Finite Group Databasebeta

← #18004311

Subgroups — #18004311

Order 4736.

452 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558332C211yesmaximal, characteristic, complemented
2#14558329C211yesmaximal, characteristic, complemented
3C2×#11924557C211yesmaximal, characteristic, complemented
4#131×D37C211yesmaximal, characteristic, complemented
5#14557807C211yesmaximal, characteristic, complemented
6#14557806C211yesmaximal, characteristic, complemented
7#14557802C211yesmaximal, characteristic, complemented
8#14557801C211yesmaximal, characteristic, complemented
9#14557797C211yesmaximal, characteristic, complemented
10#14557796C211yesmaximal, characteristic, complemented
11#14557793C211yesmaximal, characteristic, complemented
12#108×D37C211yesmaximal, characteristic, complemented
13#14557516C211yesmaximal, characteristic, complemented
14#14557514C211yesmaximal, characteristic, complemented
15C37×#471C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18#41×D37C2211yescharacteristic
19#11924569C2211yescharacteristic
20#11924568—21no—
21#11924567C2211yescharacteristic
22#11924566C2211yescharacteristic
23#11924565—21no—
24#11924564C2211yescharacteristic
25#11924563—21no—
26#11924562C2211yescharacteristic
27#11924561C2211yescharacteristic
28#11924560—21no—
29#11924559—21no—
30#11924557—21no—
31#11924557—21no—
32#11924557—21no—
33#11924557—21no—
34#11924557—21no—
35#11924557—21no—
36#11924555—21no—
37C2×#10596942C2211yescharacteristic, complemented
38C2×#10596930C2211yescharacteristic, complemented
39C2×#10596939C2211yescharacteristic, complemented
40#11924544—21no—
41#11924544C2211yescharacteristic
42#11924543C2211yescharacteristic
43#11924542—21no—
44#11924542C2211yescharacteristic
45M16×D37—21no—
46M16×D37C2211yescharacteristic
47M16×D37C2211yescharacteristic
48M16×D37C2211yescharacteristic
49C2×C8×D37—21no—
50C2×C8×D37C2211yescharacteristic
51#11924472C2211yescharacteristic, complemented
52#11924471C2211yescharacteristic, complemented
53#11924471C2211yescharacteristic, complemented
54#11924455C2211yescharacteristic, complemented
55#11924454C2211yescharacteristic, complemented
56#11924454C2211yescharacteristic, complemented
57#11924453C2211yescharacteristic, complemented
58#11924452C2211yescharacteristic, complemented
59#11924452C2211yescharacteristic, complemented
60#137×C37C2211yescharacteristic
61AGL(1,ℤ/8)×C37C2211yescharacteristic
62C2×SD16×C37C2211yescharacteristic, complemented
63#131×C37C2211yescharacteristic
64#108×C37C2211yescharacteristic, complemented
65#101×C37C2211yescharacteristic, complemented
66#100×C37C2211yescharacteristic, complemented
67#41×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C22×Dic37—21no—
72#10596966—21no—
73#10596966—21no—
74#10596966—21no—
75#10596966—21no—
76#10596966D411yescharacteristic
77Q8×D37D411yescharacteristic
78#10596964—21no—
79#10596964—21no—
80#10596964—21no—
81#10596964—21no—
82#10596964—21no—
83#10596964D411yescharacteristic
84D4×D37—21no—
85D4×D37D411yescharacteristic
86#10596962—21no—
87#10596962C2311yescharacteristic
88C2×D148—21no—
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37—21no—
92C2×C4×D37C2311yescharacteristic
93C2×Dic74C2311yescharacteristic
94Q16×C37—21no—
95SD16×C37—21no—
96SD16×C37—21no—
97SD16×C37—21no—
98SD16×C37—21no—
99D8×C37—21no—
100M16×C37—21no—
101M16×C37C2311yescharacteristic
102M16×C37C2311yescharacteristic
103M16×C37C2311yescharacteristic
104C2×C8×C37—21no—
105C2×C8×C37C2311yescharacteristic
106#10596942—21no—
107#10596942—21no—
108#10596942—21no—
109#10596942—21no—
110#10596941—21no—
111#10596941—21no—
112#10596940—21no—
113#10596940—21no—
114#10596939—21no—
115#10596939—21no—
116#10596939—21no—
117#10596939—21no—
118#10596934—21no—
119#10596934C2311yescharacteristic
120#10596934C2311yescharacteristic
121#10596934C2311yescharacteristic
122C2×#64436—21no—
123C2×#64436C2311yescharacteristic
124Dic148—21no—
125D296—21no—
126#10596930—21no—
127#10596930—21no—
128#10596930—21no—
129#10596930—21no—
130#10596929—21no—
131#10596929—21no—
132#10596929—21no—
133#10596929—21no—
134#10596929—21no—
135C8×D37—21no—
136C8×D37—21no—
137C8×D37—21no—
138C8×D37—21no—
139C8×D37—21no—
140C8×D37D411yescharacteristic
141C8×D37D411yescharacteristic
142C8×D37D411yescharacteristic
143C8×D37D411yescharacteristic
144C23×C37—21no—
145C22×D37—21no—
146C22×D37—21no—
147C22×D37#4111yescharacteristic
148Q8×C37—21no—
149Q8×C37—21no—
150Q8×C37C2×D411yescharacteristic
151D4×C37—21no—
152D4×C37—21no—
153D4×C37—21no—
154D4×C37C2×D411yescharacteristic
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37C2411yescharacteristic
158C22⋊D37—21no—
159C22⋊D37—21no—
160C22⋊D37—21no—
161C22⋊D37—41no—
162C22⋊D37—41no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—41no—
166C2×Dic37—41no—
167C2×Dic37#4111yescharacteristic
168D148—21no—
169D148—21no—
170D148—21no—
171D148—41no—
172D148—41no—
173D148C2×D411yescharacteristic
174C4×D37—21no—
175C4×D37—21no—
176C4×D37—21no—
177C4×D37—41no—
178C4×D37—41no—
179C4×D37C2×D411yescharacteristic
180C4×D37C2×D411yescharacteristic
181C4×D37C2×D411yescharacteristic
182C4×D37C2×D411yescharacteristic
183Dic74—21no—
184Dic74—21no—
185Dic74—21no—
186Dic74C2×D411yescharacteristic
187C8×C37—21no—
188C8×C37—21no—
189C8×C37—21no—
190C8×C37C2×D411yescharacteristic
191C8×C37C2×D411yescharacteristic
192#64436—21no—
193#64436—21no—
194#64436—21no—
195#64436C2×D411yescharacteristic
196#64436C2×D411yescharacteristic
197C22×C37—21no—
198C22×C37—41no—
199C22×C37—81no—
200C22×C37C2×#4111yescharacteristic
201C2×D37—21no—
202C2×D37—41no—
203C2×D37—42no—
204C2×D37—41no—
205C2×D37—81no—
206C2×D37#12111yescharacteristic
207C2×D37#12111yescharacteristic
208C4×C37—21no—
209C4×C37—41no—
210C4×C37C22×D411yescharacteristic
211C4×C37C22×D411yescharacteristic
212Dic37—21no—
213Dic37—41no—
214Dic37#12111yescharacteristic
215Dic37#12111yescharacteristic
216#3067—371nomaximal, Sylow
217C2×C37—21no—
218C2×C37—41no—
219C2×C37—81no—
220C2×C37C2×#12111yescharacteristic
221D37—21no—
222D37—21no—
223D37—41no—
224D37—81no—
225#575—371no—
226#575—371no—
227C2×#135—371no—
228C2×#131—371no—
229#473—371no—
230#473—371no—
231#472—371no—
232#472—371no—
233#471—371no—
234#471—371no—
235#471—371no—
236#471D3711yescharacteristic, complemented
237C2×#108—371no—
238#413—371no—
239#413—371no—
240C37#306711yescharacteristic, complemented, Sylow
241C2×#41—371no—
242C2×#41—371no—
243C2×#41—371no—
244#137—371no—
245#137—371no—
246#137—371no—
247#137—741no—
248#137—741no—
249#137C2×D3711yescharacteristic
250AGL(1,ℤ/8)—371no—
251AGL(1,ℤ/8)—371no—
252AGL(1,ℤ/8)—371no—
253AGL(1,ℤ/8)—741no—
254AGL(1,ℤ/8)—741no—
255AGL(1,ℤ/8)C2×D3711yescharacteristic
256#135—741no—
257#135—741no—
258#135—741no—
259#135—741no—
260#135—741no—
261#135—741no—
262#135—741no—
263#135—741no—
264C2×Q16—371no—
265C2×SD16—371no—
266C2×SD16C2×D3711yescharacteristic, complemented
267C2×D8—371no—
268#131—371no—
269#131—371no—
270#131—371no—
271#131—741no—
272#131—741no—
273#131C2×D3711yescharacteristic
274C2×M16—371no—
275C2×M16—371no—
276C2×M16—371no—
277C2×M16—741no—
278C22×C8—371no—
279C22×C8—741no—
280#108—371no—
281#108—371no—
282#108—371no—
283#108C2×D3711yescharacteristic, complemented
284#101—371no—
285#101—371no—
286#101—371no—
287#101C2×D3711yescharacteristic, complemented
288#100—371no—
289#100—371no—
290#100—371no—
291#100C2×D3711yescharacteristic, complemented
292#41—371no—
293#41—371no—
294#41—371no—
295#41—741no—
296#41—741no—
297#41—741no—
298#41—741no—
299#41—741no—
300#41—741no—
301#41—741no—
302#41—741no—
303#41—741no—
304#41—741no—
305#41C22×D3711yescharacteristic
306C2×Q8—371no—
307C2×Q8—371no—
308C2×Q8C22×D3711yescharacteristic
309C2×D4—371no—
310C2×D4—371no—
311C2×D4—741no—
312C2×D4—741no—
313C2×D4—741no—
314C2×D4C22×D3711yescharacteristic
315C22×C4—371no—
316C22×C4—741no—
317C22×C4—741no—
318C22×C4—741no—
319Q16—21no—
320Q16—741no—
321Q16—741no—
322Q16—741no—
323Q16—741no—
324Q16—741no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—741no—
330SD16—741no—
331SD16—741no—
332SD16—741no—
333SD16—741no—
334SD16—741no—
335SD16—741no—
336SD16—741no—
337D8—21no—
338D8—741no—
339D8—741no—
340D8—741no—
341D8—741no—
342D8—741no—
343M16—21no—
344M16—371no—
345M16—371no—
346M16—371no—
347M16—741no—
348M16—741no—
349M16—741no—
350M16—741no—
351M16—741no—
352M16—741no—
353M16C22×D3711yescharacteristic
354M16C22×D3711yescharacteristic
355M16C22×D3711yescharacteristic
356C2×C8—21no—
357C2×C8—371no—
358C2×C8—371no—
359C2×C8—371no—
360C2×C8—371no—
361C2×C8—371no—
362C2×C8—741no—
363C2×C8—741no—
364C2×C8—741no—
365C2×C8—741no—
366C2×C8—741no—
367C2×C8—741no—
368C2×C8C22×D3711yescharacteristic
369C23—21no—
370C23—371no—
371C23—741no—
372C23—741no—
373Q8—21no—
374Q8—21no—
375Q8—371no—
376Q8—741no—
377Q8—741no—
378Q8—741no—
379Q8D4×D3711yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—371no—
384D4—741no—
385D4—741no—
386D4—741no—
387D4—741no—
388D4—741no—
389D4—741no—
390D4—1481no—
391D4—1481no—
392D4—1481no—
393D4—1481no—
394D4D4×D3711yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—371no—
398C2×C4—371no—
399C2×C4—371no—
400C2×C4—371no—
401C2×C4—371no—
402C2×C4—741no—
403C2×C4—741no—
404C2×C4—741no—
405C2×C4—741no—
406C2×C4—741no—
407C2×C4—1481no—
408C2×C4—1481no—
409C2×C4—1481no—
410C2×C4—1481no—
411C2×C4C23×D3711yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—371no—
416C8—371no—
417C8—741no—
418C8—741no—
419C8—741no—
420C8D4×D3711yescharacteristic
421C8D4×D3711yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—371no—
426C22—371no—
427C22—2961no—
428C22—741no—
429C22—1481no—
430C22—1482no—
431C22—1481no—
432C22#41×D3711yescharacteristic
433C4—21no—
434C4—41no—
435C4—371no—
436C4—371no—
437C4—741no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4C2×D4×D3711yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—2961no—
445C2—741no—
446C2—741no—
447C2—1481no—
448C2#121×D3711yescharacteristic
subgroupG/H
centerC2#121×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#471C2
socleC2×C37C2×#121
hypercenter#471D37
hypocenterC37#3067
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14558332C2semidirect
2. #14558329C2semidirect
3. C2×#11924557C2semidirect
4. #131×D37C2semidirect
5. #14557807C2semidirect
6. #14557806C2semidirect
7. #14557802C2semidirect
8. #14557801C2semidirect
9. #14557797C2semidirect
10. #14557796C2semidirect
11. #14557793C2semidirect
12. #108×D37C2semidirect
13. #14557516C2semidirect
14. #14557514C2semidirect
15. C37×#471C2semidirect
37. C2×#10596942C22semidirect
38. C2×#10596930C22semidirect
39. C2×#10596939C22semidirect
51. #11924472C22semidirect
52. #11924471C22semidirect
53. #11924471C22semidirect
54. #11924455C22semidirect
55. #11924454C22semidirect
56. #11924454C22semidirect
57. #11924453C22semidirect
58. #11924452C22semidirect
59. #11924452C22semidirect
62. C2×SD16×C37C22semidirect
64. #108×C37C22semidirect
65. #101×C37C22semidirect
66. #100×C37C22semidirect
236. #471D37semidirect
240. C37#3067semidirect
266. C2×SD16C2×D37semidirect
283. #108C2×D37semidirect
287. #101C2×D37semidirect
291. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583322
#145583292
C2×#119245572
#131×D372
#145578072
#145578062
#145578022
#145578012
#145577972
#145577962
#145577932
#108×D372
#145575162
#145575142
C37×#4712
#306737