Finite Group Databasebeta

← #18007680

Subgroups — #18007680

Order 4736.

380 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#14558268C211yesmaximal, characteristic, complemented
2#14557923C211yesmaximal, characteristic, complemented
3#14557920C211yesmaximal, characteristic, complemented
4#14557915C211yesmaximal, characteristic, complemented
5#14557755C211yesmaximal, characteristic, complemented
6#14557752C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557728C211yesmaximal, characteristic, complemented
10#14557725C211yesmaximal, characteristic, complemented
11#14557664C211yesmaximal, characteristic, complemented
12#14557633C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, characteristic, complemented
14C4×#10596939C211yesmaximal, characteristic, complemented
15C37×#559C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21C2×#10596939C2211yescharacteristic
22C2×#10596939C2211yescharacteristic
23C2×#10596939C2211yescharacteristic
24C2×#10596939C2211yescharacteristic
25#11924533C2211yescharacteristic
26#11924525—21no—
27#11924524C2211yescharacteristic
28#11924524C2211yescharacteristic
29#11924521—21no—
30#11924521—21no—
31C4×Dic74C2211yescharacteristic
32C4×D148C2211yescharacteristic
33C4×D148C2211yescharacteristic
34#11924498—21no—
35#11924469C2211yescharacteristic
36C4⋊#64436C2211yescharacteristic
37C4⋊#64436C2211yescharacteristic
38C4⋊#64436C2211yescharacteristic
39#11924460C2211yescharacteristic
40#11924459C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45#11924447C2211yescharacteristic
46#11924447C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#127×C37C2211yescharacteristic
49#124×C37—21no—
50#124×C37C2211yescharacteristic
51#124×C37C2211yescharacteristic
52#123×C37—21no—
53#123×C37—21no—
54C4×Q8×C37C2211yescharacteristic
55C4×Q8×C37C2211yescharacteristic
56C4×D4×C37—21no—
57C4×D4×C37C2211yescharacteristic
58C4×D4×C37C2211yescharacteristic
59C2×Q8×C37D411yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148C2311yescharacteristic
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×Dic74C2311yescharacteristic
74C4⋊C4×C37—21no—
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37D411yescharacteristic
77C4⋊C4×C37D411yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C42×C37—21no—
86C42×C37C2311yescharacteristic
87C42×C37C2311yescharacteristic
88C42×C37C2311yescharacteristic
89#10596942—41no—
90#10596941—22no—
91#10596941—41no—
92#10596940—22no—
93#10596940—41no—
94#10596939—22no—
95#10596939—41no—
96#10596939—41no—
97#10596939—41no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104C4⋊Dic37C2311yescharacteristic
105#10596936—21no—
106C4×Dic37—21no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37—21no—
113C22×D37—21no—
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—41no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—42no—
123D4×C37—81no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—81no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C2×Dic37—21no—
136C2×Dic37—21no—
137D148—21no—
138D148—21no—
139D148—21no—
140D148—21no—
141D148—42no—
142D148—81no—
143C4×D37—81no—
144C4×D37—81no—
145Dic74—21no—
146Dic74—21no—
147#64436—21no—
148#64436—21no—
149#64436—21no—
150#64436#4112yes—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37C22×D411yescharacteristic
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174Dic37—41no—
175Dic37—41no—
176#3403—371nomaximal, Sylow
177C2×C37—81no—
178C2×C37—81no—
179C2×C37#55011yescharacteristic
180C2×C37#57511yescharacteristic
181C2×C37#57611yescharacteristic
182D37—81no—
183D37—81no—
184#559—371no—
185#559D3711yescharacteristic, complemented
186#496—371no—
187#496—371no—
188#495—371no—
189#464—371no—
190#464—371no—
191#463—371no—
192#463—371no—
193#459—371no—
194#459—371no—
195#446—371no—
196#440—371no—
197#440—371no—
198C4×D8—371no—
199C37#340311yescharacteristic, complemented, Sylow
200C2×Q16—371no—
201C2×SD16—371no—
202C2×SD16—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C2×D8—371no—
207C2×D8—371no—
208C2×D8—371no—
209#127—371no—
210#127C2×D3711yescharacteristic
211#124—21no—
212#124—371no—
213#124—371no—
214#124—741no—
215#124C2×D3711yescharacteristic
216#124C2×D3711yescharacteristic
217#123—21no—
218#123—21no—
219#123—741no—
220#123—741no—
221C4×Q8—371no—
222C4×Q8C2×D3711yescharacteristic
223C4×Q8C2×D3711yescharacteristic
224C4×D4—21no—
225C4×D4—371no—
226C4×D4—371no—
227C4×D4—741no—
228C4×D4C2×D3711yescharacteristic
229C4×D4C2×D3711yescharacteristic
230#107—371no—
231C4⋊C8—371no—
232C4⋊C8—371no—
233C4⋊C8—371no—
234#103—371no—
235#103—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#97—371no—
241#97—371no—
242C4×C8—371no—
243C2×Q8—371no—
244C2×Q8C22⋊D3711yescharacteristic
245C2×Q8C22×D3711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—371no—
249C2×D4—371no—
250C2×D4—741no—
251C2×D4—741no—
252C2×D4C22×D3711yescharacteristic
253C2×D4C22×D3711yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—741no—
257C22×C4—741no—
258Q16—1481no—
259SD16—742no—
260SD16—742no—
261SD16—1481no—
262SD16—1481no—
263D8—742no—
264D8—1481no—
265D8—1481no—
266D8—1481no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—371no—
271C4⋊C4—21no—
272C4⋊C4—371no—
273C4⋊C4—741no—
274C4⋊C4C22⋊D3711yescharacteristic
275C4⋊C4C22⋊D3711yescharacteristic
276C4⋊C4C22⋊D3711yescharacteristic
277C4⋊C4C22×D3711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C42—21no—
291C42—741no—
292C42C22×D3711yescharacteristic
293C42C22×D3711yescharacteristic
294C42C22×D3711yescharacteristic
295C23—21no—
296C23—21no—
297C23—741no—
298C23—741no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—741no—
303Q8—741no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—2961no—
311D4—741no—
312D4—741no—
313D4—741no—
314D4—741no—
315D4—1482no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—2961no—
321C2×C4—2961no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4C2×C22⋊D3711yescharacteristic
325C2×C4C2×C22⋊D3711yescharacteristic
326C2×C4C2×C22⋊D3711yescharacteristic
327C2×C4C2×C22⋊D3711yescharacteristic
328C2×C4C2×C22⋊D3711yescharacteristic
329C2×C4C2×C22⋊D3711yescharacteristic
330C2×C4C23×D3711yescharacteristic
331C8—372no—
332C8—741no—
333C8—741no—
334C8—741no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1481no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22C22×C22⋊D3711yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—1481no—
357C4—1481no—
358C4#41×D3711yescharacteristic
359C4#1192458211yescharacteristic
360C2—81no—
361C2—81no—
362C2—2961no—
363C2—2961no—
364C2#1455820211yescharacteristic
365C2#1455833111yescharacteristic
366C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#559C2
socleC22×C37C22×D4
hypercenter#559D37
hypocenterC37#3403
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14558268C2semidirect
2. #14557923C2semidirect
3. #14557920C2semidirect
4. #14557915C2semidirect
5. #14557755C2semidirect
6. #14557752C2semidirect
7. #14557748C2semidirect
8. #14557745C2semidirect
9. #14557728C2semidirect
10. #14557725C2semidirect
11. #14557664C2semidirect
12. #14557633C2semidirect
13. #14557631C2semidirect
14. C4×#10596939C2semidirect
15. C37×#559C2semidirect
185. #559D37semidirect
199. C37#3403semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145579232
#145579202
#145579152
#145577552
#145577522
#145577482
#145577452
#145577282
#145577252
#145576642
#145576332
#145576312
C4×#105969392
C37×#5592
#340337