Finite Group Databasebeta

← #18007187

Subgroups — #18007187

Order 4736.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558246C211yesmaximal, characteristic, complemented
2#14558184C211yesmaximal, characteristic, complemented
3#14557930C211yesmaximal, characteristic, complemented
4#14557860C211yesmaximal, characteristic, complemented
5#14557857C211yesmaximal, characteristic, complemented
6#14557853C211yesmaximal, characteristic, complemented
7#14557851C211yesmaximal, characteristic, complemented
8#14557822C211yesmaximal, characteristic, complemented
9#14557812C211yesmaximal, characteristic, complemented
10#14557787C211yesmaximal, characteristic, complemented
11#14557786C211yesmaximal, characteristic, complemented
12#14557615C211yesmaximal, characteristic, complemented
13#14557609C211yesmaximal, characteristic, complemented
14#14557574C211yesmaximal, characteristic, complemented
15C37×#428C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×D296C2211yescharacteristic
18C2×#10596929C2211yescharacteristic
19#11924535C2211yescharacteristic
20#11924535C2211yescharacteristic
21#11924524—21no—
22#11924522—21no—
23#11924521—21no—
24#11924519—21no—
25#11924514—21no—
26#11924511C2211yescharacteristic
27#11924511C2211yescharacteristic
28#11924510C2211yescharacteristic
29#11924510C2211yescharacteristic
30#11924509—21no—
31#11924498C2211yescharacteristic
32#11924498C2211yescharacteristic
33C4×C22⋊D37C2211yescharacteristic
34#11924494C2211yescharacteristic
35#11924493—21no—
36C4⋊C4×D37C2211yescharacteristic
37#11924469C2211yescharacteristic
38#11924468C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×M16×C37C2211yescharacteristic
53#117×C37C2211yescharacteristic
54C2×C4⋊C4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#107×C37C2211yescharacteristic
57#106×C37C2211yescharacteristic
58#106×C37C2211yescharacteristic
59C22×C4×C37—21no—
60C22×C4×C37C2311yescharacteristic
61C2×C22⋊D37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37D411yescharacteristic
64#10596962—44no—
65C2×D148—21no—
66C2×D148—21no—
67C2×D148C2311yescharacteristic
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×C4×D37C2311yescharacteristic
73C2×Dic74—21no—
74C2×Dic74—21no—
75M16×C37—22no—
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C42×C37—21no—
85C22⋊Dic37D411yescharacteristic
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938D411yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936D411yescharacteristic
100C4×Dic37—21no—
101C4×Dic37C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104D296—22no—
105#10596929—22no—
106C23×C37C2×D411yescharacteristic
107C22×D37—21no—
108C22×D37—21no—
109C22×D37C2×D411yescharacteristic
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—42no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2411yescharacteristic
119C22⋊D37—22no—
120C22⋊D37—42no—
121C22⋊D37—81no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37C2×D411yescharacteristic
125C2×Dic37C2×D411yescharacteristic
126C2×Dic37C2×D411yescharacteristic
127D148—21no—
128D148—21no—
129D148—21no—
130D148—21no—
131D148—42no—
132D148—81no—
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—42no—
136C4×D37—42no—
137C4×D37—42no—
138Dic74—42no—
139Dic74—81no—
140C8×C37—21no—
141C8×C37#4112yescomplemented
142#64436—21no—
143#64436—21no—
144C22×C37—21no—
145C22×C37—21no—
146C22×C37—21no—
147C22×C37C22×D411yescharacteristic
148C2×D37—21no—
149C2×D37—21no—
150C2×D37—21no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37C2×#4111yescharacteristic
163C4×C372−1+411yescharacteristic
164Dic37—21no—
165Dic37—21no—
166Dic37—41no—
167Dic37—41no—
168Dic37AGL(1,ℤ/8)12yes—
169#3354—371nomaximal, Sylow
170C2×C37—41no—
171C2×C37#54711yescharacteristic
172C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C37#57711yescharacteristic
174D37—41no—
175D37—81no—
176D37—81no—
177#555—371no—
178#547—371no—
179#498—371no—
180#482—371no—
181#482—371no—
182#481—371no—
183#481—371no—
184#476—371no—
185#474—371no—
186#469—371no—
187#469—371no—
188C4×D8—371no—
189#436—371no—
190#428—371no—
191#428D3711yescharacteristic, complemented
192C37#335411yescharacteristic, complemented, Sylow
193C2×#41—741no—
194C2×D8—371no—
195C2×M16—371no—
196C2×M16C2×D3711yescharacteristic
197C4⋊Q8—371no—
198C4⋊Q8—371no—
199#124—741no—
200#124—741no—
201#123—741no—
202#123—741no—
203C22⋊Q8—741no—
204#121—371no—
205#121—371no—
206#121—371no—
207#121—371no—
208#121—741no—
209C4×D4—371no—
210C4×D4—371no—
211C4×D4—371no—
212#117—371no—
213#117—741no—
214#117C2×D3711yescharacteristic
215C2×C4⋊C4—371no—
216C2×C4⋊C4C2×D3711yescharacteristic
217#107—371no—
218#107C2×D3711yescharacteristic
219#107C2×D3711yescharacteristic
220#106—371no—
221#106—371no—
222#106—371no—
223#106—371no—
224#106C2×D3711yescharacteristic
225#106C2×D3711yescharacteristic
226C4⋊C8—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233C22⋊C8—371no—
234C22⋊C8—371no—
235C4×C8—371no—
236#41—1484no—
237C2×Q8—741no—
238C2×Q8—741no—
239C2×D4—371no—
240C2×D4—371no—
241C2×D4—371no—
242C2×D4—741no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4—741no—
246C22×C4—21no—
247C22×C4—371no—
248C22×C4—741no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4C22×D3711yescharacteristic
252D8—742no—
253M16—22no—
254M16—742no—
255C2×C8—371no—
256C2×C8—371no—
257C2×C8C22×D3711yescharacteristic
258C2×C8C22×D3711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—371no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4C22×D3711yescharacteristic
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C4⋊C4C22×D3711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—371no—
272C22⋊C4—371no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C42—21no—
281C42—371no—
282C42—741no—
283C23—371no—
284C23—741no—
285C23—741no—
286C23D4×D3711yescharacteristic
287Q8—2961no—
288Q8—1482no—
289D4—2961no—
290D4—2961no—
291D4—742no—
292D4—741no—
293D4—741no—
294D4—741no—
295D4—741no—
296D4—1482no—
297D4—1482no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—371no—
306C2×C4—371no—
307C2×C4—371no—
308C2×C4—741no—
309C2×C4—741no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—1482no—
313C2×C4—1482no—
314C2×C4—1482no—
315C2×C4D4×D3711yescharacteristic
316C2×C4C23×D3711yescharacteristic
317C8—21no—
318C8—741no—
319C8—741no—
320C8#1059696212yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—741no—
325C22—741no—
326C22—741no—
327C22—1481no—
328C22—1481no—
329C22—1481no—
330C22—1481no—
331C22—1481no—
332C22—1481no—
333C22C2×D4×D3711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—372no—
340C4—741no—
341C4—741no—
342C4—1481no—
343C4—1481no—
344C4C2×#1059696211yescharacteristic
345C4#1192458411yescharacteristic
346C2—41no—
347C2—2961no—
348C2—2961no—
349C2—1481no—
350C2#1455818411yescharacteristic
351C2AGL(1,ℤ/8)×D3711yescharacteristic
352C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#428C2
socleC22×C37C22×D4
hypercenter#428D37
hypocenterC37#3354
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #14558246C2semidirect
2. #14558184C2semidirect
3. #14557930C2semidirect
4. #14557860C2semidirect
5. #14557857C2semidirect
6. #14557853C2semidirect
7. #14557851C2semidirect
8. #14557822C2semidirect
9. #14557812C2semidirect
10. #14557787C2semidirect
11. #14557786C2semidirect
12. #14557615C2semidirect
13. #14557609C2semidirect
14. #14557574C2semidirect
15. C37×#428C2semidirect
141. C8×C37#41semidirect
191. #428D37semidirect
192. C37#3354semidirect
320. C8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145582462
#145581842
#145579302
#145578602
#145578572
#145578532
#145578512
#145578222
#145578122
#145577872
#145577862
#145576152
#145576092
#145575742
C37×#4282
#335437