Finite Group Databasebeta

← #18004851

Subgroups — #18004851

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#14558150C211yesmaximal, characteristic, complemented
2#14558016C211yesmaximal, characteristic, complemented
3#14557869C211yesmaximal, characteristic, complemented
4#14557844C211yesmaximal, characteristic, complemented
5#14557826C211yesmaximal, characteristic, complemented
6#14557811C211yesmaximal, characteristic, complemented
7#14557753C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557634C211yesmaximal, characteristic, complemented
11#14557630C211yesmaximal, characteristic, complemented
12#14557625C211yesmaximal, characteristic, complemented
13D8×Dic37C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic
16C2×#10596942C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18#11924535C2211yescharacteristic
19#11924529—21no—
20#11924523—21no—
21#11924523C2211yescharacteristic
22#11924517—21no—
23#11924515C2211yescharacteristic
24#11924513—21no—
25Q8×Dic37C2211yescharacteristic
26Q8×Dic37C2211yescharacteristic
27#11924501C2211yescharacteristic
28D4×Dic37—21no—
29D4×Dic37—21no—
30D4×Dic37C2211yescharacteristic
31D4×Dic37C2211yescharacteristic
32D4×Dic37C2211yescharacteristic
33#11924495—21no—
34#11924495C2211yescharacteristic
35C2×C4⋊Dic37—21no—
36C2×C4⋊Dic37C2211yescharacteristic
37#11924470C2211yescharacteristic
38#11924470C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×#41×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—22no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C22×Dic37—21no—
69C22×Dic37—21no—
70C22×Dic37—21no—
71C22×Dic37—21no—
72C2×Dic74—21no—
73C2×Dic74C2311yescharacteristic
74SD16×C37—22no—
75D8×C37—22no—
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊Dic37—21no—
81C22⋊Dic37—21no—
82C22⋊Dic37—21no—
83C22⋊Dic37—21no—
84C22⋊Dic37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87C22⋊Dic37D411yescharacteristic
88#10596942—22no—
89#10596940—22no—
90C4⋊Dic37—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37D411yescharacteristic
94C4⋊Dic37D411yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37—21no—
110C23×C37C2×D411yescharacteristic
111Q8×C37—21no—
112Q8×C37#4112yes—
113D4×C37—24no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—81no—
118D4×C37#4112yes—
119C2×C4×C37—24no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2411yescharacteristic
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—81no—
131C2×Dic37—81no—
132C2×Dic37—81no—
133C2×Dic37—81no—
134C2×Dic37C2×D411yescharacteristic
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138Dic74—21no—
139Dic74—21no—
140Dic74—81no—
141C8×C37—21no—
142C8×C37—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×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C4×C37—21no—
156C4×C37—22no—
157C4×C37—41no—
158C4×C37C2×#4111yescharacteristic
159C4×C37C2×#4111yescharacteristic
160Dic37—21no—
161Dic37—21no—
162Dic37—21no—
163Dic37—21no—
164Dic37—41no—
165Dic37—41no—
166Dic37—41no—
167Dic37—41no—
168#3124—371nomaximal, Sylow
169C2×C37—41no—
170C2×C37—42no—
171C2×C37—81no—
172C2×C37#52511yescharacteristic
173C2×C37#57611yescharacteristic
174C2×C37#57811yescharacteristic
175#542—371no—
176#520—371no—
177#484—371no—
178#480—371no—
179#477—371no—
180#474—371no—
181#464—371no—
182#463—371no—
183#452—371no—
184#449D3711yescharacteristic
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×SD16C2×D3711yescharacteristic
195C2×D8C2×D3711yescharacteristic
196C4⋊Q8—371no—
197#126—741no—
198#124—371no—
199#124—741no—
200#123—741no—
201C22⋊Q8—371no—
202C22⋊Q8—741no—
203#121C2×D3711yescharacteristic
204C4×Q8—371no—
205C4×Q8—371no—
206C4×Q8—371no—
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—371no—
210C4×D4—741no—
211C4×D4—741no—
212#117—371no—
213#117—741no—
214C2×C4⋊C4—371no—
215C2×C4⋊C4—741no—
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#103C2×D3711yescharacteristic
226#102—371no—
227#102—371no—
228#102—371no—
229#102C2×D3711yescharacteristic
230C22⋊C8—371no—
231C22⋊C8C2×D3711yescharacteristic
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—21no—
241C2×D4C22×D3711yescharacteristic
242C2×D4C22×D3711yescharacteristic
243C22×C4—21no—
244C22×C4—741no—
245C22×C4—741no—
246C22×C4—741no—
247C22×C4—741no—
248C22×C4C22×D3711yescharacteristic
249Q16—742no—
250SD16—22no—
251SD16—742no—
252D8—22no—
253C2×C8—371no—
254C2×C8—371no—
255C2×C8C22×D3711yescharacteristic
256C2×C8C22×D3711yescharacteristic
257C4⋊C4—371no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4C22×D3711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—371no—
271C22⋊C4—371no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C42—371no—
279C42—371no—
280C42—741no—
281C42—741no—
282C42—741no—
283C23—21no—
284C23—21no—
285C23D4×D3711yescharacteristic
286Q8—21no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290Q8#1059696412yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1059696412yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—371no—
303C2×C4—371no—
304C2×C4—371no—
305C2×C4—371no—
306C2×C4—2961no—
307C2×C4—2961no—
308C2×C4—2961no—
309C2×C4—2961no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4D4×D3711yescharacteristic
315C2×C4C23×D3711yescharacteristic
316C8—21no—
317C8—21no—
318C8—741no—
319C8—741no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D3711yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—741no—
334C4—741no—
335C4—741no—
336C4—741no—
337C4—1481no—
338C4—1481no—
339C4—1481no—
340C4—1481no—
341C4C2×#1059696411yescharacteristic
342C4C2×#1059696411yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1455803911yescharacteristic
347C2#1455833711yescharacteristic
348C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3124
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14558150C2semidirect
2. #14558016C2semidirect
3. #14557869C2semidirect
4. #14557844C2semidirect
5. #14557826C2semidirect
6. #14557811C2semidirect
7. #14557753C2semidirect
8. #14557746C2semidirect
9. #14557695C2semidirect
10. #14557634C2semidirect
11. #14557630C2semidirect
12. #14557625C2semidirect
13. D8×Dic37C2semidirect
14. #14557591C2semidirect
190. C37#3124semidirect

Maximal subgroups

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

subgroupindex
#145581502
#145580162
#145578692
#145578442
#145578262
#145578112
#145577532
#145577462
#145576952
#145576342
#145576302
#145576252
D8×Dic372
#145575912
C37×#4492
#312437