Finite Group Databasebeta

← #18006504

Subgroups — #18006504

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#14558235C211yesmaximal, characteristic, complemented
2#14558189C211yesmaximal, characteristic, complemented
3#14557886C211yesmaximal, characteristic, complemented
4#14557876C211yesmaximal, characteristic, complemented
5#14557849C211yesmaximal, characteristic, complemented
6#14557839C211yesmaximal, characteristic, complemented
7#14557761C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557675C211yesmaximal, characteristic, complemented
10#14557671C211yesmaximal, characteristic, complemented
11#14557624C211yesmaximal, characteristic, complemented
12C8×C22⋊D37C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14C2×#11924461C211yesmaximal, characteristic, complemented
15C37×#466C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924529—21no—
22#11924527C2211yescharacteristic
23#11924523C2211yescharacteristic
24#11924522—21no—
25#11924520—21no—
26#11924516C2211yescharacteristic
27#11924513—21no—
28#11924508—21no—
29#11924508—21no—
30#11924507C2211yescharacteristic
31#11924501C2211yescharacteristic
32D4×Dic37—21no—
33D4×Dic37—21no—
34D4×Dic37C2211yescharacteristic
35C4×C22⋊D37C2211yescharacteristic
36#11924494C2211yescharacteristic
37C2×C4⋊Dic37C2211yescharacteristic
38#11924467C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924461C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×D8×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#121×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#107×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37D411yescharacteristic
67C22×Dic37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70C22×Dic37—21no—
71#10596964—22no—
72#10596964—41no—
73C2×C4×D37C2311yescharacteristic
74C2×Dic74—22no—
75C2×Dic74—21no—
76C2×Dic74—41no—
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79D8×C37—41no—
80C2×C8×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37D411yescharacteristic
92#10596940—22no—
93#10596940—41no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104#10596936D411yescharacteristic
105C4×Dic37—21no—
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—42no—
120D4×C37—42no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—22no—
128C22⋊D37—42no—
129C22⋊D37—81no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—42no—
135C2×Dic37—42no—
136C2×Dic37—81no—
137C2×Dic37—81no—
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140C2×Dic37C2×D411yescharacteristic
141C4×D37—21no—
142C4×D37—21no—
143Dic74—21no—
144Dic74—21no—
145Dic74—21no—
146Dic74—42no—
147Dic74#4112yes—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37#13512yes—
161C22×C37C22×D411yescharacteristic
162C2×D37—21no—
163C2×D37—21no—
164C2×D37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37C2×#4111yescharacteristic
169C4×C37H(5,𝔽2)11yescharacteristic
170Dic37—22no—
171Dic37—21no—
172Dic37—21no—
173Dic37—21no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37—81no—
180C2×C37—81no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—41no—
185#553—371no—
186#548—371no—
187#488—371no—
188#485—371no—
189#481—371no—
190#479—371no—
191#466D3711yescharacteristic, complemented
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×D8C2×D3711yescharacteristic
206C22×C8—371no—
207C22×C8C2×D3711yescharacteristic
208#126—741no—
209#125—371no—
210#124—371no—
211#124—741no—
212#123—741no—
213C22⋊Q8—371no—
214C22⋊Q8—741no—
215#121—371no—
216#121—741no—
217#121—741no—
218#121C2×D3711yescharacteristic
219#121C2×D3711yescharacteristic
220C4×Q8—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224C4×D4—741no—
225#117—371no—
226C2×C4⋊C4—371no—
227#107C2×D3711yescharacteristic
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#102C2×D3711yescharacteristic
240#102C2×D3711yescharacteristic
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—371no—
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4C22×D3711yescharacteristic
264SD16—742no—
265SD16—1481no—
266D8—41no—
267C2×C8—41no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—371no—
286C22⋊C4—371no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C42—371no—
294C42—741no—
295C42—741no—
296C23—21no—
297C23—21no—
298C23—371no—
299C23D4×D3711yescharacteristic
300Q8—372no—
301Q8—741no—
302Q8—741no—
303Q8—741no—
304Q8—1482no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—42no—
311D4—2961no—
312D4—742no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—371no—
319C2×C4—371no—
320C2×C4—371no—
321C2×C4—2961no—
322C2×C4—2961no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—1482no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—741no—
346C22—741no—
347C22—741no—
348C22#1192455512yes—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—741no—
354C4—741no—
355C4—741no—
356C4—742no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458111yescharacteristic
362C2—22no—
363C2—81no—
364C2—81no—
365C2—1481no—
366C2#1455817211yescharacteristic
367C2C2×#1192455511yescharacteristic
368C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#466C2
socleC22×C37C22×D4
hypercenter#466D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14558235C2semidirect
2. #14558189C2semidirect
3. #14557886C2semidirect
4. #14557876C2semidirect
5. #14557849C2semidirect
6. #14557839C2semidirect
7. #14557761C2semidirect
8. #14557746C2semidirect
9. #14557675C2semidirect
10. #14557671C2semidirect
11. #14557624C2semidirect
12. C8×C22⋊D37C2semidirect
13. #14557526C2semidirect
14. C2×#11924461C2semidirect
15. C37×#466C2semidirect
191. #466D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145582352
#145581892
#145578862
#145578762
#145578492
#145578392
#145577612
#145577462
#145576752
#145576712
#145576242
C8×C22⋊D372
#145575262
C2×#119244612
C37×#4662
#330137