Finite Group Databasebeta

← #18004846

Subgroups — #18004846

Order 4736.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558144C211yesmaximal, characteristic, complemented
2#14558005C211yesmaximal, characteristic
3#14557873C211yesmaximal, characteristic, complemented
4#14557872C211yesmaximal, characteristic, complemented
5#14557834C211yesmaximal, characteristic, complemented
6#14557833C211yesmaximal, characteristic, complemented
7#14557735C211yesmaximal, characteristic, complemented
8#14557682C211yesmaximal, characteristic
9#14557682C211yesmaximal, characteristic
10#14557636C211yesmaximal, characteristic, complemented
11#14557634C211yesmaximal, characteristic, complemented
12SD16×Dic37C211yesmaximal, characteristic, complemented
13#14557618C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#461C211yesmaximal, characteristic, complemented
16C2×D4×D37C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19#11924531—21no—
20#11924531—21no—
21#11924528C2211yescharacteristic, complemented
22#11924526—21no—
23#11924526—21no—
24#11924512C2211yescharacteristic
25#11924512C2211yescharacteristic
26Q8×Dic37C2211yescharacteristic, complemented
27Q8×Dic37C2211yescharacteristic, complemented
28C4×D148C2211yescharacteristic
29D4×Dic37C2211yescharacteristic
30#11924498C2211yescharacteristic
31C4×C22⋊D37—21no—
32#11924496—21no—
33#11924494C2211yescharacteristic
34#11924493C2211yescharacteristic
35C2×#10596938—21no—
36C22⋊C4×D37—21no—
37#11924470C2211yescharacteristic, complemented
38#11924469C2211yescharacteristic, complemented
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41C4⋊#64436C2211yescharacteristic, complemented
42#11924460C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C2×SD16×C37C2211yescharacteristic
53C2×SD16×C37C2211yescharacteristic
54C4⋊Q8×C37C2211yescharacteristic, complemented
55C4×D4×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58#103×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37—21no—
64C2×C22⋊D37—21no—
65C22×Dic37—21no—
66D4×D37—22no—
67D4×D37—22no—
68C2×D148C2311yescharacteristic
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×C4×D37C2311yescharacteristic
72SD16×C37—22no—
73SD16×C37—22no—
74C2×C8×C37C2311yescharacteristic
75C2×C8×C37C2311yescharacteristic
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C42×C37C2311yescharacteristic
81C22⋊Dic37—21no—
82#10596941—22no—
83#10596941—22no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938D411yescharacteristic
90#10596938D411yescharacteristic
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95C4⋊Dic37C2311yescharacteristic
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C22×D37—21no—
110C22×D37—24no—
111C22×D37—81no—
112C22×D37—81no—
113C22×D37C2×D411yescharacteristic
114Q8×C37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118D4×C37—21no—
119D4×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—81no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—24no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—81no—
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—21no—
136D148#4112yes—
137C4×D37—21no—
138C4×D37—21no—
139C4×D37—81no—
140C4×D37—81no—
141C8×C37—21no—
142C8×C37—21no—
143#64436—21no—
144#64436—21no—
145C22×C37—22no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37C22×D411yescharacteristic
149C2×D37—21no—
150C2×D37—22no—
151C2×D37—21no—
152C2×D37—21no—
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—84no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37C2×#4111yescharacteristic
162C4×C37C2×#4111yescharacteristic
163Dic37—21no—
164Dic37—21no—
165Dic37—21no—
166Dic37—41no—
167Dic37—41no—
168Dic37—41no—
169#3123—371nomaximal, Sylow
170C2×C37—42no—
171C2×C37#52511yescharacteristic
172C2×C37#57711yescharacteristic
173C2×C37#57711yescharacteristic
174D37—41no—
175D37—42no—
176#541—371no—
177#518—371no—
178#485—371no—
179#485—371no—
180#478—371no—
181#478—371no—
182#461—371no—
183#461D3711yescharacteristic, complemented
184#450—371no—
185#450—371no—
186#440—371no—
187#440—371no—
188C4×SD16—371no—
189C4×SD16—371no—
190#433—371no—
191C37#312311yescharacteristic, complemented, Sylow
192C22×D4—371no—
193C2×SD16—371no—
194C2×SD16—371no—
195C2×SD16C2×D3711yescharacteristic
196C2×SD16C2×D3711yescharacteristic
197C4⋊Q8C2×D3711yescharacteristic, complemented
198#126—741no—
199#126—741no—
200#125—371no—
201#125—741no—
202#125—741no—
203C22⋊Q8—371no—
204C22⋊Q8—371no—
205C4×Q8—371no—
206C4×Q8—371no—
207C4×D4—371no—
208C4×D4—371no—
209C4×D4—371no—
210C4×D4—741no—
211C4×D4—741no—
212C4×D4C2×D3711yescharacteristic
213#117—371no—
214#117—371no—
215C2×C22⋊C4—741no—
216C2×C22⋊C4—741no—
217#107—371no—
218#107—371no—
219#106—371no—
220#106—371no—
221C4⋊C8—371no—
222C4⋊C8C2×D3711yescharacteristic, complemented
223#103—371no—
224#103—371no—
225#103C2×D3711yescharacteristic, complemented
226#103C2×D3711yescharacteristic, complemented
227#102—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231C22⋊C8—371no—
232C22⋊C8—371no—
233#97—371no—
234C4×C8—371no—
235C24—741no—
236C2×Q8C22×D3711yescharacteristic
237C2×Q8C22×D3711yescharacteristic
238C2×D4—371no—
239C2×D4—741no—
240C2×D4—742no—
241C2×D4—742no—
242C2×D4C22×D3711yescharacteristic
243C22×C4—21no—
244C22×C4—371no—
245C22×C4—741no—
246C22×C4—741no—
247C22×C4—741no—
248SD16—22no—
249SD16—22no—
250SD16—742no—
251SD16—742no—
252C2×C8—371no—
253C2×C8—371no—
254C2×C8C22×D3711yescharacteristic
255C2×C8C22×D3711yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—371no—
259C4⋊C4—371no—
260C4⋊C4—371no—
261C4⋊C4—371no—
262C4⋊C4—371no—
263C4⋊C4—741no—
264C4⋊C4—741no—
265C4⋊C4—741no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4C22×D3711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—371no—
272C22⋊C4—371no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C42—371no—
280C42—741no—
281C42—741no—
282C42—741no—
283C42C22×D3711yescharacteristic
284C23—21no—
285C23—371no—
286C23—2961no—
287C23—2961no—
288C23—744no—
289C23—741no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—372no—
296D4—744no—
297D4—741no—
298D4#1059696412yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—371no—
304C2×C4—371no—
305C2×C4—371no—
306C2×C4—2961no—
307C2×C4—2961no—
308C2×C4—2961no—
309C2×C4—741no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4D4×D3711yescharacteristic
315C2×C4D4×D3711yescharacteristic
316C2×C4C23×D3711yescharacteristic
317C8—21no—
318C8—21no—
319C8—741no—
320C8—741no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2964no—
325C22—741no—
326C22—742no—
327C22—741no—
328C22—741no—
329C22—1481no—
330C22—1481no—
331C22C2×D4×D3711yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—741no—
338C4—741no—
339C4—741no—
340C4—1481no—
341C4—1481no—
342C4—1481no—
343C4#41×D3711yescharacteristic
344C4C2×#1059696411yescharacteristic
345C2—42no—
346C2—1481no—
347C2—1482no—
348C2#1455804311yescharacteristic
349C2#1455833911yescharacteristic
350C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#461C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#461D37
hypocenterC37#3123
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14558144C2semidirect
3. #14557873C2semidirect
4. #14557872C2semidirect
5. #14557834C2semidirect
6. #14557833C2semidirect
7. #14557735C2semidirect
10. #14557636C2semidirect
11. #14557634C2semidirect
12. SD16×Dic37C2semidirect
13. #14557618C2semidirect
14. #14557593C2semidirect
15. C37×#461C2semidirect
21. #11924528C22semidirect
26. Q8×Dic37C22semidirect
27. Q8×Dic37C22semidirect
37. #11924470C22semidirect
38. #11924469C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. C4⋊#64436C22semidirect
42. #11924460C22semidirect
43. #11924460C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
54. C4⋊Q8×C37C22semidirect
56. C4⋊C8×C37C22semidirect
57. #103×C37C22semidirect
58. #103×C37C22semidirect
183. #461D37semidirect
191. C37#3123semidirect
197. C4⋊Q8C2×D37semidirect
222. C4⋊C8C2×D37semidirect
225. #103C2×D37semidirect
226. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581442
#145580052
#145578732
#145578722
#145578342
#145578332
#145577352
#145576822
#145576362
#145576342
SD16×Dic372
#145576182
#145575932
C37×#4612
#312337