Finite Group Databasebeta

← #18006134

Subgroups — #18006134

Order 4736.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924555C211yesmaximal, characteristic, complemented
3#14558201C211yesmaximal, characteristic, complemented
4#14558177C211yesmaximal, characteristic, complemented
5#14557921C211yesmaximal, characteristic, complemented
6#14557777C211yesmaximal, characteristic, complemented
7#14557768C211yesmaximal, characteristic, complemented
8#14557754C211yesmaximal, characteristic, complemented
9#14557726C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557679C211yesmaximal, characteristic, complemented
12#14557675C211yesmaximal, characteristic, complemented
13#14557630C211yesmaximal, characteristic, complemented
14#14557607C211yesmaximal, characteristic, complemented
15C37×#447C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×#10596964C2211yescharacteristic, complemented
19#11924562—24no—
20#11924555—24no—
21C2×Dic148C2211yescharacteristic, complemented
22C2×#10596930C2211yescharacteristic, complemented
23C2×#10596940C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596940C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596934C2211yescharacteristic
29C2×C8×D37C2211yescharacteristic, complemented
30#11924532—21no—
31#11924532C2211yescharacteristic, complemented
32#11924523C2211yescharacteristic
33#11924517—21no—
34#11924515C2211yescharacteristic
35#11924511C2211yescharacteristic, complemented
36#11924509—21no—
37#11924508—21no—
38#11924508—21no—
39#11924507C2211yescharacteristic
40#11924505—21no—
41#11924501C2211yescharacteristic, complemented
42D4×Dic37C2211yescharacteristic
43C4×C22⋊D37C2211yescharacteristic
44#11924496—21no—
45C2×C22⋊Dic37—21no—
46#11924469C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic, complemented
51#11924457C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C22×D4×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56C2×D8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic
60C22⋊C8×C37C2211yescharacteristic
61C24×C37—21no—
62C2×D4×C37—22no—
63C2×D4×C37—21no—
64C2×D4×C37—21no—
65C2×D4×C37—41no—
66C2×D4×C37C2311yescharacteristic
67C2×D4×C37C2311yescharacteristic
68C2×D4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37D411yescharacteristic
77C22×Dic37—21no—
78C22×Dic37—21no—
79C22×Dic37—21no—
80#10596964—22no—
81#10596964—22no—
82#10596964—41no—
83#10596964—41no—
84#10596962—22no—
85#10596962—41no—
86C2×D148—21no—
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91C2×Dic74C2311yescharacteristic
92D8×C37—22no—
93D8×C37—41no—
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C4⋊C4×C37C2311yescharacteristic
97C22⋊C4×C37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102C22⋊Dic37—21no—
103C22⋊Dic37D411yescharacteristic
104#10596940—22no—
105#10596940—22no—
106#10596940D414yescomplemented
107#10596939—22no—
108#10596939—22no—
109#10596938—21no—
110#10596938D411yescharacteristic
111C4⋊Dic37C2311yescharacteristic
112#10596936—21no—
113#10596936—21no—
114#10596936D411yescharacteristic
115C4×Dic37—21no—
116C4×Dic37C2311yescharacteristic
117#10596934—22no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120Dic148—22no—
121#10596930—41no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—81no—
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131C22×D37C2×D411yescharacteristic
132D4×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—42no—
138D4×C37—81no—
139D4×C37C2×D412yes—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2411yescharacteristic
145C22⋊D37—41no—
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—42no—
150C22⋊D37—81no—
151C22⋊D37—81no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156C2×Dic37—42no—
157C2×Dic37—81no—
158C2×Dic37C2×D411yescharacteristic
159C2×Dic37C2×D411yescharacteristic
160C2×Dic37C2×D411yescharacteristic
161D148—21no—
162D148—21no—
163D148—81no—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—42no—
167Dic74—21no—
168Dic74—21no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—22no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—21no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—84no—
188C22×C37C22×D411yescharacteristic
189C2×D37—21no—
190C2×D37—21no—
191C2×D37—21no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C4×C37—21no—
196C4×C37—41no—
197C4×C37C22×D411yescharacteristic
198C4×C37H(5,𝔽2)11yescharacteristic
199Dic37—22no—
200Dic37—21no—
201Dic37—21no—
202Dic37—21no—
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—41no—
207C2×C37—42no—
208C2×C37—81no—
209C2×C37—81no—
210C2×C37D4211yescharacteristic
211C2×C37#57511yescharacteristic
212C2×C37#57611yescharacteristic
213D37—41no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550—371no—
218#546—371no—
219#496—371no—
220#468—371no—
221#466—371no—
222#464—371no—
223#459—371no—
224#452—371no—
225#449—371no—
226#449—371no—
227#447D3711yescharacteristic, complemented
228#440—371no—
229#435—371no—
230C37#326811yescharacteristic, complemented, Sylow
231C2×#41—371no—
232C2×#41—371no—
233C2×#41—371no—
234C22×D4C2×D3711yescharacteristic
235AGL(1,ℤ/8)—744no—
236#135—744no—
237C2×Q16—371no—
238C2×SD16—371no—
239C2×SD16—371no—
240C2×SD16—371no—
241C2×SD16—371no—
242C2×D8—371no—
243C2×D8—371no—
244C2×D8C2×D3711yescharacteristic
245C2×D8C2×D3711yescharacteristic
246C2×M16—371no—
247C22×C8—371no—
248#127—371no—
249#127—741no—
250#124—371no—
251#123—741no—
252C22⋊Q8—371no—
253#121—371no—
254#121—371no—
255#121—741no—
256#121—741no—
257#121—741no—
258#121C2×D3711yescharacteristic
259#120—741no—
260C4×Q8—371no—
261C4×D4—371no—
262C4×D4—371no—
263C4×D4—741no—
264C2×C22⋊C4—741no—
265#107—371no—
266C4⋊C8—371no—
267#103—371no—
268#103—371no—
269#102—371no—
270#102—371no—
271#102C2×D3711yescharacteristic
272#102C2×D3711yescharacteristic
273C22⋊C8—371no—
274C22⋊C8C2×D3711yescharacteristic
275#97—371no—
276C24—21no—
277#41—742no—
278#41—742no—
279#41—742no—
280#41—1481no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8—371no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—371no—
290C2×D4—371no—
291C2×D4—741no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4C22×D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—371no—
302C22×C4—741no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4C22×D3711yescharacteristic
307Q16—742no—
308SD16—374no—
309SD16—742no—
310SD16—742no—
311SD16—1481no—
312D8—22no—
313D8—41no—
314D8—742no—
315D8—742no—
316M16—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—742no—
320C2×C8C22×D3711yescharacteristic
321C2×C8C22×D3711yescharacteristic
322C4⋊C4—371no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4—741no—
326C4⋊C4C22×D3711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—371no—
329C22⋊C4—371no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C42—371no—
337C42—741no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—371no—
345C23—741no—
346C23D4×D3711yescharacteristic
347Q8—372no—
348Q8—741no—
349Q8—741no—
350Q8—741no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—2961no—
359D4—2961no—
360D4—2961no—
361D4—741no—
362D4—741no—
363D4—1481no—
364D4—1482no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4D4×D3712yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—371no—
373C2×C4—371no—
374C2×C4—371no—
375C2×C4—2961no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—1482no—
382C2×C4—1482no—
383C2×C4—1482no—
384C2×C4D4×D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—21no—
388C8—372no—
389C8—741no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—741no—
404C22—741no—
405C22—741no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C2×D4×D3711yescharacteristic
410C4—21no—
411C4—41no—
412C4—741no—
413C4—741no—
414C4—741no—
415C4—742no—
416C4—1481no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458111yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—2961no—
425C2—1481no—
426C2#1455816511yescharacteristic
427C2#1455832911yescharacteristic
428C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#447C2
socleC22×C37C22×D4
hypercenter#447D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924555C2semidirect
3. #14558201C2semidirect
4. #14558177C2semidirect
5. #14557921C2semidirect
6. #14557777C2semidirect
7. #14557768C2semidirect
8. #14557754C2semidirect
9. #14557726C2semidirect
10. #14557697C2semidirect
11. #14557679C2semidirect
12. #14557675C2semidirect
13. #14557630C2semidirect
14. #14557607C2semidirect
15. C37×#447C2semidirect
18. C2×#10596964C22semidirect
21. C2×Dic148C22semidirect
22. C2×#10596930C22semidirect
25. C2×#10596940C22semidirect
29. C2×C8×D37C22semidirect
31. #11924532C22semidirect
35. #11924511C22semidirect
41. #11924501C22semidirect
46. #11924469C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924459C22semidirect
50. #11924458C22semidirect
51. #11924457C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
106. #10596940D4semidirect
227. #447D37semidirect
230. C37#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245552
#145582012
#145581772
#145579212
#145577772
#145577682
#145577542
#145577262
#145576972
#145576792
#145576752
#145576302
#145576072
C37×#4472
#326837