic
103C22⋊D37—24no—
104C22⋊D37—42no—
105C22⋊D37—82no—
106C22⋊D37—82no—
107C2×Dic37—21no—
108C2×Dic37—21no—
109C2×Dic37C2×D412yes—
110C2×Dic37C2×D412yes—
111D148—21no—
112D148—21no—
113D148—21no—
114D148C2×D412yes—
115C4×D37—24no—
116C4×D37—42no—
117C4×D37—82no—
118Dic74—21no—
119Dic74—21no—
120Dic74—21no—
121Dic74C2×D412yes—
122C8×C37—21no—
123C8×C37—21no—
124#64436—22no—
125C22×C37—21no—
126C22×C37—21no—
127C22×C37—42no—
128C22×C37—42no—
129C22×C37—42no—
130C22×C37—84no—
131C22×C37#12112yes—
132C22×C37C22×D411yescharacteristic
133C2×D37—22no—
134C2×D37—41no—
135C2×D37—41no—
136C2×D37—41no—
137C2×D37—41no—
138C2×D37—41no—
139C4×C37—42no—
140C4×C37#12112yes—
141C4×C37C22×D411yescharacteristic
142C4×C37C2×#4111yescharacteristic
143Dic37—22no—
144Dic37—22no—
145Dic37—22no—
146Dic37—41no—
147#3045—371nomaximal, Sylow
148C2×C37—22no—
149C2×C37—82no—
150C2×C37C2×#12111yescharacteristic
151C2×C37#57611yescharacteristic
152C2×C37#57711yescharacteristic
153D37—42no—
154D37—81no—
155C2×AGL(1,ℤ/8)—371no—
156C2×#135—371no—
157#535—371no—
158#520—371no—
159#464—372no—
160#463—372no—
161#460—372no—
162#459—372no—
163#424—371no—
164#417—371no—
165C2×#102D3711yescharacteristic, complemented
166C37#304511yescharacteristic, complemented, Sylow
167C2×#41—371no—
168C2×#41—371no—
169C22×D4C2×D3711yescharacteristic
170AGL(1,ℤ/8)—744no—
171#135—744no—
172C2×Q16—371no—
173C2×SD16—372no—
174C2×SD16—371no—
175C2×SD16—371no—
176C2×D8—372no—
177C2×D8—371no—
178C2×M16—371no—
179C22×C8C2×D3711yescharacteristic
180#127—372no—
181#124—372no—
182#121—741no—
183#121—741no—
184#120—742no—
185C4×Q8—372no—
186C4×D4—372no—
187C4×D4—742no—
188#117—371no—
189#117—741no—
190C2×C4⋊C4—741no—
191C2×C4⋊C4C2×D3711yescharacteristic
192C4⋊C8—372no—
193C4⋊C8—372no—
194#103—372no—
195#102—372no—
196#102C2×D3712yes—
197#102C2×D3712yes—
198C24—21no—
199#41—374no—
200#41—742no—
201#41—742no—
202#41—742no—
203C2×Q8—371no—
204C2×Q8—371no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—371no—
209C2×D4—371no—
210C2×D4—742no—
211C2×D4—742no—
212C2×D4—741no—
213C2×D4—741no—
214C2×D4C22×D3712yes—
215C22×C4—21no—
216C22×C4—742no—
217C22×C4—741no—
218C22×C4—741no—
219C22×C4C22×D3711yescharacteristic
220Q16—742no—
221SD16—742no—
222SD16—742no—
223SD16—744no—
224D8—742no—
225D8—744no—
226M16—742no—
227C2×C8—22no—
228C2×C8—372no—
229C2×C8C22×D3711yescharacteristic
230C2×C8C22×D3711yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—371no—
233C4⋊C4—371no—
234C4⋊C4—742no—
235C4⋊C4C22×D3712yes—
236C22⋊C4—372no—
237C22⋊C4—742no—
238C22⋊C4—742no—
239C22⋊C4—742no—
240C42—372no—
241C42—742no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—741no—
247C23—741no—
248C23D4×D3711yescharacteristic
249Q8—372no—
250Q8—741no—
251Q8—741no—
252Q8—741no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—372no—
257D4—2962no—
258D4—2962no—
259D4—744no—
260D4—741no—
261D4—741no—
262D4—741no—
263D4—1482no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—372no—
267C2×C4—372no—
268C2×C4—2962no—
269C2×C4—741no—
270C2×C4—744no—
271C2×C4—741no—
272C2×C4—1482no—
273C2×C4#1059696212yes—
274C2×C4D4×D3711yescharacteristic
275C2×C4D4×D3712yes—
276C2×C4C23×D3711yescharacteristic
277C8—21no—
278C8—21no—
279C8—742no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—742no—
287C22—1481no—
288C22—1481no—
289C22—1481no—
290C22—1481no—
291C22—1481no—
292C22#1192450912yes—
293C22C2×D4×D3711yescharacteristic
294C4—42no—
295C4—742no—
296C4—742no—
297C4—742no—
298C4—1481no—
299C4#1192450912yes—
300C4C2×D4×D3711yescharacteristic
301C4C2×#1059696211yescharacteristic
302C2—22no—
303C2—82no—
304C2—2961no—
305C2—1482no—
306C2C2×#1192450911yescharacteristic
307C2#1455833411yescharacteristic
308C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC22×C37C22×D4
hypercenterC2×#102D37
hypocenterC37#3045
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×#11924558C2semidirect
3. #14558100C2semidirect
4. #14558014C2semidirect
5. #14557754C2semidirect
6. #14557747C2semidirect
7. #14557732C2semidirect
8. #14557727C2semidirect
9. #14557559C2semidirect
10. #14557532C2semidirect
11. C2×#102×C37C2semidirect
16. C2×Dic148C22semidirect
17. C2×#10596930C22semidirect
18. C2×#10596930C22semidirect
20. C2×D296C22semidirect
28. #11924501C22semidirect
29. #11924498C22semidirect
34. #11924465C22semidirect
35. #11924465C22semidirect
36. #11924459C22semidirect
37. #11924456C22semidirect
57. #10596962D4semidirect
165. C2×#102D37semidirect
166. C37#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245582
#145581002
#145580142
#145577542
#145577472
#145577322
#145577272
#145575592
#145575322
C2×#102×C372
#304537