Finite Group Databasebeta

← #18007304

Subgroups — #18007304

Order 4736.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558242C211yesmaximal, characteristic, complemented
2#14558204C211yesmaximal, characteristic, complemented
3#14557898C211yesmaximal, characteristic, complemented
4#14557896C211yesmaximal, characteristic, complemented
5#14557878C211yesmaximal, characteristic, complemented
6#14557833C211yesmaximal, characteristic, complemented
7#14557832C211yesmaximal, characteristic, complemented
8#14557822C211yesmaximal, characteristic, complemented
9#14557728C211yesmaximal, characteristic, complemented
10#14557726C211yesmaximal, characteristic, complemented
11#14557726C211yesmaximal, characteristic, complemented
12#14557661C211yesmaximal, characteristic, complemented
13#14557642C211yesmaximal, characteristic, complemented
14#14557613C211yesmaximal, characteristic, complemented
15C37×#442C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×#10596939C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19#11924535C2211yescharacteristic
20#11924533C2211yescharacteristic
21#11924532C2211yescharacteristic
22#11924532C2211yescharacteristic
23#11924528C2211yescharacteristic
24#11924527C2211yescharacteristic
25#11924515—21no—
26#11924513—21no—
27#11924513—21no—
28#11924510—21no—
29#11924509—21no—
30#11924509—21no—
31C4×Dic74C2211yescharacteristic
32D4×Dic37C2211yescharacteristic
33D4×Dic37C2211yescharacteristic
34#11924498C2211yescharacteristic
35#11924498C2211yescharacteristic
36C2×#10596936—21no—
37#11924469C2211yescharacteristic
38#11924467C2211yescharacteristic
39C4⋊#64436C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924458C2211yescharacteristic
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×D8×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×D4×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69#10596962—44no—
70C2×D148—21no—
71C2×D148—21no—
72C2×D148C2311yescharacteristic
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×Dic74—21no—
77C2×Dic74D411yescharacteristic
78D8×C37—22no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C42×C37C2311yescharacteristic
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88#10596939—22no—
89#10596939—22no—
90#10596938—21no—
91#10596938—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37D411yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C23×C37—21no—
107C23×C37—21no—
108C22×D37—21no—
109C22×D37—21no—
110D4×C37—21no—
111D4×C37—21no—
112D4×C37—21no—
113D4×C37#4112yescomplemented
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—42no—
117C2×C4×C37—81no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—42no—
122C22⋊D37—42no—
123C22⋊D37—81no—
124C22⋊D37—81no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—42no—
128C2×Dic37—81no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135D148—21no—
136D148—21no—
137D148—42no—
138D148—81no—
139C4×D37—42no—
140C4×D37—42no—
141Dic74—22no—
142Dic74—81no—
143C8×C37—21no—
144C8×C37—21no—
145#64436—21no—
146#64436—21no—
147C22×C37—22no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37C22×D411yescharacteristic
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C4×C37—21no—
161C4×C37—21no—
162C4×C37—41no—
163C4×C37—41no—
164C4×C37C2×#4111yescharacteristic
165C4×C372−1+411yescharacteristic
166Dic37—21no—
167Dic37—21no—
168Dic37—21no—
169Dic37—41no—
170Dic37—41no—
171Dic37AGL(1,ℤ/8)12yes—
172#3366—371nomaximal, Sylow
173C2×C37—42no—
174C2×C37—81no—
175C2×C37#54811yescharacteristic
176C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C37#57611yescharacteristic
178D37—81no—
179D37—81no—
180#554—371no—
181#550—371no—
182#490—371no—
183#490—371no—
184#486—371no—
185#478—371no—
186#478—371no—
187#476—371no—
188#459—371no—
189#459—371no—
190#459—371no—
191#446—371no—
192#442—371no—
193#442D3711yescharacteristic, complemented
194C4×D8—371no—
195C37#336611yescharacteristic, complemented, Sylow
196C2×#41—741no—
197C2×D8—371no—
198C2×D8—371no—
199C2×D8C2×D3711yescharacteristic
200C4⋊Q8—371no—
201#127—371no—
202#127—371no—
203#127—371no—
204#125—371no—
205#125—371no—
206C22⋊Q8—741no—
207C22⋊Q8—741no—
208C22⋊Q8—741no—
209#121—741no—
210#121—741no—
211#121—741no—
212C4×Q8—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—371no—
217C4×D4C2×D3711yescharacteristic
218C4×D4C2×D3711yescharacteristic
219C2×C4⋊C4—741no—
220#107—371no—
221#106—371no—
222#106C2×D3711yescharacteristic
223C4⋊C8—371no—
224C4⋊C8—371no—
225C4⋊C8—371no—
226#102—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102C2×D3711yescharacteristic
235#102C2×D3711yescharacteristic
236#97—371no—
237#97C2×D3711yescharacteristic
238C4×C8—371no—
239#41—1484no—
240C2×Q8—371no—
241C2×Q8—741no—
242C2×D4—371no—
243C2×D4—371no—
244C2×D4—741no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C2×D4C22×D3711yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
258D8—22no—
259D8—742no—
260D8—742no—
261C2×C8—371no—
262C2×C8—371no—
263C2×C8C22×D3711yescharacteristic
264C2×C8C22×D3711yescharacteristic
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C42—371no—
284C42—371no—
285C42C22×D3711yescharacteristic
286C23—21no—
287C23—21no—
288C23—741no—
289C23—741no—
290Q8—2961no—
291Q8—742no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—2961no—
296D4—2961no—
297D4—2961no—
298D4—741no—
299D4—741no—
300D4—741no—
301D4—741no—
302D4—1482no—
303D4—1482no—
304D4—1482no—
305D4#1059696212yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—371no—
311C2×C4—371no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—2961no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—1482no—
318C2×C4—1482no—
319C2×C4—1482no—
320C2×C4D4×D3711yescharacteristic
321C2×C4D4×D3711yescharacteristic
322C2×C4C23×D3711yescharacteristic
323C8—21no—
324C8—21no—
325C8—741no—
326C8—741no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22—1481no—
338C22—1481no—
339C22C2×D4×D3711yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—372no—
345C4—741no—
346C4—741no—
347C4—741no—
348C4—1481no—
349C4—1481no—
350C4C2×#1059696211yescharacteristic
351C4#1192458311yescharacteristic
352C2—42no—
353C2—81no—
354C2—2961no—
355C2—2961no—
356C2#1455819211yescharacteristic
357C2AGL(1,ℤ/8)×D3711yescharacteristic
358C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#442C2
socleC22×C37C22×D4
hypercenter#442D37
hypocenterC37#3366
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14558242C2semidirect
2. #14558204C2semidirect
3. #14557898C2semidirect
4. #14557896C2semidirect
5. #14557878C2semidirect
6. #14557833C2semidirect
7. #14557832C2semidirect
8. #14557822C2semidirect
9. #14557728C2semidirect
10. #14557726C2semidirect
11. #14557726C2semidirect
12. #14557661C2semidirect
13. #14557642C2semidirect
14. #14557613C2semidirect
15. C37×#442C2semidirect
113. D4×C37#41semidirect
193. #442D37semidirect
195. C37#3366semidirect
305. D4#10596962semidirect

Maximal subgroups

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

subgroupindex
#145582422
#145582042
#145578982
#145578962
#145578782
#145578332
#145578322
#145578222
#145577282
#145577262
#145576612
#145576422
#145576132
C37×#4422
#336637