Finite Group Databasebeta

← #18007326

Subgroups — #18007326

Order 4736.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558259C211yesmaximal, characteristic, complemented
2#14558204C211yesmaximal, characteristic
3#14557898C211yesmaximal, characteristic, complemented
4#14557896C211yesmaximal, characteristic, complemented
5#14557878C211yesmaximal, characteristic, complemented
6#14557836C211yesmaximal, characteristic, complemented
7#14557833C211yesmaximal, characteristic, complemented
8#14557812C211yesmaximal, characteristic, complemented
9#14557733C211yesmaximal, characteristic, complemented
10#14557731C211yesmaximal, characteristic, complemented
11#14557731C211yesmaximal, characteristic, complemented
12#14557661C211yesmaximal, characteristic, complemented
13#14557636C211yesmaximal, characteristic, complemented
14#14557618C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19#11924535—21no—
20#11924535C2211yescharacteristic
21#11924533C2211yescharacteristic
22#11924532C2211yescharacteristic
23#11924532C2211yescharacteristic
24#11924528—21no—
25#11924528C2211yescharacteristic
26#11924527—21no—
27#11924527C2211yescharacteristic
28#11924510—21no—
29#11924509—21no—
30#11924509—21no—
31Q8×Dic37C2211yescharacteristic
32Q8×Dic37C2211yescharacteristic
33C4×Dic74—21no—
34C4×Dic74C2211yescharacteristic
35#11924498C2211yescharacteristic
36#11924498C2211yescharacteristic
37#11924469C2211yescharacteristic
38#11924467C2211yescharacteristic
39C4⋊#64436C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924458C2211yescharacteristic
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66#10596962—44no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148C2311yescharacteristic
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×Dic74—21no—
74C2×Dic74D411yescharacteristic
75SD16×C37—22no—
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C42×C37—21no—
83C42×C37C2311yescharacteristic
84#10596941—22no—
85#10596941—22no—
86#10596938—21no—
87#10596938—21no—
88C4⋊Dic37—21no—
89C4⋊Dic37—21no—
90C4⋊Dic37—21no—
91C4⋊Dic37D411yescharacteristic
92C4⋊Dic37C2311yescharacteristic
93C4⋊Dic37C2311yescharacteristic
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936D411yescharacteristic
99#10596936D411yescharacteristic
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C23×C37—21no—
107C22×D37—21no—
108C22×D37—21no—
109Q8×C37—21no—
110Q8×C37#4112yescomplemented
111D4×C37—21no—
112D4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—42no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C22⋊D37—42no—
121C22⋊D37—42no—
122C22⋊D37—81no—
123C22⋊D37—81no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C2×Dic37C2×D411yescharacteristic
130D148—21no—
131D148—21no—
132D148—21no—
133D148—21no—
134D148—42no—
135D148—81no—
136C4×D37—42no—
137C4×D37—42no—
138Dic74—22no—
139Dic74—42no—
140C8×C37—21no—
141C8×C37—21no—
142#64436—21no—
143#64436—21no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37C22×D411yescharacteristic
148C2×D37—41no—
149C2×D37—41no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C4×C37—22no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37C2×#4111yescharacteristic
160C4×C372−1+411yescharacteristic
161Dic37—21no—
162Dic37—21no—
163Dic37—21no—
164Dic37—41no—
165Dic37—41no—
166Dic37AGL(1,ℤ/8)12yes—
167#3368—371nomaximal, Sylow
168C2×C37—81no—
169C2×C37#54811yescharacteristic
170C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C37#57711yescharacteristic
172D37—81no—
173D37—81no—
174#557—371no—
175#550—371no—
176#490—371no—
177#490—371no—
178#486—371no—
179#478—371no—
180#478—371no—
181#474—371no—
182#460—371no—
183#460—371no—
184#460—371no—
185#446—371no—
186#440—371no—
187#440D3711yescharacteristic, complemented
188C4×SD16—371no—
189C37#336811yescharacteristic, complemented, Sylow
190C2×#41—741no—
191C2×SD16—371no—
192C2×SD16—371no—
193C2×SD16C2×D3711yescharacteristic
194C4⋊Q8—371no—
195C4⋊Q8—741no—
196#127—371no—
197#127—371no—
198#127—371no—
199#125—371no—
200#125—371no—
201#125—741no—
202#125—741no—
203#121—741no—
204#121—741no—
205#121—741no—
206C4×Q8—371no—
207C4×Q8—371no—
208C4×Q8—371no—
209C4×Q8—741no—
210C4×Q8C2×D3711yescharacteristic
211C4×D4—371no—
212C4×D4—371no—
213C4×D4C2×D3711yescharacteristic
214#107—371no—
215#107C2×D3711yescharacteristic
216#106—371no—
217C4⋊C8—371no—
218C4⋊C8—371no—
219C4⋊C8—371no—
220#103C2×D3711yescharacteristic
221#102—371no—
222#102—371no—
223#102—371no—
224#102—371no—
225#102—371no—
226#102—371no—
227#102—371no—
228#102—371no—
229#102C2×D3711yescharacteristic
230#97—371no—
231#97C2×D3711yescharacteristic
232C4×C8—371no—
233#41—1484no—
234C2×Q8—371no—
235C2×Q8—741no—
236C2×Q8C22×D3711yescharacteristic
237C2×D4—371no—
238C2×D4—371no—
239C2×D4—741no—
240C2×D4—741no—
241C2×D4—741no—
242C2×D4—741no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4C22×D3711yescharacteristic
246C22×C4—21no—
247C22×C4—741no—
248C22×C4—741no—
249SD16—22no—
250SD16—742no—
251SD16—742no—
252C2×C8—371no—
253C2×C8—371no—
254C2×C8C22×D3711yescharacteristic
255C2×C8C22×D3711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4C22×D3711yescharacteristic
270C4⋊C4C22×D3711yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C42—21no—
275C42—371no—
276C42—371no—
277C42—741no—
278C42—741no—
279C42C22×D3711yescharacteristic
280C23—21no—
281C23—741no—
282C23—741no—
283Q8—21no—
284Q8—742no—
285Q8—1482no—
286Q8#1059696212yescomplemented
287D4—21no—
288D4—21no—
289D4—2961no—
290D4—2961no—
291D4—2961no—
292D4—741no—
293D4—741no—
294D4—741no—
295D4—741no—
296D4—1482no—
297D4—1482no—
298D4—1482no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—371no—
304C2×C4—371no—
305C2×C4—371no—
306C2×C4—371no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4—1482no—
310C2×C4—1482no—
311C2×C4D4×D3711yescharacteristic
312C2×C4D4×D3711yescharacteristic
313C2×C4C23×D3711yescharacteristic
314C8—21no—
315C8—21no—
316C8—741no—
317C8—741no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1481no—
322C22—1481no—
323C22—1481no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22C2×D4×D3711yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—372no—
334C4—741no—
335C4—741no—
336C4—741no—
337C4—1481no—
338C4—1481no—
339C4C2×#1059696211yescharacteristic
340C4#1192458311yescharacteristic
341C2—81no—
342C2—2961no—
343C2—2961no—
344C2#1455819211yescharacteristic
345C2AGL(1,ℤ/8)×D3711yescharacteristic
346C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
prime radical#14558204C2
hypercenter#440D37
hypocenterC37#3368
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14558259C2semidirect
3. #14557898C2semidirect
4. #14557896C2semidirect
5. #14557878C2semidirect
6. #14557836C2semidirect
7. #14557833C2semidirect
8. #14557812C2semidirect
9. #14557733C2semidirect
10. #14557731C2semidirect
11. #14557731C2semidirect
12. #14557661C2semidirect
13. #14557636C2semidirect
14. #14557618C2semidirect
15. C37×#440C2semidirect
110. Q8×C37#41semidirect
187. #440D37semidirect
189. C37#3368semidirect
286. Q8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145582592
#145582042
#145578982
#145578962
#145578782
#145578362
#145578332
#145578122
#145577332
#145577312
#145576612
#145576362
#145576182
C37×#4402
#336837