Finite Group Databasebeta

← #18007322

Subgroups — #18007322

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#14558260C211yesmaximal, characteristic, complemented
2#14558203C211yesmaximal, characteristic
3#14557896C211yesmaximal, characteristic, complemented
4#14557878C211yesmaximal, characteristic, complemented
5#14557831C211yesmaximal, characteristic, complemented
6#14557830C211yesmaximal, characteristic, complemented
7#14557811C211yesmaximal, characteristic, complemented
8#14557732C211yesmaximal, characteristic, complemented
9#14557732C211yesmaximal, characteristic, complemented
10#14557730C211yesmaximal, characteristic, complemented
11#14557661C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13#14557630C211yesmaximal, characteristic, complemented
14#14557624C211yesmaximal, characteristic, complemented
15C37×#490C211yesmaximal, characteristic, complemented
16C2×#10596964—21no—
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20#11924535—21no—
21#11924535C2211yescharacteristic
22#11924532C2211yescharacteristic
23#11924532C2211yescharacteristic
24#11924527C2211yescharacteristic
25#11924526—21no—
26#11924526—21no—
27#11924508—21no—
28#11924508—21no—
29#11924507—21no—
30C4×Dic74C2211yescharacteristic
31C4×Dic74C2211yescharacteristic
32#11924501—21no—
33#11924501C2211yescharacteristic
34#11924501C2211yescharacteristic
35C4×D148C2211yescharacteristic
36D4×Dic37C2211yescharacteristic
37D4×Dic37C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#127×C37C2211yescharacteristic
53#125×C37C2211yescharacteristic
54#102×C37C2211yescharacteristic
55#102×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69#10596964—44no—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×Dic74—21no—
73C2×Dic74D411yescharacteristic
74C2×Dic74C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C42×C37C2311yescharacteristic
82C22⋊Dic37—21no—
83C22⋊Dic37—21no—
84#10596940—22no—
85#10596940—22no—
86#10596938—21no—
87C4⋊Dic37—21no—
88C4⋊Dic37D411yescharacteristic
89C4⋊Dic37C2311yescharacteristic
90C4⋊Dic37C2311yescharacteristic
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
105#10596930—22no—
106C23×C37—21no—
107C23×C37—21no—
108C22×D37—21no—
109D4×C37—21no—
110D4×C37—21no—
111D4×C37—21no—
112D4×C37—21no—
113D4×C37—42no—
114D4×C37—81no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
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×Dic37—21no—
127C2×Dic37—42no—
128C2×Dic37—42no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135C4×D37—42no—
136Dic74—21no—
137Dic74—22no—
138Dic74—42no—
139Dic74#4112yescomplemented
140C8×C37—21no—
141C8×C37—21no—
142#64436—21no—
143#64436—21no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37C22×D411yescharacteristic
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37C2×#4111yescharacteristic
159C4×C372−1+411yescharacteristic
160Dic37—22no—
161Dic37—21no—
162Dic37—21no—
163Dic37—21no—
164Dic37—41no—
165Dic37—41no—
166Dic37AGL(1,ℤ/8)12yes—
167#3368—371nomaximal, Sylow
168C2×C37—81no—
169C2×C37—81no—
170C2×C37#54811yescharacteristic
171C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C37#57711yescharacteristic
173D37—81no—
174#557—371no—
175#550—371no—
176#490—371no—
177#490D3711yescharacteristic, complemented
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#440—371no—
188C4×SD16—371no—
189C37#336811yescharacteristic, complemented, Sylow
190C2×#41—741no—
191C2×SD16—371no—
192C2×SD16—371no—
193C2×SD16—371no—
194C4⋊Q8—371no—
195C4⋊Q8—741no—
196#127—371no—
197#127—371no—
198#127C2×D3711yescharacteristic
199#125—371no—
200#125—741no—
201#125—741no—
202#125C2×D3711yescharacteristic
203#121—741no—
204#121—741no—
205#121—741no—
206C4×Q8—371no—
207C4×Q8—371no—
208C4×Q8—371no—
209C4×Q8—371no—
210C4×Q8—741no—
211C4×D4—371no—
212C4×D4—371no—
213C4×D4—371no—
214#107—371no—
215#107—371no—
216#106—371no—
217C4⋊C8—371no—
218C4⋊C8—371no—
219C4⋊C8—371no—
220#103—371no—
221#102—371no—
222#102—371no—
223#102—371no—
224#102—371no—
225#102—371no—
226#102C2×D3711yescharacteristic
227#102C2×D3711yescharacteristic
228#102C2×D3711yescharacteristic
229#102C2×D3711yescharacteristic
230#97—371no—
231#97C2×D3711yescharacteristic
232C4×C8—371no—
233#41—1484no—
234C2×Q8—371no—
235C2×Q8—371no—
236C2×Q8—741no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—371no—
240C2×D4—741no—
241C2×D4—741no—
242C2×D4—741no—
243C2×D4—741no—
244C2×D4C22×D3711yescharacteristic
245C2×D4C22×D3711yescharacteristic
246C22×C4—741no—
247C22×C4—741no—
248C22×C4—741no—
249SD16—742no—
250SD16—742no—
251SD16—742no—
252C2×C8—371no—
253C2×C8—371no—
254C2×C8C22×D3711yescharacteristic
255C2×C8C22×D3711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—371no—
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—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C42—371no—
275C42—371no—
276C42—741no—
277C42—741no—
278C42—741no—
279C42C22×D3711yescharacteristic
280C23—21no—
281C23—21no—
282C23—741no—
283Q8—372no—
284Q8—742no—
285Q8—741no—
286Q8—1482no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—2961no—
294D4—2961no—
295D4—741no—
296D4—741no—
297D4—1482no—
298D4—1482no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—371no—
304C2×C4—371no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4—1482no—
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—41no—
322C22—41no—
323C22—41no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22C2×D4×D3711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—372no—
333C4—741no—
334C4—741no—
335C4—741no—
336C4—742no—
337C4—1481no—
338C4—1481no—
339C4#41×D3711yescharacteristic
340C4#1192458311yescharacteristic
341C2—81no—
342C2—81no—
343C2—2961no—
344C2#1455819111yescharacteristic
345C2AGL(1,ℤ/8)×D3711yescharacteristic
346C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#490C2
socleC22×C37C22×D4
prime radical#14558203C2
hypercenter#490D37
hypocenterC37#3368
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14558260C2semidirect
3. #14557896C2semidirect
4. #14557878C2semidirect
5. #14557831C2semidirect
6. #14557830C2semidirect
7. #14557811C2semidirect
8. #14557732C2semidirect
9. #14557732C2semidirect
10. #14557730C2semidirect
11. #14557661C2semidirect
12. #14557635C2semidirect
13. #14557630C2semidirect
14. #14557624C2semidirect
15. C37×#490C2semidirect
139. Dic74#41semidirect
177. #490D37semidirect
189. C37#3368semidirect

Maximal subgroups

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

subgroupindex
#145582602
#145582032
#145578962
#145578782
#145578312
#145578302
#145578112
#145577322
#145577302
#145576612
#145576352
#145576302
#145576242
C37×#4902
#336837