Finite Group Databasebeta

← #18006571

Subgroups — #18006571

Order 4736.

394 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#14558236C211yesmaximal, characteristic, complemented
2#14558186C211yesmaximal, characteristic, complemented
3#14557872C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557782C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557735C211yesmaximal, characteristic, complemented
9#14557681C211yesmaximal, characteristic, complemented
10#14557681C211yesmaximal, characteristic, complemented
11#14557646C211yesmaximal, characteristic, complemented
12#14557606C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14#14557528C211yesmaximal, characteristic, complemented
15C37×#491C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596966C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×D296C2211yescharacteristic
21C2×#10596929C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic
23#11924531—21no—
24#11924521—21no—
25#11924521—21no—
26#11924521—21no—
27#11924512C2211yescharacteristic
28#11924512C2211yescharacteristic
29#11924511—21no—
30#11924511—21no—
31#11924511C2211yescharacteristic
32#11924511C2211yescharacteristic
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic
35C4×D148C2211yescharacteristic
36#11924498—21no—
37#11924494C2211yescharacteristic
38C4⋊C4×D37—21no—
39C4⋊C4×D37C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924467C2211yescharacteristic
43C4⋊#64436C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924448C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53#125×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61#10596966—22no—
62#10596966—22no—
63#10596966—41no—
64#10596966—41no—
65C2×D148—21no—
66C2×D148—21no—
67C2×D148—21no—
68C2×D148—21no—
69C2×D148D411yescharacteristic
70C2×D148C2311yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37C2311yescharacteristic
78C2×C4×D37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37—21no—
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C42×C37C2311yescharacteristic
88#10596941—41no—
89#10596941—41no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938D411yescharacteristic
98#10596938D411yescharacteristic
99C4⋊Dic37D411yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104#10596936—21no—
105C4×Dic37—21no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108D296—22no—
109#10596929—41no—
110C8×D37—41no—
111C22×D37—21no—
112C22×D37—21no—
113C22×D37C2×D411yescharacteristic
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37C2×D411yescharacteristic
129C2×Dic37C2×D411yescharacteristic
130D148—21no—
131D148—21no—
132D148—21no—
133D148—41no—
134D148—42no—
135D148—42no—
136D148—42no—
137D148—81no—
138D148#4112yes—
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144C4×D37—42no—
145C4×D37—42no—
146C4×D37—81no—
147C4×D37—81no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37C22×D411yescharacteristic
153C2×D37—21no—
154C2×D37—21no—
155C2×D37—22no—
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37C2×#4111yescharacteristic
172C4×C37H(5,𝔽2)11yescharacteristic
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176Dic37—41no—
177#3307—371nomaximal, Sylow
178C2×C37#54611yescharacteristic
179C2×C37#57511yescharacteristic
180C2×C37#57711yescharacteristic
181D37—41no—
182D37—41no—
183D37—42no—
184D37—81no—
185#553—371no—
186#547—371no—
187#491D3711yescharacteristic, complemented
188#485—371no—
189#483—371no—
190#478—371no—
191#468—371no—
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196#442—371no—
197#435—371no—
198#417—371no—
199#416—371no—
200C37#330711yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C2×#41—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C2×M16—371no—
207C22×C8—371no—
208C4⋊Q8C2×D3711yescharacteristic
209#126—741no—
210#125C2×D3711yescharacteristic
211#123—741no—
212#123—741no—
213#123—741no—
214C22⋊Q8—371no—
215C22⋊Q8—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224#117—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—741no—
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103C2×D3711yescharacteristic
234#103C2×D3711yescharacteristic
235#103C2×D3711yescharacteristic
236#103C2×D3711yescharacteristic
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8—371no—
242C22⋊C8—371no—
243#97C2×D3711yescharacteristic
244#41—742no—
245#41—742no—
246#41—1481no—
247#41—1481no—
248C2×Q8C22×D3711yescharacteristic
249C2×Q8C22×D3711yescharacteristic
250C2×D4—371no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C22×C4—371no—
258C22×C4—371no—
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4—741no—
264SD16—1481no—
265SD16—1481no—
266D8—742no—
267M16—1481no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—371no—
278C4⋊C4—371no—
279C4⋊C4—371no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4—741no—
283C4⋊C4C22×D3711yescharacteristic
284C4⋊C4C22×D3711yescharacteristic
285C22⋊C4—371no—
286C22⋊C4—371no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—371no—
297C23—371no—
298C23—741no—
299C23—741no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—372no—
305D4—2961no—
306D4—741no—
307D4—741no—
308D4—741no—
309D4—1481no—
310D4—1482no—
311D4—1482no—
312D4—1482no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—371no—
318C2×C4—371no—
319C2×C4—2961no—
320C2×C4—2961no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—1482no—
328C2×C4—1482no—
329C2×C4—1482no—
330C2×C4D4×D3711yescharacteristic
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—741no—
338C22—741no—
339C22—741no—
340C22—741no—
341C22—741no—
342C22—741no—
343C22—742no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—741no—
357C4—741no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458211yescharacteristic
362C2—2961no—
363C2—1481no—
364C2—1481no—
365C2—1482no—
366C2#1455817611yescharacteristic
367C2#1455833211yescharacteristic
368C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#491C2
socleC22×C37C22×D4
hypercenter#491D37
hypocenterC37#3307
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14558236C2semidirect
2. #14558186C2semidirect
3. #14557872C2semidirect
4. #14557862C2semidirect
5. #14557830C2semidirect
6. #14557782C2semidirect
7. #14557765C2semidirect
8. #14557735C2semidirect
9. #14557681C2semidirect
10. #14557681C2semidirect
11. #14557646C2semidirect
12. #14557606C2semidirect
13. #14557533C2semidirect
14. #14557528C2semidirect
15. C37×#491C2semidirect
187. #491D37semidirect
200. C37#3307semidirect

Maximal subgroups

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

subgroupindex
#145582362
#145581862
#145578722
#145578622
#145578302
#145577822
#145577652
#145577352
#145576812
#145576462
#145576062
#145575332
#145575282
C37×#4912
#330737