Finite Group Databasebeta

← #18005311

Subgroups — #18005311

Order 4736.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558087C211yesmaximal, characteristic, complemented
2#14558080C211yesmaximal, characteristic
3#14557937C211yesmaximal, characteristic, complemented
4#14557904C211yesmaximal, characteristic, complemented
5#14557882C211yesmaximal, characteristic, complemented
6#14557878C211yesmaximal, characteristic, complemented
7#14557782C211yesmaximal, characteristic, complemented
8#14557780C211yesmaximal, characteristic, complemented
9#14557778C211yesmaximal, characteristic, complemented
10#14557776C211yesmaximal, characteristic, complemented
11#14557635C211yesmaximal, characteristic, complemented
12#14557633C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, characteristic, complemented
14#14557485C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21C2×#10596929C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924535C2211yescharacteristic
24#11924534C2211yescharacteristic
25#11924532C2211yescharacteristic
26#11924526—21no—
27#11924522—21no—
28#11924516C2211yescharacteristic
29#11924514—21no—
30#11924512C2211yescharacteristic
31#11924511C2211yescharacteristic
32#11924509—21no—
33#11924507C2211yescharacteristic
34C4×Dic74—21no—
35C4×Dic74C2211yescharacteristic
36C4×D148C2211yescharacteristic
37C4×C22⋊D37—21no—
38#11924493—21no—
39C42×D37C2211yescharacteristic
40#11924470C2211yescharacteristic
41#11924469C2211yescharacteristic
42#11924469C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924447C2211yescharacteristic
50C8×Dic37C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C4×Q8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65#10596962—44no—
66C2×D148—21no—
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×C4×D37D411yescharacteristic
70C2×C4×D37D411yescharacteristic
71C2×C4×D37C2311yescharacteristic
72C2×Dic74—21no—
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75SD16×C37—22no—
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37—21no—
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C42×C37—21no—
83C42×C37C2311yescharacteristic
84C22⋊Dic37—21no—
85#10596941—22no—
86#10596940—22no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37C2311yescharacteristic
93C4⋊Dic37C2311yescharacteristic
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100C4×Dic37—21no—
101C4×Dic37D411yescharacteristic
102C4×Dic37D411yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596930—22no—
107#10596929—22no—
108#10596929—22no—
109C23×C37—21no—
110C22×D37—21no—
111C22×D37C2×D411yescharacteristic
112Q8×C37—21no—
113Q8×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—42no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2411yescharacteristic
123C22⋊D37—42no—
124C22⋊D37—42no—
125C22⋊D37—42no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132D148—21no—
133D148—21no—
134D148—42no—
135C4×D37—21no—
136C4×D37—21no—
137C4×D37—22no—
138C4×D37—22no—
139C4×D37—42no—
140Dic74—21no—
141Dic74—21no—
142Dic74—42no—
143Dic74—42no—
144C8×C37—21no—
145C8×C37#4112yescomplemented
146#64436—21no—
147#64436#4112yescomplemented
148C22×C37—41no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37C22×D411yescharacteristic
152C2×D37—21no—
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C4×C37—21no—
159C4×C37—21no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37C2×#4111yescharacteristic
164C4×C37C2×#4111yescharacteristic
165Dic37—21no—
166Dic37—41no—
167Dic37—41no—
168Dic37—41no—
169Dic37AGL(1,ℤ/8)12yes—
170Dic37#13712yes—
171#3182—371nomaximal, Sylow
172C2×C37—81no—
173C2×C37#53211yescharacteristic
174C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C37C2×#13711yescharacteristic
176D37—41no—
177D37—81no—
178#533—371no—
179#532—371no—
180#500—371no—
181#492—371no—
182#487—371no—
183#486—371no—
184#468—371no—
185#468—371no—
186#468—371no—
187#468—371no—
188#440—371no—
189#440—371no—
190#440—371no—
191#440D3711yescharacteristic, complemented
192C4×M16—371no—
193C37#318211yescharacteristic, complemented, Sylow
194C2×#41—741no—
195C2×SD16—371no—
196C2×SD16—371no—
197C2×SD16—371no—
198C2×SD16C2×D3711yescharacteristic
199C2×M16—371no—
200C2×M16—371no—
201C4⋊Q8—371no—
202C4⋊Q8—371no—
203C4⋊Q8—371no—
204#127—371no—
205#125—741no—
206#124—741no—
207C22⋊Q8—371no—
208C22⋊Q8—371no—
209C22⋊Q8—741no—
210#121—371no—
211#121—371no—
212#121—741no—
213C4×Q8—371no—
214C4×Q8—741no—
215C4×Q8C2×D3711yescharacteristic
216C4×D4—371no—
217C4×D4—741no—
218C4×D4C2×D3711yescharacteristic
219#117—741no—
220C2×C42—371no—
221#107—371no—
222#107—371no—
223#107—371no—
224#107C2×D3711yescharacteristic
225#103—371no—
226#103—371no—
227#103—371no—
228#103C2×D3711yescharacteristic
229#102—371no—
230#102—371no—
231#102—371no—
232#102C2×D3711yescharacteristic
233#97—371no—
234#97C2×D3711yescharacteristic
235C4×C8—371no—
236C4×C8—371no—
237#41—1484no—
238C2×Q8—371no—
239C2×Q8—741no—
240C2×Q8—741no—
241C2×Q8C22×D3711yescharacteristic
242C2×D4—371no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4C22×D3711yescharacteristic
248C22×C4—21no—
249C22×C4—371no—
250C22×C4—371no—
251C22×C4—371no—
252C22×C4—741no—
253SD16—22no—
254SD16—742no—
255SD16—742no—
256SD16—742no—
257M16—742no—
258M16—742no—
259C2×C8—371no—
260C2×C8—371no—
261C2×C8C22×D3711yescharacteristic
262C2×C8C22×D3711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4C22×D3711yescharacteristic
274C4⋊C4C22×D3711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C42—21no—
282C42—371no—
283C42—371no—
284C42—371no—
285C42—741no—
286C42C22×D3711yescharacteristic
287C23—21no—
288C23—371no—
289C23—741no—
290Q8—21no—
291Q8—21no—
292Q8—741no—
293Q8—741no—
294Q8—1482no—
295Q8—1482no—
296D4—21no—
297D4—21no—
298D4—741no—
299D4—741no—
300D4—1482no—
301D4—1482no—
302D4—1482no—
303D4—1482no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—371no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—742no—
312C2×C4—742no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—1482no—
319C2×C4D4×D3711yescharacteristic
320C2×C4D4×D3711yescharacteristic
321C2×C4C23×D3711yescharacteristic
322C8—21no—
323C8—372no—
324C8—741no—
325C8#1059696212yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—741no—
330C22—741no—
331C22—741no—
332C22—1481no—
333C22—1481no—
334C22—1481no—
335C22C2×D4×D3711yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—372no—
342C4—372no—
343C4—741no—
344C4—1481no—
345C4—1481no—
346C4—1481no—
347C4#41×D3711yescharacteristic
348C4C2×#1059696211yescharacteristic
349C2—81no—
350C2—2961no—
351C2—1481no—
352C2#1455808011yescharacteristic
353C2AGL(1,ℤ/8)×D3711yescharacteristic
354C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
prime radical#14558080C2
hypercenter#440D37
hypocenterC37#3182
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14558087C2semidirect
3. #14557937C2semidirect
4. #14557904C2semidirect
5. #14557882C2semidirect
6. #14557878C2semidirect
7. #14557782C2semidirect
8. #14557780C2semidirect
9. #14557778C2semidirect
10. #14557776C2semidirect
11. #14557635C2semidirect
12. #14557633C2semidirect
13. #14557631C2semidirect
14. #14557485C2semidirect
15. C37×#440C2semidirect
145. C8×C37#41semidirect
147. #64436#41semidirect
191. #440D37semidirect
193. C37#3182semidirect
325. C8#10596962semidirect

Maximal subgroups

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

subgroupindex
#145580872
#145580802
#145579372
#145579042
#145578822
#145578782
#145577822
#145577802
#145577782
#145577762
#145576352
#145576332
#145576312
#145574852
C37×#4402
#318237