Finite Group Databasebeta

← #18007343

Subgroups — #18007343

Order 4736.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558243C211yesmaximal, characteristic, complemented
2#14557897C211yesmaximal, characteristic, complemented
3#14557892C211yesmaximal, characteristic, complemented
4#14557887C211yesmaximal, characteristic, complemented
5#14557840C211yesmaximal, characteristic, complemented
6#14557833C211yesmaximal, characteristic, complemented
7#14557813C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557745C211yesmaximal, characteristic, complemented
10#14557725C211yesmaximal, characteristic
11#14557664C211yesmaximal, characteristic, complemented
12#14557643C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, characteristic, complemented
14C4×#10596939C211yesmaximal, characteristic, complemented
15C37×#559C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17C2×#10596939C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19#11924536C2211yescharacteristic
20#11924528C2211yescharacteristic
21#11924528C2211yescharacteristic
22#11924514—21no—
23#11924514—21no—
24#11924512—21no—
25C4×D148C2211yescharacteristic
26C4×D148C2211yescharacteristic
27C4×D148C2211yescharacteristic
28C4⋊C4×D37—21no—
29#11924469C2211yescharacteristic
30#11924469C2211yescharacteristic
31#11924467C2211yescharacteristic
32C4⋊#64436C2211yescharacteristic
33C4⋊#64436C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924460C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
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×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×Dic74—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37D411yescharacteristic
74C4⋊C4×C37D411yescharacteristic
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C22⋊C4×C37—21no—
78C22⋊C4×C37—21no—
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C42×C37—21no—
84C42×C37C2311yescharacteristic
85C42×C37C2311yescharacteristic
86C42×C37C2311yescharacteristic
87#10596941—22no—
88#10596939—22no—
89#10596939—22no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C2×#64436C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C23×C37—21no—
106C23×C37—21no—
107C22×D37—21no—
108Q8×C37—21no—
109Q8×C37—21no—
110Q8×C37—41no—
111D4×C37—21no—
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—42no—
116D4×C37—81no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—81no—
120C2×C4×C37—81no—
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131D148—21no—
132D148#4112yes—
133C4×D37—42no—
134C4×D37—81no—
135C4×D37—81no—
136Dic74—81no—
137#64436—21no—
138#64436—21no—
139#64436—21no—
140#64436—21no—
141C22×C37—41no—
142C22×C37—41no—
143C22×C37—41no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37—41no—
147C22×C37C22×D411yescharacteristic
148C2×D37—22no—
149C2×D37—41no—
150C2×D37—41no—
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37C2×#4111yescharacteristic
160C4×C372−1+411yescharacteristic
161Dic37—41no—
162Dic37—41no—
163Dic37—41no—
164#3370—371nomaximal, Sylow
165C2×C37—81no—
166C2×C37—81no—
167C2×C37#54811yescharacteristic
168C2×C37#57511yescharacteristic
169C2×C37#57611yescharacteristic
170D37—42no—
171#559D3711yescharacteristic, complemented
172#554—371no—
173#490—371no—
174#489—371no—
175#488—371no—
176#479—371no—
177#478—371no—
178#474—371no—
179#463—371no—
180#463—371no—
181#459—371no—
182#446—371no—
183#442—371no—
184#440—371no—
185C4×D8—371no—
186C37#337011yescharacteristic, complemented, Sylow
187C2×SD16—371no—
188C2×D8—371no—
189C2×D8—371no—
190C4⋊Q8—371no—
191#127C2×D3711yescharacteristic
192#125—371no—
193#125—371no—
194#124—21no—
195#124C2×D3711yescharacteristic
196#124C2×D3711yescharacteristic
197#123—21no—
198#123—21no—
199C22⋊Q8—741no—
200C22⋊Q8—741no—
201C22⋊Q8—741no—
202C4×Q8C2×D3711yescharacteristic
203C4×Q8C2×D3711yescharacteristic
204C4×D4—21no—
205C4×D4—371no—
206C4×D4—371no—
207C4×D4—371no—
208C4×D4C2×D3711yescharacteristic
209C4×D4C2×D3711yescharacteristic
210C2×C4⋊C4—741no—
211#107—371no—
212#107—371no—
213#106—371no—
214C4⋊C8—371no—
215C4⋊C8—371no—
216C4⋊C8—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#102—371no—
221#102—371no—
222#102—371no—
223#102—371no—
224#102—371no—
225#102—371no—
226#102—371no—
227#97—371no—
228#97—371no—
229C4×C8—371no—
230C2×Q8—741no—
231C2×Q8C22⋊D3711yescharacteristic
232C2×Q8C22×D3711yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—371no—
236C2×D4C22×D3711yescharacteristic
237C2×D4C22×D3711yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—741no—
241C22×C4—741no—
242C22×C4—741no—
243SD16—742no—
244D8—742no—
245D8—742no—
246C2×C8—371no—
247C2×C8—371no—
248C2×C8—371no—
249C2×C8—371no—
250C4⋊C4—21no—
251C4⋊C4—371no—
252C4⋊C4—371no—
253C4⋊C4—371no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4C22⋊D3711yescharacteristic
260C4⋊C4C22⋊D3711yescharacteristic
261C4⋊C4C22⋊D3711yescharacteristic
262C4⋊C4C22×D3711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C42—21no—
273C42C22×D3711yescharacteristic
274C42C22×D3711yescharacteristic
275C42C22×D3711yescharacteristic
276C23—21no—
277C23—21no—
278C23—741no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—2961no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—372no—
290D4—741no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—2961no—
296C2×C4—2961no—
297C2×C4—741no—
298C2×C4—741no—
299C2×C4—741no—
300C2×C4—1482no—
301C2×C4C2×C22⋊D3711yescharacteristic
302C2×C4C2×C22⋊D3711yescharacteristic
303C2×C4C2×C22⋊D3711yescharacteristic
304C2×C4C2×C22⋊D3711yescharacteristic
305C2×C4C2×C22⋊D3711yescharacteristic
306C2×C4C2×C22⋊D3711yescharacteristic
307C2×C4C23×D3711yescharacteristic
308C8—741no—
309C8—741no—
310C8—741no—
311C8—741no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—742no—
319C22—1481no—
320C22—1481no—
321C22C22×C22⋊D3711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—1481no—
331C4—1481no—
332C4—1481no—
333C4#41×D3711yescharacteristic
334C4#1192458311yescharacteristic
335C2—81no—
336C2—81no—
337C2—1482no—
338C2#1455819011yescharacteristic
339C2#1455833111yescharacteristic
340C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#559C2
socleC22×C37C22×D4
prime radical#14557725C2
hypercenter#559D37
hypocenterC37#3370
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. #14558243C2semidirect
2. #14557897C2semidirect
3. #14557892C2semidirect
4. #14557887C2semidirect
5. #14557840C2semidirect
6. #14557833C2semidirect
7. #14557813C2semidirect
8. #14557745C2semidirect
9. #14557745C2semidirect
11. #14557664C2semidirect
12. #14557643C2semidirect
13. #14557631C2semidirect
14. C4×#10596939C2semidirect
15. C37×#559C2semidirect
171. #559D37semidirect
186. C37#3370semidirect

Maximal subgroups

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

subgroupindex
#145582432
#145578972
#145578922
#145578872
#145578402
#145578332
#145578132
#145577452
#145577252
#145576642
#145576432
#145576312
C4×#105969392
C37×#5592
#337037