Finite Group Databasebeta

← #18007196

Subgroups — #18007196

Order 4736.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558229C211yesmaximal, characteristic, complemented
2#14557932C211yesmaximal, characteristic, complemented
3#14557857C211yesmaximal, characteristic, complemented
4#14557854C211yesmaximal, characteristic, complemented
5#14557846C211yesmaximal, characteristic, complemented
6#14557844C211yesmaximal, characteristic, complemented
7#14557833C211yesmaximal, characteristic, complemented
8#14557830C211yesmaximal, characteristic, complemented
9#14557784C211yesmaximal, characteristic, complemented
10#14557784C211yesmaximal, characteristic, complemented
11C4×#10596939C211yesmaximal, characteristic, complemented
12#14557611C211yesmaximal, characteristic, complemented
13#14557576C211yesmaximal, characteristic, complemented
14#14557573C211yesmaximal, characteristic, complemented
15C37×#553C211yesmaximal, characteristic, complemented
16C2×#10596939C2211yescharacteristic
17C2×#10596934C2211yescharacteristic
18C2×#10596934C2211yescharacteristic
19#11924531—21no—
20#11924528C2211yescharacteristic
21#11924518—21no—
22#11924510C2211yescharacteristic
23#11924510C2211yescharacteristic
24#11924508—21no—
25C4×D148C2211yescharacteristic
26#11924496—21no—
27#11924495C2211yescharacteristic
28C2×C4⋊Dic37C2211yescharacteristic
29#11924469C2211yescharacteristic
30#11924469C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924469C2211yescharacteristic
33#11924469C2211yescharacteristic
34#11924467C2211yescharacteristic
35#11924467C2211yescharacteristic
36#11924467C2211yescharacteristic
37#11924467C2211yescharacteristic
38C4⋊#64436C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
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—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37D411yescharacteristic
84C22⋊C4×C37D411yescharacteristic
85C42×C37—21no—
86C42×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98C4×Dic37—21no—
99#10596934—22no—
100#10596934—22no—
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C23×C37—21no—
106C23×C37C2×D411yescharacteristic
107C23×C37C2×D411yescharacteristic
108C22×D37—21no—
109D4×C37—21no—
110D4×C37—21no—
111D4×C37—41no—
112D4×C37—42no—
113D4×C37—81no—
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×C37—21no—
121C2×C4×C37—81no—
122C2×C4×C37—81no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—42no—
129C22⋊D37—81no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—81no—
134D148—21no—
135D148—21no—
136C4×D37—81no—
137#64436—21no—
138#64436—21no—
139#64436—21no—
140#64436#4112yes—
141C22×C37—21no—
142C22×C37—21no—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37—21no—
146C22×C37—21no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37C22×D411yescharacteristic
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37C2×#4111yescharacteristic
162C4×C372−1+411yescharacteristic
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166#3355—371nomaximal, Sylow
167C2×C37—41no—
168C2×C37—41no—
169C2×C37—81no—
170C2×C37#54711yescharacteristic
171C2×C37#57511yescharacteristic
172C2×C37#57611yescharacteristic
173D37—81no—
174#553—371no—
175#553D3711yescharacteristic, complemented
176#499—371no—
177#482—371no—
178#482—371no—
179#480—371no—
180#480—371no—
181#478—371no—
182#478—371no—
183#469—371no—
184#469—371no—
185C4×D8—371no—
186#436—371no—
187#428—371no—
188#428—371no—
189C37#335511yescharacteristic, complemented, Sylow
190C2×D8—371no—
191C2×M16—371no—
192C2×M16—371no—
193#126—21no—
194#126—741no—
195#125—371no—
196#125C2×D3711yescharacteristic
197#123—21no—
198#123—741no—
199#121—21no—
200#121—371no—
201#121—371no—
202#121—741no—
203#121C2×D3711yescharacteristic
204#121C2×D3711yescharacteristic
205C4×D4—21no—
206C4×D4—371no—
207C4×D4—741no—
208C4×D4C2×D3711yescharacteristic
209C4×D4C2×D3711yescharacteristic
210#117—371no—
211#117C2×D3711yescharacteristic
212C2×C4⋊C4—371no—
213C2×C4⋊C4C2×D3711yescharacteristic
214#107—371no—
215#107—371no—
216#107—371no—
217#107—371no—
218#107—371no—
219#106—371no—
220#106—371no—
221#106—371no—
222#106—371no—
223C4⋊C8—371no—
224#102—371no—
225#102—371no—
226#102—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230C22⋊C8—371no—
231C22⋊C8—371no—
232C4×C8—371no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—371no—
236C2×D4—741no—
237C2×D4—741no—
238C2×D4C22⋊D3711yescharacteristic
239C2×D4C22×D3711yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—741no—
243C22×C4—741no—
244C22×C4C22×D3711yescharacteristic
245C22×C4C22×D3711yescharacteristic
246D8—742no—
247M16—742no—
248M16—742no—
249C2×C8—371no—
250C2×C8—371no—
251C2×C8—371no—
252C2×C8—371no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4C22⋊D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C4⋊C4C22×D3711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4C22⋊D3711yescharacteristic
275C22⋊C4C22⋊D3711yescharacteristic
276C42—21no—
277C42—741no—
278C42C22×D3711yescharacteristic
279C23—21no—
280C23—741no—
281C23C2×C22⋊D3711yescharacteristic
282C23C2×C22⋊D3711yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—2961no—
289D4—741no—
290D4—741no—
291D4—1482no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—2961no—
302C2×C4—2961no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4C2×C22⋊D3711yescharacteristic
307C2×C4C2×C22⋊D3711yescharacteristic
308C2×C4C2×C22⋊D3711yescharacteristic
309C2×C4C2×C22⋊D3711yescharacteristic
310C2×C4C23×D3711yescharacteristic
311C8—372no—
312C8—741no—
313C8—741no—
314C8—741no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1481no—
325C22—1481no—
326C22—1481no—
327C22C22×C22⋊D3711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1481no—
336C4—1481no—
337C4—1481no—
338C4#41×D3711yescharacteristic
339C4#1192458311yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—2961no—
344C2#1455818211yescharacteristic
345C2#1455833111yescharacteristic
346C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#553C2
socleC22×C37C22×D4
hypercenter#553D37
hypocenterC37#3355
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. #14558229C2semidirect
2. #14557932C2semidirect
3. #14557857C2semidirect
4. #14557854C2semidirect
5. #14557846C2semidirect
6. #14557844C2semidirect
7. #14557833C2semidirect
8. #14557830C2semidirect
9. #14557784C2semidirect
10. #14557784C2semidirect
11. C4×#10596939C2semidirect
12. #14557611C2semidirect
13. #14557576C2semidirect
14. #14557573C2semidirect
15. C37×#553C2semidirect
175. #553D37semidirect
189. C37#3355semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145579322
#145578572
#145578542
#145578462
#145578442
#145578332
#145578302
#145577842
C4×#105969392
#145576112
#145575762
#145575732
C37×#5532
#335537