Finite Group Databasebeta

← #18006126

Subgroups — #18006126

Order 4736.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924564C211yesmaximal, characteristic, complemented
2C2×#11924558C211yesmaximal, characteristic, complemented
3#14558188C211yesmaximal, characteristic, complemented
4#14558179C211yesmaximal, characteristic, complemented
5#14557927C211yesmaximal, characteristic, complemented
6#14557791C211yesmaximal, characteristic, complemented
7#14557762C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557739C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557697C211yesmaximal, characteristic, complemented
12#14557686C211yesmaximal, characteristic, complemented
13#14557680C211yesmaximal, characteristic, complemented
14#14557646C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596962C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic
20#11924564—24no—
21#11924558—24no—
22C2×Dic148C2211yescharacteristic, complemented
23C2×Dic148C2211yescharacteristic, complemented
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic
26C2×#10596930C2211yescharacteristic
27C2×#10596930C2211yescharacteristic
28C2×#10596930C2211yescharacteristic, complemented
29C2×D296C2211yescharacteristic
30C2×D296C2211yescharacteristic
31#11924536C2211yescharacteristic, complemented
32#11924524C2211yescharacteristic
33#11924521—21no—
34#11924518—21no—
35#11924518—21no—
36#11924515C2211yescharacteristic
37#11924515C2211yescharacteristic
38#11924515C2211yescharacteristic, complemented
39#11924510C2211yescharacteristic
40#11924509—21no—
41#11924507—21no—
42#11924504—21no—
43C4×D148C2211yescharacteristic
44C4×D148C2211yescharacteristic, complemented
45C4⋊C4×D37—21no—
46C22⋊C4×D37—21no—
47#11924468C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924461C2211yescharacteristic, complemented
50#11924461C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic
52#11924458C2211yescharacteristic
53#11924458C2211yescharacteristic, complemented
54C2×M16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic, complemented
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C22⋊C8×C37C2211yescharacteristic, complemented
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37D411yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69#10596962—22no—
70#10596962—22no—
71#10596962—22no—
72#10596962—41no—
73#10596962—41no—
74#10596962—41no—
75C2×D148—22no—
76C2×D148—21no—
77C2×D148—41no—
78C2×D148C2311yescharacteristic
79C2×D148C2311yescharacteristic
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88C2×Dic74C2311yescharacteristic
89M16×C37—22no—
90C2×C8×C37—22no—
91C2×C8×C37C2311yescharacteristic
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C2×C8×C37C2311yescharacteristic
95C4⋊C4×C37D411yescharacteristic
96C22⋊C4×C37D411yescharacteristic
97C22⋊C4×C37D411yescharacteristic
98C42×C37C2311yescharacteristic
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107C4⋊Dic37—21no—
108C4⋊Dic37—21no—
109C4⋊Dic37C2311yescharacteristic
110C4⋊Dic37C2311yescharacteristic
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114Dic148—22no—
115Dic148—41no—
116D296—22no—
117D296D414yescomplemented
118#10596930—22no—
119#10596930—22no—
120#10596930—22no—
121#10596930—22no—
122#10596930—41no—
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—81no—
131D4×C37—41no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C22⋊D37—42no—
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—81no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150D148—21no—
151D148—21no—
152D148—21no—
153D148—21no—
154D148—42no—
155D148C2×D412yes—
156D148C2×D412yes—
157C4×D37—42no—
158C4×D37—42no—
159C4×D37—42no—
160C4×D37—42no—
161C4×D37—81no—
162Dic74—21no—
163Dic74—21no—
164Dic74—21no—
165Dic74—21no—
166Dic74—21no—
167Dic74—21no—
168C8×C37—21no—
169C8×C37—21no—
170C8×C37—21no—
171C8×C37C2×D412yes—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37C22×D411yescharacteristic
179C2×D37—22no—
180C2×D37—22no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C2×D37—84no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37—21no—
193C4×C37C22×D411yescharacteristic
194C4×C37H(5,𝔽2)11yescharacteristic
195Dic37—41no—
196Dic37—41no—
197Dic37—41no—
198Dic37—41no—
199Dic37—41no—
200#3267—371nomaximal, Sylow
201C2×C37—41no—
202C2×C37—41no—
203C2×C37D4211yescharacteristic
204C2×C37#57511yescharacteristic
205C2×C37#57711yescharacteristic
206D37—42no—
207D37—42no—
208D37—81no—
209C2×AGL(1,ℤ/8)—371no—
210C2×#135—371no—
211#547—371no—
212#546—371no—
213#497—371no—
214#470—371no—
215#465—371no—
216#463—371no—
217#461—371no—
218#452—371no—
219#452—371no—
220#450—371no—
221#449—371no—
222#442—371no—
223#435D3711yescharacteristic, complemented
224C37#326711yescharacteristic, complemented, Sylow
225C2×#41—371no—
226C2×#41—371no—
227C2×#41—371no—
228C22×D4—371no—
229AGL(1,ℤ/8)—744no—
230#135—744no—
231C2×Q16—371no—
232C2×Q16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×SD16—371no—
238C2×D8—371no—
239C2×D8—371no—
240C2×M16C2×D3711yescharacteristic
241C22×C8C2×D3711yescharacteristic, complemented
242C4⋊Q8—371no—
243#124—371no—
244#123—741no—
245#123—741no—
246#123—741no—
247C22⋊Q8—371no—
248C22⋊Q8—371no—
249C22⋊Q8—371no—
250#121—371no—
251#121—741no—
252#121—741no—
253#120—741no—
254C4×D4—371no—
255C4×D4—371no—
256C4×D4C2×D3711yescharacteristic
257C2×C4⋊C4—741no—
258C2×C22⋊C4—741no—
259#106—371no—
260C4⋊C8C2×D3711yescharacteristic, complemented
261#103—371no—
262#103—371no—
263#103—371no—
264#102—371no—
265#102—371no—
266#102—371no—
267C22⋊C8C2×D3711yescharacteristic
268C22⋊C8C2×D3711yescharacteristic, complemented
269#97C2×D3711yescharacteristic, complemented
270C24—741no—
271#41—742no—
272#41—742no—
273#41—742no—
274#41—1481no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8—371no—
279C2×Q8—371no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—371no—
283C2×D4—742no—
284C2×D4—741no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—1481no—
290C2×D4D14811yescharacteristic
291C22×C4—741no—
292C22×C4—741no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4C22×D3711yescharacteristic
297C22×C4C22×D3711yescharacteristic
298Q16—742no—
299Q16—1481no—
300SD16—742no—
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—1481no—
305D8—374no—
306D8—742no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D3711yescharacteristic
310C2×C8C22×D3711yescharacteristic
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C4⋊C4—371no—
314C4⋊C4—371no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4—741no—
320C4⋊C4D14811yescharacteristic
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4D14811yescharacteristic
330C22⋊C4D14811yescharacteristic
331C42C22×D3711yescharacteristic
332C23—2961no—
333C23—741no—
334C23—741no—
335C23—741no—
336C23—1482no—
337C23—1482no—
338C23C2×D14811yescharacteristic
339C23C2×D14811yescharacteristic
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—741no—
344Q8—741no—
345Q8—741no—
346D4—41no—
347D4—372no—
348D4—372no—
349D4—2961no—
350D4—741no—
351D4—741no—
352D4—741no—
353D4—741no—
354D4—1482no—
355D4—1482no—
356D4—1482no—
357D4—1482no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—2961no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4—1482no—
372C2×C4C2×D14811yescharacteristic
373C2×C4C2×D14811yescharacteristic
374C2×C4C2×D14811yescharacteristic
375C2×C4C2×D14811yescharacteristic
376C2×C4C23×D3711yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D3712yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—2964no—
388C22—742no—
389C22—742no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22—1481no—
396C22—1481no—
397C22C22×D14811yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—1481no—
403C4—1481no—
404C4—1481no—
405C4—1481no—
406C4—1481no—
407C4C2×D4×D3711yescharacteristic
408C4#1192458211yescharacteristic
409C2—41no—
410C2—41no—
411C2—2961no—
412C2—1482no—
413C2—1482no—
414C2D4×D14811yescharacteristic
415C2#1455833311yescharacteristic
416C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3267
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924558C2semidirect
3. #14558188C2semidirect
4. #14558179C2semidirect
5. #14557927C2semidirect
6. #14557791C2semidirect
7. #14557762C2semidirect
8. #14557749C2semidirect
9. #14557739C2semidirect
10. #14557697C2semidirect
11. #14557697C2semidirect
12. #14557686C2semidirect
13. #14557680C2semidirect
14. #14557646C2semidirect
15. C37×#435C2semidirect
18. C2×#10596962C22semidirect
22. C2×Dic148C22semidirect
23. C2×Dic148C22semidirect
28. C2×#10596930C22semidirect
31. #11924536C22semidirect
38. #11924515C22semidirect
44. C4×D148C22semidirect
47. #11924468C22semidirect
48. #11924461C22semidirect
49. #11924461C22semidirect
50. #11924461C22semidirect
53. #11924458C22semidirect
55. C22×C8×C37C22semidirect
57. C4⋊C8×C37C22semidirect
59. C22⋊C8×C37C22semidirect
60. #97×C37C22semidirect
117. D296D4semidirect
223. #435D37semidirect
224. C37#3267semidirect
241. C22×C8C2×D37semidirect
260. C4⋊C8C2×D37semidirect
268. C22⋊C8C2×D37semidirect
269. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245582
#145581882
#145581792
#145579272
#145577912
#145577622
#145577492
#145577392
#145576972
#145576862
#145576802
#145576462
C37×#4352
#326737