Finite Group Databasebeta

← #18006500

Subgroups — #18006500

Order 4736.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558229C211yesmaximal, characteristic, complemented
2#14558192C211yesmaximal, characteristic, complemented
3#14557888C211yesmaximal, characteristic, complemented
4#14557875C211yesmaximal, characteristic, complemented
5#14557852C211yesmaximal, characteristic, complemented
6#14557841C211yesmaximal, characteristic, complemented
7#14557769C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557749C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557674C211yesmaximal, characteristic, complemented
12C4×#10596930C211yesmaximal, characteristic, complemented
13#14557530C211yesmaximal, characteristic, complemented
14C2×#11924461C211yesmaximal, characteristic, complemented
15C8×D4×C37C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924531—21no—
22#11924528C2211yescharacteristic
23#11924524C2211yescharacteristic
24#11924522—21no—
25#11924518—21no—
26#11924515C2211yescharacteristic
27#11924514—21no—
28#11924510C2211yescharacteristic
29#11924510C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924508—21no—
32#11924508—21no—
33C4×Dic74C2211yescharacteristic
34C4×D148C2211yescharacteristic
35#11924496—21no—
36#11924496—21no—
37#11924495C2211yescharacteristic
38C2×C4⋊Dic37C2211yescharacteristic
39#11924470C2211yescharacteristic
40#11924468C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924461C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52C22×C8×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55C4⋊C8×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C2×D4×C37D411yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C22×Dic37—21no—
67C22×Dic37—21no—
68#10596962—22no—
69#10596962—41no—
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×Dic74—22no—
75C2×Dic74—21no—
76C2×Dic74—41no—
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79C2×C8×C37—41no—
80C2×C8×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C4⋊C4×C37D411yescharacteristic
86C22⋊C4×C37D411yescharacteristic
87C22⋊C4×C37D411yescharacteristic
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106C4×Dic37—21no—
107C4×Dic37—21no—
108D296—41no—
109#10596930—22no—
110#10596930—41no—
111C23×C37C2×D411yescharacteristic
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—21no—
115D4×C37—22no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—42no—
126C22⋊D37—42no—
127C22⋊D37—42no—
128C22⋊D37—81no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—42no—
136C2×Dic37—81no—
137D148—21no—
138D148—21no—
139D148—21no—
140D148—21no—
141C4×D37—42no—
142C4×D37—81no—
143Dic74—21no—
144Dic74—21no—
145Dic74—21no—
146Dic74—42no—
147Dic74#4112yes—
148C8×C37—21no—
149C8×C37—21no—
150C8×C37—21no—
151C8×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37#13512yes—
158C22×C37C22×D411yescharacteristic
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—22no—
172Dic37—41no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37—41no—
180C2×C37#54611yescharacteristic
181C2×C37C2×#13511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—81no—
184D37—81no—
185#553—371no—
186#548—371no—
187#488—371no—
188#485—371no—
189#481—371no—
190#479—371no—
191#466—371no—
192#465—371no—
193#463—371no—
194#449—371no—
195#448—371no—
196C4×SD16—371no—
197C8×D4D3711yescharacteristic, complemented
198#416—371no—
199C2×#103—371no—
200C37#330111yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C22×Q8—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C22×C8C2×D3711yescharacteristic
207C22×C8C2×D3711yescharacteristic
208#126—741no—
209#125—371no—
210#124—371no—
211#124—741no—
212#123—741no—
213C22⋊Q8—371no—
214C22⋊Q8—741no—
215#121—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×Q8—371no—
221C4×D4—371no—
222C4×D4—741no—
223C4×D4—741no—
224C4×D4C2×D3711yescharacteristic
225#117—371no—
226C2×C4⋊C4—371no—
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8C2×D3711yescharacteristic
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8C2×D3711yescharacteristic
242C22⋊C8C2×D3711yescharacteristic
243C4×C8C2×D3711yescharacteristic
244#41—742no—
245#41—1481no—
246C2×Q8—371no—
247C2×Q8—371no—
248C2×Q8—742no—
249C2×Q8—741no—
250C2×Q8—1481no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C2×D4D14811yescharacteristic
258C22×C4—741no—
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263C22×C4C22×D3711yescharacteristic
264SD16—742no—
265SD16—1481no—
266D8—1481no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D3711yescharacteristic
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4D14811yescharacteristic
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4D14811yescharacteristic
292C22⋊C4D14811yescharacteristic
293C42—741no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—741no—
297C23—741no—
298C23C2×D14811yescharacteristic
299C23C2×D14811yescharacteristic
300Q8—372no—
301Q8—741no—
302Q8—741no—
303Q8—741no—
304Q8—1482no—
305D4—22no—
306D4—2961no—
307D4—741no—
308D4—741no—
309D4—741no—
310D4—741no—
311D4—1482no—
312D4—1482no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2961no—
319C2×C4—2961no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—1482no—
327C2×C4—1482no—
328C2×C4C2×D14811yescharacteristic
329C2×C4C2×D14811yescharacteristic
330C2×C4C2×D14811yescharacteristic
331C2×C4C2×D14811yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22#1192455812yes—
349C22C22×D14811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—742no—
355C4—1481no—
356C4—1481no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458111yescharacteristic
362C2—22no—
363C2—41no—
364C2—2961no—
365C2—2961no—
366C2#1455817811yescharacteristic
367C2C2×#1192455811yescharacteristic
368C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC8×D4×C37C2
socleC22×C37C22×D4
hypercenterC8×D4D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14558192C2semidirect
3. #14557888C2semidirect
4. #14557875C2semidirect
5. #14557852C2semidirect
6. #14557841C2semidirect
7. #14557769C2semidirect
8. #14557762C2semidirect
9. #14557749C2semidirect
10. #14557680C2semidirect
11. #14557674C2semidirect
12. C4×#10596930C2semidirect
13. #14557530C2semidirect
14. C2×#11924461C2semidirect
15. C8×D4×C37C2semidirect
197. C8×D4D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145581922
#145578882
#145578752
#145578522
#145578412
#145577692
#145577622
#145577492
#145576802
#145576742
C4×#105969302
#145575302
C2×#119244612
C8×D4×C372
#330137