Finite Group Databasebeta

← #18006372

Subgroups — #18006372

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#14558350C211yesmaximal, characteristic, complemented
2#14558347C211yesmaximal, characteristic, complemented
3#14558345C211yesmaximal, characteristic, complemented
4#14558340C211yesmaximal, characteristic, complemented
5#14557927C211yesmaximal, characteristic, complemented
6#14557809C211yesmaximal, characteristic, complemented
7#14557808C211yesmaximal, characteristic, complemented
8#14557797C211yesmaximal, characteristic, complemented
9#14557796C211yesmaximal, characteristic, complemented
10#14557717C211yesmaximal, characteristic, complemented
11#14557717C211yesmaximal, characteristic, complemented
12#14557712C211yesmaximal, characteristic, complemented
13#14557707C211yesmaximal, characteristic, complemented
14#14557656C211yesmaximal, characteristic, complemented
15C37×#444C211yesmaximal, characteristic, complemented
16#11924583C2211yescharacteristic
17#11924583C2211yescharacteristic
18#11924583C2211yescharacteristic, complemented
19#11924582C2211yescharacteristic
20#11924569—21no—
21#11924569—21no—
22#11924569—21no—
23#11924569C2211yescharacteristic
24#11924569C2211yescharacteristic
25#11924569C2211yescharacteristic, complemented
26#11924568—21no—
27#11924566C2211yescharacteristic
28#11924566C2211yescharacteristic
29#11924566C2211yescharacteristic, complemented
30#11924565—21no—
31#11924565—21no—
32#11924564—21no—
33#11924564C2211yescharacteristic
34#11924561C2211yescharacteristic
35#11924560—21no—
36#11924558—21no—
37#11924558—21no—
38#11924558C2211yescharacteristic
39#11924557—21no—
40#11924555—21no—
41C2×Dic148—21no—
42C2×Dic148C2211yescharacteristic, complemented
43C2×Dic148C2211yescharacteristic, complemented
44Q16×D37—21no—
45C2×#10596930—21no—
46C2×#10596930C2211yescharacteristic
47C2×#10596930C2211yescharacteristic
48SD16×D37—21no—
49#11924542C2211yescharacteristic
50#11924542C2211yescharacteristic, complemented
51#11924536C2211yescharacteristic, complemented
52#11924524C2211yescharacteristic
53#11924472C2211yescharacteristic, complemented
54#11924464C2211yescharacteristic
55#11924464C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924454C2211yescharacteristic, complemented
58#11924454C2211yescharacteristic, complemented
59#11924452C2211yescharacteristic
60#135×C37C2211yescharacteristic
61#131×C37C2211yescharacteristic
62#131×C37C2211yescharacteristic, complemented
63#108×C37C2211yescharacteristic, complemented
64#104×C37C2211yescharacteristic
65#104×C37C2211yescharacteristic, complemented
66#97×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68#41×C37C2311yescharacteristic
69#10596966—21no—
70Q8×D37—21no—
71Q8×D37—21no—
72Q8×D37—21no—
73#10596964—21no—
74#10596964—21no—
75#10596964—21no—
76#10596964—41no—
77#10596964—41no—
78#10596964—41no—
79D4×D37—21no—
80D4×D37—41no—
81#10596962—21no—
82#10596962—21no—
83#10596962—21no—
84#10596962—21no—
85#10596962C2311yescharacteristic
86#10596962C2311yescharacteristic
87C2×D148—21no—
88C2×D148C2311yescharacteristic
89C2×Dic74—21no—
90C2×Dic74—21no—
91C2×Dic74—21no—
92C2×Dic74C2311yescharacteristic
93C2×Dic74C2311yescharacteristic
94C2×Dic74C2311yescharacteristic
95Q16×C37D411yescharacteristic
96SD16×C37D411yescharacteristic
97SD16×C37D411yescharacteristic
98D8×C37D411yescharacteristic
99M16×C37—21no—
100M16×C37—21no—
101M16×C37C2311yescharacteristic
102M16×C37C2311yescharacteristic
103C2×C8×C37—21no—
104C2×C8×C37—21no—
105C2×C8×C37C2311yescharacteristic
106C2×C8×C37C2311yescharacteristic
107C42×C37C2311yescharacteristic
108#10596942—21no—
109#10596942—21no—
110#10596942—21no—
111#10596941—21no—
112#10596940—21no—
113#10596940—21no—
114#10596940—21no—
115#10596939—21no—
116#10596938—41no—
117C4⋊Dic37—41no—
118#10596934C2311yescharacteristic
119#10596934C2311yescharacteristic
120Dic148—21no—
121Dic148—21no—
122Dic148—21no—
123Dic148—21no—
124Dic148—21no—
125Dic148—21no—
126Dic148—21no—
127Dic148D411yescharacteristic
128D296—21no—
129D296D411yescharacteristic
130#10596930—21no—
131#10596930—21no—
132#10596930—21no—
133#10596930—21no—
134#10596930—21no—
135#10596930—21no—
136#10596930—21no—
137#10596930—21no—
138#10596930D411yescharacteristic
139#10596930D411yescharacteristic
140#10596929—21no—
141#10596929—21no—
142C8×D37—21no—
143C8×D37—21no—
144C22×D37—21no—
145C22×D37—41no—
146Q8×C37C2×D411yescharacteristic
147Q8×C37C2×D411yescharacteristic
148D4×C37—21no—
149D4×C37—21no—
150D4×C37C2×D411yescharacteristic
151D4×C37C2×D411yescharacteristic
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37C2411yescharacteristic
156C22⋊D37—21no—
157C22⋊D37—21no—
158C22⋊D37—41no—
159C22⋊D37—41no—
160C22⋊D37—41no—
161C22⋊D37—41no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—41no—
166C2×Dic37—41no—
167C2×Dic37—41no—
168D148—21no—
169D148—21no—
170D148—41no—
171D148C2×D411yescharacteristic
172D148C2×D411yescharacteristic
173C4×D37—21no—
174C4×D37—21no—
175C4×D37—41no—
176C4×D37—41no—
177C4×D37—41no—
178C4×D37—41no—
179Dic74—21no—
180Dic74—21no—
181Dic74—21no—
182Dic74—21no—
183Dic74—21no—
184Dic74—21no—
185Dic74—41no—
186Dic74—41no—
187Dic74—41no—
188Dic74C2×D411yescharacteristic
189Dic74C2×D411yescharacteristic
190C8×C37—21no—
191C8×C37—21no—
192C8×C37C2×D411yescharacteristic
193C8×C37C2×D411yescharacteristic
194C8×C37C2×D411yescharacteristic
195C8×C37C2×D411yescharacteristic
196#64436—21no—
197#64436—21no—
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×C37C22×D411yescharacteristic
210C4×C37C22×D411yescharacteristic
211Dic37—21no—
212Dic37—21no—
213Dic37—41no—
214Dic37—41no—
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#456—371no—
235#455—371no—
236#454—371no—
237#444—371no—
238#444D3711yescharacteristic, complemented
239C37#328911yescharacteristic, complemented, Sylow
2402−1+4—371no—
2412−1+4—371no—
2422−1+4—371no—
243H(5,𝔽2)—371no—
244#137—371no—
245#137—371no—
246#137—371no—
247#137—371no—
248#137—371no—
249#137—371no—
250#137—741no—
251#137—741no—
252#137—741no—
253#137—741no—
254#137—741no—
255#137—741no—
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—741no—
262#135—741no—
263#135—741no—
264#135—741no—
265#135C2×D3711yescharacteristic
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#131C2×D3711yescharacteristic
277#131C2×D3711yescharacteristic, complemented
278C4⋊Q8—371no—
279#124—371no—
280#108—371no—
281#108C2×D3711yescharacteristic, complemented
282#104—371no—
283#104—371no—
284#104C2×D3711yescharacteristic
285#104C2×D3711yescharacteristic, complemented
286#101—371no—
287#101—371no—
288#101—371no—
289#100—371no—
290#97C2×D3711yescharacteristic, complemented
291#41—371no—
292#41—371no—
293#41—741no—
294#41—741no—
295#41—741no—
296#41—741no—
297#41—741no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—1481no—
302#41—1481no—
303#41—1481no—
304#41C22×D3711yescharacteristic
305#41C22×D3711yescharacteristic
306C2×Q8—371no—
307C2×Q8—371no—
308C2×Q8—371no—
309C2×Q8—741no—
310C2×Q8—741no—
311C2×Q8—741no—
312C2×Q8—741no—
313C2×Q8—741no—
314C2×Q8—741no—
315C2×D4—371no—
316C2×D4—741no—
317C2×D4—741no—
318C2×D4—1481no—
319Q16—371no—
320Q16—741no—
321Q16—741no—
322Q16—741no—
323Q16—741no—
324Q16—741no—
325Q16—741no—
326Q16—741no—
327Q16—741no—
328Q16—741no—
329Q16—741no—
330Q16D14811yescharacteristic
331SD16—371no—
332SD16—371no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337SD16—741no—
338SD16—741no—
339SD16—741no—
340SD16—741no—
341SD16—741no—
342SD16—741no—
343SD16—741no—
344SD16—741no—
345SD16D14811yescharacteristic
346SD16D14811yescharacteristic
347D8—371no—
348D8—741no—
349D8—741no—
350D8D14811yescharacteristic
351M16—21no—
352M16—21no—
353M16—371no—
354M16—371no—
355M16—741no—
356M16—741no—
357M16C22×D3711yescharacteristic
358M16C22×D3711yescharacteristic
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—741no—
362C2×C8—741no—
363C2×C8C22×D3711yescharacteristic
364C2×C8C22×D3711yescharacteristic
365C4⋊C4—1481no—
366C22⋊C4—1481no—
367C42C22×D3711yescharacteristic
368C23—741no—
369C23—1481no—
370Q8—371no—
371Q8—371no—
372Q8—741no—
373Q8—741no—
374Q8—741no—
375Q8—741no—
376Q8—741no—
377Q8—741no—
378Q8—1481no—
379Q8—1481no—
380Q8—1481no—
381Q8C2×D14811yescharacteristic
382Q8C2×D14811yescharacteristic
383D4—21no—
384D4—21no—
385D4—371no—
386D4—371no—
387D4—741no—
388D4—741no—
389D4—741no—
390D4—741no—
391D4—1481no—
392D4—1481no—
393D4—1481no—
394D4—1481no—
395D4—1481no—
396D4C2×D14811yescharacteristic
397D4C2×D14811yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—741no—
402C2×C4—741no—
403C2×C4—741no—
404C2×C4—741no—
405C2×C4—741no—
406C2×C4—1481no—
407C2×C4—1481no—
408C2×C4—1481no—
409C2×C4—1481no—
410C2×C4—1481no—
411C2×C4—1481no—
412C2×C4—1481no—
413C2×C4C23×D3711yescharacteristic
414C8—21no—
415C8—21no—
416C8—741no—
417C8—741no—
418C8C2×D14811yescharacteristic
419C8C2×D14811yescharacteristic
420C8D4×D3711yescharacteristic
421C8D4×D3711yescharacteristic
422C22—21no—
423C22—21no—
424C22—2961no—
425C22—741no—
426C22—741no—
427C22—5921no—
428C22—1481no—
429C22#1192458211yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—741no—
434C4—741no—
435C4—1481no—
436C4—1481no—
437C4—1481no—
438C4C2×D4×D3711yescharacteristic
439C4C22×D14811yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—2961no—
444C2—1481no—
445C2—1481no—
446C2D4×D14811yescharacteristic
subgroupG/H
centerC2D4×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#444C2
socleC2×C37D42
hypercenter#444D37
hypocenterC37#3289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #14558350C2semidirect
2. #14558347C2semidirect
3. #14558345C2semidirect
4. #14558340C2semidirect
5. #14557927C2semidirect
6. #14557809C2semidirect
7. #14557808C2semidirect
8. #14557797C2semidirect
9. #14557796C2semidirect
10. #14557717C2semidirect
11. #14557717C2semidirect
12. #14557712C2semidirect
13. #14557707C2semidirect
14. #14557656C2semidirect
15. C37×#444C2semidirect
18. #11924583C22semidirect
25. #11924569C22semidirect
29. #11924566C22semidirect
42. C2×Dic148C22semidirect
43. C2×Dic148C22semidirect
50. #11924542C22semidirect
51. #11924536C22semidirect
53. #11924472C22semidirect
55. #11924464C22semidirect
56. #11924454C22semidirect
57. #11924454C22semidirect
58. #11924454C22semidirect
62. #131×C37C22semidirect
63. #108×C37C22semidirect
65. #104×C37C22semidirect
66. #97×C37C22semidirect
238. #444D37semidirect
239. C37#3289semidirect
277. #131C2×D37semidirect
281. #108C2×D37semidirect
285. #104C2×D37semidirect
290. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583502
#145583472
#145583452
#145583402
#145579272
#145578092
#145578082
#145577972
#145577962
#145577172
#145577122
#145577072
#145576562
C37×#4442
#328937