Subgroups — #383×D₁₃₇ #31783177

Order 17536.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#22577271	C₂	1	1	yes	maximal, characteristic, complemented
3	#22577270	C₂	1	6	yes	maximal, complemented
4	#95×D₁₃₇	C₂	1	6	yes	maximal
5	#383×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₃₇	C₂²	1	4	yes	—
7	C₂²×C₄×D₁₃₇	C₂²	1	3	yes	—
8	C₂×C₄×Dic₁₃₇	C₂²	1	3	yes	—
9	C₄²×D₁₃₇	C₄	1	8	yes	complemented
10	#17983995	C₂²	1	12	yes	—
11	#17983995	C₂²	1	6	yes	—
12	C₂×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
13	#95×C₁₃₇	C₂²	1	6	yes	—
14	C₂³×D₁₃₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₃₇	C₂³	1	4	yes	—
16	C₂²×Dic₁₃₇	C₂³	1	3	yes	—
17	C₂×C₄×D₁₃₇	—	2	12	no	—
18	C₂×C₄×D₁₃₇	—	2	24	no	—
19	C₂×C₄×D₁₃₇	C₂×C₄	1	12	yes	—
20	C₄×Dic₁₃₇	C₂×C₄	1	12	yes	complemented
21	C₂²×C₄×C₁₃₇	C₂³	1	4	yes	—
22	C₂²×C₄×C₁₃₇	C₂³	1	3	yes	—
23	C₄²×C₁₃₇	C₂×C₄	1	4	yes	complemented
24	C₂²×D₁₃₇	C₂²×C₄	1	2	yes	—
25	C₂²×D₁₃₇	#41	1	12	yes	—
26	C₂×Dic₁₃₇	—	2	6	no	—
27	C₂×Dic₁₃₇	—	2	12	no	—
28	C₂×Dic₁₃₇	C₂²×C₄	1	6	yes	—
29	C₄×D₁₃₇	—	2	24	no	—
30	C₄×D₁₃₇	—	4	16	no	—
31	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
32	C₂×C₄×C₁₃₇	—	2	6	no	—
33	C₂×C₄×C₁₃₇	—	2	12	no	—
34	C₂×C₄×C₁₃₇	C₂²×C₄	1	6	yes	—
35	C₂²×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
36	C₂²×C₁₃₇	C₂×#41	1	6	yes	—
37	C₂×D₁₃₇	#117	1	12	yes	—
38	C₂×D₁₃₇	#126	1	16	yes	—
39	C₄×C₁₃₇	—	2	6	no	—
40	C₄×C₁₃₇	—	4	4	no	—
41	Dic₁₃₇	—	2	6	no	—
42	Dic₁₃₇	—	4	4	no	—
43	C₂×C₁₃₇	C₂×#117	1	3	yes	—
44	C₂×C₁₃₇	C₂×#126	1	4	yes	—
45	D₁₃₇	#383	1	8	yes	direct product factor
46	C₁₃₇	C₂×#383	1	1	yes	characteristic, complemented, Sylow
47	C₂×#383	—	137	1	no	maximal, Sylow
48	C₂²×C₄²	—	137	1	no	—
49	#383	—	137	1	no	—
50	#383	—	137	6	no	—
51	#383	D₁₃₇	1	1	yes	characteristic, direct product factor
52	C₂×#95	—	137	6	no	—
53	C₂³×C₄	—	137	4	no	—
54	C₂³×C₄	—	137	3	no	—
55	C₂×C₄²	—	137	3	no	—
56	C₂×C₄²	—	137	8	no	—
57	C₂×C₄²	C₂×D₁₃₇	1	1	yes	characteristic
58	#95	—	137	6	no	—
59	#95	—	137	12	no	—
60	#95	C₂×D₁₃₇	1	6	yes	—
61	C₂⁴	—	137	1	no	—
62	C₂²×C₄	—	274	12	no	—
63	C₂²×C₄	—	274	24	no	—
64	C₂²×C₄	—	137	4	no	—
65	C₂²×C₄	—	137	3	no	—
66	C₂²×C₄	—	137	12	no	—
67	C₂²×C₄	C₂²×D₁₃₇	1	4	yes	—
68	C₂²×C₄	C₂²×D₁₃₇	1	3	yes	—
69	C₄²	—	137	12	no	—
70	C₄²	C₄×D₁₃₇	1	4	yes	complemented
71	C₂³	—	137	2	no	—
72	C₂³	—	137	12	no	—
73	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	274	24	no	—
77	C₂×C₄	—	274	6	no	—
78	C₂×C₄	—	274	12	no	—
79	C₂×C₄	—	548	16	no	—
80	C₂×C₄	—	137	6	no	—
81	C₂×C₄	C₂×C₄×D₁₃₇	1	6	yes	—
82	C₂²	—	137	16	no	—
83	C₂²	—	137	12	no	—
84	C₂²	C₂²×C₄×D₁₃₇	1	1	yes	characteristic
85	C₂²	#41×D₁₃₇	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	274	6	no	—
89	C₄	—	548	4	no	—
90	C₂	—	137	8	no	—
91	C₂	#117×D₁₃₇	1	3	yes	—
92	C₂	#126×D₁₃₇	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃₇
commutator	C₂²×C₁₃₇	C₂³×C₄
Fitting	#383×C₁₃₇	C₂
socle, cosocle	C₂³×C₁₃₇	C₂⁴
prime radical	C₂³×D₁₃₇	C₂³
hypercenter	#383	D₁₃₇
hypocenter	C₁₃₇	C₂×#383
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #22577271	C₂	semidirect
3. #22577270	C₂	semidirect
5. #383×C₁₃₇	C₂	semidirect
9. C₄²×D₁₃₇	C₄	semidirect
20. C₄×Dic₁₃₇	C₂×C₄	semidirect
23. C₄²×C₁₃₇	C₂×C₄	semidirect
45. D₁₃₇	#383	direct (N × H)
46. C₁₃₇	C₂×#383	semidirect
51. #383	D₁₃₇	direct (N × H)
70. C₄²	C₄×D₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₁₃₇	2
#22577271	2
#22577270	2
#95×D₁₃₇	2
#383×C₁₃₇	2
C₂×#383	137

Subgroups — #383×D137 #31783177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #383×D₁₃₇ #31783177