Finite Group Databasebeta

← #18004792

Subgroups — #18004792

Order 4736.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558137C211yesmaximal, characteristic, complemented
2#14558012C211yesmaximal, characteristic, complemented
3#14557850C211yesmaximal, characteristic, complemented
4#14557845C211yesmaximal, characteristic, complemented
5#14557841C211yesmaximal, characteristic, complemented
6#14557833C211yesmaximal, characteristic, complemented
7#14557730C211yesmaximal, characteristic, complemented
8#14557675C211yesmaximal, characteristic, complemented
9#14557675C211yesmaximal, characteristic, complemented
10#14557645C211yesmaximal, characteristic, complemented
11#14557630C211yesmaximal, characteristic, complemented
12#14557624C211yesmaximal, characteristic, complemented
13D8×Dic37C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#459C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19#11924528C2211yescharacteristic
20#11924517—21no—
21#11924517—21no—
22#11924508—21no—
23#11924508—21no—
24#11924507C2211yescharacteristic
25#11924507C2211yescharacteristic
26C4×Dic74C2211yescharacteristic
27#11924501C2211yescharacteristic
28D4×Dic37C2211yescharacteristic
29D4×Dic37C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31C4×C22⋊D37—21no—
32#11924496—21no—
33#11924493C2211yescharacteristic
34#11924492—21no—
35C2×#10596936—21no—
36C4⋊C4×D37C2211yescharacteristic
37#11924470C2211yescharacteristic
38#11924469C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×D8×C37C2211yescharacteristic
53C2×D8×C37C2211yescharacteristic
54#127×C37C2211yescharacteristic
55C4×D4×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C22×Dic37—21no—
69C22×Dic37—21no—
70C22×Dic37—21no—
71C22×Dic37—21no—
72#10596964—22no—
73#10596964—22no—
74C2×C4×D37—21no—
75C2×C4×D37C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77D8×C37—22no—
78D8×C37—22no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C22⋊C4×C37—21no—
83C42×C37C2311yescharacteristic
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37—21no—
87C22⋊Dic37—21no—
88C22⋊Dic37—21no—
89#10596940—22no—
90#10596940—22no—
91#10596938D411yescharacteristic
92#10596938D411yescharacteristic
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936D411yescharacteristic
102#10596936D411yescharacteristic
103C4×Dic37—21no—
104C4×Dic37—21no—
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C22×D37C2×D411yescharacteristic
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—81no—
118D4×C37—81no—
119D4×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—81no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—24no—
126C22⋊D37—81no—
127C22⋊D37—81no—
128C2×Dic37—24no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—81no—
134C2×Dic37—81no—
135C2×Dic37—81no—
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138C2×Dic37C2×D411yescharacteristic
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—81no—
142Dic74—21no—
143Dic74#4112yes—
144C8×C37—21no—
145C8×C37—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—22no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37C22×D411yescharacteristic
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—21no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—41no—
164C4×C37C2×#4111yescharacteristic
165C4×C37C2×#4111yescharacteristic
166Dic37—22no—
167Dic37—21no—
168Dic37—21no—
169Dic37—21no—
170Dic37—41no—
171Dic37—41no—
172Dic37—41no—
173#3119—371nomaximal, Sylow
174C2×C37—42no—
175C2×C37—81no—
176C2×C37—81no—
177C2×C37#52511yescharacteristic
178C2×C37#57611yescharacteristic
179C2×C37#57711yescharacteristic
180D37—41no—
181#540—371no—
182#520—371no—
183#481—371no—
184#480—371no—
185#479—371no—
186#478—371no—
187#460—371no—
188#459D3711yescharacteristic, complemented
189#449—371no—
190#449—371no—
191#442—371no—
192#440—371no—
193C4×SD16—371no—
194C4×D8—371no—
195#433—371no—
196C37#311911yescharacteristic, complemented, Sylow
197C2×#41—371no—
198C2×SD16—371no—
199C2×SD16—371no—
200C2×D8C2×D3711yescharacteristic
201C2×D8C2×D3711yescharacteristic
202#127C2×D3711yescharacteristic
203#125—371no—
204#123—741no—
205#123—741no—
206#121—371no—
207#121—371no—
208#121—741no—
209#121—741no—
210C4×Q8—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—741no—
216C4×D4—741no—
217C4×D4C2×D3711yescharacteristic
218#117—371no—
219#117—741no—
220C2×C4⋊C4—371no—
221C2×C4⋊C4—741no—
222#107—371no—
223#107—371no—
224#106—371no—
225#106—371no—
226C4⋊C8—371no—
227C4⋊C8C2×D3711yescharacteristic
228#103—371no—
229#103—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102C2×D3711yescharacteristic
235#102C2×D3711yescharacteristic
236C22⋊C8—371no—
237C22⋊C8—371no—
238#97—371no—
239C4×C8—371no—
240#41—742no—
241#41—742no—
242C2×Q8—371no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C2×D4C22×D3711yescharacteristic
249C2×D4C22×D3711yescharacteristic
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—371no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4—741no—
258SD16—742no—
259SD16—742no—
260D8—22no—
261D8—22no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8C22×D3711yescharacteristic
265C2×C8C22×D3711yescharacteristic
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—371no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4—741no—
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—371no—
279C22⋊C4—371no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C42—371no—
286C42—741no—
287C42—741no—
288C42C22×D3711yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—371no—
293Q8—372no—
294Q8—741no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—2961no—
303D4—2961no—
304D4—744no—
305D4#1059696412yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—371no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—2961no—
312C2×C4—2961no—
313C2×C4—2961no—
314C2×C4—2961no—
315C2×C4—744no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4D4×D3711yescharacteristic
323C2×C4D4×D3711yescharacteristic
324C2×C4C23×D3711yescharacteristic
325C8—21no—
326C8—21no—
327C8—741no—
328C8—741no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—741no—
339C22—741no—
340C22—741no—
341C22C2×D4×D3711yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—741no—
346C4—742no—
347C4—741no—
348C4—741no—
349C4—1481no—
350C4—1481no—
351C4—1481no—
352C4#41×D3711yescharacteristic
353C4C2×#1059696411yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—1481no—
358C2#1455804311yescharacteristic
359C2#1455833411yescharacteristic
360C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#459C2
socleC22×C37C22×D4
hypercenter#459D37
hypocenterC37#3119
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14558137C2semidirect
2. #14558012C2semidirect
3. #14557850C2semidirect
4. #14557845C2semidirect
5. #14557841C2semidirect
6. #14557833C2semidirect
7. #14557730C2semidirect
8. #14557675C2semidirect
9. #14557675C2semidirect
10. #14557645C2semidirect
11. #14557630C2semidirect
12. #14557624C2semidirect
13. D8×Dic37C2semidirect
14. #14557593C2semidirect
15. C37×#459C2semidirect
188. #459D37semidirect
196. C37#3119semidirect

Maximal subgroups

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

subgroupindex
#145581372
#145580122
#145578502
#145578452
#145578412
#145578332
#145577302
#145576752
#145576452
#145576302
#145576242
D8×Dic372
#145575932
C37×#4592
#311937