Finite Group Databasebeta

← #18006327

Subgroups — #18006327

Order 4736.

494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 494 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×#11924557C212yesmaximal, complemented
2#14558205C211yesmaximal, characteristic, complemented
3#14558187C211yesmaximal, characteristic, complemented
4#14557906C211yesmaximal, characteristic, complemented
5#14557763C212yesmaximal, complemented
6#14557743C211yesmaximal, characteristic, complemented
7#14557728C211yesmaximal, characteristic, complemented
8#14557698C212yesmaximal, complemented
9#14557679C212yesmaximal, complemented
10C8×D148C211yesmaximal, characteristic, complemented
11C4×SD16×C37C211yesmaximal, characteristic, complemented
12C2×#10596966C2212yes—
13C2×#10596964C2212yes—
14#11924557—28no—
15C2×#10596942C2212yes—
16C2×#10596930C2212yes—
17C2×#10596930C2212yes—
18C2×#10596939C2212yes—
19C2×C8×D37C2212yes—
20#11924536C2211yescharacteristic
21#11924533—21no—
22#11924533C2211yescharacteristic
23#11924520—22no—
24#11924516C2212yes—
25#11924511—22no—
26#11924511C2212yes—
27#11924510—21no—
28C4×D148—21no—
29C4×D148C2211yescharacteristic
30C2×C4⋊Dic37—21no—
31C4⋊#64436C2211yescharacteristic
32#11924459C2212yes—
33#11924456C2212yes—
34#11924448C2212yes—
35C2×SD16×C37C2211yescharacteristic
36C4×Q8×C37C2211yescharacteristic
37C4×D4×C37C2211yescharacteristic
38#106×C37C2211yescharacteristic
39#103×C37C2211yescharacteristic
40#102×C37C2211yescharacteristic
41C4×C8×C37C2211yescharacteristic
42C2×Q8×C37C2311yescharacteristic
43C2×D4×C37C2311yescharacteristic
44C22×C4×C37—21no—
45C2×C22⋊D37—22no—
46C22×Dic37—22no—
47#10596966—24no—
48#10596966—42no—
49#10596964—24no—
50#10596964—42no—
51C2×D148—22no—
52C2×D148—21no—
53C2×D148—22no—
54C2×D148—21no—
55C2×D148D411yescharacteristic
56C2×D148C2312yes—
57C2×C4×D37—22no—
58C2×C4×D37C2312yes—
59C2×Dic74C2312yes—
60SD16×C37D414yescomplemented
61C2×C8×C37C2311yescharacteristic
62C2×C8×C37C2311yescharacteristic
63C4⋊C4×C37—21no—
64C4⋊C4×C37C2311yescharacteristic
65C4⋊C4×C37C2311yescharacteristic
66C22⋊C4×C37—21no—
67C42×C37—21no—
68C42×C37C2311yescharacteristic
69#10596942—24no—
70#10596939—24no—
71#10596938—22no—
72#10596938—22no—
73#10596938D412yes—
74C4⋊Dic37—21no—
75C4⋊Dic37—21no—
76C4⋊Dic37—22no—
77C4⋊Dic37D411yescharacteristic
78C2×#64436C2312yes—
79#10596930—24no—
80#10596930—42no—
81C8×D37—24no—
82C23×C37—21no—
83C22×D37—22no—
84C22×D37C2×D412yes—
85Q8×C37—21no—
86Q8×C37C2×D412yes—
87D4×C37—21no—
88D4×C37C2×D412yes—
89C2×C4×C37—21no—
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37—42no—
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2411yescharacteristic
96C22⋊D37—44no—
97C2×Dic37—22no—
98C2×Dic37—44no—
99C2×Dic37C2×D412yes—
100D148—22no—
101D148—22no—
102D148—22no—
103D148—44no—
104D148—42no—
105D148—81no—
106D148—82no—
107C4×D37—22no—
108C4×D37—22no—
109C4×D37—44no—
110Dic74—22no—
111Dic74—22no—
112C8×C37—21no—
113C8×C37C2×D412yes—
114#64436—22no—
115C22×C37—22no—
116C22×C37—41no—
117C22×C37—41no—
118C22×C37C22×D411yescharacteristic
119C2×D37—22no—
120C2×D37—22no—
121C2×D37—22no—
122C2×D37—42no—
123C2×D37—42no—
124C2×D37—42no—
125C4×C37—22no—
126C4×C37—21no—
127C4×C37—41no—
128C4×C37—41no—
129C4×C37#13512yescomplemented
130C4×C37C22×D411yescharacteristic
131C4×C37H(5,𝔽2)11yescharacteristic
132Dic37—22no—
133Dic37—42no—
134#3284—371nomaximal, Sylow
135C2×C37—42no—
136C2×C37D4211yescharacteristic
137C2×C37C2×#13511yescharacteristic
138C2×C37#57711yescharacteristic
139D37—42no—
140D37—82no—
141C2×#135—372no—
142#550—371no—
143#547—371no—
144#492—371no—
145#465—372no—
146#462—371no—
147#459—371no—
148#452—372no—
149#449—372no—
150C4×SD16D3711yescharacteristic, complemented
151C8×D4—371no—
152C37#328411yescharacteristic, complemented, Sylow
153C2×#41—372no—
154C2×#41—372no—
155#135—748no—
156C2×Q16—372no—
157C2×SD16—372no—
158C2×SD16—372no—
159C2×SD16C2×D3711yescharacteristic
160C2×D8—372no—
161C22×C8—372no—
162C4⋊Q8—371no—
163#127—371no—
164#127—741no—
165#123—742no—
166C22⋊Q8—372no—
167#121—372no—
168#121—742no—
169#121—741no—
170C4×Q8C2×D3711yescharacteristic
171C4×D4—371no—
172C4×D4—741no—
173C4×D4C2×D3711yescharacteristic
174C2×C4⋊C4—741no—
175#106C2×D3711yescharacteristic
176C4⋊C8—371no—
177#103—372no—
178#103C2×D3711yescharacteristic
179#102—372no—
180#102C2×D3711yescharacteristic
181C22⋊C8—372no—
182C4×C8C2×D3711yescharacteristic
183#41—744no—
184#41—744no—
185#41—1482no—
186#41—1482no—
187C2×Q8—372no—
188C2×Q8C22×D3711yescharacteristic
189C2×D4—371no—
190C2×D4—372no—
191C2×D4—742no—
192C2×D4—742no—
193C2×D4—742no—
194C2×D4—741no—
195C2×D4—741no—
196C2×D4C22×D3711yescharacteristic
197C22×C4—21no—
198C22×C4—372no—
199C22×C4—742no—
200C22×C4—742no—
201Q16—744no—
202SD16—744no—
203SD16—1482no—
204SD16D14814yescomplemented
205D8—744no—
206C2×C8—372no—
207C2×C8—744no—
208C2×C8C22×D3711yescharacteristic
209C2×C8C22×D3711yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—371no—
212C4⋊C4—742no—
213C4⋊C4—741no—
214C4⋊C4—741no—
215C4⋊C4C22×D3711yescharacteristic
216C4⋊C4C22×D3711yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—372no—
219C22⋊C4—742no—
220C22⋊C4—742no—
221C42—21no—
222C42C22×D3711yescharacteristic
223C23—21no—
224C23—372no—
225C23—742no—
226Q8—21no—
227Q8—742no—
228Q8—742no—
229Q8C2×D14812yes—
230D4—21no—
231D4—2961no—
232D4—2962no—
233D4—742no—
234D4—742no—
235D4—742no—
236D4—1484no—
237D4—1484no—
238D4—1482no—
239D4C2×D14812yes—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—372no—
245C2×C4—742no—
246C2×C4—742no—
247C2×C4—742no—
248C2×C4—1484no—
249C2×C4—1484no—
250C2×C4D4×D3711yescharacteristic
251C2×C4D4×D3711yescharacteristic
252C2×C4C23×D3711yescharacteristic
253C8—21no—
254C8—742no—
255C8C2×D14812yes—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—742no—
260C22—742no—
261C22—742no—
262C22—1482no—
263C22—1482no—
264C22—1482no—
265C22C2×D4×D3711yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—41no—
270C4—742no—
271C4—1482no—
272C4#1192455712yescomplemented
273C4C22×D14811yescharacteristic
274C4#1192458211yescharacteristic
275C2—42no—
276C2—2962no—
277C2—1482no—
278C2D4×D14811yescharacteristic
279C2C2×#1192455711yescharacteristic
280C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×SD16×C37C2
socleC22×C37C22×D4
hypercenterC4×SD16D37
hypocenterC37#3284
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11924557C2semidirect
2. #14558205C2semidirect
3. #14558187C2semidirect
4. #14557906C2semidirect
5. #14557763C2semidirect
6. #14557743C2semidirect
7. #14557728C2semidirect
8. #14557698C2semidirect
9. #14557679C2semidirect
10. C8×D148C2semidirect
11. C4×SD16×C37C2semidirect
60. SD16×C37D4semidirect
129. C4×C37#135semidirect
150. C4×SD16D37semidirect
152. C37#3284semidirect
204. SD16D148semidirect
272. C4#11924557semidirect

Maximal subgroups

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

subgroupindex
C2×#119245572
#145582052
#145581872
#145579062
#145577632
#145577432
#145577282
#145576982
#145576792
C8×D1482
C4×SD16×C372
#328437