Finite Group Databasebeta

← #18004879

Subgroups — #18004879

Order 4736.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558148C211yesmaximal, characteristic, complemented
2#14558015C211yesmaximal, characteristic, complemented
3#14557865C211yesmaximal, characteristic, complemented
4#14557850C211yesmaximal, characteristic, complemented
5#14557822C211yesmaximal, characteristic, complemented
6#14557816C211yesmaximal, characteristic, complemented
7#14557753C211yesmaximal, characteristic, complemented
8#14557747C211yesmaximal, characteristic, complemented
9#14557698C211yesmaximal, characteristic, complemented
10#14557677C211yesmaximal, characteristic
11#14557643C211yesmaximal, characteristic, complemented
12#14557638C211yesmaximal, characteristic, complemented
13C4×#10596930C211yesmaximal, characteristic, complemented
14#14557592C211yesmaximal, characteristic, complemented
15C4×SD16×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20#11924535C2211yescharacteristic
21#11924529—21no—
22#11924523C2211yescharacteristic
23#11924522—21no—
24#11924519—21no—
25#11924516C2211yescharacteristic
26#11924515—21no—
27#11924507C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29C4×Dic74C2211yescharacteristic
30C4×D148—21no—
31C4×D148C2211yescharacteristic
32#11924498—21no—
33#11924498C2211yescharacteristic
34#11924493—21no—
35#11924493C2211yescharacteristic
36C4⋊C4×D37—21no—
37C4⋊C4×D37C2211yescharacteristic
38#11924468C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924447C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63#10596966—22no—
64#10596966—22no—
65C2×D148—21no—
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37C2311yescharacteristic
72C2×Dic74—21no—
73C2×Dic74C2311yescharacteristic
74SD16×C37—22no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C42×C37—21no—
82C42×C37C2311yescharacteristic
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86#10596942—22no—
87#10596939—22no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938D411yescharacteristic
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107#10596930—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37C2×D411yescharacteristic
111Q8×C37—21no—
112Q8×C37#4112yes—
113D4×C37—21no—
114D4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—81no—
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2411yescharacteristic
122C22⋊D37—81no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129D148—24no—
130D148—21no—
131D148#4112yes—
132C4×D37—24no—
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—81no—
136C4×D37—81no—
137C4×D37—81no—
138Dic74—21no—
139Dic74—21no—
140Dic74—81no—
141C8×C37—21no—
142C8×C37—21no—
143#64436—21no—
144#64436—21no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37C22×D411yescharacteristic
149C2×D37—21no—
150C2×D37—22no—
151C2×D37—21no—
152C2×D37—21no—
153C2×D37—41no—
154C2×D37—41no—
155C4×C37—22no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37C2×#4111yescharacteristic
161C4×C37C2×#4111yescharacteristic
162Dic37—21no—
163Dic37—21no—
164Dic37—21no—
165Dic37—41no—
166Dic37—41no—
167Dic37—41no—
168#3125—371nomaximal, Sylow
169C2×C37—81no—
170C2×C37#52511yescharacteristic
171C2×C37#57711yescharacteristic
172C2×C37#57711yescharacteristic
173D37—41no—
174D37—42no—
175#542—371no—
176#520—371no—
177#483—371no—
178#481—371no—
179#476—371no—
180#475—371no—
181#464—371no—
182#463—371no—
183#452—371no—
184#449—371no—
185#442—371no—
186#441—371no—
187C4×SD16—371no—
188C4×SD16D3711yescharacteristic, complemented
189#433—371no—
190C37#312511yescharacteristic, complemented, Sylow
191C2×#41—371no—
192C2×Q16—371no—
193C2×SD16—371no—
194C2×SD16C2×D3711yescharacteristic
195C2×D8—371no—
196C4⋊Q8—371no—
197#126—741no—
198#124—371no—
199#124—741no—
200#123—741no—
201C22⋊Q8—371no—
202C22⋊Q8—741no—
203#121—371no—
204C4×Q8—371no—
205C4×Q8—371no—
206C4×Q8C2×D3711yescharacteristic
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—741no—
210C4×D4—741no—
211C4×D4C2×D3711yescharacteristic
212#117—371no—
213#117—741no—
214C2×C4⋊C4—371no—
215C2×C4⋊C4—741no—
216#106—371no—
217#106—371no—
218#106—371no—
219#106C2×D3711yescharacteristic
220C4⋊C8—371no—
221C4⋊C8—371no—
222#103—371no—
223#103—371no—
224#103—371no—
225#103C2×D3711yescharacteristic
226#102—371no—
227#102—371no—
228#102—371no—
229#102C2×D3711yescharacteristic
230C22⋊C8—371no—
231C22⋊C8—371no—
232#97—371no—
233C4×C8C2×D3711yescharacteristic
234#41—742no—
235#41—742no—
236C2×Q8—371no—
237C2×Q8—741no—
238C2×Q8C22×D3711yescharacteristic
239C2×D4—371no—
240C2×D4—741no—
241C2×D4—741no—
242C2×D4C22×D3711yescharacteristic
243C22×C4—21no—
244C22×C4—371no—
245C22×C4—741no—
246C22×C4—741no—
247C22×C4—741no—
248C22×C4—741no—
249Q16—742no—
250SD16—22no—
251SD16—742no—
252D8—742no—
253C2×C8—371no—
254C2×C8—371no—
255C2×C8C22×D3711yescharacteristic
256C2×C8C22×D3711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—371no—
271C22⋊C4—371no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C42—21no—
279C42—371no—
280C42—741no—
281C42—741no—
282C42C22×D3711yescharacteristic
283C23—21no—
284C23—371no—
285C23—741no—
286Q8—21no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290Q8#1059696212yes—
291D4—21no—
292D4—21no—
293D4—372no—
294D4—2961no—
295D4—744no—
296D4—741no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—371no—
304C2×C4—2961no—
305C2×C4—2961no—
306C2×C4—2961no—
307C2×C4—744no—
308C2×C4—741no—
309C2×C4—741no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4D4×D3711yescharacteristic
314C2×C4D4×D3711yescharacteristic
315C2×C4C23×D3711yescharacteristic
316C8—21no—
317C8—21no—
318C8—741no—
319C8—741no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—742no—
324C22—741no—
325C22—741no—
326C22—741no—
327C22—1481no—
328C22—1481no—
329C22C2×D4×D3711yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—741no—
336C4—741no—
337C4—741no—
338C4—1481no—
339C4—1481no—
340C4—1481no—
341C4#41×D3711yescharacteristic
342C4C2×#1059696211yescharacteristic
343C2—81no—
344C2—1481no—
345C2—1482no—
346C2#1455804211yescharacteristic
347C2#1455833911yescharacteristic
348C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×SD16×C37C2
socleC22×C37C22×D4
prime radical#14557677C2
hypercenterC4×SD16D37
hypocenterC37#3125
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14558148C2semidirect
2. #14558015C2semidirect
3. #14557865C2semidirect
4. #14557850C2semidirect
5. #14557822C2semidirect
6. #14557816C2semidirect
7. #14557753C2semidirect
8. #14557747C2semidirect
9. #14557698C2semidirect
11. #14557643C2semidirect
12. #14557638C2semidirect
13. C4×#10596930C2semidirect
14. #14557592C2semidirect
15. C4×SD16×C37C2semidirect
188. C4×SD16D37semidirect
190. C37#3125semidirect

Maximal subgroups

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

subgroupindex
#145581482
#145580152
#145578652
#145578502
#145578222
#145578162
#145577532
#145577472
#145576982
#145576772
#145576432
#145576382
C4×#105969302
#145575922
C4×SD16×C372
#312537