Finite Group Databasebeta

← #18005045

Subgroups — #18005045

Order 4736.

656 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924563C212yesmaximal, complemented
2C2×#11924560C212yesmaximal, complemented
3#14558082C211yesmaximal, characteristic, complemented
4#127×D37C211yesmaximal, characteristic, complemented
5#14557923C211yesmaximal, characteristic, complemented
6#14557922C211yesmaximal, characteristic, complemented
7#14557920C211yesmaximal, characteristic, complemented
8#14557908C212yesmaximal, complemented
9#14557904C212yesmaximal, complemented
10#14557485C211yesmaximal, characteristic, complemented
11C37×#496C211yesmaximal, characteristic, complemented
12C2×#10596966C2211yescharacteristic
13C2×#10596964C2211yescharacteristic
14C2×D4×D37—22no—
15C2×D4×D37C2212yes—
16#11924563—28no—
17#11924560—28no—
18C2×#10596930C2212yescomplemented
19C2×#10596940C2212yescomplemented
20C2×#10596941C2212yescomplemented
21C2×D296C2212yescomplemented
22C2×#10596939C2212yescomplemented
23C2×#10596939C2212yescomplemented
24C2×#10596929C2212yes—
25#11924534C2211yescharacteristic, complemented
26#11924533C2211yescharacteristic
27#11924532—22no—
28#11924532C2212yes—
29#11924532C2211yescharacteristic, complemented
30#11924524C2211yescharacteristic, complemented
31#11924509—22no—
32#11924496—22no—
33C42×D37C2211yescharacteristic
34#11924447C2211yescharacteristic, complemented
35C8×Dic37C2212yescomplemented
36C2×SD16×C37C2212yescomplemented
37C2×D8×C37C2212yescomplemented
38#127×C37C2211yescharacteristic
39#124×C37C2211yescharacteristic, complemented
40#97×C37C2211yescharacteristic, complemented
41C23×D37—22no—
42C2×Q8×C37C2311yescharacteristic
43C2×D4×C37—22no—
44C2×D4×C37C2312yes—
45C2×D4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C2×C22⋊D37—22no—
48C2×C22⋊D37—22no—
49C2×C22⋊D37—24no—
50C22×Dic37—21no—
51#10596966—24no—
52#10596964—24no—
53D4×D37—24no—
54D4×D37—24no—
55D4×D37—48no—
56C2×D148—21no—
57C2×D148—22no—
58C2×D148C2311yescharacteristic
59C2×D148C2312yes—
60C2×C4×D37—21no—
61C2×C4×D37D412yes—
62C2×C4×D37C2311yescharacteristic
63C2×Dic74C2311yescharacteristic
64SD16×C37—24no—
65D8×C37—24no—
66C2×C8×C37C2312yes—
67C22⋊C4×C37—22no—
68C42×C37C2311yescharacteristic
69#10596941—24no—
70#10596940—24no—
71#10596939—24no—
72#10596939—24no—
73#10596938—22no—
74#10596936—22no—
75C4×Dic37D412yes—
76C4×Dic37C2311yescharacteristic
77C2×#64436C2312yes—
78D296—24no—
79#10596930—24no—
80#10596929D418yescomplemented
81C23×C37—21no—
82C23×C37—22no—
83C22×D37—21no—
84C22×D37—22no—
85C22×D37—48no—
86C22×D37—44no—
87C22×D37C2×D411yescharacteristic
88Q8×C37—22no—
89D4×C37—22no—
90D4×C37—22no—
91D4×C37—22no—
92D4×C37—44no—
93C2×C4×C37—21no—
94C2×C4×C37C2×D412yes—
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—42no—
97C22⋊D37—44no—
98C22⋊D37—48no—
99C22⋊D37—44no—
100C2×Dic37—21no—
101C2×Dic37—42no—
102C2×Dic37C2×D411yescharacteristic
103C2×Dic37C2×D412yes—
104D148—22no—
105D148—22no—
106D148—22no—
107D148—44no—
108D148—42no—
109C4×D37—24no—
110C4×D37—42no—
111C4×D37C2×D414yes—
112Dic74—22no—
113C8×C37C2×D414yescomplemented
114#64436C2×D414yescomplemented
115C22×C37—41no—
116C22×C37—42no—
117C22×C37—44no—
118C22×C37—42no—
119C22×C37C22×D411yescharacteristic
120C2×D37—22no—
121C2×D37—41no—
122C2×D37—42no—
123C2×D37—44no—
124C2×D37—42no—
125C2×D37—88no—
126C2×D37#12712yes—
127C4×C37—22no—
128C4×C37—41no—
129C4×C37C22×D412yes—
130Dic37—41no—
131Dic37#12712yes—
132Dic37AGL(1,ℤ/8)14yescomplemented
133#3151—371nomaximal, Sylow
134C2×C37—82no—
135C2×C37—81no—
136C2×C37C2×#12711yescharacteristic
137C2×C37C2×AGL(1,ℤ/8)12yes—
138D37—22no—
139D37—81no—
140D37—82no—
141C2×AGL(1,ℤ/8)—372no—
142C2×AGL(1,ℤ/8)—372no—
143#532—371no—
144C2×#127—371no—
145#496—371no—
146#496—371no—
147#496—371no—
148#496D3711yescharacteristic, complemented
149#493—372no—
150#492—372no—
151C4×M16—371no—
152C37#315111yescharacteristic, complemented, Sylow
153C2×#41—371no—
154C2×#41—371no—
155C22×D4—372no—
156C22×D4—742no—
157AGL(1,ℤ/8)—748no—
158AGL(1,ℤ/8)—748no—
159C2×SD16—372no—
160C2×SD16—372no—
161C2×SD16—372no—
162C2×SD16C2×D3712yescomplemented
163C2×D8—372no—
164C2×D8—372no—
165C2×D8—372no—
166C2×D8C2×D3712yescomplemented
167C2×M16—372no—
168C4⋊Q8—371no—
169#127—372no—
170#127—371no—
171#127—371no—
172#127—742no—
173#127C2×D3711yescharacteristic
174#124—371no—
175#124C2×D3711yescharacteristic, complemented
176#121—742no—
177C4×D4—742no—
178C2×C42—371no—
179#97—371no—
180#97C2×D3711yescharacteristic, complemented
181C4×C8—372no—
182C24—742no—
183#41—744no—
184#41—744no—
185C2×Q8—371no—
186C2×Q8C22×D3711yescharacteristic
187C2×D4—22no—
188C2×D4—371no—
189C2×D4—372no—
190C2×D4—741no—
191C2×D4—744no—
192C2×D4—744no—
193C2×D4—742no—
194C2×D4—744no—
195C2×D4—742no—
196C2×D4—741no—
197C2×D4—742no—
198C2×D4—1488no—
199C2×D4C22×D3711yescharacteristic
200C2×D4C22×D3712yes—
201C22×C4—371no—
202C22×C4—372no—
203C22×C4—741no—
204C22×C4—741no—
205SD16—24no—
206SD16—744no—
207SD16—744no—
208SD16—744no—
209D8—24no—
210D8—744no—
211D8—744no—
212D8—744no—
213M16—378no—
214C2×C8—372no—
215C2×C8C22×D3712yes—
216C4⋊C4—742no—
217C22⋊C4—22no—
218C22⋊C4—742no—
219C42—372no—
220C42—371no—
221C42C22×D3711yescharacteristic
222C23—21no—
223C23—22no—
224C23—371no—
225C23—741no—
226C23—742no—
227C23—1484no—
228C23—1488no—
229Q8—22no—
230Q8—742no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—742no—
236D4—742no—
237D4—742no—
238D4—1484no—
239D4—1482no—
240D4—1484no—
241D4—1488no—
242D4—1484no—
243D4—1482no—
244C2×C4—21no—
245C2×C4—372no—
246C2×C4—371no—
247C2×C4—374no—
248C2×C4—744no—
249C2×C4—741no—
250C2×C4—1482no—
251C2×C4—1482no—
252C2×C4D4×D3712yes—
253C2×C4C23×D3711yescharacteristic
254C8—374no—
255C8D4×D3714yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—372no—
261C22—2968no—
262C22—742no—
263C22—1484no—
264C22—1482no—
265C22—1481no—
266C22—1482no—
267C22C2×D4×D3711yescharacteristic
268C4—22no—
269C4—41no—
270C4—374no—
271C4—372no—
272C4—1481no—
273C4C2×D4×D3712yes—
274C2—82no—
275C2—81no—
276C2—2962no—
277C2—2961no—
278C2—742no—
279C2#127×D3711yescharacteristic
280C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC22×C37C22×D4
hypercenter#496D37
hypocenterC37#3151
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C2×#11924560C2semidirect
3. #14558082C2semidirect
4. #127×D37C2semidirect
5. #14557923C2semidirect
6. #14557922C2semidirect
7. #14557920C2semidirect
8. #14557908C2semidirect
9. #14557904C2semidirect
10. #14557485C2semidirect
11. C37×#496C2semidirect
18. C2×#10596930C22semidirect
19. C2×#10596940C22semidirect
20. C2×#10596941C22semidirect
21. C2×D296C22semidirect
22. C2×#10596939C22semidirect
23. C2×#10596939C22semidirect
25. #11924534C22semidirect
29. #11924532C22semidirect
30. #11924524C22semidirect
34. #11924447C22semidirect
35. C8×Dic37C22semidirect
36. C2×SD16×C37C22semidirect
37. C2×D8×C37C22semidirect
39. #124×C37C22semidirect
40. #97×C37C22semidirect
80. #10596929D4semidirect
113. C8×C37C2×D4semidirect
114. #64436C2×D4semidirect
132. Dic37AGL(1,ℤ/8)semidirect
148. #496D37semidirect
152. C37#3151semidirect
162. C2×SD16C2×D37semidirect
166. C2×D8C2×D37semidirect
175. #124C2×D37semidirect
180. #97C2×D37semidirect
255. C8D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×#119245602
#145580822
#127×D372
#145579232
#145579222
#145579202
#145579082
#145579042
#145574852
C37×#4962
#315137