Finite Group Databasebeta

← #18006410

Subgroups — #18006410

Order 4736.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
1#14558187C211yesmaximal, characteristic, complemented
2D4×D148C211yesmaximal, characteristic, complemented
3#14557880C211yesmaximal, characteristic, complemented
4#14557847C212yesmaximal, complemented
5#14557814C211yesmaximal, characteristic, complemented
6#14557769C212yesmaximal, complemented
7#14557729C211yesmaximal, characteristic, complemented
8#14557669C212yesmaximal, complemented
9C4×D296C211yesmaximal, characteristic, complemented
10C2×#11924458C212yesmaximal, complemented
11C8×D4×C37C211yesmaximal, characteristic, complemented
12C2×#10596964—21no—
13C22×D148C2212yes—
14C2×D4×D37—21no—
15C2×D296C2211yescharacteristic
16C2×D296C2212yescomplemented
17#11924536C2211yescharacteristic, complemented
18#11924533C2211yescharacteristic
19#11924520—22no—
20#11924516—21no—
21#11924511—21no—
22#11924510C2212yes—
23#11924510C2212yescomplemented
24#11924506—22no—
25C4×D148C2211yescharacteristic
26C4×D148C2211yescharacteristic, complemented
27C2×C4⋊Dic37C2212yescomplemented
28#11924470C2212yescomplemented
29#11924470C2211yescharacteristic, complemented
30#11924458C2211yescharacteristic
31#11924458C2212yes—
32#11924458C2212yescomplemented
33#11924458C2211yescharacteristic, complemented
34#11924458C2212yescomplemented
35#11924458C2212yescomplemented
36C22×C8×C37C2212yescomplemented
37C4×D4×C37C2211yescharacteristic
38C4⋊C8×C37C2211yescharacteristic, complemented
39C22⋊C8×C37C2212yescomplemented
40C4×C8×C37C2211yescharacteristic, complemented
41C23×D37—22no—
42C2×D4×C37D411yescharacteristic
43C22×C4×C37C2312yes—
44C2×C22⋊D37—22no—
45C2×C22⋊D37—22no—
46C22×Dic37—22no—
47#10596964—44no—
48D4×D37—44no—
49C2×D148—24no—
50C2×D148—22no—
51C2×D148—21no—
52C2×D148—21no—
53C2×D148—42no—
54C2×D148C2311yescharacteristic
55C2×D148C2312yes—
56C2×D148C2311yescharacteristic
57C2×C4×D37—21no—
58C2×C4×D37—21no—
59C2×Dic74—21no—
60C2×C8×C37—42no—
61C2×C8×C37C2311yescharacteristic
62C2×C8×C37C2312yes—
63C2×C8×C37C2311yescharacteristic
64C4⋊C4×C37D411yescharacteristic
65C22⋊C4×C37D412yes—
66C42×C37C2311yescharacteristic
67#10596938—21no—
68#10596938—21no—
69#10596938—22no—
70#10596938—22no—
71C4⋊Dic37—22no—
72C4⋊Dic37—21no—
73C4⋊Dic37C2311yescharacteristic
74C4⋊Dic37C2312yes—
75C4⋊Dic37C2311yescharacteristic
76D296—22no—
77D296—42no—
78C23×C37C2×D412yes—
79C22×D37—21no—
80C22×D37—21no—
81C22×D37—22no—
82C22×D37—44no—
83C22×D37—44no—
84C22×D37—82no—
85D4×C37D814yescomplemented
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D412yes—
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2411yescharacteristic
92C22⋊D37—44no—
93C22⋊D37—44no—
94C2×Dic37—22no—
95C2×Dic37—21no—
96C2×Dic37—21no—
97C2×Dic37—44no—
98D148—21no—
99D148—22no—
100D148—21no—
101D148—21no—
102D148—22no—
103D148—44no—
104D148—42no—
105D148—81no—
106D148#4112yescomplemented
107C4×D37—42no—
108C4×D37—42no—
109Dic74—42no—
110C8×C37—21no—
111C8×C37—22no—
112C8×C37—21no—
113C22×C37—22no—
114C22×C37—22no—
115C22×C37C2×D814yes—
116C22×C37C22×D411yescharacteristic
117C2×D37—22no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—42no—
121C2×D37—41no—
122C2×D37—41no—
123C2×D37—42no—
124C2×D37—42no—
125C2×D37—41no—
126C2×D37—88no—
127C4×C37—22no—
128C4×C37—21no—
129C4×C37C2×D812yes—
130C4×C37C2×#4111yescharacteristic
131C4×C37H(5,𝔽2)11yescharacteristic
132Dic37—42no—
133Dic37—41no—
134Dic37—41no—
135#3294—371nomaximal, Sylow
136C2×C37—24no—
137C2×C37#54611yescharacteristic
138C2×C37C22×D811yescharacteristic
139C2×C37#57711yescharacteristic
140D37—42no—
141D37—81no—
142D37—82no—
143#547—371no—
144D42—371no—
145#486—371no—
146#480—372no—
147#474—371no—
148#466—372no—
149#459—371no—
150#447—372no—
151C4×D8—371no—
152C8×D4D3711yescharacteristic, complemented
153C2×#102—372no—
154C37#329411yescharacteristic, complemented, Sylow
155C2×#41—741no—
156C22×D4—372no—
157C22×D4—741no—
158C2×D8—371no—
159C2×D8—372no—
160C22×C8C2×D3712yescomplemented
161C4⋊Q8—371no—
162#127—371no—
163#123—742no—
164C22⋊Q8—741no—
165#121—372no—
166#121—372no—
167#121—741no—
168#120—742no—
169C4×D4—371no—
170C4×D4—371no—
171C4×D4C2×D3711yescharacteristic
172C2×C4⋊C4—372no—
173#107—371no—
174#107—372no—
175C4⋊C8C2×D3711yescharacteristic, complemented
176#102—371no—
177#102—372no—
178#102—372no—
179#102—372no—
180#102—371no—
181#102—372no—
182C22⋊C8C2×D3712yescomplemented
183C4×C8C2×D3711yescharacteristic, complemented
184C24—742no—
185#41—1484no—
186C2×Q8—741no—
187C2×D4—371no—
188C2×D4—372no—
189C2×D4—371no—
190C2×D4—744no—
191C2×D4—742no—
192C2×D4—742no—
193C2×D4—741no—
194C2×D4—742no—
195C2×D4—741no—
196C2×D4—1482no—
197C2×D4—1484no—
198C2×D4D14811yescharacteristic
199C22×C4—742no—
200C22×C4—741no—
201C22×C4—741no—
202C22×C4C22×D3712yes—
203D8—742no—
204D8—1482no—
205C2×C8—42no—
206C2×C8C22×D3711yescharacteristic
207C2×C8C22×D3711yescharacteristic
208C2×C8C22×D3712yes—
209C4⋊C4—371no—
210C4⋊C4—372no—
211C4⋊C4—371no—
212C4⋊C4—742no—
213C4⋊C4—741no—
214C4⋊C4D14811yescharacteristic
215C22⋊C4—741no—
216C22⋊C4—741no—
217C22⋊C4—742no—
218C22⋊C4—742no—
219C22⋊C4D14812yes—
220C42C22×D3711yescharacteristic
221C23—2962no—
222C23—741no—
223C23—741no—
224C23—742no—
225C23—1484no—
226C23—1484no—
227C23C2×D14812yes—
228Q8—1482no—
229D4—372no—
230D4—2961no—
231D4—741no—
232D4—742no—
233D4—741no—
234D4—741no—
235D4—742no—
236D4—1484no—
237D4—1484no—
238D4—1484no—
239D4—1482no—
240D4D29614yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—741no—
244C2×C4—741no—
245C2×C4—742no—
246C2×C4—1484no—
247C2×C4—1482no—
248C2×C4—1482no—
249C2×C4C2×D14811yescharacteristic
250C2×C4C2×D14812yes—
251C2×C4C2×D14811yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—2968no—
259C22—742no—
260C22—1481no—
261C22—1482no—
262C22—1482no—
263C22—1481no—
264C22—1482no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22C2×D29614yes—
269C22C22×D14811yescharacteristic
270C4—21no—
271C4—22no—
272C4—1481no—
273C4—1481no—
274C4—1482no—
275C4C2×D29612yes—
276C4#41×D3711yescharacteristic
277C4#1192458111yescharacteristic
278C2—24no—
279C2—2962no—
280C2—2961no—
281C2—1482no—
282C2#1455817811yescharacteristic
283C2C22×D29611yescharacteristic
284C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC8×D4×C37C2
socleC22×C37C22×D4
hypercenterC8×D4D37
hypocenterC37#3294
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14558187C2semidirect
2. D4×D148C2semidirect
3. #14557880C2semidirect
4. #14557847C2semidirect
5. #14557814C2semidirect
6. #14557769C2semidirect
7. #14557729C2semidirect
8. #14557669C2semidirect
9. C4×D296C2semidirect
10. C2×#11924458C2semidirect
11. C8×D4×C37C2semidirect
16. C2×D296C22semidirect
17. #11924536C22semidirect
23. #11924510C22semidirect
26. C4×D148C22semidirect
27. C2×C4⋊Dic37C22semidirect
28. #11924470C22semidirect
29. #11924470C22semidirect
32. #11924458C22semidirect
33. #11924458C22semidirect
34. #11924458C22semidirect
35. #11924458C22semidirect
36. C22×C8×C37C22semidirect
38. C4⋊C8×C37C22semidirect
39. C22⋊C8×C37C22semidirect
40. C4×C8×C37C22semidirect
85. D4×C37D8semidirect
106. D148#41semidirect
152. C8×D4D37semidirect
154. C37#3294semidirect
160. C22×C8C2×D37semidirect
175. C4⋊C8C2×D37semidirect
182. C22⋊C8C2×D37semidirect
183. C4×C8C2×D37semidirect
240. D4D296semidirect

Maximal subgroups

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

subgroupindex
#145581872
D4×D1482
#145578802
#145578472
#145578142
#145577692
#145577292
#145576692
C4×D2962
C2×#119244582
C8×D4×C372
#329437