Finite Group Databasebeta

← #18007282

Subgroups — #18007282

Order 4736.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558259C211yesmaximal, characteristic, complemented
2#14558255C211yesmaximal, characteristic
3#14557889C211yesmaximal, characteristic
4#14557888C211yesmaximal, characteristic
5#14557882C211yesmaximal, characteristic, complemented
6#14557840C211yesmaximal, characteristic, complemented
7#14557839C211yesmaximal, characteristic, complemented
8#14557812C211yesmaximal, characteristic
9#14557757C211yesmaximal, characteristic
10#14557755C211yesmaximal, characteristic
11#14557741C211yesmaximal, characteristic, complemented
12C8×Dic74C211yesmaximal, characteristic, complemented
13#14557625C211yesmaximal, characteristic, complemented
14#14557618C211yesmaximal, characteristic
15C4×Q16×C37C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18#11924535—21no—
19#11924535C2211yescharacteristic
20#11924534C2211yescharacteristic
21#11924531—21no—
22#11924530—21no—
23#11924528—21no—
24#11924528C2211yescharacteristic
25#11924527—21no—
26#11924527C2211yescharacteristic
27#11924525C2211yescharacteristic
28#11924524C2211yescharacteristic
29#11924514—21no—
30Q8×Dic37C2211yescharacteristic
31Q8×Dic37C2211yescharacteristic
32C4×Dic74—21no—
33C4×Dic74C2211yescharacteristic
34#11924501C2211yescharacteristic
35#11924498C2211yescharacteristic
36#11924493—21no—
37#11924469C2211yescharacteristic
38#11924467C2211yescharacteristic
39C4⋊#64436C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924456C2211yescharacteristic
50C8×Dic37C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×Q16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×Dic74—21no—
64C2×Dic74D411yescharacteristic
65C2×Dic74C2311yescharacteristic
66Q16×C37—22no—
67C2×C8×C37C2311yescharacteristic
68C2×C8×C37C2311yescharacteristic
69C4⋊C4×C37—21no—
70C4⋊C4×C37—21no—
71C4⋊C4×C37C2311yescharacteristic
72C4⋊C4×C37C2311yescharacteristic
73C42×C37—21no—
74C42×C37—21no—
75C42×C37C2311yescharacteristic
76#10596942—22no—
77#10596941—22no—
78#10596938—21no—
79#10596938—21no—
80#10596938—21no—
81#10596938—21no—
82#10596938—21no—
83C4⋊Dic37—21no—
84C4⋊Dic37—21no—
85C4⋊Dic37—21no—
86C4⋊Dic37D411yescharacteristic
87C4⋊Dic37C2311yescharacteristic
88C4⋊Dic37C2311yescharacteristic
89#10596936—21no—
90#10596936—21no—
91#10596936—21no—
92#10596936—21no—
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936D411yescharacteristic
97#10596936D411yescharacteristic
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37C2311yescharacteristic
102C4×Dic37C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C22×D37—21no—
106Q8×C37—21no—
107Q8×C37—21no—
108Q8×C37—21no—
109Q8×C37#4112yes—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2411yescharacteristic
117C2×Dic37—21no—
118C2×Dic37—21no—
119C2×Dic37—21no—
120C2×Dic37C2×D411yescharacteristic
121C2×Dic37C2×D411yescharacteristic
122C2×Dic37C2×D411yescharacteristic
123C2×Dic37C2×D411yescharacteristic
124D148—21no—
125D148—21no—
126C4×D37—42no—
127Dic74—22no—
128Dic74—21no—
129Dic74—21no—
130Dic74—42no—
131C8×C37—21no—
132C8×C37—21no—
133#64436—21no—
134#64436—21no—
135C22×C37C22×D411yescharacteristic
136C2×D37—41no—
137C2×D37—41no—
138C2×D37—41no—
139C4×C37—22no—
140C4×C37—21no—
141C4×C37—21no—
142C4×C37—41no—
143C4×C37—41no—
144C4×C37—41no—
145C4×C37C2×#4111yescharacteristic
146C4×C372−1+411yescharacteristic
147Dic37—21no—
148Dic37—21no—
149Dic37—21no—
150Dic37—41no—
151Dic37—41no—
152Dic37—41no—
153Dic37#13512yes—
154#3364—371nomaximal, Sylow
155C2×C37#54811yescharacteristic
156C2×C37C2×#13511yescharacteristic
157C2×C37#57811yescharacteristic
158D37—81no—
159#557—371no—
160#556—371no—
161#488—371no—
162#488—371no—
163#487—371no—
164#479—371no—
165#479—371no—
166#474—371no—
167#464—371no—
168#464—371no—
169#462—371no—
170C8×Q8—371no—
171C4×Q16—371no—
172C4×Q16D3711yescharacteristic, complemented
173C4×SD16—371no—
174C37#336411yescharacteristic, complemented, Sylow
175C2×Q16—371no—
176C2×Q16C2×D3711yescharacteristic
177C2×SD16—371no—
178C4⋊Q8—371no—
179C4⋊Q8—371no—
180C4⋊Q8—741no—
181#126—741no—
182#126—741no—
183#125—371no—
184#125—371no—
185#125—741no—
186#125—741no—
187#124—371no—
188#124—371no—
189C22⋊Q8—741no—
190C4×Q8—371no—
191C4×Q8—371no—
192C4×Q8—371no—
193C4×Q8—371no—
194C4×Q8—741no—
195C4×Q8C2×D3711yescharacteristic
196C4×Q8C2×D3711yescharacteristic
197C4×D4—371no—
198#117—741no—
199#107—371no—
200#107C2×D3711yescharacteristic
201#106—371no—
202C4⋊C8—371no—
203C4⋊C8—371no—
204C4⋊C8—371no—
205#103—371no—
206#103—371no—
207#103—371no—
208#103—371no—
209#103—371no—
210#103C2×D3711yescharacteristic
211#103C2×D3711yescharacteristic
212#102—371no—
213#102—371no—
214#102—371no—
215C4×C8—371no—
216C4×C8—371no—
217C4×C8C2×D3711yescharacteristic
218C2×Q8—371no—
219C2×Q8—371no—
220C2×Q8—741no—
221C2×Q8C22×D3711yescharacteristic
222C2×Q8C22×D3711yescharacteristic
223C2×D4—371no—
224C22×C4—741no—
225Q16—22no—
226Q16—742no—
227SD16—742no—
228C2×C8—371no—
229C2×C8—371no—
230C2×C8C22×D3711yescharacteristic
231C2×C8C22×D3711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—371no—
235C4⋊C4—371no—
236C4⋊C4—371no—
237C4⋊C4—371no—
238C4⋊C4—371no—
239C4⋊C4—741no—
240C4⋊C4—741no—
241C4⋊C4—741no—
242C4⋊C4—741no—
243C4⋊C4—741no—
244C4⋊C4—741no—
245C4⋊C4—741no—
246C4⋊C4—741no—
247C4⋊C4—741no—
248C4⋊C4—741no—
249C4⋊C4C22×D3711yescharacteristic
250C4⋊C4C22×D3711yescharacteristic
251C22⋊C4—741no—
252C22⋊C4—741no—
253C22⋊C4—741no—
254C22⋊C4—741no—
255C22⋊C4—741no—
256C42—21no—
257C42—21no—
258C42—371no—
259C42—371no—
260C42—741no—
261C42—741no—
262C42—741no—
263C42C22×D3711yescharacteristic
264C23—741no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—742no—
269Q8—741no—
270Q8—741no—
271Q8—1482no—
272Q8#1059696212yes—
273D4—741no—
274D4—741no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—371no—
280C2×C4—371no—
281C2×C4—371no—
282C2×C4—371no—
283C2×C4—741no—
284C2×C4—741no—
285C2×C4—741no—
286C2×C4—1482no—
287C2×C4D4×D3711yescharacteristic
288C2×C4D4×D3711yescharacteristic
289C2×C4C23×D3711yescharacteristic
290C8—21no—
291C8—21no—
292C8—741no—
293C8—741no—
294C22—1481no—
295C22—1481no—
296C22—1481no—
297C22C2×D4×D3711yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—372no—
305C4—741no—
306C4—741no—
307C4—741no—
308C4—1481no—
309C4—1481no—
310C4—1481no—
311C4C2×#1059696211yescharacteristic
312C4#1192458311yescharacteristic
313C2—2961no—
314C2#1455819211yescharacteristic
315C2#135×D3711yescharacteristic
316C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×Q16×C37C2
socleC22×C37C22×D4
prime radicalC2×D148C23
hypercenterC4×Q16D37
hypocenterC37#3364
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #14558259C2semidirect
5. #14557882C2semidirect
6. #14557840C2semidirect
7. #14557839C2semidirect
11. #14557741C2semidirect
12. C8×Dic74C2semidirect
13. #14557625C2semidirect
15. C4×Q16×C37C2semidirect
172. C4×Q16D37semidirect
174. C37#3364semidirect

Maximal subgroups

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

subgroupindex
#145582592
#145582552
#145578892
#145578882
#145578822
#145578402
#145578392
#145578122
#145577572
#145577552
#145577412
C8×Dic742
#145576252
#145576182
C4×Q16×C372
#336437