Finite Group Databasebeta

← #18005284

Subgroups — #18005284

Order 4736.

374 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#14558157C211yesmaximal, characteristic, complemented
2#14558139C211yesmaximal, characteristic, complemented
3#14557922C211yesmaximal, characteristic, complemented
4#14557890C211yesmaximal, characteristic, complemented
5#14557881C211yesmaximal, characteristic, complemented
6#14557787C211yesmaximal, characteristic, complemented
7#14557780C211yesmaximal, characteristic, complemented
8#14557770C211yesmaximal, characteristic, complemented
9#14557763C211yesmaximal, characteristic, complemented
10#14557644C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557620C211yesmaximal, characteristic, complemented
13#14557615C211yesmaximal, characteristic, complemented
14#14557490C211yesmaximal, characteristic, complemented
15C37×#501C211yesmaximal, characteristic, complemented
16C2×#10596930C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×D296C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924533C2211yescharacteristic
23#11924531—21no—
24#11924525—21no—
25#11924524C2211yescharacteristic
26#11924521—21no—
27#11924521—21no—
28#11924521—21no—
29#11924516C2211yescharacteristic
30#11924512—21no—
31#11924511—21no—
32#11924511—21no—
33#11924511C2211yescharacteristic
34#11924511C2211yescharacteristic
35#11924511C2211yescharacteristic
36#11924501C2211yescharacteristic
37#11924498C2211yescharacteristic
38#11924498C2211yescharacteristic
39#11924498C2211yescharacteristic
40#11924493C2211yescharacteristic
41#11924459C2211yescharacteristic
42#11924459C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924456C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924446C2211yescharacteristic
50C4×#64436C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53#125×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#106×C37C2211yescharacteristic
57#106×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×D148—21no—
61C2×D148—21no—
62C2×D148—21no—
63C2×D148—21no—
64C2×D148—21no—
65C2×D148C2311yescharacteristic
66C2×D148C2311yescharacteristic
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37C2311yescharacteristic
72C2×Dic74C2311yescharacteristic
73C2×C8×C37C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C42×C37C2311yescharacteristic
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938D411yescharacteristic
93#10596938D411yescharacteristic
94C4⋊Dic37—21no—
95#10596936—21no—
96#10596936D411yescharacteristic
97#10596936D411yescharacteristic
98C4×Dic37—21no—
99C4×Dic37C2311yescharacteristic
100C2×#64436C2311yescharacteristic
101C2×#64436C2311yescharacteristic
102D296—22no—
103D296—22no—
104#10596930—22no—
105#10596930—22no—
106#10596929—22no—
107C8×D37—22no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37C2×D411yescharacteristic
112Q8×C37—81no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C2×Dic37—21no—
121C2×Dic37C2×D411yescharacteristic
122C2×Dic37C2×D411yescharacteristic
123C2×Dic37C2×D411yescharacteristic
124D148—21no—
125D148—21no—
126D148—21no—
127D148—21no—
128D148—21no—
129D148—21no—
130D148—81no—
131D148—81no—
132D148—81no—
133D148—81no—
134D148—81no—
135C4×D37—21no—
136C4×D37—21no—
137C4×D37—81no—
138C4×D37—81no—
139C4×D37—81no—
140Dic74—21no—
141Dic74—21no—
142C8×C37#4112yes—
143C8×C37#4112yes—
144#64436—21no—
145#64436—21no—
146C22×C37C22×D411yescharacteristic
147C2×D37—21no—
148C2×D37—21no—
149C2×D37—21no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37C2×#4111yescharacteristic
166C4×C37C2×#4111yescharacteristic
167Dic37—21no—
168Dic37—21no—
169Dic37—21no—
170Dic37—41no—
171#3179—371nomaximal, Sylow
172C2×C37#53211yescharacteristic
173C2×C37#57611yescharacteristic
174C2×C37#57711yescharacteristic
175D37—41no—
176D37—81no—
177D37—81no—
178D37—81no—
179#542—371no—
180#540—371no—
181#501D3711yescharacteristic, complemented
182#496—371no—
183#488—371no—
184#486—371no—
185#469—371no—
186#468—371no—
187#466—371no—
188#465—371no—
189#442—371no—
190#440—371no—
191C4×SD16—371no—
192C4×D8—371no—
193#405—371no—
194C37#317911yescharacteristic, complemented, Sylow
195C2×SD16—371no—
196C2×SD16—371no—
197C2×D8—371no—
198C2×D8—371no—
199C2×M16—371no—
200C22×C8—371no—
201C4⋊Q8C2×D3711yescharacteristic
202#127—371no—
203#126—741no—
204#125C2×D3711yescharacteristic
205#124—371no—
206#124—741no—
207#123—741no—
208#123—741no—
209#123—741no—
210C22⋊Q8—371no—
211C22⋊Q8—741no—
212#121—371no—
213#121—371no—
214#121—371no—
215#121—741no—
216#121—741no—
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221#117—371no—
222#107C2×D3711yescharacteristic
223#107C2×D3711yescharacteristic
224#106C2×D3711yescharacteristic
225#106C2×D3711yescharacteristic
226#103—371no—
227#103—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#97—371no—
235#97C2×D3711yescharacteristic
236C4×C8—371no—
237C4×C8—371no—
238C2×Q8—21no—
239C2×Q8—371no—
240C2×D4—371no—
241C2×D4—371no—
242C2×D4—371no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C22×C4—371no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4—741no—
252SD16—742no—
253SD16—742no—
254D8—742no—
255D8—742no—
256M16—742no—
257C2×C8—371no—
258C2×C8—371no—
259C2×C8—742no—
260C2×C8C22×D3711yescharacteristic
261C2×C8C22×D3711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4C22×D3711yescharacteristic
270C4⋊C4C22×D3711yescharacteristic
271C4⋊C4C22×D3711yescharacteristic
272C4⋊C4C22×D3711yescharacteristic
273C22⋊C4—371no—
274C22⋊C4—371no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C42—371no—
285C42—741no—
286C42C22×D3711yescharacteristic
287C23—371no—
288C23—741no—
289C23—741no—
290C23—741no—
291Q8—81no—
292Q8—741no—
293Q8—741no—
294D4—2961no—
295D4—2961no—
296D4—2961no—
297D4—2961no—
298D4—2961no—
299D4—741no—
300D4—741no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—741no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—371no—
312C2×C4—2961no—
313C2×C4—2961no—
314C2×C4—2961no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4D4×D3711yescharacteristic
319C2×C4D4×D3711yescharacteristic
320C2×C4C23×D3711yescharacteristic
321C8—741no—
322C8—741no—
323C8#1059696612yes—
324C8#1059696612yes—
325C22—741no—
326C22—741no—
327C22—741no—
328C22—1481no—
329C22—1481no—
330C22—1481no—
331C22—1481no—
332C22—1481no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22C2×D4×D3711yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—741no—
345C4—741no—
346C4—741no—
347C4—1481no—
348C4C2×#1059696611yescharacteristic
349C4C2×#1059696611yescharacteristic
350C2—2961no—
351C2—2961no—
352C2—2961no—
353C2—1481no—
354C2#1455808411yescharacteristic
355C2#1455833711yescharacteristic
356C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#501C2
socleC22×C37C22×D4
hypercenter#501D37
hypocenterC37#3179
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14558157C2semidirect
2. #14558139C2semidirect
3. #14557922C2semidirect
4. #14557890C2semidirect
5. #14557881C2semidirect
6. #14557787C2semidirect
7. #14557780C2semidirect
8. #14557770C2semidirect
9. #14557763C2semidirect
10. #14557644C2semidirect
11. #14557632C2semidirect
12. #14557620C2semidirect
13. #14557615C2semidirect
14. #14557490C2semidirect
15. C37×#501C2semidirect
181. #501D37semidirect
194. C37#3179semidirect

Maximal subgroups

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

subgroupindex
#145581572
#145581392
#145579222
#145578902
#145578812
#145577872
#145577802
#145577702
#145577632
#145576442
#145576322
#145576202
#145576152
#145574902
C37×#5012
#317937