Finite Group Databasebeta

← #18005264

Subgroups — #18005264

Order 4736.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic
2#14558145C211yesmaximal, characteristic, complemented
3#14557942C211yesmaximal, characteristic, complemented
4#14557927C211yesmaximal, characteristic, complemented
5#14557888C211yesmaximal, characteristic, complemented
6#14557884C211yesmaximal, characteristic, complemented
7#14557791C211yesmaximal, characteristic, complemented
8#14557779C211yesmaximal, characteristic
9#14557774C211yesmaximal, characteristic, complemented
10#14557762C211yesmaximal, characteristic
11#14557641C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13C4×Dic148C211yesmaximal, characteristic, complemented
14C4×#10596930C211yesmaximal, characteristic, complemented
15C37×#405C211yesmaximal, characteristic, complemented
16C2×Dic148C2211yescharacteristic
17C2×Dic148C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20#11924536C2211yescharacteristic
21#11924536C2211yescharacteristic
22#11924531—21no—
23#11924529—21no—
24#11924529—21no—
25#11924528C2211yescharacteristic
26#11924526—21no—
27#11924526—21no—
28#11924524C2211yescharacteristic
29#11924522—21no—
30#11924518—21no—
31#11924515C2211yescharacteristic
32#11924515C2211yescharacteristic
33#11924515C2211yescharacteristic
34#11924514—21no—
35#11924510C2211yescharacteristic
36C4×Dic74C2211yescharacteristic
37C4×Dic74C2211yescharacteristic
38C4×Dic74C2211yescharacteristic
39C4×D148C2211yescharacteristic
40#11924470C2211yescharacteristic
41#11924470C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924468C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924461C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52C2×M16×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#117×C37C2211yescharacteristic
55#97×C37C2211yescharacteristic
56#97×C37C2211yescharacteristic
57C4×C8×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C2×C22⋊D37—21no—
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×Dic74—21no—
64C2×Dic74C2311yescharacteristic
65C2×Dic74C2311yescharacteristic
66C2×Dic74C2311yescharacteristic
67M16×C37—22no—
68C2×C8×C37—22no—
69C2×C8×C37C2311yescharacteristic
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37D411yescharacteristic
74C4⋊C4×C37D411yescharacteristic
75C22⋊C4×C37D411yescharacteristic
76C22⋊C4×C37D411yescharacteristic
77C42×C37C2311yescharacteristic
78C42×C37C2311yescharacteristic
79C22⋊Dic37—21no—
80C22⋊Dic37—21no—
81C22⋊Dic37—21no—
82#10596938—21no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86C4⋊Dic37—21no—
87C4⋊Dic37—21no—
88C4⋊Dic37—21no—
89C4⋊Dic37C2311yescharacteristic
90C4⋊Dic37C2311yescharacteristic
91C4⋊Dic37C2311yescharacteristic
92C4⋊Dic37C2311yescharacteristic
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104Dic148—22no—
105Dic148—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37C2×D411yescharacteristic
113C2×C4×C37C2×D411yescharacteristic
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2411yescharacteristic
118C22⋊D37—81no—
119C2×Dic37—21no—
120C2×Dic37—21no—
121C2×Dic37—21no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126D148—21no—
127D148—21no—
128C4×D37—81no—
129Dic74—21no—
130Dic74—21no—
131Dic74—21no—
132Dic74—21no—
133Dic74—21no—
134Dic74—21no—
135Dic74—81no—
136C8×C37—21no—
137C8×C37—21no—
138C8×C37#4112yes—
139C8×C37#4112yes—
140C22×C37—21no—
141C22×C37—21no—
142C22×C37—21no—
143C22×C37C22×D411yescharacteristic
144C2×D37—41no—
145C2×D37—41no—
146C2×D37—41no—
147C4×C37—21no—
148C4×C37—21no—
149C4×C37—21no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37C2×#4111yescharacteristic
153C4×C37C2×#4111yescharacteristic
154Dic37—41no—
155Dic37—41no—
156Dic37—41no—
157Dic37—41no—
158Dic37—41no—
159Dic37—41no—
160Dic37—41no—
161#3178—371nomaximal, Sylow
162C2×C37—41no—
163C2×C37#53211yescharacteristic
164C2×C37#57711yescharacteristic
165C2×C37#57811yescharacteristic
166D37—81no—
167#542—371no—
168#541—371no—
169#501—371no—
170#497—371no—
171#488—371no—
172#487—371no—
173#470—371no—
174#468—371no—
175#467—371no—
176#465—371no—
177#441—371no—
178#440—371no—
179C4×Q16—371no—
180C4×SD16—371no—
181#405D3711yescharacteristic, complemented
182C37#317811yescharacteristic, complemented, Sylow
183C2×Q16—371no—
184C2×Q16—371no—
185C2×SD16—371no—
186C2×SD16—371no—
187C2×M16C2×D3711yescharacteristic
188C22×C8C2×D3711yescharacteristic
189C4⋊Q8—371no—
190C4⋊Q8—371no—
191#126—741no—
192#126—741no—
193#126—741no—
194#125—371no—
195#125—741no—
196#125—741no—
197#124—371no—
198#124—741no—
199#123—741no—
200C22⋊Q8—371no—
201C22⋊Q8—371no—
202C22⋊Q8—371no—
203C22⋊Q8—741no—
204#121—371no—
205C4×Q8—371no—
206C4×Q8—371no—
207C4×Q8—371no—
208C4×D4—371no—
209#117C2×D3711yescharacteristic
210#107—371no—
211#107—371no—
212#106—371no—
213#106—371no—
214#103—371no—
215#103—371no—
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#102—371no—
221#102—371no—
222#97C2×D3711yescharacteristic
223#97C2×D3711yescharacteristic
224C4×C8C2×D3711yescharacteristic
225C4×C8C2×D3711yescharacteristic
226C2×Q8—371no—
227C2×Q8—371no—
228C2×Q8—371no—
229C2×Q8—741no—
230C2×D4—371no—
231C2×D4—741no—
232C22×C4—741no—
233C22×C4C22×D3711yescharacteristic
234Q16—742no—
235Q16—742no—
236SD16—742no—
237SD16—742no—
238M16—22no—
239C2×C8—22no—
240C2×C8C22×D3711yescharacteristic
241C2×C8C22×D3711yescharacteristic
242C2×C8C22×D3711yescharacteristic
243C2×C8C22×D3711yescharacteristic
244C4⋊C4—371no—
245C4⋊C4—371no—
246C4⋊C4—371no—
247C4⋊C4—371no—
248C4⋊C4—741no—
249C4⋊C4—741no—
250C4⋊C4—741no—
251C4⋊C4—741no—
252C4⋊C4—741no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4D14811yescharacteristic
260C4⋊C4D14811yescharacteristic
261C22⋊C4—741no—
262C22⋊C4—741no—
263C22⋊C4—741no—
264C22⋊C4—741no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4D14811yescharacteristic
269C22⋊C4D14811yescharacteristic
270C42—741no—
271C42—741no—
272C42—741no—
273C42C22×D3711yescharacteristic
274C42C22×D3711yescharacteristic
275C23—741no—
276C23C2×D14811yescharacteristic
277Q8—2961no—
278Q8—741no—
279Q8—741no—
280Q8—741no—
281Q8—741no—
282Q8—741no—
283Q8—741no—
284D4—2961no—
285D4—741no—
286D4—741no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—2961no—
290C2×C4—741no—
291C2×C4—741no—
292C2×C4—741no—
293C2×C4—741no—
294C2×C4—741no—
295C2×C4—741no—
296C2×C4—741no—
297C2×C4C2×D14811yescharacteristic
298C2×C4C2×D14811yescharacteristic
299C2×C4C2×D14811yescharacteristic
300C2×C4C2×D14811yescharacteristic
301C2×C4C2×D14811yescharacteristic
302C2×C4C23×D3711yescharacteristic
303C8—21no—
304C8—21no—
305C8#1059696212yes—
306C8#1059696212yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—1481no—
311C22—1481no—
312C22—1481no—
313C22C22×D14811yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—1481no—
320C4—1481no—
321C4—1481no—
322C4—1481no—
323C4—1481no—
324C4—1481no—
325C4—1481no—
326C4C2×#1059696211yescharacteristic
327C4C2×#1059696211yescharacteristic
328C2—41no—
329C2—2961no—
330C2#1455808311yescharacteristic
331C2#1455834511yescharacteristic
332C2#1455835011yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#405C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#405D37
hypocenterC37#3178
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
2. #14558145C2semidirect
3. #14557942C2semidirect
4. #14557927C2semidirect
5. #14557888C2semidirect
6. #14557884C2semidirect
7. #14557791C2semidirect
9. #14557774C2semidirect
11. #14557641C2semidirect
12. #14557635C2semidirect
13. C4×Dic148C2semidirect
14. C4×#10596930C2semidirect
15. C37×#405C2semidirect
181. #405D37semidirect
182. C37#3178semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145581452
#145579422
#145579272
#145578882
#145578842
#145577912
#145577792
#145577742
#145577622
#145576412
#145576352
C4×Dic1482
C4×#105969302
C37×#4052
#317837