Subgroups — D₁₃₇⋊#108 #22578416

Order 8768.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₇⋊M₁₆	C₂	1	2	yes	maximal
2	#17984159	C₂	1	2	yes	maximal, complemented
3	#17984158	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#14555520	C₂²	1	4	yes	—
6	#14555519	—	2	2	no	—
7	#14555518	—	2	2	no	—
8	C₂×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
9	C₂×#11764040	C₄	1	1	yes	characteristic
10	C₈×D₁₃₇	C₄	1	1	yes	characteristic
11	C₈×D₁₃₇	C₄	1	1	yes	characteristic
12	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
13	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
15	#11764047	—	2	4	no	—
16	C₂²×D₁₃₇	Q₈	1	1	yes	characteristic
17	C₂×Dic₁₃₇	D₄	1	1	yes	characteristic
18	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₃₇	D₄	1	1	yes	characteristic
20	C₄×D₁₃₇	Q₈	1	1	yes	characteristic
21	C₄×D₁₃₇	C₂³	1	1	yes	characteristic
22	#11764040	C₂×C₄	1	1	yes	characteristic
23	#11764040	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
25	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
26	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₁₃₇	—	2	2	no	—
29	C₂×D₁₃₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₁₃₇	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₃₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₁₃₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₁₃₇	—	2	1	no	—
36	C₂×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₁₃₇	—	2	1	no	—
38	D₁₃₇	#108	1	2	yes	complemented
39	C₁₃₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
40	C₂×#108	—	137	1	no	maximal, Sylow
41	C₂×M₁₆	—	137	2	no	—
42	C₂²×C₈	—	137	1	no	—
43	#108	—	137	2	no	—
44	#108	—	137	2	no	—
45	C₂²×C₄	—	137	1	no	—
46	M₁₆	—	274	2	no	—
47	M₁₆	—	137	4	no	—
48	C₂×C₈	—	274	2	no	—
49	C₂×C₈	—	137	1	no	—
50	C₂×C₈	—	137	1	no	—
51	C₂×C₈	—	137	1	no	—
52	C₂×C₈	—	137	1	no	—
53	C₂×C₈	—	137	1	no	—
54	C₂×C₈	#10587739	1	1	yes	characteristic
55	C₂³	—	137	1	no	—
56	C₂×C₄	—	137	1	no	—
57	C₂×C₄	—	137	1	no	—
58	C₂×C₄	—	137	1	no	—
59	C₂×C₄	—	137	1	no	—
60	C₂×C₄	—	137	1	no	—
61	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
62	C₈	—	274	4	no	—
63	C₈	—	137	1	no	—
64	C₈	—	137	1	no	—
65	C₈	C₂×#10587739	1	1	yes	characteristic
66	C₈	C₂×#10587739	1	1	yes	characteristic
67	C₂²	—	274	2	no	—
68	C₂²	—	137	1	no	—
69	C₂²	—	137	1	no	—
70	C₂²	C₄⋊#10587739	1	1	yes	characteristic
71	C₄	—	137	1	no	—
72	C₄	—	137	1	no	—
73	C₄	C₄⋊#10587739	1	1	yes	characteristic
74	C₄	C₂²×#10587739	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	274	1	no	—
77	C₂	—	137	2	no	—
78	C₂	C₂×C₄⋊#10587739	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#10587739
commutator	C₄×C₁₃₇	C₂²×C₄
Frattini	C₄	C₂²×#10587739
Fitting	C₂×C₈×C₁₃₇	C₄
socle	C₂×C₁₃₇	C₂×C₄⋊C₄
hypercenter	C₂×C₈	#10587739
hypocenter	C₁₃₇	C₂×#108
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #17984159	C₂	semidirect
3. #17984158	C₂	semidirect
38. D₁₃₇	#108	semidirect
39. C₁₃₇	C₂×#108	semidirect

Subgroups — D137⋊#108 #22578416

Conjugacy classes of subgroups

Complements

Subgroups — D₁₃₇⋊#108 #22578416