Finite Group Databasebeta

← #18006509

Subgroups — #18006509

Order 4736.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558251C211yesmaximal, characteristic, complemented
2#14558182C211yesmaximal, characteristic
3#14557882C211yesmaximal, characteristic, complemented
4#14557874C211yesmaximal, characteristic, complemented
5#14557873C211yesmaximal, characteristic, complemented
6#14557811C211yesmaximal, characteristic, complemented
7#14557774C211yesmaximal, characteristic, complemented
8#14557773C211yesmaximal, characteristic, complemented
9#14557742C211yesmaximal, characteristic, complemented
10#14557696C211yesmaximal, characteristic, complemented
11#14557695C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#14557526C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924534C2211yescharacteristic
23#11924530—21no—
24#11924529—21no—
25#11924522—21no—
26#11924519—21no—
27#11924517—21no—
28#11924516C2211yescharacteristic
29#11924515C2211yescharacteristic
30#11924515C2211yescharacteristic
31#11924512C2211yescharacteristic
32#11924508—21no—
33C4×Dic74—21no—
34#11924501C2211yescharacteristic
35D4×Dic37C2211yescharacteristic
36C4×C22⋊D37C2211yescharacteristic
37#11924494C2211yescharacteristic
38C2×#10596936—21no—
39#11924470C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#117×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×C22⋊D37D411yescharacteristic
68C22×Dic37—21no—
69C22×Dic37—21no—
70#10596964—22no—
71#10596964—41no—
72C2×C4×D37C2311yescharacteristic
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C2×C8×C37—41no—
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C42×C37—21no—
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596942—41no—
88#10596940—22no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936D411yescharacteristic
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109Dic148—41no—
110C8×D37—41no—
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C22×D37C2×D411yescharacteristic
114Q8×C37—21no—
115Q8×C37—21no—
116D4×C37—21no—
117D4×C37—42no—
118D4×C37#4112yes—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—42no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—22no—
128C22⋊D37—42no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—42no—
134C2×Dic37—42no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138C4×D37—21no—
139C4×D37—21no—
140Dic74—21no—
141Dic74—21no—
142Dic74—21no—
143Dic74—21no—
144Dic74—42no—
145C8×C37—21no—
146C8×C37—21no—
147#64436—21no—
148#64436—21no—
149C22×C37—22no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C4×C37—21no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37C2×#4111yescharacteristic
164C4×C37H(5,𝔽2)11yescharacteristic
165Dic37—21no—
166Dic37—21no—
167Dic37—41no—
168Dic37—41no—
169Dic37—41no—
170Dic37—41no—
171Dic37#13512yes—
172#3302—371nomaximal, Sylow
173C2×C37—41no—
174C2×C37—42no—
175C2×C37#54611yescharacteristic
176C2×C37C2×#13511yescharacteristic
177C2×C37#57811yescharacteristic
178D37—41no—
179#556—371no—
180#547—371no—
181#487—371no—
182#485—371no—
183#485—371no—
184#474—371no—
185#467—371no—
186#467—371no—
187#462—371no—
188#452—371no—
189#452—371no—
190C4×SD16—371no—
191C8×D4—371no—
192#416—371no—
193#416D3711yescharacteristic, complemented
194C37#330211yescharacteristic, complemented, Sylow
195C2×#41—371no—
196C2×#41C2×D3711yescharacteristic
197C2×Q16—371no—
198C2×Q16—371no—
199C2×SD16—371no—
200C22×C8—371no—
201C22×C8C2×D3711yescharacteristic
202C4⋊Q8—371no—
203C4⋊Q8—371no—
204#126—741no—
205#126—741no—
206#124—741no—
207#123—741no—
208#123—741no—
209C22⋊Q8—371no—
210C22⋊Q8—371no—
211C22⋊Q8—371no—
212C22⋊Q8—371no—
213#121—741no—
214C4×Q8—371no—
215C4×Q8—741no—
216C4×D4—371no—
217C4×D4—371no—
218#117—371no—
219#117C2×D3711yescharacteristic
220C2×C4⋊C4—741no—
221#107—371no—
222#107—371no—
223#106—371no—
224C4⋊C8—371no—
225#103—371no—
226#103—371no—
227#103—371no—
228#103—371no—
229#103—371no—
230#103C2×D3711yescharacteristic
231#103C2×D3711yescharacteristic
232#102—371no—
233#102C2×D3711yescharacteristic
234#102C2×D3711yescharacteristic
235C22⋊C8—371no—
236C22⋊C8—371no—
237C4×C8—371no—
238#41—22no—
239#41—41no—
240#41—742no—
241#41—1481no—
242C2×Q8—371no—
243C2×Q8—371no—
244C2×Q8—741no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—21no—
247C2×D4—371no—
248C2×D4—741no—
249C2×D4C22×D3711yescharacteristic
250C22×C4—21no—
251C22×C4—371no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4C22×D3711yescharacteristic
255Q16—1481no—
256Q16—1481no—
257SD16—742no—
258C2×C8—41no—
259C2×C8—371no—
260C2×C8—371no—
261C2×C8—1481no—
262C2×C8C22×D3711yescharacteristic
263C2×C8C22×D3711yescharacteristic
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
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—371no—
279C22⋊C4—371no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C42—21no—
287C42—371no—
288C42—741no—
289C42—741no—
290C23—21no—
291C23—371no—
292C23D4×D3711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—741no—
296Q8—741no—
297Q8—741no—
298Q8—741no—
299Q8—1482no—
300D4—21no—
301D4—42no—
302D4—742no—
303D4—1482no—
304D4#1059696212yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—371no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—1482no—
321C2×C4—1482no—
322C2×C4D4×D3711yescharacteristic
323C2×C4C23×D3711yescharacteristic
324C8—21no—
325C8—21no—
326C8—741no—
327C8—741no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—741no—
335C22—741no—
336C22—741no—
337C22C2×D4×D3711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—372no—
343C4—741no—
344C4—741no—
345C4—1481no—
346C4—1481no—
347C4—1481no—
348C4—1481no—
349C4C2×#1059696211yescharacteristic
350C4#1192458111yescharacteristic
351C2—41no—
352C2—42no—
353C2—1481no—
354C2#1455817311yescharacteristic
355C2#135×D3711yescharacteristic
356C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
prime radical#14558182C2
hypercenter#416D37
hypocenterC37#3302
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14558251C2semidirect
3. #14557882C2semidirect
4. #14557874C2semidirect
5. #14557873C2semidirect
6. #14557811C2semidirect
7. #14557774C2semidirect
8. #14557773C2semidirect
9. #14557742C2semidirect
10. #14557696C2semidirect
11. #14557695C2semidirect
12. #14557624C2semidirect
13. C8×C22⋊D37C2semidirect
14. #14557526C2semidirect
15. C37×#416C2semidirect
193. #416D37semidirect
194. C37#3302semidirect

Maximal subgroups

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

subgroupindex
#145582512
#145581822
#145578822
#145578742
#145578732
#145578112
#145577742
#145577732
#145577422
#145576962
#145576952
#145576242
C8×C22⋊D372
#145575262
C37×#4162
#330237