Finite Group Databasebeta

← #18006137

Subgroups — #18006137

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×#11924561C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558179C211yesmaximal, characteristic, complemented
4#14557920C211yesmaximal, characteristic, complemented
5#14557777C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557755C211yesmaximal, characteristic, complemented
8#14557725C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557676C211yesmaximal, characteristic, complemented
12#14557666C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15C37×#550C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×D148C2211yescharacteristic
18#11924561—24no—
19#11924556—24no—
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic, complemented
23C2×#10596941C2211yescharacteristic
24C2×#10596941C2211yescharacteristic
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic
32#11924521—21no—
33#11924515C2211yescharacteristic
34#11924510C2211yescharacteristic
35#11924509—21no—
36#11924504—21no—
37C4×D148C2211yescharacteristic
38C22⋊C4×D37—21no—
39#11924469C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924460C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic, complemented
44#11924457C2211yescharacteristic, complemented
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47C22⋊#64436C2211yescharacteristic
48C22⋊#64436C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50C2×#41×C37C2211yescharacteristic
51C2×#41×C37C2211yescharacteristic, complemented
52#127×C37—21no—
53#127×C37C2211yescharacteristic, complemented
54#121×C37—21no—
55#121×C37—21no—
56#121×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic, complemented
58C4×Q8×C37C2211yescharacteristic, complemented
59C4×D4×C37—21no—
60C4×D4×C37C2211yescharacteristic
61C23×D37—21no—
62#41×C37—22no—
63#41×C37—22no—
64#41×C37—41no—
65#41×C37—41no—
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37—21no—
71C2×D4×C37—21no—
72C2×D4×C37—21no—
73C2×D4×C37D411yescharacteristic
74C2×D4×C37C2311yescharacteristic
75C2×D4×C37C2311yescharacteristic
76C22×C4×C37—21no—
77C22×C4×C37—21no—
78C22×C4×C37C2311yescharacteristic
79C22×C4×C37C2311yescharacteristic
80C2×C22⋊D37—21no—
81C2×C22⋊D37—21no—
82#10596962—22no—
83#10596962—41no—
84C2×D148—22no—
85C2×D148—21no—
86C2×D148—41no—
87C2×D148C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×C4×D37—21no—
90C2×C4×D37—21no—
91C2×Dic74C2311yescharacteristic
92C4⋊C4×C37—21no—
93C4⋊C4×C37D411yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37D411yescharacteristic
98C22⋊C4×C37D411yescharacteristic
99C42×C37—21no—
100C42×C37C2311yescharacteristic
101C22⋊Dic37—21no—
102#10596942—22no—
103#10596941—22no—
104#10596941D414yescomplemented
105#10596940—22no—
106#10596940—41no—
107#10596939—22no—
108#10596939—22no—
109#10596939—22no—
110#10596939—41no—
111#10596938—21no—
112#10596938—21no—
113#10596938—21no—
114#10596938—21no—
115C4⋊Dic37C2311yescharacteristic
116#10596936—21no—
117#10596934—22no—
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37—21no—
124C23×C37—21no—
125C23×C37C2×D411yescharacteristic
126C23×C37C2×D411yescharacteristic
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—81no—
132Q8×C37—21no—
133Q8×C37C2×D412yes—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—21no—
138D4×C37—41no—
139D4×C37—42no—
140D4×C37—42no—
141D4×C37—42no—
142D4×C37—81no—
143D4×C37—81no—
144D4×C37—81no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—42no—
152C2×C4×C37—42no—
153C2×C4×C37C2×D411yescharacteristic
154C2×C4×C37C2×D411yescharacteristic
155C2×C4×C37C2×D411yescharacteristic
156C2×C4×C37C2×D411yescharacteristic
157C2×C4×C37C2411yescharacteristic
158C22⋊D37—42no—
159C22⋊D37—81no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162D148—21no—
163D148—21no—
164D148—21no—
165D148—42no—
166D148C2×D412yes—
167C4×D37—42no—
168C4×D37—81no—
169Dic74—21no—
170Dic74—21no—
171#64436—21no—
172#64436—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37C22×D411yescharacteristic
188C2×D37—22no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C4×C37—21no—
196C4×C37—21no—
197C4×C37—22no—
198C4×C37—21no—
199C4×C37—21no—
200C4×C37—41no—
201C4×C37C22×D411yescharacteristic
202C4×C37H(5,𝔽2)11yescharacteristic
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—41no—
207C2×C37—41no—
208C2×C37—81no—
209C2×C37—81no—
210C2×C37D4211yescharacteristic
211C2×C37#57511yescharacteristic
212C2×C37#57611yescharacteristic
213D37—42no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550D3711yescharacteristic, complemented
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#447—371no—
228#440—371no—
229#435—371no—
230C37#326811yescharacteristic, complemented, Sylow
231C2×#41—371no—
232C2×#41C2×D3711yescharacteristic
233C2×#41C2×D3711yescharacteristic, complemented
234C22×D4—371no—
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×D8—371no—
245C2×D8—371no—
246C2×M16—371no—
247C22×C8—371no—
248#127—21no—
249#127C2×D3711yescharacteristic, complemented
250#124—371no—
251#123—741no—
252C22⋊Q8—371no—
253#121—21no—
254#121—21no—
255#121—371no—
256#121—741no—
257#121C2×D3711yescharacteristic
258#121C2×D3711yescharacteristic, complemented
259#120—741no—
260C4×Q8C2×D3711yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—371no—
263C4×D4C2×D3711yescharacteristic
264C2×C22⋊C4—741no—
265#107—371no—
266C4⋊C8—371no—
267#103—371no—
268#103—371no—
269#102—371no—
270#102—371no—
271#102—371no—
272#102—371no—
273C22⋊C8—371no—
274C22⋊C8—371no—
275#97—371no—
276C24—741no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—742no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—371no—
292C2×D4—371no—
293C2×D4—742no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—1481no—
298C2×D4C22⋊D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4C22×D3711yescharacteristic
306C22×C4C22×D3711yescharacteristic
307Q16—742no—
308SD16—374no—
309SD16—742no—
310SD16—742no—
311SD16—1481no—
312D8—742no—
313D8—742no—
314D8—742no—
315D8—1481no—
316M16—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—371no—
320C2×C8—371no—
321C2×C8—742no—
322C4⋊C4—21no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4C22⋊D3711yescharacteristic
326C4⋊C4C22×D3711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4C22⋊D3711yescharacteristic
335C22⋊C4C22⋊D3711yescharacteristic
336C42—21no—
337C42C22×D3711yescharacteristic
338C23—21no—
339C23—21no—
340C23—2961no—
341C23—741no—
342C23—741no—
343C23—1482no—
344C23—1482no—
345C23C2×C22⋊D3711yescharacteristic
346C23C2×C22⋊D3711yescharacteristic
347Q8—21no—
348Q8—741no—
349Q8—741no—
350Q8D4×D3712yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—372no—
363D4—2961no—
364D4—741no—
365D4—741no—
366D4—741no—
367D4—1482no—
368D4—1482no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—2961no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—1482no—
381C2×C4C2×C22⋊D3711yescharacteristic
382C2×C4C2×C22⋊D3711yescharacteristic
383C2×C4C2×C22⋊D3711yescharacteristic
384C2×C4C2×C22⋊D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—372no—
387C8—741no—
388C8—741no—
389C8—741no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—2964no—
403C22—742no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C22×C22⋊D3711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—1481no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458111yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—2961no—
425C2—1482no—
426C2D4×C22⋊D3711yescharacteristic
427C2#1455833111yescharacteristic
428C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#550C2
socleC22×C37C22×D4
hypercenter#550D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#11924561C2semidirect
2. C2×#11924556C2semidirect
3. #14558179C2semidirect
4. #14557920C2semidirect
5. #14557777C2semidirect
6. #14557767C2semidirect
7. #14557755C2semidirect
8. #14557725C2semidirect
9. #14557695C2semidirect
10. #14557678C2semidirect
11. #14557676C2semidirect
12. #14557666C2semidirect
13. #14557631C2semidirect
14. #14557605C2semidirect
15. C37×#550C2semidirect
20. C2×#10596942C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596940C22semidirect
30. C22×#64436C22semidirect
39. #11924469C22semidirect
40. C4⋊#64436C22semidirect
41. #11924460C22semidirect
42. #11924459C22semidirect
43. #11924457C22semidirect
44. #11924457C22semidirect
48. C22⋊#64436C22semidirect
49. #11924447C22semidirect
51. C2×#41×C37C22semidirect
53. #127×C37C22semidirect
57. #121×C37C22semidirect
58. C4×Q8×C37C22semidirect
104. #10596941D4semidirect
217. #550D37semidirect
230. C37#3268semidirect
233. C2×#41C2×D37semidirect
249. #127C2×D37semidirect
258. #121C2×D37semidirect
260. C4×Q8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245612
C2×#119245562
#145581792
#145579202
#145577772
#145577672
#145577552
#145577252
#145576952
#145576782
#145576762
#145576662
#145576312
#145576052
C37×#5502
#326837