Finite Group Databasebeta

← #18005066

Subgroups — #18005066

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×#11924567C211yesmaximal, characteristic, complemented
2C2×#11924562C211yesmaximal, characteristic, complemented
3C2×#11924558C211yesmaximal, characteristic, complemented
4#14558107C211yesmaximal, characteristic, complemented
5#14558100C211yesmaximal, characteristic, complemented
6#14557924C212yesmaximal, complemented
7#14557919C212yesmaximal, complemented
8#14557914C212yesmaximal, complemented
9#14557904C212yesmaximal, complemented
10#14557488C211yesmaximal, characteristic, complemented
11C22×SD16×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14#11924567—24no—
15#11924562—24no—
16#11924558—24no—
17C2×Dic148C2211yescharacteristic, complemented
18C2×#10596942C2212yescomplemented
19C2×#10596930C2211yescharacteristic, complemented
20C2×#10596930C2211yescharacteristic, complemented
21C2×#10596940C2212yes—
22C2×#10596941C2212yescomplemented
23C2×D296C2211yescharacteristic, complemented
24C2×#10596939C2212yes—
25C2×#10596934C2211yescharacteristic
26#11924534C2212yescomplemented
27#11924532C2212yes—
28#11924525C2212yescomplemented
29#11924523C2212yes—
30#11924519—22no—
31#11924512—22no—
32#11924507—22no—
33#11924505—22no—
34#11924495C2211yescharacteristic
35#11924446C2212yescomplemented
36C8×Dic37C2212yescomplemented
37C22×Q8×C37C2211yescharacteristic
38C22×D4×C37C2211yescharacteristic
39C2×SD16×C37—24no—
40C2×SD16×C37C2212yes—
41C2×SD16×C37C2212yes—
42C22×C8×C37C2211yescharacteristic
43C24×C37—21no—
44C2×Q8×C37—21no—
45C2×Q8×C37—22no—
46C2×Q8×C37—22no—
47C2×Q8×C37C2312yes—
48C2×D4×C37—22no—
49C2×D4×C37—22no—
50C2×D4×C37—21no—
51C2×D4×C37C2312yes—
52C22×C4×C37—21no—
53C22×C4×C37C2311yescharacteristic
54C2×C22⋊D37—21no—
55C2×C22⋊D37—21no—
56C2×C22⋊D37—24no—
57#10596962—22no—
58#10596962—22no—
59#10596962—22no—
60#10596962—22no—
61C2×D148C2311yescharacteristic
62C2×D148C2311yescharacteristic
63C2×C4×D37—21no—
64C2×C4×D37—21no—
65C2×Dic74C2311yescharacteristic
66C2×Dic74C2311yescharacteristic
67SD16×C37—24no—
68SD16×C37—24no—
69C2×C8×C37D414yescomplemented
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C22⋊Dic37—24no—
73C22⋊Dic37D412yes—
74#10596942—24no—
75#10596941—24no—
76#10596940—24no—
77#10596939—24no—
78#10596938—24no—
79C4⋊Dic37D412yes—
80#10596936—24no—
81C4×Dic37C2312yes—
82#10596934D414yescomplemented
83C2×#64436C2312yes—
84Dic148—22no—
85D296—22no—
86#10596930—22no—
87#10596930—22no—
88C23×C37—22no—
89C23×C37—42no—
90C23×C37—82no—
91C23×C37C2×D411yescharacteristic
92C22×D37—21no—
93C22×D37—21no—
94Q8×C37—22no—
95Q8×C37—22no—
96Q8×C37—42no—
97D4×C37—22no—
98D4×C37—22no—
99D4×C37—42no—
100C2×C4×C37—22no—
101C2×C4×C37—42no—
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37C2×D412yes—
104C2×C4×C37C2×D412yes—
105C2×C4×C37C2411yescharacteristic
106C22⋊D37—42no—
107C22⋊D37—42no—
108C22⋊D37—84no—
109C2×Dic37—21no—
110C2×Dic37—21no—
111C2×Dic37C2×D414yes—
112D148—21no—
113D148—21no—
114D148—21no—
115D148—21no—
116C4×D37—42no—
117C4×D37—42no—
118Dic74—21no—
119Dic74—21no—
120Dic74—21no—
121Dic74—21no—
122C8×C37C2×D412yes—
123C8×C37C2×D412yes—
124#64436C2×D414yes—
125C22×C37—22no—
126C22×C37—42no—
127C22×C37—44no—
128C22×C37—84no—
129C22×C37#12712yes—
130C22×C37C22×D411yescharacteristic
131C2×D37—41no—
132C2×D37—41no—
133C2×D37—42no—
134C2×D37—42no—
135C4×C37—42no—
136C4×C37#12712yes—
137C4×C37C22×D411yescharacteristic
138C4×C37C22×D411yescharacteristic
139Dic37—24no—
140Dic37—41no—
141Dic37—41no—
142#3154—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—82no—
145C2×C37C2×#12711yescharacteristic
146C2×C37#57712yes—
147D37—81no—
148D37—81no—
149C2×#137—371no—
150C2×AGL(1,ℤ/8)—371no—
151C2×#135—371no—
152C22×SD16D3711yescharacteristic, complemented
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×#41—371no—
163C22×Q8C2×D3711yescharacteristic
164C22×D4C2×D3711yescharacteristic
165#137—744no—
166AGL(1,ℤ/8)—744no—
167#135—744no—
168C2×Q16—372no—
169C2×Q16—371no—
170C2×SD16—24no—
171C2×SD16—372no—
172C2×SD16—372no—
173C2×SD16—371no—
174C2×SD16—371no—
175C2×SD16C2×D3712yes—
176C2×SD16C2×D3712yes—
177C2×D8—372no—
178C2×D8—371no—
179C2×M16—371no—
180C22×C8C2×D3711yescharacteristic
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—21no—
193#41—742no—
194#41—742no—
195#41—742no—
196#41—742no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—371no—
201C2×Q8—371no—
202C2×Q8C22×D3712yes—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—371no—
207C2×D4—371no—
208C2×D4—744no—
209C2×D4—741no—
210C2×D4—741no—
211C2×D4C22×D3712yes—
212C22×C4—21no—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4C22×D3711yescharacteristic
216Q16—744no—
217Q16—742no—
218SD16—24no—
219SD16—24no—
220SD16—744no—
221SD16—744no—
222SD16—742no—
223SD16—742no—
224D8—744no—
225D8—742no—
226M16—374no—
227C2×C8—372no—
228C2×C8C22⋊D3714yescomplemented
229C2×C8C22×D3711yescharacteristic
230C2×C8C22×D3711yescharacteristic
231C4⋊C4—372no—
232C4⋊C4—744no—
233C22⋊C4—372no—
234C22⋊C4—744no—
235C22⋊C4—744no—
236C42—372no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—741no—
241C23—741no—
242C23D4×D3711yescharacteristic
243Q8—22no—
244Q8—22no—
245Q8—42no—
246Q8—741no—
247Q8—741no—
248Q8—741no—
249Q8—741no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—2964no—
254D4—741no—
255D4—741no—
256D4—741no—
257D4—741no—
258D4—1482no—
259D4—1482no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—374no—
263C2×C4—741no—
264C2×C4—741no—
265C2×C4—1482no—
266C2×C4—1482no—
267C2×C4D4×D3711yescharacteristic
268C2×C4D4×D3712yes—
269C2×C4C2×C22⋊D3712yes—
270C2×C4C23×D3711yescharacteristic
271C8—374no—
272C8C2×C22⋊D3712yes—
273C8C2×C22⋊D3712yes—
274C22—22no—
275C22—42no—
276C22—44no—
277C22—84no—
278C22—1481no—
279C22—1481no—
280C22—1482no—
281C22—1482no—
282C22#1192453212yes—
283C22C2×D4×D3711yescharacteristic
284C4—42no—
285C4—744no—
286C4—1481no—
287C4—1481no—
288C4#1192453212yes—
289C4C2×D4×D3711yescharacteristic
290C4C22×C22⋊D3711yescharacteristic
291C2—22no—
292C2—82no—
293C2—2961no—
294C2—2961no—
295C2C2×#1192453211yescharacteristic
296C2#1455833912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×SD16×C37C2
socleC22×C37C22×D4
hypercenterC22×SD16D37
hypocenterC37#3154
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
2. C2×#11924562C2semidirect
3. C2×#11924558C2semidirect
4. #14558107C2semidirect
5. #14558100C2semidirect
6. #14557924C2semidirect
7. #14557919C2semidirect
8. #14557914C2semidirect
9. #14557904C2semidirect
10. #14557488C2semidirect
11. C22×SD16×C37C2semidirect
17. C2×Dic148C22semidirect
18. C2×#10596942C22semidirect
19. C2×#10596930C22semidirect
20. C2×#10596930C22semidirect
22. C2×#10596941C22semidirect
23. C2×D296C22semidirect
26. #11924534C22semidirect
28. #11924525C22semidirect
35. #11924446C22semidirect
36. C8×Dic37C22semidirect
69. C2×C8×C37D4semidirect
82. #10596934D4semidirect
152. C22×SD16D37semidirect
160. C37#3154semidirect
228. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C2×#119245622
C2×#119245582
#145581072
#145581002
#145579242
#145579192
#145579142
#145579042
#145574882
C22×SD16×C372
#315437