Finite Group Databasebeta

← #18006491

Subgroups — #18006491

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#14558230C211yesmaximal, characteristic, complemented
2#14558190C211yesmaximal, characteristic, complemented
3#14557886C211yesmaximal, characteristic, complemented
4#14557875C211yesmaximal, characteristic, complemented
5#14557850C211yesmaximal, characteristic, complemented
6#14557842C211yesmaximal, characteristic, complemented
7#14557766C211yesmaximal, characteristic, complemented
8#14557760C211yesmaximal, characteristic, complemented
9#14557746C211yesmaximal, characteristic, complemented
10#14557670C211yesmaximal, characteristic, complemented
11SD16×Dic37C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C22×#64436C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924529—21no—
21#11924527C2211yescharacteristic
22#11924523—21no—
23#11924523C2211yescharacteristic
24#11924517—21no—
25#11924515—21no—
26#11924515C2211yescharacteristic
27#11924507—21no—
28#11924507—21no—
29#11924507C2211yescharacteristic
30#11924507C2211yescharacteristic
31Q8×Dic37C2211yescharacteristic
32D4×Dic37C2211yescharacteristic
33C4×C22⋊D37—21no—
34C4×C22⋊D37C2211yescharacteristic
35#11924496—21no—
36#11924495C2211yescharacteristic
37C4⋊C4×D37C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37D411yescharacteristic
71C22×Dic37—21no—
72Q8×D37—22no—
73Q8×D37—41no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37C2311yescharacteristic
77C2×Dic74—21no—
78C2×Dic74C2311yescharacteristic
79SD16×C37—22no—
80D8×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37D411yescharacteristic
93#10596940—41no—
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936D411yescharacteristic
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436—41no—
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37#4112yes—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—42no—
122D4×C37—81no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—42no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—22no—
131C22⋊D37—42no—
132C22⋊D37—42no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—81no—
138C2×Dic37C2×D411yescharacteristic
139C2×Dic37C2×D411yescharacteristic
140C2×Dic37C2×D411yescharacteristic
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144C4×D37—81no—
145Dic74—21no—
146Dic74—21no—
147Dic74—42no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37C22×D411yescharacteristic
162C2×D37—21no—
163C2×D37—21no—
164C2×D37#13512yes—
165C4×C37—22no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37C2×#4111yescharacteristic
169C4×C37H(5,𝔽2)11yescharacteristic
170Dic37—21no—
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—41no—
179C2×C37—81no—
180C2×C37—81no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—22no—
185#553—371no—
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#449D3711yescharacteristic, complemented
195#448—371no—
196C4×SD16—371no—
197C8×D4—371no—
198#416—371no—
199C2×#103—371no—
200C37#330111yescharacteristic, complemented, Sylow
201C2×#41C2×D3711yescharacteristic
202C22×Q8—371no—
203C2×SD16—371no—
204C2×SD16C2×D3711yescharacteristic
205C2×D8C2×D3711yescharacteristic
206C22×C8—371no—
207C22×C8—371no—
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—371no—
217#121—741no—
218#121—741no—
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#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#103C2×D3711yescharacteristic
237#102—371no—
238#102—371no—
239#102—371no—
240#102C2×D3711yescharacteristic
241C22⋊C8—371no—
242C22⋊C8C2×D3711yescharacteristic
243C4×C8—371no—
244#41—22no—
245#41—41no—
246C2×Q8—371no—
247C2×Q8—741no—
248C2×Q8—742no—
249C2×Q8—1481no—
250C2×Q8C22×D3711yescharacteristic
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—371no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4C22×D3711yescharacteristic
264SD16—22no—
265SD16—1481no—
266D8—41no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—1481no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—371no—
285C22⋊C4—371no—
286C22⋊C4—741no—
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—21no—
301Q8—741no—
302Q8—741no—
303Q8—1482no—
304Q8#1059696412yes—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—81no—
311D4—742no—
312D4—1482no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—371no—
320C2×C4—371no—
321C2×C4—371no—
322C2×C4—2961no—
323C2×C4—2961no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—372no—
347C22—741no—
348C22—741no—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—741no—
354C4—741no—
355C4—741no—
356C4—1481no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696411yescharacteristic
361C4#1192458111yescharacteristic
362C2—41no—
363C2—81no—
364C2—81no—
365C2—742no—
366C2#1455817011yescharacteristic
367C2#135×D3711yescharacteristic
368C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14558230C2semidirect
2. #14558190C2semidirect
3. #14557886C2semidirect
4. #14557875C2semidirect
5. #14557850C2semidirect
6. #14557842C2semidirect
7. #14557766C2semidirect
8. #14557760C2semidirect
9. #14557746C2semidirect
10. #14557670C2semidirect
11. SD16×Dic37C2semidirect
12. #14557596C2semidirect
13. #14557529C2semidirect
14. #103×D37C2semidirect
15. C37×#449C2semidirect
194. #449D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145582302
#145581902
#145578862
#145578752
#145578502
#145578422
#145577662
#145577602
#145577462
#145576702
SD16×Dic372
#145575962
#145575292
#103×D372
C37×#4492
#330137