Finite Group Databasebeta

← #18007300

Subgroups — #18007300

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#14558239C211yesmaximal, characteristic, complemented
2#14558203C211yesmaximal, characteristic, complemented
3#14557896C211yesmaximal, characteristic, complemented
4#14557878C211yesmaximal, characteristic, complemented
5#14557835C211yesmaximal, characteristic, complemented
6#14557830C211yesmaximal, characteristic, complemented
7#14557821C211yesmaximal, characteristic, complemented
8#14557727C211yesmaximal, characteristic, complemented
9#14557727C211yesmaximal, characteristic, complemented
10#14557725C211yesmaximal, characteristic, complemented
11#14557661C211yesmaximal, characteristic, complemented
12#14557646C211yesmaximal, characteristic, complemented
13#14557642C211yesmaximal, characteristic, complemented
14#14557613C211yesmaximal, characteristic, complemented
15C37×#490C211yesmaximal, characteristic, complemented
16C2×#10596964—21no—
17C2×D296C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20#11924535C2211yescharacteristic
21#11924532C2211yescharacteristic
22#11924532C2211yescharacteristic
23#11924527C2211yescharacteristic
24#11924516—21no—
25#11924514—21no—
26#11924514—21no—
27#11924508—21no—
28#11924508—21no—
29#11924507—21no—
30C4×Dic74C2211yescharacteristic
31C4×D148C2211yescharacteristic
32C4×D148C2211yescharacteristic
33D4×Dic37C2211yescharacteristic
34D4×Dic37C2211yescharacteristic
35#11924498C2211yescharacteristic
36#11924498C2211yescharacteristic
37C4⋊C4×D37—21no—
38#11924469C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52#127×C37C2211yescharacteristic
53#125×C37C2211yescharacteristic
54#102×C37C2211yescharacteristic
55#102×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69#10596964—44no—
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×Dic74—21no—
77C2×Dic74D411yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C42×C37C2311yescharacteristic
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87#10596939—22no—
88#10596939—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37D411yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936D411yescharacteristic
100#10596936D411yescharacteristic
101C4×Dic37C2311yescharacteristic
102C4×Dic37C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105D296—22no—
106C23×C37—21no—
107C23×C37—21no—
108C22×D37—21no—
109C22×D37—21no—
110D4×C37—21no—
111D4×C37—21no—
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—42no—
115D4×C37—81no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
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—42no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135D148—21no—
136D148#4112yescomplemented
137C4×D37—42no—
138C4×D37—42no—
139C4×D37—81no—
140C4×D37—81no—
141Dic74—22no—
142Dic74—81no—
143C8×C37—21no—
144C8×C37—21no—
145#64436—21no—
146#64436—21no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37C22×D411yescharacteristic
154C2×D37—22no—
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—81no—
174C2×C37—81no—
175C2×C37#54811yescharacteristic
176C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C37#57611yescharacteristic
178D37—42no—
179D37—81no—
180#554—371no—
181#550—371no—
182#490—371no—
183#490D3711yescharacteristic, complemented
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#442—371no—
194C4×D8—371no—
195C37#336611yescharacteristic, complemented, Sylow
196C2×#41—741no—
197C2×D8—371no—
198C2×D8—371no—
199C2×D8—371no—
200C4⋊Q8—371no—
201#127—371no—
202#127—371no—
203#127C2×D3711yescharacteristic
204#125—371no—
205#125C2×D3711yescharacteristic
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×D4—371no—
218C4×D4—371no—
219C2×C4⋊C4—741no—
220#107—371no—
221#106—371no—
222#106—371no—
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#102C2×D3711yescharacteristic
233#102C2×D3711yescharacteristic
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—21no—
243C2×D4—21no—
244C2×D4—371no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C2×D4C22×D3711yescharacteristic
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
258D8—742no—
259D8—742no—
260D8—742no—
261C2×C8—371no—
262C2×C8—371no—
263C2×C8C22×D3711yescharacteristic
264C2×C8C22×D3711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—371no—
271C4⋊C4—371no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—741no—
278C22⋊C4—741no—
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—21no—
296D4—42no—
297D4—81no—
298D4—372no—
299D4—2961no—
300D4—2961no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—1482no—
305D4—1482no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—371no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—371no—
312C2×C4—2961no—
313C2×C4—2961no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—1482no—
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—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—742no—
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—
350C4#41×D3711yescharacteristic
351C4#1192458311yescharacteristic
352C2—81no—
353C2—81no—
354C2—2961no—
355C2—1482no—
356C2#1455819111yescharacteristic
357C2AGL(1,ℤ/8)×D3711yescharacteristic
358C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#490C2
socleC22×C37C22×D4
hypercenter#490D37
hypocenterC37#3366
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14558239C2semidirect
2. #14558203C2semidirect
3. #14557896C2semidirect
4. #14557878C2semidirect
5. #14557835C2semidirect
6. #14557830C2semidirect
7. #14557821C2semidirect
8. #14557727C2semidirect
9. #14557727C2semidirect
10. #14557725C2semidirect
11. #14557661C2semidirect
12. #14557646C2semidirect
13. #14557642C2semidirect
14. #14557613C2semidirect
15. C37×#490C2semidirect
136. D148#41semidirect
183. #490D37semidirect
195. C37#3366semidirect

Maximal subgroups

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

subgroupindex
#145582392
#145582032
#145578962
#145578782
#145578352
#145578302
#145578212
#145577272
#145577252
#145576612
#145576462
#145576422
#145576132
C37×#4902
#336637