Finite Group Databasebeta

← #18004797

Subgroups — #18004797

Order 4736.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558138C211yesmaximal, characteristic, complemented
2#14558013C211yesmaximal, characteristic, complemented
3#14557852C211yesmaximal, characteristic, complemented
4#14557847C211yesmaximal, characteristic, complemented
5#14557841C211yesmaximal, characteristic, complemented
6#14557834C211yesmaximal, characteristic, complemented
7#14557734C211yesmaximal, characteristic, complemented
8#14557729C211yesmaximal, characteristic, complemented
9#14557680C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557646C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13C4×#10596930C211yesmaximal, characteristic, complemented
14C4×D296C211yesmaximal, characteristic, complemented
15C37×#433C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924533C2211yescharacteristic
22#11924528C2211yescharacteristic
23#11924521—21no—
24#11924521—21no—
25#11924510C2211yescharacteristic
26#11924510C2211yescharacteristic
27#11924509—21no—
28#11924509—21no—
29C4×Dic74C2211yescharacteristic
30C4×Dic74C2211yescharacteristic
31C4×D148C2211yescharacteristic
32C4×D148C2211yescharacteristic
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic
35#11924496—21no—
36#11924496—21no—
37#11924494—21no—
38C2×C4⋊Dic37C2211yescharacteristic
39C4⋊C4×D37—21no—
40#11924470C2211yescharacteristic
41#11924470C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924468C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52#117×C37C2211yescharacteristic
53C4⋊C8×C37C2211yescharacteristic
54C4⋊C8×C37C2211yescharacteristic
55C22⋊C8×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57#97×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C2×C22⋊D37—21no—
61C2×C22⋊D37—21no—
62C2×C22⋊D37—21no—
63C22×Dic37—21no—
64#10596962—22no—
65#10596962—22no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148C2311yescharacteristic
69C2×D148C2311yescharacteristic
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37D411yescharacteristic
82C4⋊C4×C37D411yescharacteristic
83C22⋊C4×C37D411yescharacteristic
84C22⋊C4×C37D411yescharacteristic
85C42×C37C2311yescharacteristic
86C42×C37C2311yescharacteristic
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104D296—22no—
105D296—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C22⋊D37—24no—
121C22⋊D37—81no—
122C22⋊D37—81no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—81no—
129D148—21no—
130D148—21no—
131D148—21no—
132D148—21no—
133D148—21no—
134D148—81no—
135D148—81no—
136D148#4112yes—
137C4×D37—24no—
138C4×D37—81no—
139C4×D37—81no—
140C4×D37—81no—
141C4×D37—81no—
142Dic74—21no—
143Dic74#4112yes—
144C8×C37—21no—
145C8×C37—21no—
146C8×C37—21no—
147C8×C37—21no—
148C22×C37—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37C22×D411yescharacteristic
152C2×D37—22no—
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37C2×#4111yescharacteristic
167C4×C37C2×#4111yescharacteristic
168Dic37—22no—
169Dic37—41no—
170Dic37—41no—
171Dic37—41no—
172Dic37—41no—
173#3119—371nomaximal, Sylow
174C2×C37—41no—
175C2×C37#52511yescharacteristic
176C2×C37#57611yescharacteristic
177C2×C37#57711yescharacteristic
178D37—42no—
179D37—81no—
180D37—81no—
181#540—371no—
182#520—371no—
183#481—371no—
184#480—371no—
185#479—371no—
186#478—371no—
187#460—371no—
188#459—371no—
189#449—371no—
190#449—371no—
191#442—371no—
192#440—371no—
193C4×SD16—371no—
194C4×D8—371no—
195#433D3711yescharacteristic, complemented
196C37#311911yescharacteristic, complemented, Sylow
197C2×#41—371no—
198C2×SD16—371no—
199C2×SD16—371no—
200C2×D8—371no—
201C2×D8—371no—
202#127—371no—
203#125—371no—
204#123—741no—
205#123—741no—
206#121—371no—
207#121—371no—
208#121—741no—
209#121—741no—
210C4×Q8—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—741no—
217C4×D4—741no—
218#117—741no—
219#117C2×D3711yescharacteristic
220C2×C4⋊C4—371no—
221C2×C4⋊C4—741no—
222#107—371no—
223#107—371no—
224#106—371no—
225#106—371no—
226C4⋊C8C2×D3711yescharacteristic
227C4⋊C8C2×D3711yescharacteristic
228#103—371no—
229#103—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236C22⋊C8C2×D3711yescharacteristic
237C22⋊C8C2×D3711yescharacteristic
238#97C2×D3711yescharacteristic
239C4×C8C2×D3711yescharacteristic
240#41—742no—
241#41—742no—
242C2×Q8—371no—
243C2×D4—371no—
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4—741no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4C22×D3711yescharacteristic
258SD16—742no—
259SD16—742no—
260D8—742no—
261D8—742no—
262C2×C8C22×D3711yescharacteristic
263C2×C8C22×D3711yescharacteristic
264C2×C8C22×D3711yescharacteristic
265C2×C8C22×D3711yescharacteristic
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4D14811yescharacteristic
276C4⋊C4D14811yescharacteristic
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4D14811yescharacteristic
284C22⋊C4D14811yescharacteristic
285C42—741no—
286C42—741no—
287C42C22×D3711yescharacteristic
288C42C22×D3711yescharacteristic
289C23—741no—
290C23—741no—
291C23—741no—
292C23C2×D14811yescharacteristic
293Q8—372no—
294Q8—741no—
295D4—372no—
296D4—2961no—
297D4—2961no—
298D4—2961no—
299D4—2961no—
300D4—744no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—741no—
305D4—741no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2961no—
309C2×C4—2961no—
310C2×C4—2961no—
311C2×C4—2961no—
312C2×C4—2961no—
313C2×C4—744no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4C2×D14811yescharacteristic
320C2×C4C2×D14811yescharacteristic
321C2×C4C2×D14811yescharacteristic
322C2×C4C2×D14811yescharacteristic
323C2×C4C2×D14811yescharacteristic
324C2×C4C23×D3711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—742no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22—1481no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22C22×D14811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—742no—
348C4—1481no—
349C4—1481no—
350C4—1481no—
351C4—1481no—
352C4#41×D3711yescharacteristic
353C4#41×D3711yescharacteristic
354C2—41no—
355C2—2961no—
356C2—2961no—
357C2—1482no—
358C2#1455804511yescharacteristic
359C2#1455833811yescharacteristic
360C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#433C2
socleC22×C37C22×D4
hypercenter#433D37
hypocenterC37#3119
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14558138C2semidirect
2. #14558013C2semidirect
3. #14557852C2semidirect
4. #14557847C2semidirect
5. #14557841C2semidirect
6. #14557834C2semidirect
7. #14557734C2semidirect
8. #14557729C2semidirect
9. #14557680C2semidirect
10. #14557680C2semidirect
11. #14557646C2semidirect
12. #14557635C2semidirect
13. C4×#10596930C2semidirect
14. C4×D296C2semidirect
15. C37×#433C2semidirect
195. #433D37semidirect
196. C37#3119semidirect

Maximal subgroups

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

subgroupindex
#145581382
#145580132
#145578522
#145578472
#145578412
#145578342
#145577342
#145577292
#145576802
#145576462
#145576352
C4×#105969302
C4×D2962
C37×#4332
#311937