Finite Group Databasebeta

← #18004825

Subgroups — #18004825

Order 4736.

370 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#14558154C211yesmaximal, characteristic
2#14557874C211yesmaximal, characteristic, complemented
3#14557857C211yesmaximal, characteristic
4#14557828C211yesmaximal, characteristic, complemented
5#14557818C211yesmaximal, characteristic, complemented
6#14557755C211yesmaximal, characteristic, complemented
7#14557755C211yesmaximal, characteristic, complemented
8#14557689C211yesmaximal, characteristic, complemented
9#14557672C211yesmaximal, characteristic
10#14557638C211yesmaximal, characteristic, complemented
11#14557631C211yesmaximal, characteristic, complemented
12C4×#10596942C211yesmaximal, characteristic, complemented
13C4×#10596941C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#519C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20#11924536C2211yescharacteristic
21#11924531—21no—
22#11924524C2211yescharacteristic
23#11924522—21no—
24#11924518—21no—
25#11924515C2211yescharacteristic
26#11924514—21no—
27#11924510C2211yescharacteristic
28C4×Dic74C2211yescharacteristic
29C4×D148C2211yescharacteristic
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
48C22×Q8×C37C2211yescharacteristic
49C4×Q8×C37—21no—
50C4×Q8×C37—21no—
51C4×Q8×C37C2211yescharacteristic
52C4×Q8×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic
55#117×C37—21no—
56#117×C37—21no—
57#117×C37C2211yescharacteristic
58#117×C37C2211yescharacteristic
59C2×Q8×C37—22no—
60C2×Q8×C37—22no—
61C2×Q8×C37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×Dic74—21no—
70C2×Dic74C2311yescharacteristic
71C4⋊C4×C37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37D411yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37D411yescharacteristic
81C22⋊C4×C37D411yescharacteristic
82C42×C37—21no—
83C42×C37—21no—
84C42×C37—21no—
85C42×C37—21no—
86C42×C37—21no—
87C42×C37C2311yescharacteristic
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90#10596942—22no—
91#10596942—22no—
92#10596941—22no—
93#10596941—22no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110Q8×C37—24no—
111Q8×C37—21no—
112Q8×C37—21no—
113Q8×C37#4112yes—
114Q8×C37#4112yes—
115C2×C4×C37—24no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—81no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132D148—21no—
133D148—21no—
134C4×D37—81no—
135Dic74—21no—
136Dic74—21no—
137Dic74—81no—
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—41no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—22no—
150C4×C37—22no—
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37C2×#4111yescharacteristic
159C4×C37C2×#4111yescharacteristic
160Dic37—41no—
161Dic37—41no—
162Dic37—41no—
163#3121—371nomaximal, Sylow
164C2×C37—41no—
165C2×C37#52511yescharacteristic
166C2×C37#57711yescharacteristic
167C2×C37#57811yescharacteristic
168D37—81no—
169#542—371no—
170#519D3711yescharacteristic, complemented
171#485—371no—
172#482—371no—
173#477—371no—
174#475—371no—
175#464—371no—
176#464—371no—
177#451—371no—
178#448—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312111yescharacteristic, complemented, Sylow
185C22×Q8C2×D3711yescharacteristic
186C2×Q16—371no—
187C2×Q16—371no—
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8—371no—
191#126—741no—
192#124—371no—
193#124—741no—
194#123—741no—
195C22⋊Q8—371no—
196C22⋊Q8—741no—
197#121—371no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—371no—
201C4×Q8C2×D3711yescharacteristic
202C4×Q8C2×D3711yescharacteristic
203C4×Q8C2×D3711yescharacteristic
204C4×Q8C2×D3711yescharacteristic
205C4×D4—371no—
206#117—21no—
207#117—21no—
208#117C2×D3711yescharacteristic
209#117C2×D3711yescharacteristic
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—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—371no—
232C2×Q8—741no—
233C2×Q8C22×D3711yescharacteristic
234C2×Q8C22×D3711yescharacteristic
235C2×D4—371no—
236C2×D4—741no—
237C22×C4—21no—
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—371no—
253C4⋊C4—371no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4C22⋊D3711yescharacteristic
258C4⋊C4C22⋊D3711yescharacteristic
259C4⋊C4C22×D3711yescharacteristic
260C4⋊C4C22×D3711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—741no—
263C22⋊C4—741no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4C22⋊D3711yescharacteristic
268C22⋊C4C22⋊D3711yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—741no—
275C42C22×D3711yescharacteristic
276C42C22×D3711yescharacteristic
277C23—741no—
278C23C2×C22⋊D3711yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—2961no—
283Q8—741no—
284Q8—741no—
285Q8#1059696212yes—
286Q8#1059696212yes—
287D4—2961no—
288D4—741no—
289D4—741no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2961no—
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—1481no—
315C22—1481no—
316C22—1481no—
317C22C22×C22⋊D3711yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—1481no—
328C4—1481no—
329C4—1481no—
330C4C2×#1059696211yescharacteristic
331C4C2×#1059696211yescharacteristic
332C2—41no—
333C2—2961no—
334C2#1455804411yescharacteristic
335C2#1455834111yescharacteristic
336C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#519C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#519D37
hypocenterC37#3121
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #14557874C2semidirect
4. #14557828C2semidirect
5. #14557818C2semidirect
6. #14557755C2semidirect
7. #14557755C2semidirect
8. #14557689C2semidirect
10. #14557638C2semidirect
11. #14557631C2semidirect
12. C4×#10596942C2semidirect
13. C4×#10596941C2semidirect
14. #14557594C2semidirect
15. C37×#519C2semidirect
170. #519D37semidirect
184. C37#3121semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145578742
#145578572
#145578282
#145578182
#145577552
#145576892
#145576722
#145576382
#145576312
C4×#105969422
C4×#105969412
#145575942
C37×#5192
#312137