Finite Group Databasebeta

← #18004858

Subgroups — #18004858

Order 4736.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14557868C211yesmaximal, characteristic, complemented
3#14557846C211yesmaximal, characteristic, complemented
4#14557828C211yesmaximal, characteristic, complemented
5#14557813C211yesmaximal, characteristic, complemented
6#14557755C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557695C211yesmaximal, characteristic, complemented
9#14557678C211yesmaximal, characteristic
10#14557633C211yesmaximal, characteristic, complemented
11#14557631C211yesmaximal, characteristic, complemented
12C4×#10596942C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#520C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20#11924536C2211yescharacteristic
21#11924531—21no—
22#11924524C2211yescharacteristic
23#11924522—21no—
24#11924518—21no—
25#11924515C2211yescharacteristic
26#11924514—21no—
27#11924510C2211yescharacteristic
28C4×Dic74C2211yescharacteristic
29C4×D148C2211yescharacteristic
30#11924469C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924469C2211yescharacteristic
33#11924469C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35C4⋊#64436C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924459C2211yescharacteristic
39#11924459C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44C22⋊#64436C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46#11924447C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48C2×#41×C37C2211yescharacteristic
49C4×Q8×C37C2211yescharacteristic
50C4×Q8×C37C2211yescharacteristic
51C4×D4×C37—21no—
52C4×D4×C37—21no—
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#117×C37—21no—
56#117×C37C2211yescharacteristic
57C2×C4⋊C4×C37—21no—
58C2×C4⋊C4×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—22no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37C2311yescharacteristic
69C2×C22⋊D37—21no—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×Dic74—21no—
73C2×Dic74C2311yescharacteristic
74C4⋊C4×C37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37D411yescharacteristic
78C4⋊C4×C37D411yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37D411yescharacteristic
84C22⋊C4×C37D411yescharacteristic
85C42×C37—21no—
86C42×C37—21no—
87C42×C37C2311yescharacteristic
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90#10596942—22no—
91#10596941—22no—
92#10596940—22no—
93#10596939—22no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111Q8×C37—21no—
112Q8×C37#4112yes—
113D4×C37—24no—
114D4×C37—21no—
115D4×C37#4112yes—
116C2×C4×C37—24no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—81no—
123C2×C4×C37—81no—
124C2×C4×C37—81no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C22⋊D37—81no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135D148—21no—
136D148—21no—
137C4×D37—81no—
138Dic74—21no—
139Dic74—21no—
140Dic74—81no—
141#64436—21no—
142#64436—21no—
143#64436—21no—
144#64436—21no—
145C22×C37—21no—
146C22×C37—22no—
147C22×C37—21no—
148C22×C37—21no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37C22×D411yescharacteristic
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C4×C37—21no—
156C4×C37—22no—
157C4×C37—21no—
158C4×C37—21no—
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37C2×#4111yescharacteristic
164C4×C37C2×#4111yescharacteristic
165Dic37—41no—
166Dic37—41no—
167Dic37—41no—
168#3124—371nomaximal, Sylow
169C2×C37—41no—
170C2×C37—42no—
171C2×C37#52511yescharacteristic
172C2×C37#57611yescharacteristic
173C2×C37#57811yescharacteristic
174D37—81no—
175#542—371no—
176#520D3711yescharacteristic, complemented
177#484—371no—
178#480—371no—
179#477—371no—
180#474—371no—
181#464—371no—
182#463—371no—
183#452—371no—
184#449—371no—
185#440—371no—
186#440—371no—
187C4×Q16—371no—
188C4×D8—371no—
189#433—371no—
190C37#312411yescharacteristic, complemented, Sylow
191C2×#41C2×D3711yescharacteristic
192C2×Q16—371no—
193C2×SD16—371no—
194C2×SD16—371no—
195C2×D8—371no—
196C4⋊Q8—371no—
197#126—741no—
198#124—371no—
199#124—741no—
200#123—741no—
201C22⋊Q8—371no—
202C22⋊Q8—741no—
203#121—371no—
204C4×Q8—371no—
205C4×Q8C2×D3711yescharacteristic
206C4×Q8C2×D3711yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—371no—
210C4×D4C2×D3711yescharacteristic
211C4×D4C2×D3711yescharacteristic
212#117—21no—
213#117C2×D3711yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D3711yescharacteristic
216#107—371no—
217#107—371no—
218#107—371no—
219#107—371no—
220C4⋊C8—371no—
221C4⋊C8—371no—
222#103—371no—
223#103—371no—
224#103—371no—
225#103—371no—
226#102—371no—
227#102—371no—
228#102—371no—
229#102—371no—
230C22⋊C8—371no—
231C22⋊C8—371no—
232#97—371no—
233C4×C8—371no—
234#41—22no—
235#41—22no—
236C2×Q8—371no—
237C2×Q8—741no—
238C2×Q8C22×D3711yescharacteristic
239C2×D4—21no—
240C2×D4—371no—
241C2×D4—741no—
242C2×D4C22×D3711yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—741no—
248C22×C4C22×D3711yescharacteristic
249Q16—742no—
250SD16—742no—
251SD16—742no—
252D8—742no—
253C2×C8—371no—
254C2×C8—371no—
255C2×C8—371no—
256C2×C8—371no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4C22⋊D3711yescharacteristic
266C4⋊C4C22⋊D3711yescharacteristic
267C4⋊C4C22×D3711yescharacteristic
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4C22⋊D3711yescharacteristic
277C22⋊C4C22⋊D3711yescharacteristic
278C42—21no—
279C42—21no—
280C42—741no—
281C42C22×D3711yescharacteristic
282C42C22×D3711yescharacteristic
283C23—21no—
284C23—741no—
285C23C2×C22⋊D3711yescharacteristic
286Q8—21no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290Q8#1059696212yes—
291D4—24no—
292D4—21no—
293D4—2961no—
294D4—741no—
295D4—741no—
296D4#1059696212yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—2961no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4—741no—
310C2×C4C2×C22⋊D3711yescharacteristic
311C2×C4C2×C22⋊D3711yescharacteristic
312C2×C4C2×C22⋊D3711yescharacteristic
313C2×C4C2×C22⋊D3711yescharacteristic
314C2×C4C2×C22⋊D3711yescharacteristic
315C2×C4C23×D3711yescharacteristic
316C8—741no—
317C8—741no—
318C8—741no—
319C8—741no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—1481no—
327C22—1481no—
328C22—1481no—
329C22C22×C22⋊D3711yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—1481no—
339C4—1481no—
340C4—1481no—
341C4C2×#1059696211yescharacteristic
342C4C2×#1059696211yescharacteristic
343C2—41no—
344C2—42no—
345C2—2961no—
346C2#1455804411yescharacteristic
347C2#1455833611yescharacteristic
348C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#520C2
socleC22×C37C22×D4
prime radical#14557678C2
hypercenter#520D37
hypocenterC37#3124
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14557868C2semidirect
3. #14557846C2semidirect
4. #14557828C2semidirect
5. #14557813C2semidirect
6. #14557755C2semidirect
7. #14557748C2semidirect
8. #14557695C2semidirect
10. #14557633C2semidirect
11. #14557631C2semidirect
12. C4×#10596942C2semidirect
13. C4×#10596939C2semidirect
14. #14557594C2semidirect
15. C37×#520C2semidirect
176. #520D37semidirect
190. C37#3124semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145578682
#145578462
#145578282
#145578132
#145577552
#145577482
#145576952
#145576782
#145576332
#145576312
C4×#105969422
C4×#105969392
#145575942
C37×#5202
#312437