Finite Group Databasebeta

← #541×D37 #18007958

Subgroups — #541×D37 #18007958

Order 4736.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558146C211yesmaximal, characteristic, complemented
2#14558145C211yesmaximal, characteristic, complemented
3#14558144C211yesmaximal, characteristic, complemented
4#14558143C212yesmaximal, complemented
5#14558142C214yesmaximal, complemented
6#14558141C212yesmaximal, complemented
7#14558140C214yesmaximal, complemented
8C4⋊Q8×D37C211yesmaximal, characteristic, complemented
9#126×D37C214yesmaximal
10#125×D37C211yesmaximal, characteristic, complemented
11#125×D37C214yesmaximal, complemented
12C22⋊Q8×D37C212yesmaximal
13C4×Q8×D37C212yesmaximal, complemented
14#117×D37C211yesmaximal, characteristic
15C37×#541C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2212yes—
17C22×C4×D37C2211yescharacteristic
18#11924536C2211yescharacteristic, complemented
19#11924535C2214yescomplemented
20#11924534C2212yescomplemented
21#11924531C2214yes—
22#11924531C2214yes—
23#11924531C2214yes—
24#11924530C2214yes—
25#11924529C2214yes—
26#11924529C2214yes—
27#11924529C2214yes—
28#11924528C2214yescomplemented
29#11924528C2211yescharacteristic, complemented
30#11924527C2214yescomplemented
31#11924527C2212yescomplemented
32#11924527C2214yescomplemented
33#11924526C2214yescomplemented
34#11924526C2214yescomplemented
35#11924526C2214yescomplemented
36#11924526C2214yescomplemented
37#11924526C2214yescomplemented
38#11924516C2212yes—
39#11924515C2212yes—
40#11924514C2214yes—
41#11924513C2214yes—
42#11924512C2212yes—
43Q8×Dic37C2212yescomplemented
44C4×Dic74C2214yescomplemented
45C4×Dic74C2212yescomplemented
46#11924501C2214yescomplemented
47#11924501C2212yescomplemented
48#11924495C2211yescharacteristic
49#11924494C2212yes—
50#11924493C2211yescharacteristic
51#11924493C2211yescharacteristic
52#11924492C2212yes—
53C4⋊C4×D37C2212yes—
54C4⋊C4×D37C2212yes—
55C4⋊C4×D37C2214yes—
56C4⋊C4×D37C2214yes—
57C4⋊C4×D37C2214yes—
58C4⋊C4×D37C2214yes—
59C22⋊C4×D37C2212yes—
60C22⋊C4×D37C2214yes—
61C42×D37C2211yescharacteristic
62C42×D37C2211yescharacteristic
63C42×D37C2214yes—
64C4⋊Q8×C37C2211yescharacteristic, complemented
65#126×C37C2214yes—
66#125×C37C2214yescomplemented
67#125×C37C2211yescharacteristic, complemented
68C22⋊Q8×C37C2212yes—
69C4×Q8×C37C2212yescomplemented
70#117×C37C2211yescharacteristic
71C23×D37C2311yescharacteristic
72C2×Q8×C37C2312yes—
73C22×C4×C37C2311yescharacteristic
74C22×Dic37C2311yescharacteristic
75Q8×D37—28no—
76C2×C4×D37—24no—
77C2×C4×D37C2312yes—
78C2×C4×D37C2312yes—
79C2×C4×D37C2314yes—
80C2×C4×D37C2314yes—
81C2×C4×D37C2311yescharacteristic
82C2×C4×D37C2311yescharacteristic
83C2×C4×D37C2311yescharacteristic
84C2×C4×D37C2311yescharacteristic
85C2×Dic74C2314yes—
86C2×Dic74C2312yes—
87C4⋊C4×C37C2312yes—
88C4⋊C4×C37C2312yes—
89C4⋊C4×C37C2314yes—
90C4⋊C4×C37C2314yes—
91C4⋊C4×C37C2314yes—
92C4⋊C4×C37C2314yes—
93C22⋊C4×C37C2312yes—
94C22⋊C4×C37C2314yes—
95C42×C37C2311yescharacteristic
96C42×C37C2311yescharacteristic
97C42×C37C2314yes—
98C22⋊Dic37C2312yes—
99C22⋊Dic37C2314yes—
100#10596938C2312yes—
101#10596938C2312yes—
102#10596938C2314yes—
103#10596938C2314yes—
104C4⋊Dic37C2312yes—
105C4⋊Dic37C2312yes—
106C4⋊Dic37C2314yes—
107C4⋊Dic37C2314yes—
108C4⋊Dic37C2314yes—
109C4⋊Dic37C2314yes—
110#10596936C2312yes—
111#10596936C2312yes—
112#10596936C2314yes—
113#10596936C2314yes—
114#10596936C2314yes—
115#10596936C2314yes—
116#10596936C2314yes—
117#10596936C2314yes—
118#10596936C2314yes—
119#10596936C2314yes—
120#10596936C2314yes—
121C4×Dic37C2312yes—
122C4×Dic37C2312yes—
123C4×Dic37C2311yescharacteristic
124C4×Dic37C2311yescharacteristic
125C4×Dic37C2314yes—
126C4×Dic37C2314yes—
127C4×Dic37C2314yes—
128C23×C37C2411yescharacteristic
129C22×D37—22no—
130C22×D37—24no—
131C22×D37C2411yescharacteristic
132C22×D37C2411yescharacteristic
133Q8×C37—24no—
134C2×C4×C37—22no—
135C2×C4×C37C2412yes—
136C2×C4×C37C2412yes—
137C2×C4×C37C2414yes—
138C2×C4×C37C2414yes—
139C2×C4×C37C2411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C2×Dic37—22no—
142C2×Dic37C2412yes—
143C2×Dic37C2412yes—
144C2×Dic37C2414yes—
145C2×Dic37C2414yes—
146C2×Dic37C2411yescharacteristic
147C2×Dic37C2411yescharacteristic
148C4×D37—22no—
149C4×D37—28no—
150C4×D37—24no—
151C4×D37—24no—
152C4×D37—28no—
153C4×D37—22no—
154C4×D37—22no—
155C4×D37#4114yes—
156Dic74—24no—
157Dic74—28no—
158C22×C37—21no—
159C22×C37—22no—
160C22×C37C2511yescharacteristic
161C2×D37—21no—
162C2×D37—22no—
163C2×D37—44no—
164C2×D37C2×#4112yes—
165C2×D372−1+414yes—
166C4×C37—24no—
167C4×C37—21no—
168C4×C37—22no—
169C4×C37—22no—
170C4×C37—24no—
171C4×C37C2×#4112yes—
172Dic37—24no—
173Dic37—21no—
174Dic37—22no—
175Dic37—22no—
176Dic37—24no—
177Dic37C2×#4112yes—
178C2×#541—371nomaximal, Sylow
179C2×C37—41no—
180C2×C37C22×#4111yescharacteristic
181C2×C37C2×2−1+412yes—
182D37—41no—
183D37#54114yesdirect product factor
184#541—371no—
185#541—374no—
186#541—374no—
187#541—371no—
188#541—372no—
189#541—372no—
190#541—371no—
191#541D3711yescharacteristic, direct product factor
192C2×C4⋊Q8—371no—
193C2×#126—374no—
194C2×#125—371no—
195C2×#125—374no—
196C2×C22⋊Q8—372no—
197C2×C4×Q8—372no—
198C2×#117—371no—
199C37C2×#54111yescharacteristic, complemented, Sylow
200C22×Q8—372no—
201C23×C4—371no—
202C4⋊Q8—372no—
203C4⋊Q8—374no—
204C4⋊Q8—371no—
205C4⋊Q8C2×D3711yescharacteristic, complemented
206#126—374no—
207#126—374no—
208#126—374no—
209#126—374no—
210#126—374no—
211#126—374no—
212#126—374no—
213#126C2×D3714yes—
214#125—374no—
215#125—374no—
216#125—374no—
217#125—374no—
218#125—374no—
219#125—372no—
220#125—374no—
221#125—374no—
222#125—371no—
223#125—374no—
224#125C2×D3711yescharacteristic, complemented
225#125C2×D3714yescomplemented
226C22⋊Q8—372no—
227C22⋊Q8—372no—
228C22⋊Q8—374no—
229C22⋊Q8—372no—
230C22⋊Q8—374no—
231C22⋊Q8C2×D3712yes—
232C4×Q8—372no—
233C4×Q8—374no—
234C4×Q8—372no—
235C4×Q8—374no—
236C4×Q8—372no—
237C4×Q8C2×D3712yescomplemented
238#117—371no—
239#117—372no—
240#117—372no—
241#117—371no—
242#117—371no—
243#117C2×D3711yescharacteristic
244C2×C4⋊C4—372no—
245C2×C4⋊C4—372no—
246C2×C4⋊C4—374no—
247C2×C4⋊C4—374no—
248C2×C4⋊C4—374no—
249C2×C4⋊C4—374no—
250C2×C22⋊C4—372no—
251C2×C22⋊C4—374no—
252C2×C42—371no—
253C2×C42—371no—
254C2×C42—374no—
255C24—371no—
256C2×Q8—374no—
257C2×Q8—372no—
258C2×Q8—748no—
259C2×Q8C22×D3712yes—
260C22×C4—371no—
261C22×C4—371no—
262C22×C4—372no—
263C22×C4—372no—
264C22×C4—374no—
265C22×C4—374no—
266C22×C4—371no—
267C22×C4—371no—
268C22×C4—371no—
269C22×C4—744no—
270C22×C4C22×D3711yescharacteristic
271C4⋊C4—372no—
272C4⋊C4—372no—
273C4⋊C4—374no—
274C4⋊C4—374no—
275C4⋊C4—374no—
276C4⋊C4—374no—
277C4⋊C4—374no—
278C4⋊C4—374no—
279C4⋊C4—374no—
280C4⋊C4—374no—
281C4⋊C4—374no—
282C4⋊C4—372no—
283C4⋊C4—372no—
284C4⋊C4—374no—
285C4⋊C4—374no—
286C4⋊C4—374no—
287C4⋊C4—374no—
288C4⋊C4C22×D3712yes—
289C4⋊C4C22×D3712yes—
290C4⋊C4C22×D3714yes—
291C4⋊C4C22×D3714yes—
292C4⋊C4C22×D3714yes—
293C4⋊C4C22×D3714yes—
294C22⋊C4—372no—
295C22⋊C4—374no—
296C22⋊C4—372no—
297C22⋊C4—372no—
298C22⋊C4—374no—
299C22⋊C4—374no—
300C22⋊C4C22×D3712yes—
301C22⋊C4C22×D3714yes—
302C42—372no—
303C42—371no—
304C42—372no—
305C42—371no—
306C42—374no—
307C42—374no—
308C42—374no—
309C42C22×D3711yescharacteristic
310C42C22×D3711yescharacteristic
311C42C22×D3714yes—
312C23—371no—
313C23—371no—
314C23—742no—
315C23—744no—
316C23C23×D3711yescharacteristic
317Q8—24no—
318Q8—748no—
319Q8—744no—
320C2×C4—22no—
321C2×C4—371no—
322C2×C4—374no—
323C2×C4—372no—
324C2×C4—372no—
325C2×C4—374no—
326C2×C4—374no—
327C2×C4—371no—
328C2×C4—742no—
329C2×C4—742no—
330C2×C4—748no—
331C2×C4—744no—
332C2×C4—744no—
333C2×C4—748no—
334C2×C4—742no—
335C2×C4—742no—
336C2×C4C23×D3712yes—
337C2×C4C23×D3712yes—
338C2×C4C23×D3714yes—
339C2×C4C23×D3714yes—
340C2×C4C23×D3711yescharacteristic
341C2×C4C23×D3711yescharacteristic
342C22—21no—
343C22—22no—
344C22—372no—
345C22—374no—
346C22—741no—
347C22—742no—
348C22—1484no—
349C22C24×D3711yescharacteristic
350C4—21no—
351C4—24no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—372no—
356C4—741no—
357C4—744no—
358C4—742no—
359C4—742no—
360C4—744no—
361C4#41×D3712yes—
362C2—41no—
363C2—374no—
364C2—1481no—
365C2C2×#41×D3711yescharacteristic
366C22−1+4×D3712yes—
subgroupG/H
center, FrattiniC22C24×D37
commutator, socle, cosocleC22×C37C25
FittingC37×#541C2
prime radicalC23×D37C23
hypercenter#541D37
hypocenterC37C2×#541
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #14558146C2semidirect
2. #14558145C2semidirect
3. #14558144C2semidirect
4. #14558143C2semidirect
5. #14558142C2semidirect
6. #14558141C2semidirect
7. #14558140C2semidirect
8. C4⋊Q8×D37C2semidirect
10. #125×D37C2semidirect
11. #125×D37C2semidirect
13. C4×Q8×D37C2semidirect
15. C37×#541C2semidirect
18. #11924536C22semidirect
19. #11924535C22semidirect
20. #11924534C22semidirect
28. #11924528C22semidirect
29. #11924528C22semidirect
30. #11924527C22semidirect
31. #11924527C22semidirect
32. #11924527C22semidirect
33. #11924526C22semidirect
34. #11924526C22semidirect
35. #11924526C22semidirect
36. #11924526C22semidirect
37. #11924526C22semidirect
43. Q8×Dic37C22semidirect
44. C4×Dic74C22semidirect
45. C4×Dic74C22semidirect
46. #11924501C22semidirect
47. #11924501C22semidirect
64. C4⋊Q8×C37C22semidirect
66. #125×C37C22semidirect
67. #125×C37C22semidirect
69. C4×Q8×C37C22semidirect
183. D37#541direct (N × H)
191. #541D37direct (N × H)
199. C37C2×#541semidirect
205. C4⋊Q8C2×D37semidirect
224. #125C2×D37semidirect
225. #125C2×D37semidirect
237. C4×Q8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581462
#145581452
#145581442
#145581432
#145581422
#145581412
#145581402
C4⋊Q8×D372
#126×D372
#125×D372
C22⋊Q8×D372
C4×Q8×D372
#117×D372
C37×#5412
C2×#54137