Finite Group Databasebeta

← #18004765

Subgroups — #18004765

Order 4736.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558065C211yesmaximal, characteristic
2C4×Q8×D37C211yesmaximal, characteristic, complemented
3#14557870C211yesmaximal, characteristic, complemented
4#14557850C211yesmaximal, characteristic
5#14557839C211yesmaximal, characteristic, complemented
6#14557838C211yesmaximal, characteristic, complemented
7#14557754C211yesmaximal, characteristic, complemented
8#14557753C211yesmaximal, characteristic, complemented
9#14557690C211yesmaximal, characteristic, complemented
10#14557670C211yesmaximal, characteristic
11#14557641C211yesmaximal, characteristic, complemented
12#14557638C211yesmaximal, characteristic, complemented
13#14557633C211yesmaximal, characteristic, complemented
14#14557588C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20#11924529—21no—
21#11924527C2211yescharacteristic
22#11924523C2211yescharacteristic
23#11924518—21no—
24#11924516C2211yescharacteristic
25#11924507C2211yescharacteristic
26Q8×Dic37C2211yescharacteristic
27C4×Dic74—21no—
28C4×Dic74C2211yescharacteristic
29C4×Dic74C2211yescharacteristic
30#11924501—21no—
31#11924501C2211yescharacteristic
32C4×C22⋊D37—21no—
33#11924495—21no—
34C4⋊C4×D37—21no—
35C4⋊C4×D37C2211yescharacteristic
36C42×D37—21no—
37C42×D37C2211yescharacteristic
38#11924469C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924447C2211yescharacteristic
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—
63Q8×D37—22no—
64Q8×D37—22no—
65C2×C4×D37—21no—
66C2×C4×D37—21no—
67C2×C4×D37D411yescharacteristic
68C2×C4×D37D411yescharacteristic
69C2×C4×D37C2311yescharacteristic
70C2×Dic74—21no—
71C2×Dic74C2311yescharacteristic
72C2×Dic74C2311yescharacteristic
73SD16×C37—22no—
74C2×C8×C37C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C4⋊C4×C37—21no—
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C42×C37—21no—
81C42×C37C2311yescharacteristic
82C22⋊Dic37—21no—
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85#10596942—22no—
86#10596940—22no—
87#10596938—21no—
88C4⋊Dic37—21no—
89C4⋊Dic37—21no—
90C4⋊Dic37—21no—
91C4⋊Dic37C2311yescharacteristic
92C4⋊Dic37C2311yescharacteristic
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37D411yescharacteristic
103C4×Dic37D411yescharacteristic
104C4×Dic37C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107Dic148—22no—
108C23×C37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37#4112yes—
112D4×C37—21no—
113D4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—42no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—42no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129C4×D37—24no—
130C4×D37—22no—
131C4×D37—21no—
132C4×D37—21no—
133C4×D37—41no—
134C4×D37—42no—
135Dic74—24no—
136Dic74—21no—
137Dic74—21no—
138Dic74—21no—
139Dic74#4112yes—
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—21no—
149C2×D37—21no—
150C2×D37#13712yes—
151C4×C37—22no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—41no—
155C4×C37—41no—
156C4×C37C2×#4111yescharacteristic
157C4×C37C2×#4111yescharacteristic
158Dic37—21no—
159Dic37—22no—
160Dic37—21no—
161Dic37—21no—
162Dic37—41no—
163Dic37—41no—
164Dic37—41no—
165#3117—371nomaximal, Sylow
166C2×C37—81no—
167C2×C37#52511yescharacteristic
168C2×C37C2×#13711yescharacteristic
169C2×C37#57511yescharacteristic
170D37—22no—
171#529—371no—
172C2×C4×Q8—371no—
173#484—371no—
174#481—371no—
175#479—371no—
176#479—371no—
177#464—371no—
178#464—371no—
179#451—371no—
180#448—371no—
181#441—371no—
182#441—371no—
183#440—371no—
184#440D3711yescharacteristic, complemented
185#432—371no—
186C37#311711yescharacteristic, complemented, Sylow
187C22×Q8—371no—
188C2×Q16—371no—
189C2×Q16—371no—
190C2×SD16—371no—
191C2×SD16C2×D3711yescharacteristic
192#126—741no—
193#125—371no—
194#124—371no—
195#123—741no—
196C22⋊Q8—371no—
197#121—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—371no—
201C4×Q8—371no—
202C4×Q8—741no—
203C4×Q8—741no—
204C4×Q8C2×D3711yescharacteristic
205C4×D4—741no—
206C4×D4C2×D3711yescharacteristic
207#117—741no—
208C2×C4⋊C4—371no—
209C2×C4⋊C4—741no—
210C2×C42—371no—
211C2×C42—741no—
212#107—371no—
213#107C2×D3711yescharacteristic
214#106—371no—
215#106—371no—
216C4⋊C8—371no—
217C4⋊C8—371no—
218#103—371no—
219#103—371no—
220#103—371no—
221#103—371no—
222#103—371no—
223#103C2×D3711yescharacteristic
224#102—371no—
225#102C2×D3711yescharacteristic
226C22⋊C8—371no—
227C22⋊C8—371no—
228#97—371no—
229#97C2×D3711yescharacteristic
230C2×Q8—371no—
231C2×Q8—371no—
232C2×Q8—741no—
233C2×Q8—742no—
234C2×Q8—742no—
235C2×Q8C22×D3711yescharacteristic
236C2×D4—741no—
237C2×D4C22×D3711yescharacteristic
238C22×C4—21no—
239C22×C4—371no—
240C22×C4—371no—
241C22×C4—371no—
242C22×C4—741no—
243C22×C4—741no—
244Q16—742no—
245Q16—742no—
246SD16—22no—
247SD16—742no—
248C2×C8—371no—
249C2×C8—371no—
250C2×C8C22×D3711yescharacteristic
251C2×C8C22×D3711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—371no—
254C4⋊C4—371no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C42—21no—
271C42—371no—
272C42—371no—
273C42—371no—
274C42—741no—
275C42—741no—
276C42—741no—
277C42—741no—
278C42C22×D3711yescharacteristic
279C23—21no—
280C23—371no—
281Q8—21no—
282Q8—372no—
283Q8—744no—
284Q8—741no—
285Q8—741no—
286Q8—741no—
287Q8#1059696212yes—
288D4—21no—
289D4—21no—
290D4—1482no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—371no—
296C2×C4—371no—
297C2×C4—371no—
298C2×C4—742no—
299C2×C4—744no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—1481no—
307C2×C4—1482no—
308C2×C4D4×D3711yescharacteristic
309C2×C4D4×D3711yescharacteristic
310C2×C4C23×D3711yescharacteristic
311C8—21no—
312C8—21no—
313C8—741no—
314C8—741no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—372no—
319C22—741no—
320C22—741no—
321C22C2×D4×D3711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—741no—
328C4—742no—
329C4—741no—
330C4—741no—
331C4—1481no—
332C4—1481no—
333C4—1481no—
334C4#41×D3711yescharacteristic
335C4C2×#1059696211yescharacteristic
336C2—81no—
337C2—742no—
338C2#1455804211yescharacteristic
339C2#137×D3711yescharacteristic
340C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
prime radical#11924507C22
hypercenter#440D37
hypocenterC37#3117
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
2. C4×Q8×D37C2semidirect
3. #14557870C2semidirect
5. #14557839C2semidirect
6. #14557838C2semidirect
7. #14557754C2semidirect
8. #14557753C2semidirect
9. #14557690C2semidirect
11. #14557641C2semidirect
12. #14557638C2semidirect
13. #14557633C2semidirect
14. #14557588C2semidirect
15. C37×#440C2semidirect
184. #440D37semidirect
186. C37#3117semidirect

Maximal subgroups

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

subgroupindex
#145580652
C4×Q8×D372
#145578702
#145578502
#145578392
#145578382
#145577542
#145577532
#145576902
#145576702
#145576412
#145576382
#145576332
#145575882
C37×#4402
#311737