Finite Group Databasebeta

← #18005075

Subgroups — #18005075

Order 4736.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#11924556C211yesmaximal, characteristic, complemented
3C22×#10596941C211yesmaximal, characteristic, complemented
4#14558107C211yesmaximal, characteristic, complemented
5#14558097C211yesmaximal, characteristic, complemented
6#14557926C212yesmaximal, complemented
7#14557919C212yesmaximal, complemented
8#14557918C212yesmaximal, complemented
9#14557904C212yesmaximal, complemented
10#14557491C211yesmaximal, characteristic, complemented
11C2×#137×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×D148C2211yescharacteristic
14#11924564—24no—
15#11924556—24no—
16C2×#10596942C2211yescharacteristic, complemented
17C2×#10596930C2212yes—
18C2×#10596940C2211yescharacteristic, complemented
19C2×#10596941—24no—
20C2×#10596941C2212yes—
21C2×#10596941C2212yes—
22C2×#10596941C2211yescharacteristic, complemented
23C2×D296C2212yes—
24C2×#10596939C2211yescharacteristic, complemented
25C22×#64436C2211yescharacteristic
26#11924534C2212yescomplemented
27#11924532C2212yes—
28#11924525C2212yes—
29#11924525C2212yescomplemented
30#11924519—22no—
31#11924512—22no—
32#11924510—22no—
33#11924504—22no—
34#11924495C2211yescharacteristic
35#11924446C2212yescomplemented
36C8×Dic37C2212yescomplemented
37C2×#41×C37C2211yescharacteristic
38C22×Q8×C37C2211yescharacteristic
39#137×C37—24no—
40C2×Q16×C37C2212yescomplemented
41C2×SD16×C37C2212yescomplemented
42C2×M16×C37C2211yescharacteristic
43C23×D37—21no—
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37—21no—
47C2×Q8×C37—22no—
48C2×Q8×C37—22no—
49C2×Q8×C37C2311yescharacteristic
50C2×Q8×C37C2312yes—
51C2×D4×C37—21no—
52C2×D4×C37C2311yescharacteristic
53C22×C4×C37—21no—
54C22×C4×C37—21no—
55C22×C4×C37C2311yescharacteristic
56C2×C22⋊D37—21no—
57C2×C22⋊D37—24no—
58#10596962—22no—
59#10596962—22no—
60C2×D148—22no—
61C2×D148—22no—
62C2×D148—21no—
63C2×D148C2312yes—
64C2×D148C2311yescharacteristic
65C2×C4×D37—21no—
66C2×Dic74C2311yescharacteristic
67Q16×C37—24no—
68SD16×C37—24no—
69M16×C37D414yescomplemented
70C2×C8×C37C2312yes—
71C22⋊Dic37D412yes—
72#10596942—22no—
73#10596941—24no—
74#10596941—24no—
75#10596941—22no—
76#10596940—22no—
77#10596939—22no—
78#10596938—24no—
79#10596938—24no—
80C4⋊Dic37D412yes—
81#10596936—24no—
82C4×Dic37C2312yes—
83C2×#64436D414yescomplemented
84C2×#64436C2311yescharacteristic
85C2×#64436C2311yescharacteristic
86D296—24no—
87#10596930—24no—
88C23×C37—21no—
89C23×C37C2×D411yescharacteristic
90C22×D37—21no—
91C22×D37—22no—
92C22×D37—42no—
93C22×D37—82no—
94Q8×C37—22no—
95Q8×C37—21no—
96Q8×C37—22no—
97Q8×C37—21no—
98Q8×C37—42no—
99D4×C37—21no—
100D4×C37—21no—
101D4×C37—42no—
102C2×C4×C37—22no—
103C2×C4×C37—21no—
104C2×C4×C37—42no—
105C2×C4×C37—42no—
106C2×C4×C37C2×D411yescharacteristic
107C2×C4×C37C2×D412yes—
108C2×C4×C37C2×D412yes—
109C2×C4×C37C2411yescharacteristic
110C22⋊D37—42no—
111C22⋊D37—84no—
112C2×Dic37—21no—
113C2×Dic37C2×D414yes—
114D148—22no—
115D148—21no—
116D148—21no—
117D148—22no—
118D148—42no—
119C4×D37—42no—
120Dic74—21no—
121Dic74—21no—
122C8×C37C2×D414yes—
123#64436C2×D412yes—
124#64436C2×D412yes—
125C22×C37—22no—
126C22×C37—41no—
127C22×C37—42no—
128C22×C37#12712yes—
129C22×C37C22×D411yescharacteristic
130C2×D37—41no—
131C2×D37—42no—
132C2×D37—44no—
133C2×D37—42no—
134C2×D37—84no—
135C4×C37—41no—
136C4×C37—42no—
137C4×C37#12712yes—
138C4×C37C22×D411yescharacteristic
139C4×C37C22×D411yescharacteristic
140Dic37—24no—
141Dic37—41no—
142#3154—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—81no—
145C2×C37C2×#12711yescharacteristic
146C2×C37#57712yes—
147D37—81no—
148D37—82no—
149C2×#137D3711yescharacteristic, complemented
150C2×AGL(1,ℤ/8)—371no—
151C2×#135—371no—
152C22×SD16—371no—
153#536—371no—
154#535—371no—
155#497—372no—
156#496—372no—
157#495—372no—
158#492—372no—
159#405—371no—
160C37#315411yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41C2×D3711yescharacteristic
163C22×Q8C2×D3711yescharacteristic
164C22×D4—371no—
165#137—24no—
166AGL(1,ℤ/8)—744no—
167#135—744no—
168C2×Q16—371no—
169C2×Q16C2×D3712yescomplemented
170C2×SD16—372no—
171C2×SD16—372no—
172C2×SD16—371no—
173C2×SD16—371no—
174C2×SD16—372no—
175C2×SD16—744no—
176C2×SD16C2×D3712yescomplemented
177C2×D8—371no—
178C2×D8—372no—
179C2×M16C2×D3711yescharacteristic
180C22×C8—371no—
181C4⋊Q8—372no—
182#127—372no—
183#124—372no—
184#124—372no—
185#123—742no—
186C22⋊Q8—742no—
187#121—742no—
188#120—742no—
189#117—371no—
190#97—372no—
191C4×C8—372no—
192C24—741no—
193#41—22no—
194#41—22no—
195#41—742no—
196#41—742no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—371no—
201C2×Q8C22×D3711yescharacteristic
202C2×Q8C22×D3712yes—
203C2×D4—21no—
204C2×D4—371no—
205C2×D4—372no—
206C2×D4—744no—
207C2×D4—741no—
208C2×D4—742no—
209C2×D4—741no—
210C2×D4—742no—
211C2×D4C22×D3711yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—741no—
215C22×C4C22×D3711yescharacteristic
216Q16—24no—
217Q16—742no—
218SD16—24no—
219SD16—742no—
220SD16—744no—
221SD16—744no—
222SD16—742no—
223SD16—744no—
224D8—742no—
225D8—744no—
226M16C22⋊D3714yescomplemented
227C2×C8—374no—
228C2×C8—371no—
229C2×C8—371no—
230C2×C8C22×D3712yes—
231C4⋊C4—372no—
232C4⋊C4—744no—
233C22⋊C4—372no—
234C22⋊C4—744no—
235C22⋊C4—744no—
236C42—372no—
237C23—21no—
238C23—2962no—
239C23—741no—
240C23—742no—
241C23—1482no—
242C23D4×D3711yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—741no—
249Q8—741no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—2964no—
254D4—741no—
255D4—742no—
256D4—741no—
257D4—742no—
258D4—1482no—
259D4—1482no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—374no—
265C2×C4—741no—
266C2×C4—1482no—
267C2×C4D4×D3711yescharacteristic
268C2×C4D4×D3712yes—
269C2×C4C2×C22⋊D3712yes—
270C2×C4C23×D3711yescharacteristic
271C8—372no—
272C8—372no—
273C8C2×C22⋊D3714yes—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—2964no—
278C22—1481no—
279C22—1482no—
280C22—1484no—
281C22—1482no—
282C22#1192453212yes—
283C22C2×D4×D3711yescharacteristic
284C4—41no—
285C4—42no—
286C4—744no—
287C4—1481no—
288C4#1192453212yes—
289C4C2×D4×D3711yescharacteristic
290C4C22×C22⋊D3711yescharacteristic
291C2—22no—
292C2—81no—
293C2—2962no—
294C2—2961no—
295C2C2×#1192453211yescharacteristic
296C2#1455834212yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#137×C37C2
socleC22×C37C22×D4
hypercenterC2×#137D37
hypocenterC37#3154
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924556C2semidirect
3. C22×#10596941C2semidirect
4. #14558107C2semidirect
5. #14558097C2semidirect
6. #14557926C2semidirect
7. #14557919C2semidirect
8. #14557918C2semidirect
9. #14557904C2semidirect
10. #14557491C2semidirect
11. C2×#137×C37C2semidirect
16. C2×#10596942C22semidirect
18. C2×#10596940C22semidirect
22. C2×#10596941C22semidirect
24. C2×#10596939C22semidirect
26. #11924534C22semidirect
29. #11924525C22semidirect
35. #11924446C22semidirect
36. C8×Dic37C22semidirect
40. C2×Q16×C37C22semidirect
41. C2×SD16×C37C22semidirect
69. M16×C37D4semidirect
83. C2×#64436D4semidirect
149. C2×#137D37semidirect
160. C37#3154semidirect
169. C2×Q16C2×D37semidirect
176. C2×SD16C2×D37semidirect
226. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245562
C22×#105969412
#145581072
#145580972
#145579262
#145579192
#145579182
#145579042
#145574912
C2×#137×C372
#315437