Finite Group Databasebeta

← #18006477

Subgroups — #18006477

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#14558192C211yesmaximal, characteristic
2#14557890C211yesmaximal, characteristic, complemented
3#14557874C211yesmaximal, characteristic, complemented
4#14557846C211yesmaximal, characteristic, complemented
5#14557837C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557755C211yesmaximal, characteristic, complemented
9#14557693C211yesmaximal, characteristic, complemented
10#14557688C211yesmaximal, characteristic, complemented
11C4×#10596942C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557527C211yesmaximal, characteristic, complemented
14C2×#11924459C211yesmaximal, characteristic, complemented
15C37×#552C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596942C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C22×#64436C2211yescharacteristic
23#11924524C2211yescharacteristic
24#11924522—21no—
25#11924515C2211yescharacteristic
26#11924514—21no—
27#11924510C2211yescharacteristic
28#11924508—21no—
29C4×Dic74C2211yescharacteristic
30#11924496—21no—
31#11924469C2211yescharacteristic
32#11924469C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924460C2211yescharacteristic
36#11924459C2211yescharacteristic
37#11924459C2211yescharacteristic
38#11924459C2211yescharacteristic
39#11924459C2211yescharacteristic
40#11924459C2211yescharacteristic
41#11924459C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#126×C37—21no—
49#125×C37—21no—
50#125×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53C22⋊Q8×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic
55C4×D4×C37C2211yescharacteristic
56#117×C37—21no—
57#117×C37C2211yescharacteristic
58C2×C4⋊C4×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37D411yescharacteristic
61C22×C4×C37—21no—
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C22×Dic37—21no—
67#10596962—22no—
68#10596962—41no—
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×Dic74—22no—
72C2×Dic74—21no—
73C2×Dic74—41no—
74C2×Dic74C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37D411yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C22⋊C4×C37—21no—
89C22⋊C4×C37D411yescharacteristic
90C22⋊C4×C37D411yescharacteristic
91C42×C37—21no—
92C42×C37—21no—
93C42×C37C2311yescharacteristic
94C22⋊Dic37—21no—
95#10596942—22no—
96#10596942—41no—
97#10596941—41no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104C4×Dic37—21no—
105C2×#64436—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37C2×D411yescharacteristic
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114Q8×C37—21no—
115Q8×C37—21no—
116D4×C37—22no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—42no—
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—42no—
132C22⋊D37—42no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—42no—
137D148—21no—
138D148—21no—
139C4×D37—42no—
140Dic74—21no—
141Dic74—21no—
142Dic74—21no—
143Dic74—42no—
144Dic74#4112yes—
145#64436—21no—
146#64436—21no—
147#64436—21no—
148#64436—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37#13512yes—
155C22×C37C22×D411yescharacteristic
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37C2×#4111yescharacteristic
168C4×C37H(5,𝔽2)11yescharacteristic
169Dic37—22no—
170Dic37—41no—
171Dic37—41no—
172#3300—371nomaximal, Sylow
173C2×C37—22no—
174C2×C37—41no—
175C2×C37#54611yescharacteristic
176C2×C37C2×#13511yescharacteristic
177C2×C37#57811yescharacteristic
178D37—81no—
179#552D3711yescharacteristic, complemented
180#548—371no—
181#488—371no—
182#485—371no—
183#480—371no—
184#479—371no—
185#467—371no—
186#465—371no—
187#464—371no—
188#452—371no—
189#451—371no—
190C4×Q16—371no—
191C8×D4—371no—
192#416—371no—
193C2×#103—371no—
194C37#330011yescharacteristic, complemented, Sylow
195C2×#41—371no—
196C22×Q8—371no—
197C2×Q16—371no—
198C2×Q16—371no—
199C2×SD16—371no—
200C22×C8—371no—
201C22×C8—371no—
202#126—21no—
203#125—21no—
204#125C2×D3711yescharacteristic
205#124—371no—
206#124—741no—
207#123—21no—
208C22⋊Q8—371no—
209C22⋊Q8—741no—
210C22⋊Q8C2×D3711yescharacteristic
211C22⋊Q8C2×D3711yescharacteristic
212#121—371no—
213#121—741no—
214C4×Q8—371no—
215C4×Q8C2×D3711yescharacteristic
216C4×D4—741no—
217C4×D4C2×D3711yescharacteristic
218#117—21no—
219#117C2×D3711yescharacteristic
220C2×C4⋊C4C2×D3711yescharacteristic
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#103—371no—
231#103—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235C22⋊C8—371no—
236C22⋊C8—371no—
237C4×C8—371no—
238#41—742no—
239#41—1481no—
240C2×Q8—371no—
241C2×Q8—371no—
242C2×Q8—742no—
243C2×Q8—741no—
244C2×Q8—1481no—
245C2×Q8C22×D3711yescharacteristic
246C2×D4—371no—
247C2×D4—741no—
248C2×D4—741no—
249C2×D4C22⋊D3711yescharacteristic
250C22×C4—21no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4C22×D3711yescharacteristic
254C22×C4C22×D3711yescharacteristic
255Q16—742no—
256Q16—1481no—
257SD16—1481no—
258C2×C8—371no—
259C2×C8—371no—
260C2×C8—371no—
261C2×C8—371no—
262C2×C8—1481no—
263C2×C8—1481no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4C22⋊D3711yescharacteristic
274C4⋊C4C22×D3711yescharacteristic
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4C22⋊D3711yescharacteristic
285C22⋊C4C22⋊D3711yescharacteristic
286C42—21no—
287C42—21no—
288C42—741no—
289C42C22×D3711yescharacteristic
290C23—741no—
291C23C2×C22⋊D3711yescharacteristic
292C23C2×C22⋊D3711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—372no—
296Q8—741no—
297Q8—741no—
298Q8—741no—
299Q8—1482no—
300D4—22no—
301D4—741no—
302D4—741no—
303D4—1482no—
304D4—1482no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—1482no—
318C2×C4—1482no—
319C2×C4C2×C22⋊D3711yescharacteristic
320C2×C4C2×C22⋊D3711yescharacteristic
321C2×C4C2×C22⋊D3711yescharacteristic
322C2×C4C2×C22⋊D3711yescharacteristic
323C2×C4C23×D3711yescharacteristic
324C8—741no—
325C8—741no—
326C8—741no—
327C8—741no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22#1192455612yes—
337C22C22×C22⋊D3711yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—742no—
347C4—1481no—
348C4—1481no—
349C4#41×D3711yescharacteristic
350C4#1192458211yescharacteristic
351C2—22no—
352C2—41no—
353C2—2961no—
354C2#1455817111yescharacteristic
355C2C2×#1192455611yescharacteristic
356C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#552C2
socleC22×C37C22×D4
prime radical#14558192C2
hypercenter#552D37
hypocenterC37#3300
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14557890C2semidirect
3. #14557874C2semidirect
4. #14557846C2semidirect
5. #14557837C2semidirect
6. #14557772C2semidirect
7. #14557764C2semidirect
8. #14557755C2semidirect
9. #14557693C2semidirect
10. #14557688C2semidirect
11. C4×#10596942C2semidirect
12. D4×#64436C2semidirect
13. #14557527C2semidirect
14. C2×#11924459C2semidirect
15. C37×#552C2semidirect
179. #552D37semidirect
194. C37#3300semidirect

Maximal subgroups

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

subgroupindex
#145581922
#145578902
#145578742
#145578462
#145578372
#145577722
#145577642
#145577552
#145576932
#145576882
C4×#105969422
D4×#644362
#145575272
C2×#119244592
C37×#5522
#330037