Finite Group Databasebeta

← #18006366

Subgroups — #18006366

Order 4736.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558349C211yesmaximal, characteristic, complemented
2#14558348C211yesmaximal, characteristic, complemented
3#14558342C211yesmaximal, characteristic, complemented
4#14558341C211yesmaximal, characteristic, complemented
5#14557925C211yesmaximal, characteristic, complemented
6#14557807C211yesmaximal, characteristic, complemented
7#14557806C211yesmaximal, characteristic, complemented
8#14557799C211yesmaximal, characteristic, complemented
9#14557798C211yesmaximal, characteristic, complemented
10#14557715C211yesmaximal, characteristic, complemented
11#14557712C211yesmaximal, characteristic, complemented
12#14557707C211yesmaximal, characteristic, complemented
13#14557652C211yesmaximal, characteristic, complemented
14#14557652C211yesmaximal, characteristic, complemented
15C37×#456C211yesmaximal, characteristic, complemented
16#11924584C2211yescharacteristic
17#11924583C2211yescharacteristic, complemented
18#11924582C2211yescharacteristic
19#11924569C2211yescharacteristic
20#11924568—21no—
21#11924568—21no—
22#11924567—21no—
23#11924567—21no—
24#11924567C2211yescharacteristic
25#11924567C2211yescharacteristic, complemented
26#11924566—21no—
27#11924566C2211yescharacteristic
28#11924565—21no—
29#11924564C2211yescharacteristic
30#11924563—21no—
31#11924561—21no—
32#11924561C2211yescharacteristic
33#11924559—21no—
34#11924557—21no—
35#11924556—21no—
36#11924556—21no—
37#11924556C2211yescharacteristic
38#11924556C2211yescharacteristic
39C2×#10596942—21no—
40C2×#10596942C2211yescharacteristic, complemented
41C2×#10596942C2211yescharacteristic, complemented
42Q16×D37—21no—
43C2×#10596941—21no—
44C2×#10596941C2211yescharacteristic
45C2×#10596941C2211yescharacteristic
46SD16×D37—21no—
47#11924544C2211yescharacteristic
48#11924544C2211yescharacteristic, complemented
49#11924543C2211yescharacteristic
50#11924543C2211yescharacteristic, complemented
51#11924524C2211yescharacteristic
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic
55#11924464C2211yescharacteristic, complemented
56#11924455C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic
59#11924447C2211yescharacteristic, complemented
602−1+4×C37C2211yescharacteristic
61#137×C37C2211yescharacteristic
62#137×C37C2211yescharacteristic, complemented
63C4⋊Q8×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic
65#104×C37C2211yescharacteristic, complemented
66#101×C37C2211yescharacteristic, complemented
67#41×C37—21no—
68#41×C37—21no—
69#41×C37—41no—
70#41×C37C2311yescharacteristic
71#41×C37C2311yescharacteristic
72C2×Q8×C37—21no—
73C2×Q8×C37—21no—
74C2×Q8×C37C2311yescharacteristic
75C2×Q8×C37C2311yescharacteristic
76#10596966—21no—
77#10596966—21no—
78#10596966—21no—
79Q8×D37—21no—
80Q8×D37—21no—
81Q8×D37—21no—
82#10596964—21no—
83#10596964—41no—
84D4×D37—21no—
85D4×D37—41no—
86#10596962—21no—
87#10596962—21no—
88#10596962—41no—
89#10596962C2311yescharacteristic
90#10596962C2311yescharacteristic
91C2×D148—21no—
92C2×D148C2311yescharacteristic
93C2×Dic74—21no—
94C2×Dic74C2311yescharacteristic
95Q16×C37—21no—
96Q16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99M16×C37C2311yescharacteristic
100M16×C37C2311yescharacteristic
101C4⋊C4×C37—41no—
102C42×C37C2311yescharacteristic
103#10596942—21no—
104#10596942—21no—
105#10596942—21no—
106#10596942—21no—
107#10596942—21no—
108#10596942—21no—
109#10596942—21no—
110#10596942D411yescharacteristic
111#10596942D411yescharacteristic
112#10596941—21no—
113#10596941—21no—
114#10596941—21no—
115#10596941—21no—
116#10596941—21no—
117#10596941—21no—
118#10596941—21no—
119#10596941D411yescharacteristic
120#10596941D411yescharacteristic
121#10596940—21no—
122#10596940D411yescharacteristic
123#10596940D411yescharacteristic
124#10596939—21no—
125#10596939D411yescharacteristic
126#10596939D411yescharacteristic
127#10596938—41no—
128#10596934—21no—
129#10596934—21no—
130#10596934C2311yescharacteristic
131#10596934C2311yescharacteristic
132C2×#64436—21no—
133C2×#64436—21no—
134C2×#64436C2311yescharacteristic
135C2×#64436C2311yescharacteristic
136Dic148—21no—
137D296—21no—
138#10596930—21no—
139#10596930—21no—
140#10596929—21no—
141#10596929—21no—
142C8×D37—21no—
143C8×D37—21no—
144C22×D37—21no—
145C22×D37—41no—
146Q8×C37—21no—
147Q8×C37—21no—
148Q8×C37—21no—
149Q8×C37—21no—
150Q8×C37—41no—
151Q8×C37C2×D411yescharacteristic
152Q8×C37C2×D411yescharacteristic
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—41no—
156D4×C37C2×D411yescharacteristic
157D4×C37C2×D411yescharacteristic
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—21no—
163C2×C4×C37—41no—
164C2×C4×C37—41no—
165C2×C4×C37C2411yescharacteristic
166C22⋊D37—21no—
167C22⋊D37—21no—
168C22⋊D37—41no—
169C22⋊D37—41no—
170C2×Dic37—21no—
171C2×Dic37—41no—
172D148—21no—
173D148—21no—
174D148—41no—
175D148—41no—
176D148C2×D411yescharacteristic
177D148C2×D411yescharacteristic
178C4×D37—21no—
179C4×D37—21no—
180C4×D37—41no—
181C4×D37—41no—
182C4×D37—41no—
183C4×D37—41no—
184Dic74—21no—
185Dic74—21no—
186Dic74—41no—
187Dic74—41no—
188Dic74C2×D411yescharacteristic
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37—21no—
192#64436—21no—
193#64436—21no—
194#64436C2×D411yescharacteristic
195#64436C2×D411yescharacteristic
196#64436C2×D411yescharacteristic
197#64436C2×D411yescharacteristic
198C22×C37—21no—
199C22×C37—21no—
200C22×C37H(5,𝔽2)11yescharacteristic
201C2×D37—21no—
202C2×D37—21no—
203C2×D37—41no—
204C2×D37—81no—
205C2×D37—161no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—41no—
209C4×C37—41no—
210C4×C37—41no—
211C4×C37C22×D411yescharacteristic
212C4×C37C22×D411yescharacteristic
213Dic37—21no—
214Dic37—21no—
215Dic37—41no—
216#3289—371nomaximal, Sylow
217C2×C37—21no—
218C2×C37—41no—
219C2×C37—41no—
220C2×C37D4211yescharacteristic
221D37—41no—
222D37—41no—
223D37—81no—
224#578—371no—
225#578—371no—
226#577—371no—
227#577—371no—
228#497—371no—
229#473—371no—
230#473—371no—
231#471—371no—
232#471—371no—
233#456—371no—
234#456D3711yescharacteristic, complemented
235#455—371no—
236#454—371no—
237#444—371no—
238#444—371no—
239C37#328911yescharacteristic, complemented, Sylow
2402−1+4—371no—
2412−1+4—371no—
2422−1+4C2×D3711yescharacteristic
243H(5,𝔽2)—371no—
244#137—371no—
245#137—371no—
246#137—371no—
247#137—371no—
248#137—741no—
249#137—741no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137C2×D3711yescharacteristic
255#137C2×D3711yescharacteristic, complemented
256AGL(1,ℤ/8)—371no—
257AGL(1,ℤ/8)—371no—
258AGL(1,ℤ/8)—741no—
259AGL(1,ℤ/8)—741no—
260#135—371no—
261#135—371no—
262#135—741no—
263#135—741no—
264#135—741no—
265#135—741no—
266C2×Q16—371no—
267C2×Q16—371no—
268C2×Q16—741no—
269C2×Q16—741no—
270C2×SD16—371no—
271C2×SD16—371no—
272C2×SD16—741no—
273C2×SD16—741no—
274#131—371no—
275#131—371no—
276#131—371no—
277#131—371no—
278C4⋊Q8C2×D3711yescharacteristic, complemented
279#124—371no—
280#108—371no—
281#108—371no—
282#104—371no—
283#104—371no—
284#104C2×D3711yescharacteristic
285#104C2×D3711yescharacteristic, complemented
286#101—371no—
287#101—371no—
288#101C2×D3711yescharacteristic, complemented
289#100—371no—
290#97—371no—
291#41—21no—
292#41—21no—
293#41—41no—
294#41—371no—
295#41—371no—
296#41—741no—
297#41—741no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—741no—
302#41—1481no—
303#41—1481no—
304#41C22×D3711yescharacteristic
305#41C22×D3711yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—371no—
309C2×Q8—741no—
310C2×Q8—741no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8C22×D3711yescharacteristic
314C2×Q8C22×D3711yescharacteristic
315C2×D4—371no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—1481no—
319Q16—21no—
320Q16—21no—
321Q16—371no—
322Q16—371no—
323Q16—741no—
324Q16—741no—
325Q16—741no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16—741no—
330Q16—741no—
331SD16—21no—
332SD16—21no—
333SD16—371no—
334SD16—371no—
335SD16—371no—
336SD16—371no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16—741no—
346SD16—741no—
347D8—371no—
348D8—371no—
349D8—741no—
350D8—741no—
351M16—371no—
352M16—371no—
353M16—741no—
354M16—741no—
355M16—741no—
356M16—741no—
357M16C22×D3711yescharacteristic
358M16C22×D3711yescharacteristic
359C2×C8—371no—
360C2×C8—371no—
361C2×C8—741no—
362C2×C8—741no—
363C2×C8—741no—
364C2×C8—741no—
365C4⋊C4—41no—
366C22⋊C4—1481no—
367C42C22×D3711yescharacteristic
368C23—741no—
369C23—1481no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—371no—
376Q8—371no—
377Q8—741no—
378Q8—741no—
379Q8—1481no—
380Q8—1481no—
381Q8D4×D3711yescharacteristic
382Q8D4×D3711yescharacteristic
383D4—21no—
384D4—21no—
385D4—41no—
386D4—371no—
387D4—371no—
388D4—741no—
389D4—741no—
390D4—741no—
391D4—741no—
392D4—1481no—
393D4—1481no—
394D4—1481no—
395D4—1481no—
396D4D4×D3711yescharacteristic
397D4D4×D3711yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—741no—
406C2×C4—741no—
407C2×C4—741no—
408C2×C4—1481no—
409C2×C4—1481no—
410C2×C4—1481no—
411C2×C4—1481no—
412C2×C4—1481no—
413C2×C4C23×D3711yescharacteristic
414C8—21no—
415C8—21no—
416C8—371no—
417C8—371no—
418C8—371no—
419C8—371no—
420C8—741no—
421C8—741no—
422C22—21no—
423C22—21no—
424C22—2961no—
425C22—741no—
426C22—741no—
427C22—5921no—
428C22—1481no—
429C22#1192458111yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—741no—
436C4—741no—
437C4—1481no—
438C4C2×D4×D3711yescharacteristic
439C4C2×D4×D3711yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—2961no—
444C2—1481no—
445C2—1481no—
446C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#456C2
socleC2×C37D42
hypercenter#456D37
hypocenterC37#3289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14558349C2semidirect
2. #14558348C2semidirect
3. #14558342C2semidirect
4. #14558341C2semidirect
5. #14557925C2semidirect
6. #14557807C2semidirect
7. #14557806C2semidirect
8. #14557799C2semidirect
9. #14557798C2semidirect
10. #14557715C2semidirect
11. #14557712C2semidirect
12. #14557707C2semidirect
13. #14557652C2semidirect
14. #14557652C2semidirect
15. C37×#456C2semidirect
17. #11924583C22semidirect
25. #11924567C22semidirect
40. C2×#10596942C22semidirect
41. C2×#10596942C22semidirect
48. #11924544C22semidirect
50. #11924543C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
55. #11924464C22semidirect
56. #11924455C22semidirect
57. #11924454C22semidirect
59. #11924447C22semidirect
62. #137×C37C22semidirect
63. C4⋊Q8×C37C22semidirect
65. #104×C37C22semidirect
66. #101×C37C22semidirect
234. #456D37semidirect
239. C37#3289semidirect
255. #137C2×D37semidirect
278. C4⋊Q8C2×D37semidirect
285. #104C2×D37semidirect
288. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583492
#145583482
#145583422
#145583412
#145579252
#145578072
#145578062
#145577992
#145577982
#145577152
#145577122
#145577072
#145576522
C37×#4562
#328937