Finite Group Databasebeta

← #18006405

Subgroups — #18006405

Order 4736.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558184C211yesmaximal, characteristic, complemented
2D4×C22⋊D37C211yesmaximal, characteristic, complemented
3#14557878C211yesmaximal, characteristic, complemented
4#14557846C211yesmaximal, characteristic, complemented
5#14557845C211yesmaximal, characteristic, complemented
6#14557811C211yesmaximal, characteristic, complemented
7#14557769C211yesmaximal, characteristic, complemented
8#14557768C211yesmaximal, characteristic, complemented
9#14557727C211yesmaximal, characteristic, complemented
10#14557668C211yesmaximal, characteristic, complemented
11#14557667C211yesmaximal, characteristic, complemented
12#14557613C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C2×#102×C37C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C22×C22⋊D37—21no—
18C2×D4×D37C2211yescharacteristic
19C2×D296C2211yescharacteristic, complemented
20C2×#10596939C2211yescharacteristic
21C2×#10596939C2211yescharacteristic, complemented
22C2×C8×D37C2211yescharacteristic, complemented
23#11924535C2211yescharacteristic, complemented
24#11924532C2211yescharacteristic
25#11924521—21no—
26#11924519—21no—
27#11924514—21no—
28#11924511C2211yescharacteristic, complemented
29#11924510C2211yescharacteristic
30#11924510C2211yescharacteristic, complemented
31#11924508—21no—
32#11924507C2211yescharacteristic
33#11924505—21no—
34#11924504—21no—
35D4×Dic37C2211yescharacteristic
36#11924498C2211yescharacteristic, complemented
37C4×C22⋊D37C2211yescharacteristic
38C4⋊C4×D37C2211yescharacteristic, complemented
39#11924470C2211yescharacteristic, complemented
40#11924469C2211yescharacteristic, complemented
41#11924469C2211yescharacteristic, complemented
42#11924465C2211yescharacteristic, complemented
43#11924458C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic, complemented
45#11924457C2211yescharacteristic
46#11924457C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52C22×D4×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic, complemented
54C2×C4⋊C4×C37C2211yescharacteristic, complemented
55#102×C37C2211yescharacteristic
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C24×C37—21no—
60C23×D37—21no—
61C2×D4×C37—22no—
62C2×D4×C37—21no—
63C2×D4×C37—41no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—44no—
75C2×C22⋊D37D411yescharacteristic
76C22×Dic37—21no—
77D4×D37—22no—
78D4×D37—41no—
79#10596962—44no—
80C2×D148—21no—
81C2×D148C2311yescharacteristic
82C2×D148C2311yescharacteristic
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37C2311yescharacteristic
86C2×Dic74—21no—
87C2×C8×C37—41no—
88C2×C8×C37C2311yescharacteristic
89C2×C8×C37C2311yescharacteristic
90C4⋊C4×C37—21no—
91C4⋊C4×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95C22⋊Dic37D411yescharacteristic
96#10596939—22no—
97#10596939—41no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938D411yescharacteristic
103C4⋊Dic37C2311yescharacteristic
104C4⋊Dic37C2311yescharacteristic
105#10596936—21no—
106#10596936—21no—
107#10596936D411yescharacteristic
108C4×Dic37C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111D296—41no—
112C8×D37—41no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—42no—
116C23×C37—42no—
117C23×C37—81no—
118C23×C37C2×D411yescharacteristic
119C22×D37—21no—
120C22×D37—21no—
121C22×D37—42no—
122C22×D37—42no—
123C22×D37—81no—
124C22×D37C2×D411yescharacteristic
125D4×C37—21no—
126D4×C37—21no—
127D4×C37—21no—
128D4×C37—42no—
129D4×C37#4112yescomplemented
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—42no—
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2411yescharacteristic
137C22⋊D37—42no—
138C22⋊D37—42no—
139C22⋊D37—42no—
140C22⋊D37—42no—
141C22⋊D37—42no—
142C22⋊D37—81no—
143C22⋊D37D814yescomplemented
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—42no—
147C2×Dic37C2×D411yescharacteristic
148C2×Dic37C2×D411yescharacteristic
149C2×Dic37C2×D411yescharacteristic
150D148—21no—
151D148—21no—
152D148—21no—
153D148—21no—
154D148—42no—
155C4×D37—21no—
156C4×D37—21no—
157C4×D37—42no—
158C4×D37—42no—
159Dic74—42no—
160C8×C37—21no—
161C8×C37—21no—
162#64436—21no—
163#64436—21no—
164C22×C37—21no—
165C22×C37—21no—
166C22×C37—22no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37—41no—
172C22×C37—84no—
173C22×C37C2×D812yes—
174C22×C37C22×D411yescharacteristic
175C2×D37—21no—
176C2×D37—21no—
177C2×D37—41no—
178C2×D37—41no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—84no—
184C2×D37C2×D812yes—
185C4×C37—21no—
186C4×C37—41no—
187C4×C37—41no—
188C4×C37C2×#4111yescharacteristic
189C4×C37H(5,𝔽2)11yescharacteristic
190Dic37—21no—
191Dic37—21no—
192Dic37—41no—
193Dic37—41no—
194Dic37C2×D812yes—
195#3294—371nomaximal, Sylow
196C2×C37—22no—
197C2×C37—42no—
198C2×C37—81no—
199C2×C37#54611yescharacteristic
200C2×C37C22×D811yescharacteristic
201C2×C37#57711yescharacteristic
202D37—22no—
203D37—81no—
204D37—81no—
205#547—371no—
206D42—371no—
207#486—371no—
208#480—371no—
209#480—371no—
210#474—371no—
211#466—371no—
212#466—371no—
213#459—371no—
214#447—371no—
215#447—371no—
216C4×D8—371no—
217C8×D4—371no—
218C2×#102—371no—
219C2×#102D3711yescharacteristic, complemented
220C37#329411yescharacteristic, complemented, Sylow
221C2×#41—741no—
222C22×D4—371no—
223C22×D4—741no—
224C22×D4C2×D3711yescharacteristic
225C2×D8—371no—
226C2×D8—371no—
227C2×D8—371no—
228C22×C8—371no—
229C22×C8C2×D3711yescharacteristic, complemented
230C4⋊Q8—371no—
231#127—371no—
232#123—741no—
233#123—741no—
234C22⋊Q8—741no—
235#121—371no—
236#121—371no—
237#121—371no—
238#121—371no—
239#121—741no—
240#120—741no—
241#120—741no—
242C4×D4—371no—
243C4×D4—371no—
244C4×D4—371no—
245C2×C4⋊C4—371no—
246C2×C4⋊C4C2×D3711yescharacteristic, complemented
247#107—371no—
248#107—371no—
249#107—371no—
250C4⋊C8—371no—
251#102—371no—
252#102—371no—
253#102—371no—
254#102—371no—
255#102—371no—
256#102—371no—
257#102C2×D3711yescharacteristic
258#102C2×D3711yescharacteristic
259#102C2×D3711yescharacteristic, complemented
260#102C2×D3711yescharacteristic, complemented
261C22⋊C8—371no—
262C22⋊C8—371no—
263C4×C8—371no—
264C24—21no—
265C24—741no—
266#41—1484no—
267C2×Q8—741no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—371no—
272C2×D4—371no—
273C2×D4—371no—
274C2×D4—741no—
275C2×D4—741no—
276C2×D4—741no—
277C2×D4—741no—
278C2×D4—742no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4—741no—
282C2×D4—1481no—
283C2×D4—1484no—
284C2×D4C22×D3711yescharacteristic
285C2×D4C22×D3711yescharacteristic
286C22×C4—21no—
287C22×C4—371no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4C22×D3711yescharacteristic
292D8—742no—
293D8—1481no—
294D8—1481no—
295C2×C8—41no—
296C2×C8—371no—
297C2×C8—371no—
298C2×C8—1481no—
299C2×C8C22×D3711yescharacteristic
300C2×C8C22×D3711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—371no—
303C4⋊C4—371no—
304C4⋊C4—371no—
305C4⋊C4—741no—
306C4⋊C4—741no—
307C4⋊C4C22×D3711yescharacteristic
308C4⋊C4C22×D3711yescharacteristic
309C22⋊C4—371no—
310C22⋊C4—371no—
311C22⋊C4—741no—
312C22⋊C4—741no—
313C22⋊C4—741no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C42—371no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—371no—
324C23—2961no—
325C23—741no—
326C23—741no—
327C23—1482no—
328C23—1482no—
329C23D4×D3711yescharacteristic
330Q8—1482no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—374no—
336D4—2961no—
337D4—741no—
338D4—741no—
339D4—741no—
340D4—741no—
341D4—1482no—
342D4—1482no—
343D4—1482no—
344D4—1482no—
345D4—1482no—
346D4—1482no—
347D4#1059696212yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—371no—
354C2×C4—371no—
355C2×C4—371no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—1482no—
361C2×C4—1482no—
362C2×C4—1482no—
363C2×C4D4×D3711yescharacteristic
364C2×C4C23×D3711yescharacteristic
365C8—21no—
366C8—21no—
367C8—741no—
368C8—741no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—372no—
379C22—2964no—
380C22—741no—
381C22—741no—
382C22—1481no—
383C22—1481no—
384C22—1481no—
385C22—1481no—
386C22—1481no—
387C22—1481no—
388C22D8×D3712yes—
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—372no—
394C4—741no—
395C4—741no—
396C4—1481no—
397C4—1481no—
398C4C2×#1059696211yescharacteristic
399C4#1192458111yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—2961no—
404C2—2961no—
405C2—742no—
406C2#1455817311yescharacteristic
407C2C2×D8×D3711yescharacteristic
408C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#102×C37C2
socleC22×C37C22×D4
hypercenterC2×#102D37
hypocenterC37#3294
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14558184C2semidirect
2. D4×C22⋊D37C2semidirect
3. #14557878C2semidirect
4. #14557846C2semidirect
5. #14557845C2semidirect
6. #14557811C2semidirect
7. #14557769C2semidirect
8. #14557768C2semidirect
9. #14557727C2semidirect
10. #14557668C2semidirect
11. #14557667C2semidirect
12. #14557613C2semidirect
13. C8×C22⋊D37C2semidirect
14. #102×D37C2semidirect
15. C2×#102×C37C2semidirect
19. C2×D296C22semidirect
21. C2×#10596939C22semidirect
22. C2×C8×D37C22semidirect
23. #11924535C22semidirect
28. #11924511C22semidirect
30. #11924510C22semidirect
36. #11924498C22semidirect
38. C4⋊C4×D37C22semidirect
39. #11924470C22semidirect
40. #11924469C22semidirect
41. #11924469C22semidirect
42. #11924465C22semidirect
43. #11924458C22semidirect
44. #11924458C22semidirect
46. #11924457C22semidirect
47. #11924456C22semidirect
48. #11924456C22semidirect
49. C22⋊#64436C22semidirect
50. #11924448C22semidirect
51. C8×Dic37C22semidirect
53. C22×C8×C37C22semidirect
54. C2×C4⋊C4×C37C22semidirect
57. #102×C37C22semidirect
58. #102×C37C22semidirect
129. D4×C37#41semidirect
143. C22⋊D37D8semidirect
219. C2×#102D37semidirect
220. C37#3294semidirect
229. C22×C8C2×D37semidirect
246. C2×C4⋊C4C2×D37semidirect
259. #102C2×D37semidirect
260. #102C2×D37semidirect
347. D4#10596962semidirect

Maximal subgroups

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

subgroupindex
#145581842
D4×C22⋊D372
#145578782
#145578462
#145578452
#145578112
#145577692
#145577682
#145577272
#145576682
#145576672
#145576132
C8×C22⋊D372
#102×D372
C2×#102×C372
#329437