Finite Group Databasebeta

← #17997720

Subgroups — #17997720

Order 4736.

496 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#14557432C211yesmaximal, characteristic, complemented
2#14557426C211yesmaximal, characteristic
3#14557426C211yesmaximal, characteristic
4#14557426C211yesmaximal, characteristic
5#14557419C211yesmaximal, characteristic, complemented
6#14557419C211yesmaximal, characteristic, complemented
7#14557419C211yesmaximal, characteristic, complemented
8#14557408C211yesmaximal, characteristic
9C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic37C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic37C211yesmaximal, characteristic
13C22⋊C4×Dic37C211yesmaximal, characteristic
14#14557379C211yesmaximal, characteristic, complemented
15C2×#126×C37C211yesmaximal, characteristic
16C23×Dic37C2211yescharacteristic
17C2×C4⋊Dic37C2211yescharacteristic
18C2×C4⋊Dic37C2211yescharacteristic
19C2×C4⋊Dic37C2211yescharacteristic
20C2×C4⋊Dic37C2211yescharacteristic
21C2×C4⋊Dic37C2211yescharacteristic
22C2×C22⋊Dic37C2211yescharacteristic
23C2×C22⋊Dic37C2211yescharacteristic
24C2×C22⋊Dic37C2211yescharacteristic
25C2×C4×Dic37C2211yescharacteristic
26C2×C4×Dic37C2211yescharacteristic
27C2×C4×Dic37C2211yescharacteristic
28C2×C4×Dic37C2211yescharacteristic
29C2×C4×Dic37C2211yescharacteristic
30C2×C4×Dic37C2211yescharacteristic
31C2×C4×Dic37C2211yescharacteristic
32#11924443C2211yescharacteristic
33#11924443C2211yescharacteristic
34#11924443C2211yescharacteristic
35#11924443C2211yescharacteristic
36#11924443C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#126×C37C418yescomplemented
45C2×C4⋊C4×C37C2211yescharacteristic
46C2×C4⋊C4×C37C2211yescharacteristic
47C2×C4⋊C4×C37C2211yescharacteristic
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C42×C37C2211yescharacteristic
52C24×C37C2311yescharacteristic
53C22×C4×C37C2311yescharacteristic
54C22×C4×C37C2311yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×Dic37—22no—
60C22×Dic37—22no—
61C22×Dic37—41no—
62C22×Dic37C2311yescharacteristic
63C22×Dic37C2311yescharacteristic
64C22×Dic37C2311yescharacteristic
65C22×Dic37C2311yescharacteristic
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C22×Dic37C2311yescharacteristic
70C4⋊C4×C37C2×C414yescomplemented
71C4⋊C4×C37C2×C414yescomplemented
72C4⋊C4×C37C2×C414yescomplemented
73C22⋊C4×C37C2×C414yes—
74C22⋊C4×C37C2×C414yes—
75C22⋊C4×C37C2×C414yes—
76C42×C37C2×C414yescomplemented
77C22⋊Dic37—22no—
78C22⋊Dic37—22no—
79C22⋊Dic37—41no—
80C4⋊Dic37—22no—
81C4⋊Dic37—22no—
82C4⋊Dic37—22no—
83C4⋊Dic37—22no—
84C4⋊Dic37—41no—
85C4×Dic37—22no—
86C4×Dic37—22no—
87C4×Dic37—22no—
88C4×Dic37—22no—
89C4×Dic37—41no—
90C4×Dic37—41no—
91C4×Dic37—41no—
92C23×C37—21no—
93C23×C37—21no—
94C23×C37—21no—
95C23×C37—21no—
96C23×C37—21no—
97C23×C37—21no—
98C23×C37C22×C412yes—
99C23×C37C2411yescharacteristic
100C2×C4×C37—21no—
101C2×C4×C37—21no—
102C2×C4×C37—21no—
103C2×C4×C37—21no—
104C2×C4×C37—21no—
105C2×C4×C37—21no—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37C22×C412yes—
113C2×C4×C37C22×C412yes—
114C2×C4×C37C22×C412yes—
115C2×C4×C37C22×C412yes—
116C2×C4×C37C22×C412yes—
117C2×C4×C37C22×C412yes—
118C2×Dic37—21no—
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—44no—
139C2×Dic37#4112yes—
140C2×Dic37#4112yes—
141C2×Dic37#4112yes—
142C2×Dic37#4112yes—
143C22×C37—22no—
144C22×C37—22no—
145C22×C37—22no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37—41no—
150C22×C37C23×C411yescharacteristic
151C22×C37C2×#4111yescharacteristic
152C22×C37C2×#4111yescharacteristic
153C22×C37C2×#4111yescharacteristic
154C22×C37C2×#4111yescharacteristic
155C22×C37H(5,𝔽2)11yescharacteristic
156C22×C372−1+411yescharacteristic
157C4×C37—22no—
158C4×C37—22no—
159C4×C37—22no—
160C4×C37—22no—
161C4×C37—22no—
162C4×C37—22no—
163Dic37—22no—
164Dic37—22no—
165Dic37—22no—
166Dic37—22no—
167Dic37—41no—
168Dic37—41no—
169Dic37—41no—
170Dic37—41no—
171#2373—371nomaximal, Sylow
172C2×C37—42no—
173C2×C37C4×#4111yescharacteristic
174C2×C37C4×#4111yescharacteristic
175C2×C37#52011yescharacteristic
176C2×C37#55111yescharacteristic
177C2×C37#55211yescharacteristic
178C2×C37#55311yescharacteristic
179C2×C37#55611yescharacteristic
180C2×#126D3711yescharacteristic
181#389—371no—
182#388—371no—
183#388—371no—
184#388—371no—
185#387—371no—
186#387—371no—
187#387—371no—
188#385—371no—
189C4×C4⋊C4—371no—
190C4×C4⋊C4—371no—
191C4×C4⋊C4—371no—
192C4×C22⋊C4—371no—
193C4×C22⋊C4—371no—
194#376—371no—
195C37#237311yescharacteristic, complemented, Sylow
196C23×C4—371no—
197#126Dic3718yescomplemented
198C2×C4⋊C4—371no—
199C2×C4⋊C4—371no—
200C2×C4⋊C4—371no—
201C2×C4⋊C4—371no—
202C2×C4⋊C4—371no—
203C2×C4⋊C4C2×D3711yescharacteristic
204C2×C4⋊C4C2×D3711yescharacteristic
205C2×C4⋊C4C2×D3711yescharacteristic
206C2×C22⋊C4—371no—
207C2×C22⋊C4—371no—
208C2×C22⋊C4—371no—
209C2×C22⋊C4C2×D3711yescharacteristic
210C2×C22⋊C4C2×D3711yescharacteristic
211C2×C22⋊C4C2×D3711yescharacteristic
212C2×C42—371no—
213C2×C42—371no—
214C2×C42—371no—
215C2×C42—371no—
216C2×C42—371no—
217C2×C42—371no—
218C2×C42—371no—
219C2×C42C2×D3711yescharacteristic
220#95—371no—
221#95—371no—
222#95—371no—
223#95—371no—
224#95—371no—
225#95—371no—
226#95—371no—
227#95—371no—
228#95—371no—
229#95—371no—
230#95—371no—
231#95—371no—
232C24C22×D3711yescharacteristic
233C22×C4—371no—
234C22×C4—371no—
235C22×C4—371no—
236C22×C4—371no—
237C22×C4—371no—
238C22×C4—371no—
239C22×C4—371no—
240C22×C4—371no—
241C22×C4—742no—
242C22×C4—742no—
243C22×C4—1481no—
244C22×C4C22×D3711yescharacteristic
245C22×C4C22×D3711yescharacteristic
246C22×C4C22×D3711yescharacteristic
247C22×C4C22×D3711yescharacteristic
248C22×C4C22×D3711yescharacteristic
249C22×C4C22×D3711yescharacteristic
250C4⋊C4—742no—
251C4⋊C4—742no—
252C4⋊C4—742no—
253C4⋊C4—742no—
254C4⋊C4—1481no—
255C4⋊C4C2×Dic3714yescomplemented
256C4⋊C4C2×Dic3714yescomplemented
257C4⋊C4C2×Dic3714yescomplemented
258C22⋊C4—742no—
259C22⋊C4—742no—
260C22⋊C4—1481no—
261C22⋊C4C2×Dic3714yes—
262C22⋊C4C2×Dic3714yes—
263C22⋊C4C2×Dic3714yes—
264C42—742no—
265C42—742no—
266C42—742no—
267C42—742no—
268C42—1481no—
269C42—1481no—
270C42—1481no—
271C42C2×Dic3714yescomplemented
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C22×Dic3712yes—
279C23C23×D3711yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—372no—
293C2×C4—372no—
294C2×C4—372no—
295C2×C4—372no—
296C2×C4—741no—
297C2×C4—741no—
298C2×C4—741no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4—741no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—1484no—
317C2×C4C22×Dic3712yes—
318C2×C4C22×Dic3712yes—
319C2×C4C22×Dic3712yes—
320C2×C4C22×Dic3712yes—
321C2×C4C22×Dic3712yes—
322C2×C4C22×Dic3712yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C23×Dic3711yescharacteristic
331C22#41×D3711yescharacteristic
332C22#41×D3711yescharacteristic
333C22#41×D3711yescharacteristic
334C22#41×D3711yescharacteristic
335C22#1192458211yescharacteristic
336C22#1192458311yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—742no—
344C4—742no—
345C4—742no—
346C4—742no—
347C4—1481no—
348C4—1481no—
349C4—1481no—
350C4—1481no—
351C2—42no—
352C2#41×Dic3711yescharacteristic
353C2#41×Dic3711yescharacteristic
354C2#1455801611yescharacteristic
355C2#1455820811yescharacteristic
356C2#1455821911yescharacteristic
357C2#1455823411yescharacteristic
358C2#1455825011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC2×#126×C37C2
socle, cosocleC23×C37C24
prime radicalC24×C37C23
hypercenterC2×#126D37
hypocenterC37#2373
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14557432C2semidirect
5. #14557419C2semidirect
6. #14557419C2semidirect
7. #14557419C2semidirect
9. C4⋊C4×Dic37C2semidirect
10. C4⋊C4×Dic37C2semidirect
11. C4×C4⋊Dic37C2semidirect
14. #14557379C2semidirect
44. #126×C37C4semidirect
70. C4⋊C4×C37C2×C4semidirect
71. C4⋊C4×C37C2×C4semidirect
72. C4⋊C4×C37C2×C4semidirect
76. C42×C37C2×C4semidirect
195. C37#2373semidirect
197. #126Dic37semidirect
255. C4⋊C4C2×Dic37semidirect
256. C4⋊C4C2×Dic37semidirect
257. C4⋊C4C2×Dic37semidirect
271. C42C2×Dic37semidirect

Maximal subgroups

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

subgroupindex
#145574322
#145574262
#145574192
#145574082
C4⋊C4×Dic372
C4×C4⋊Dic372
C22⋊C4×Dic372
#145573792
C2×#126×C372
#237337