Finite Group Databasebeta

← #18004804

Subgroups — #18004804

Order 4736.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558013C211yesmaximal, characteristic
2#14557866C211yesmaximal, characteristic, complemented
3#14557861C211yesmaximal, characteristic, complemented
4#14557837C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557740C211yesmaximal, characteristic, complemented
7#14557735C211yesmaximal, characteristic, complemented
8#14557693C211yesmaximal, characteristic
9#14557693C211yesmaximal, characteristic
10#14557638C211yesmaximal, characteristic, complemented
11#14557631C211yesmaximal, characteristic, complemented
12C4×#10596942C211yesmaximal, characteristic, complemented
13C4×#10596941C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#541C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21C4×Dic74C2211yescharacteristic
22C4×Dic74C2211yescharacteristic
23C4×D148C2211yescharacteristic
24C4×D148C2211yescharacteristic
25#11924496—21no—
26#11924496—21no—
27#11924494—21no—
28C2×C4⋊Dic37C2211yescharacteristic
29C4⋊C4×D37—21no—
30#11924469C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35C4⋊#64436C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924460C2211yescharacteristic
39#11924460C2211yescharacteristic
40#11924459C2211yescharacteristic
41#11924459C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44C22⋊#64436C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46#11924447C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48C4⋊Q8×C37C2211yescharacteristic
49#126×C37—21no—
50#126×C37—21no—
51#125×C37—21no—
52#125×C37—21no—
53#125×C37C2211yescharacteristic
54C22⋊Q8×C37C2211yescharacteristic
55C22⋊Q8×C37C2211yescharacteristic
56C4×Q8×C37C2211yescharacteristic
57C4×Q8×C37C2211yescharacteristic
58#117×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C22×Dic37—21no—
64#10596962—22no—
65#10596962—22no—
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×Dic74C2311yescharacteristic
71C4⋊C4×C37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37D411yescharacteristic
80C4⋊C4×C37D411yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C22⋊C4×C37D411yescharacteristic
86C22⋊C4×C37D411yescharacteristic
87C42×C37—21no—
88C42×C37—21no—
89C42×C37C2311yescharacteristic
90C42×C37C2311yescharacteristic
91#10596942—22no—
92#10596942—22no—
93#10596941—22no—
94#10596941—22no—
95#10596938—21no—
96#10596938—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936—21no—
101#10596936—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110Q8×C37—21no—
111Q8×C37—21no—
112Q8×C37—21no—
113Q8×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C22⋊D37—24no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—81no—
131D148—21no—
132D148#4112yes—
133C4×D37—24no—
134C4×D37—81no—
135C4×D37—81no—
136Dic74—21no—
137Dic74#4112yes—
138#64436—21no—
139#64436—21no—
140#64436—21no—
141#64436—21no—
142C22×C37—21no—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37C22×D411yescharacteristic
146C2×D37—22no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—21no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—41no—
155C4×C37—41no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37C2×#4111yescharacteristic
159C4×C37C2×#4111yescharacteristic
160Dic37—22no—
161Dic37—41no—
162Dic37—41no—
163#3120—371nomaximal, Sylow
164C2×C37—41no—
165C2×C37#52511yescharacteristic
166C2×C37#57711yescharacteristic
167C2×C37#57811yescharacteristic
168D37—42no—
169#541D3711yescharacteristic, complemented
170#520—371no—
171#484—371no—
172#483—371no—
173#479—371no—
174#478—371no—
175#462—371no—
176#461—371no—
177#452—371no—
178#452—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312011yescharacteristic, complemented, Sylow
185C2×#41—371no—
186C2×Q16—371no—
187C2×Q16—371no—
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8C2×D3711yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D3711yescharacteristic
196C22⋊Q8C2×D3711yescharacteristic
197C22⋊Q8C2×D3711yescharacteristic
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8C2×D3711yescharacteristic
201C4×Q8C2×D3711yescharacteristic
202C4×D4—371no—
203C4×D4—371no—
204C4×D4—741no—
205C4×D4—741no—
206#117—741no—
207#117C2×D3711yescharacteristic
208C2×C4⋊C4—371no—
209C2×C4⋊C4—741no—
210#107—371no—
211#107—371no—
212#106—371no—
213#106—371no—
214C4⋊C8—371no—
215C4⋊C8—371no—
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103—371no—
221#103—371no—
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8—371no—
226#97—371no—
227C4×C8—371no—
228#41—742no—
229#41—742no—
230C2×Q8—371no—
231C2×Q8C22×D3711yescharacteristic
232C2×Q8C22×D3711yescharacteristic
233C2×D4—371no—
234C2×D4—741no—
235C22×C4—741no—
236C22×C4—741no—
237C22×C4—741no—
238C22×C4—741no—
239C22×C4C22×D3711yescharacteristic
240Q16—742no—
241Q16—742no—
242SD16—742no—
243SD16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8—371no—
247C2×C8—371no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4C22⋊D3711yescharacteristic
262C4⋊C4C22⋊D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4C22⋊D3711yescharacteristic
270C22⋊C4C22⋊D3711yescharacteristic
271C42—21no—
272C42—21no—
273C42—741no—
274C42—741no—
275C42C22×D3711yescharacteristic
276C42C22×D3711yescharacteristic
277C23—741no—
278C23C2×C22⋊D3711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—372no—
284Q8—741no—
285D4—372no—
286D4—744no—
287D4—741no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2961no—
295C2×C4—2961no—
296C2×C4—2961no—
297C2×C4—744no—
298C2×C4—741no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4C2×C22⋊D3711yescharacteristic
302C2×C4C2×C22⋊D3711yescharacteristic
303C2×C4C2×C22⋊D3711yescharacteristic
304C2×C4C2×C22⋊D3711yescharacteristic
305C2×C4C2×C22⋊D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—741no—
308C8—741no—
309C8—741no—
310C8—741no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—742no—
315C22—1481no—
316C22—1481no—
317C22C22×C22⋊D3711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—742no—
328C4—1481no—
329C4—1481no—
330C4#41×D3711yescharacteristic
331C4#41×D3711yescharacteristic
332C2—41no—
333C2—1482no—
334C2#1455804011yescharacteristic
335C2#1455834111yescharacteristic
336C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#541C2
socleC22×C37C22×D4
prime radicalC2×#10596962C22
hypercenter#541D37
hypocenterC37#3120
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14557866C2semidirect
3. #14557861C2semidirect
4. #14557837C2semidirect
5. #14557830C2semidirect
6. #14557740C2semidirect
7. #14557735C2semidirect
10. #14557638C2semidirect
11. #14557631C2semidirect
12. C4×#10596942C2semidirect
13. C4×#10596941C2semidirect
14. #14557594C2semidirect
15. C37×#541C2semidirect
169. #541D37semidirect
184. C37#3120semidirect

Maximal subgroups

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

subgroupindex
#145580132
#145578662
#145578612
#145578372
#145578302
#145577402
#145577352
#145576932
#145576382
#145576312
C4×#105969422
C4×#105969412
#145575942
C37×#5412
#312037