Finite Group Databasebeta

← #18004214

Subgroups — #18004214

Order 4736.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924560C211yesmaximal, characteristic, complemented
2C2×M16×D37C211yesmaximal, characteristic, complemented
3#14558043C211yesmaximal, characteristic, complemented
4#121×D37C211yesmaximal, characteristic, complemented
5#14557784C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557777C211yesmaximal, characteristic, complemented
8#14557768C211yesmaximal, characteristic, complemented
9#14557766C211yesmaximal, characteristic, complemented
10#14557763C211yesmaximal, characteristic, complemented
11#14557761C211yesmaximal, characteristic, complemented
12#14557572C211yesmaximal, characteristic, complemented
13#14557536C211yesmaximal, characteristic, complemented
14#14557531C211yesmaximal, characteristic, complemented
15C37×#469C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×D4×D37—21no—
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20#11924560—24no—
21C2×#10596930C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic, complemented
23C2×#10596939C2211yescharacteristic, complemented
24C2×#10596934C2211yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×#10596929C2211yescharacteristic
27M16×D37—24no—
28C2×C8×D37C2211yescharacteristic, complemented
29C2×C8×D37C2211yescharacteristic, complemented
30#11924518—21no—
31#11924516C2211yescharacteristic, complemented
32#11924515C2211yescharacteristic, complemented
33#11924511C2211yescharacteristic
34#11924510C2211yescharacteristic
35#11924509—21no—
36#11924508—21no—
37#11924507C2211yescharacteristic
38#11924507C2211yescharacteristic, complemented
39#11924504—21no—
40D4×Dic37—21no—
41#11924496—21no—
42#11924494C2211yescharacteristic
43C4⋊C4×D37C2211yescharacteristic
44C22⋊C4×D37—21no—
45#11924470C2211yescharacteristic, complemented
46#11924469C2211yescharacteristic, complemented
47#11924467C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic, complemented
51#11924457C2211yescharacteristic, complemented
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic, complemented
54C2×D8×C37C2211yescharacteristic, complemented
55C2×M16×C37C2211yescharacteristic, complemented
56#121×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic, complemented
58#106×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37D411yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37—21no—
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C22×Dic37—21no—
74C22×Dic37D411yescharacteristic
75#10596964—22no—
76#10596964—22no—
77D4×D37—22no—
78D4×D37—22no—
79D4×D37—44no—
80C2×D148—21no—
81C2×D148C2311yescharacteristic
82C2×C4×D37—22no—
83C2×C4×D37—22no—
84C2×C4×D37—21no—
85C2×C4×D37D411yescharacteristic
86C2×C4×D37D411yescharacteristic
87C2×C4×D37C2311yescharacteristic
88C2×C4×D37C2311yescharacteristic
89C2×Dic74C2311yescharacteristic
90D8×C37—22no—
91M16×C37—22no—
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101#10596940—22no—
102#10596939—22no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107C4⋊Dic37—21no—
108C4⋊Dic37C2311yescharacteristic
109C4⋊Dic37C2311yescharacteristic
110#10596936—21no—
111#10596936—21no—
112C4×Dic37—21no—
113#10596934—22no—
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116#10596930—22no—
117#10596929—22no—
118#10596929D414yescomplemented
119C8×D37—22no—
120C8×D37—22no—
121C23×C37—21no—
122C23×C37—21no—
123C23×C37C2×D411yescharacteristic
124C22×D37—22no—
125C22×D37—22no—
126C22×D37—21no—
127C22×D37—41no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37C2×D411yescharacteristic
132C22×D37C2×D411yescharacteristic
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—42no—
138D4×C37—42no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2411yescharacteristic
145C22⋊D37—42no—
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—42no—
150C2×Dic37—22no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—42no—
155C2×Dic37C2×D411yescharacteristic
156C2×Dic37C2×D411yescharacteristic
157D148—21no—
158D148—21no—
159D148—42no—
160C4×D37—22no—
161C4×D37—21no—
162C4×D37—21no—
163C4×D37—22no—
164C4×D37—42no—
165C4×D37C2×D412yes—
166C4×D37#4112yes—
167Dic74—21no—
168Dic74—21no—
169C8×C37—21no—
170C8×C37C2×D412yescomplemented
171#64436—21no—
172#64436C2×D412yescomplemented
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37C22×D411yescharacteristic
183C2×D37—21no—
184C2×D37—21no—
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—44no—
188C2×D37—41no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—84no—
192C2×D37#12112yes—
193C2×D37AGL(1,ℤ/8)12yescomplemented
194C4×C37—21no—
195C4×C37—41no—
196C4×C37—41no—
197C4×C37C22×D411yescharacteristic
198C4×C37C2×#4111yescharacteristic
199Dic37—21no—
200Dic37—41no—
201Dic37—41no—
202Dic37—41no—
203Dic37#12112yes—
204#3055—371nomaximal, Sylow
205C2×C37—41no—
206C2×C37—81no—
207C2×C37—81no—
208C2×C37C2×#12111yescharacteristic
209C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
210C2×C37#57511yescharacteristic
211D37—22no—
212D37—22no—
213D37—81no—
214C2×AGL(1,ℤ/8)—371no—
215C22×M16—371no—
216#525—371no—
217C2×#121—371no—
218#469—371no—
219#469D3711yescharacteristic, complemented
220#468—371no—
221#468—371no—
222#466—371no—
223#466—371no—
224#465—371no—
225#465—371no—
226#428—371no—
227#418—371no—
228#417—371no—
229C37#305511yescharacteristic, complemented, Sylow
230C2×#41—371no—
231C22×D4—371no—
232C22×D4—741no—
233C23×C4—371no—
234AGL(1,ℤ/8)—744no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×D8—371no—
238C2×D8C2×D3711yescharacteristic, complemented
239C2×M16—371no—
240C2×M16—371no—
241C2×M16—371no—
242C2×M16—744no—
243C2×M16C2×D3711yescharacteristic, complemented
244C22×C8—371no—
245C22×C8—371no—
246#123—741no—
247C22⋊Q8—371no—
248C22⋊Q8—371no—
249#121—371no—
250#121—371no—
251#121—371no—
252#121—371no—
253#121—741no—
254#121—741no—
255#121C2×D3711yescharacteristic
256#121C2×D3711yescharacteristic, complemented
257#120—741no—
258C4×D4—741no—
259C4×D4—741no—
260#117—371no—
261C2×C4⋊C4—371no—
262C2×C22⋊C4—741no—
263#107—371no—
264#107—371no—
265#106—371no—
266#106C2×D3711yescharacteristic, complemented
267#103—371no—
268#103—371no—
269#102—371no—
270#102—371no—
271#102—371no—
272#102—371no—
273#102C2×D3711yescharacteristic, complemented
274#102C2×D3711yescharacteristic, complemented
275C24—371no—
276C24—741no—
277#41—742no—
278#41—742no—
279C2×Q8—371no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—371no—
283C2×D4—741no—
284C2×D4—742no—
285C2×D4—742no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—1484no—
292C2×D4C22×D3711yescharacteristic
293C2×D4C22×D3711yescharacteristic
294C22×C4—371no—
295C22×C4—371no—
296C22×C4—371no—
297C22×C4—371no—
298C22×C4—371no—
299C22×C4—742no—
300C22×C4—742no—
301C22×C4—741no—
302C22×C4—741no—
303C22×C4C22×D3711yescharacteristic
304SD16—742no—
305SD16—742no—
306D8—22no—
307D8—742no—
308M16—22no—
309M16—374no—
310M16—742no—
311M16—742no—
312C2×C8—371no—
313C2×C8—371no—
314C2×C8—742no—
315C2×C8—742no—
316C2×C8C22×D3711yescharacteristic
317C2×C8C22×D3711yescharacteristic
318C4⋊C4—371no—
319C4⋊C4—371no—
320C4⋊C4—741no—
321C4⋊C4—741no—
322C4⋊C4—741no—
323C4⋊C4C22×D3711yescharacteristic
324C4⋊C4C22×D3711yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C42—741no—
335C23—21no—
336C23—21no—
337C23—371no—
338C23—371no—
339C23—742no—
340C23—742no—
341C23—741no—
342C23—1481no—
343C23—1482no—
344C23—1482no—
345C23—1482no—
346C23D4×D3711yescharacteristic
347Q8—741no—
348Q8—741no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—42no—
355D4—741no—
356D4—741no—
357D4—1482no—
358D4—1482no—
359D4—1482no—
360D4—1482no—
361D4—1482no—
362D4—1482no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—371no—
368C2×C4—372no—
369C2×C4—372no—
370C2×C4—371no—
371C2×C4—742no—
372C2×C4—742no—
373C2×C4—742no—
374C2×C4—741no—
375C2×C4—741no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—1482no—
380C2×C4—1482no—
381C2×C4D4×D3711yescharacteristic
382C2×C4C23×D3711yescharacteristic
383C8—21no—
384C8—372no—
385C8—741no—
386C8D4×D3712yescomplemented
387C22—21no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—372no—
397C22—372no—
398C22—2964no—
399C22—741no—
400C22—741no—
401C22—741no—
402C22—741no—
403C22—1484no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22C2×D4×D3711yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—372no—
412C4—741no—
413C4—1481no—
414C4—1481no—
415C4—1481no—
416C4C2×D4×D3711yescharacteristic
417C4#41×D3711yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—2961no—
422C2—742no—
423C2—742no—
424C2#121×D3711yescharacteristic
425C2AGL(1,ℤ/8)×D3711yescharacteristic
426C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3055
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. C2×M16×D37C2semidirect
3. #14558043C2semidirect
4. #121×D37C2semidirect
5. #14557784C2semidirect
6. #14557779C2semidirect
7. #14557777C2semidirect
8. #14557768C2semidirect
9. #14557766C2semidirect
10. #14557763C2semidirect
11. #14557761C2semidirect
12. #14557572C2semidirect
13. #14557536C2semidirect
14. #14557531C2semidirect
15. C37×#469C2semidirect
21. C2×#10596930C22semidirect
22. C2×#10596940C22semidirect
23. C2×#10596939C22semidirect
24. C2×#10596934C22semidirect
28. C2×C8×D37C22semidirect
29. C2×C8×D37C22semidirect
31. #11924516C22semidirect
32. #11924515C22semidirect
38. #11924507C22semidirect
45. #11924470C22semidirect
46. #11924469C22semidirect
47. #11924467C22semidirect
48. #11924461C22semidirect
49. #11924459C22semidirect
50. #11924458C22semidirect
51. #11924457C22semidirect
52. #11924457C22semidirect
53. #11924456C22semidirect
54. C2×D8×C37C22semidirect
55. C2×M16×C37C22semidirect
57. #121×C37C22semidirect
58. #106×C37C22semidirect
59. #102×C37C22semidirect
60. #102×C37C22semidirect
118. #10596929D4semidirect
170. C8×C37C2×D4semidirect
172. #64436C2×D4semidirect
193. C2×D37AGL(1,ℤ/8)semidirect
219. #469D37semidirect
229. C37#3055semidirect
238. C2×D8C2×D37semidirect
243. C2×M16C2×D37semidirect
256. #121C2×D37semidirect
266. #106C2×D37semidirect
273. #102C2×D37semidirect
274. #102C2×D37semidirect
386. C8D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
C2×M16×D372
#145580432
#121×D372
#145577842
#145577792
#145577772
#145577682
#145577662
#145577632
#145577612
#145575722
#145575362
#145575312
C37×#4692
#305537