Finite Group Databasebeta

← #18006492

Subgroups — #18006492

Order 4736.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558192C211yesmaximal, characteristic, complemented
2#14557890C211yesmaximal, characteristic, complemented
3#14557874C211yesmaximal, characteristic, complemented
4#14557851C211yesmaximal, characteristic, complemented
5#14557837C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557760C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557671C211yesmaximal, characteristic, complemented
11C4×#10596940C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557527C211yesmaximal, characteristic, complemented
14C2×#11924459C211yesmaximal, characteristic, complemented
15C37×#553C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C22×#64436C2211yescharacteristic
23#11924524C2211yescharacteristic
24#11924522—21no—
25#11924515C2211yescharacteristic
26#11924514—21no—
27#11924510C2211yescharacteristic
28#11924508—21no—
29C4×Dic74C2211yescharacteristic
30#11924496—21no—
31#11924469C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924459C2211yescharacteristic
36#11924459C2211yescharacteristic
37#11924459C2211yescharacteristic
38#11924459C2211yescharacteristic
39#11924459C2211yescharacteristic
40#11924459C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#126×C37—21no—
49#125×C37C2211yescharacteristic
50#123×C37—21no—
51#121×C37—21no—
52#121×C37C2211yescharacteristic
53#121×C37C2211yescharacteristic
54C4×D4×C37—21no—
55C4×D4×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57#117×C37C2211yescharacteristic
58C2×C4⋊C4×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37D411yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37—21no—
64C22×C4×C37—21no—
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C22×Dic37—21no—
70#10596962—22no—
71#10596962—41no—
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×Dic74—22no—
75C2×Dic74—21no—
76C2×Dic74—41no—
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37D411yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C22⋊C4×C37—21no—
89C22⋊C4×C37—21no—
90C22⋊C4×C37D411yescharacteristic
91C22⋊C4×C37D411yescharacteristic
92C42×C37—21no—
93C42×C37C2311yescharacteristic
94C22⋊Dic37—21no—
95#10596940—22no—
96#10596940—41no—
97#10596939—41no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104C4×Dic37—21no—
105C2×#64436—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115D4×C37—22no—
116D4×C37—21no—
117D4×C37—21no—
118D4×C37—42no—
119D4×C37—81no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—81no—
128C2×C4×C37—81no—
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2411yescharacteristic
134C22⋊D37—42no—
135C22⋊D37—42no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—42no—
140D148—21no—
141D148—21no—
142C4×D37—42no—
143Dic74—21no—
144Dic74—21no—
145Dic74—21no—
146Dic74—42no—
147Dic74#4112yes—
148#64436—21no—
149#64436—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37#13512yes—
161C22×C37C22×D411yescharacteristic
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174Dic37—22no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37—41no—
180C2×C37—81no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—81no—
185#553D3711yescharacteristic, complemented
186#548—371no—
187#488—371no—
188#485—371no—
189#481—371no—
190#479—371no—
191#466—371no—
192#465—371no—
193#463—371no—
194#449—371no—
195#448—371no—
196C4×SD16—371no—
197C8×D4—371no—
198#416—371no—
199C2×#103—371no—
200C37#330111yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C22×Q8—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C22×C8—371no—
207C22×C8—371no—
208#126—21no—
209#125C2×D3711yescharacteristic
210#124—371no—
211#124—741no—
212#123—21no—
213C22⋊Q8—371no—
214C22⋊Q8—741no—
215#121—21no—
216#121—371no—
217#121—741no—
218#121C2×D3711yescharacteristic
219#121C2×D3711yescharacteristic
220C4×Q8—371no—
221C4×D4—21no—
222C4×D4—741no—
223C4×D4C2×D3711yescharacteristic
224C4×D4C2×D3711yescharacteristic
225#117C2×D3711yescharacteristic
226C2×C4⋊C4C2×D3711yescharacteristic
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8—371no—
242C22⋊C8—371no—
243C4×C8—371no—
244#41—742no—
245#41—1481no—
246C2×Q8—371no—
247C2×Q8—371no—
248C2×Q8—742no—
249C2×Q8—741no—
250C2×Q8—1481no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—371no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22⋊D3711yescharacteristic
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263C22×C4C22×D3711yescharacteristic
264SD16—742no—
265SD16—1481no—
266D8—1481no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—371no—
271C2×C8—1481no—
272C2×C8—1481no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4C22⋊D3711yescharacteristic
280C4⋊C4C22×D3711yescharacteristic
281C4⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4C22⋊D3711yescharacteristic
292C22⋊C4C22⋊D3711yescharacteristic
293C42—21no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—741no—
298C23C2×C22⋊D3711yescharacteristic
299C23C2×C22⋊D3711yescharacteristic
300Q8—372no—
301Q8—741no—
302Q8—741no—
303Q8—741no—
304Q8—1482no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—741no—
311D4—741no—
312D4—1482no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—1482no—
327C2×C4—1482no—
328C2×C4C2×C22⋊D3711yescharacteristic
329C2×C4C2×C22⋊D3711yescharacteristic
330C2×C4C2×C22⋊D3711yescharacteristic
331C2×C4C2×C22⋊D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—741no—
334C8—741no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22#1192455612yes—
349C22C22×C22⋊D3711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—742no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458211yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—2961no—
366C2#1455817111yescharacteristic
367C2C2×#1192455611yescharacteristic
368C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#553C2
socleC22×C37C22×D4
hypercenter#553D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14558192C2semidirect
2. #14557890C2semidirect
3. #14557874C2semidirect
4. #14557851C2semidirect
5. #14557837C2semidirect
6. #14557767C2semidirect
7. #14557760C2semidirect
8. #14557748C2semidirect
9. #14557676C2semidirect
10. #14557671C2semidirect
11. C4×#10596940C2semidirect
12. D4×#64436C2semidirect
13. #14557527C2semidirect
14. C2×#11924459C2semidirect
15. C37×#553C2semidirect
185. #553D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145581922
#145578902
#145578742
#145578512
#145578372
#145577672
#145577602
#145577482
#145576762
#145576712
C4×#105969402
D4×#644362
#145575272
C2×#119244592
C37×#5532
#330137