Finite Group Databasebeta

← #18006135

Subgroups — #18006135

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×#11924560C211yesmaximal, characteristic, complemented
2C2×#11924557C211yesmaximal, characteristic, complemented
3#14558203C211yesmaximal, characteristic, complemented
4#14558176C211yesmaximal, characteristic, complemented
5#14557776C211yesmaximal, characteristic, complemented
6#14557766C211yesmaximal, characteristic, complemented
7#14557752C211yesmaximal, characteristic, complemented
8#14557725C211yesmaximal, characteristic, complemented
9#14557692C211yesmaximal, characteristic, complemented
10#14557677C211yesmaximal, characteristic, complemented
11#14557675C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13#14557635C211yesmaximal, characteristic, complemented
14#14557606C211yesmaximal, characteristic, complemented
15C37×#496C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×#10596964C2211yescharacteristic, complemented
19C2×D4×D37C2211yescharacteristic
20#11924560—24no—
21#11924557—24no—
22C2×#10596942C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596929C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic, complemented
29#11924532—21no—
30#11924518—21no—
31#11924512C2211yescharacteristic
32#11924509—21no—
33#11924508—21no—
34#11924508—21no—
35#11924507C2211yescharacteristic
36#11924507C2211yescharacteristic
37#11924507C2211yescharacteristic, complemented
38#11924506—21no—
39C4×Dic74C2211yescharacteristic, complemented
40C4×D148C2211yescharacteristic
41C4×D148C2211yescharacteristic
42D4×Dic37—21no—
43C22⋊C4×D37—21no—
44#11924470C2211yescharacteristic, complemented
45C4⋊#64436C2211yescharacteristic, complemented
46#11924461C2211yescharacteristic, complemented
47#11924460C2211yescharacteristic, complemented
48#11924458C2211yescharacteristic
49#11924457C2211yescharacteristic
50#11924457C2211yescharacteristic, complemented
51#11924457C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic
53#11924448C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×SD16×C37C2211yescharacteristic, complemented
56C2×D8×C37C2211yescharacteristic
57C2×D8×C37C2211yescharacteristic
58#127×C37C2211yescharacteristic, complemented
59#124×C37C2211yescharacteristic
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37—21no—
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C2×D4×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—
74C22×Dic37—21no—
75C22×Dic37—21no—
76#10596966—22no—
77#10596966—41no—
78#10596964—22no—
79#10596964—22no—
80#10596964—41no—
81#10596964—41no—
82D4×D37—22no—
83D4×D37—41no—
84C2×D148—21no—
85C2×D148D411yescharacteristic
86C2×D148C2311yescharacteristic
87C2×C4×D37—21no—
88C2×C4×D37—21no—
89C2×C4×D37C2311yescharacteristic
90C2×C4×D37C2311yescharacteristic
91C2×Dic74C2311yescharacteristic
92SD16×C37—22no—
93SD16×C37—41no—
94D8×C37—22no—
95D8×C37—41no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C42×C37C2311yescharacteristic
101C22⋊Dic37—21no—
102C22⋊Dic37—21no—
103C22⋊Dic37—21no—
104#10596942—22no—
105#10596940—22no—
106#10596939—22no—
107#10596939—22no—
108#10596938—21no—
109#10596938—21no—
110#10596938D411yescharacteristic
111#10596938D411yescharacteristic
112C4⋊Dic37D411yescharacteristic
113C4⋊Dic37C2311yescharacteristic
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936—21no—
117C4×Dic37—21no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120#10596930D414yescomplemented
121#10596929—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—21no—
126C22×D37—21no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—81no—
130C22×D37C2×D411yescharacteristic
131C22×D37C2×D411yescharacteristic
132Q8×C37—21no—
133Q8×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—21no—
138D4×C37—21no—
139D4×C37—21no—
140D4×C37—42no—
141D4×C37—81no—
142C2×C4×C37—21no—
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2411yescharacteristic
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—81no—
150C22⋊D37—81no—
151C22⋊D37—81no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156C2×Dic37—42no—
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159D148—21no—
160D148—41no—
161D148—42no—
162D148C2×D412yes—
163C4×D37—21no—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—21no—
167C4×D37—42no—
168C4×D37—81no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37C2×D412yes—
173#64436—21no—
174#64436—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37C22×D411yescharacteristic
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—22no—
188C2×D37—21no—
189C2×D37—21no—
190C2×D37—21no—
191C2×D37—21no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C4×C37—21no—
196C4×C37—21no—
197C4×C37—41no—
198C4×C37C22×D411yescharacteristic
199C4×C37H(5,𝔽2)11yescharacteristic
200Dic37—22no—
201Dic37—21no—
202Dic37—21no—
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—81no—
207C2×C37—81no—
208C2×C37—81no—
209C2×C37D4211yescharacteristic
210C2×C37#57511yescharacteristic
211C2×C37#57611yescharacteristic
212D37—41no—
213D37—41no—
214D37—42no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550—371no—
218#546—371no—
219#496D3711yescharacteristic, complemented
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×#41—371no—
233C2×#41—371no—
234C22×D4—371no—
235AGL(1,ℤ/8)—744no—
236#135—744no—
237C2×Q16—371no—
238C2×SD16—371no—
239C2×SD16—371no—
240C2×SD16C2×D3711yescharacteristic, complemented
241C2×SD16C2×D3711yescharacteristic, complemented
242C2×D8—371no—
243C2×D8—371no—
244C2×D8C2×D3711yescharacteristic
245C2×D8C2×D3711yescharacteristic
246C2×M16—371no—
247C22×C8—371no—
248#127—741no—
249#127C2×D3711yescharacteristic, complemented
250#124C2×D3711yescharacteristic
251#123—741no—
252C22⋊Q8—371no—
253#121—371no—
254#121—371no—
255#121—371no—
256#121—741no—
257#121—741no—
258#121—741no—
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#102—371no—
272#102—371no—
273C22⋊C8—371no—
274C22⋊C8—371no—
275#97C2×D3711yescharacteristic, complemented
276C24—741no—
277#41—742no—
278#41—742no—
279#41—742no—
280#41—1481no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—742no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—1481no—
298C2×D4C22×D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—371no—
302C22×C4—371no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4—741no—
307Q16—742no—
308SD16—22no—
309SD16—41no—
310SD16—374no—
311SD16—742no—
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—371no—
325C4⋊C4—741no—
326C4⋊C4—741no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—371no—
330C22⋊C4—371no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C42—741no—
337C42C22×D3711yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—371no—
342C23—371no—
343C23—2961no—
344C23—741no—
345C23—1482no—
346C23—1482no—
347Q8—21no—
348Q8—21no—
349Q8—372no—
350Q8—741no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—372no—
360D4—2961no—
361D4—2961no—
362D4—2961no—
363D4—741no—
364D4—1481no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4—1482no—
369C2×C4—21no—
370C2×C4—371no—
371C2×C4—371no—
372C2×C4—2961no—
373C2×C4—741no—
374C2×C4—741no—
375C2×C4—741no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—1482no—
381C2×C4—1482no—
382C2×C4—1482no—
383C2×C4D4×D3711yescharacteristic
384C2×C4D4×D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—741no—
388C8—741no—
389C8D4×D3712yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2964no—
400C22—741no—
401C22—741no—
402C22—741no—
403C22—741no—
404C22—741no—
405C22—741no—
406C22—742no—
407C22—1481no—
408C22—1481no—
409C22C2×D4×D3711yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—741no—
414C4—741no—
415C4—742no—
416C4—1481no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458111yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—1481no—
424C2—1482no—
425C2—1481no—
426C2#1455816811yescharacteristic
427C2#1455832911yescharacteristic
428C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#496C2
socleC22×C37C22×D4
hypercenter#496D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. C2×#11924557C2semidirect
3. #14558203C2semidirect
4. #14558176C2semidirect
5. #14557776C2semidirect
6. #14557766C2semidirect
7. #14557752C2semidirect
8. #14557725C2semidirect
9. #14557692C2semidirect
10. #14557677C2semidirect
11. #14557675C2semidirect
12. #14557665C2semidirect
13. #14557635C2semidirect
14. #14557606C2semidirect
15. C37×#496C2semidirect
18. C2×#10596964C22semidirect
22. C2×#10596942C22semidirect
28. C2×C8×D37C22semidirect
37. #11924507C22semidirect
39. C4×Dic74C22semidirect
44. #11924470C22semidirect
45. C4⋊#64436C22semidirect
46. #11924461C22semidirect
47. #11924460C22semidirect
50. #11924457C22semidirect
51. #11924457C22semidirect
53. #11924448C22semidirect
54. C2×SD16×C37C22semidirect
55. C2×SD16×C37C22semidirect
58. #127×C37C22semidirect
60. #97×C37C22semidirect
120. #10596930D4semidirect
219. #496D37semidirect
230. C37#3268semidirect
240. C2×SD16C2×D37semidirect
241. C2×SD16C2×D37semidirect
249. #127C2×D37semidirect
275. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
C2×#119245572
#145582032
#145581762
#145577762
#145577662
#145577522
#145577252
#145576922
#145576772
#145576752
#145576652
#145576352
#145576062
C37×#4962
#326837