Subgroups — #22581232

Order 8896.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984841	C₂	1	1	yes	maximal, characteristic, complemented
2	#17984804	C₂	1	1	yes	maximal, characteristic
3	#17984775	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984764	C₂	1	1	yes	maximal, characteristic
6	#17984762	C₂	1	1	yes	maximal, characteristic
7	#107×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₇₈	—	2	1	no	—
9	C₂×D₅₅₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₁₃₉	—	2	1	no	—
11	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
13	Dic₁₃₉⋊C₄	—	2	1	no	—
14	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
15	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×D₁₃₉	—	2	1	no	—
20	Dic₂₇₈	—	4	2	no	—
21	D₅₅₆	—	2	1	no	—
22	D₅₅₆	Q₈	1	2	yes	complemented
23	C₂×Dic₁₃₉	—	2	1	no	—
24	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
25	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
26	C₄×D₁₃₉	—	4	2	no	—
27	C₁₃₉⋊C₈	—	2	1	no	—
28	C₂×C₄×C₁₃₉	—	2	1	no	—
29	C₂×C₄×C₁₃₉	—	2	1	no	—
30	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
31	C₈×C₁₃₉	—	2	1	no	—
32	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
33	C₂×D₁₃₉	—	2	2	no	—
34	C₂×D₁₃₉	—	4	1	no	—
35	C₂×D₁₃₉	—	4	1	no	—
36	C₄×C₁₃₉	—	4	1	no	—
37	C₄×C₁₃₉	—	4	1	no	—
38	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₁₃₉	#41	1	1	yes	characteristic
40	Dic₁₃₉	—	2	1	no	—
41	Dic₁₃₉	—	4	1	no	—
42	Dic₁₃₉	D₈	1	2	yes	—
43	C₂×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₁₃₉	C₂×D₈	1	1	yes	characteristic
45	C₂×C₁₃₉	#137	1	1	yes	characteristic
46	D₁₃₉	—	4	2	no	—
47	C₁₃₉	#474	1	1	yes	characteristic, complemented, Sylow
48	#474	—	139	1	no	maximal, Sylow
49	C₄⋊Q₈	—	139	1	no	—
50	C₄×D₄	—	139	1	no	—
51	#107	—	139	1	no	—
52	#107	D₁₃₉	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	139	1	no	—
54	#102	—	139	1	no	—
55	#102	—	139	1	no	—
56	C₂×Q₈	—	278	1	no	—
57	C₂×D₄	—	139	1	no	—
58	C₂²×C₄	—	278	1	no	—
59	C₂×C₈	—	139	1	no	—
60	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
61	C₄⋊C₄	—	278	1	no	—
62	C₄⋊C₄	—	139	1	no	—
63	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	278	1	no	—
66	C₄²	—	139	1	no	—
67	C₂³	—	278	1	no	—
68	Q₈	—	556	2	no	—
69	D₄	—	278	1	no	—
70	D₄	—	139	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	278	1	no	—
74	C₂×C₄	—	556	2	no	—
75	C₂×C₄	—	139	1	no	—
76	C₂×C₄	—	139	1	no	—
77	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	278	1	no	—
80	C₂²	—	278	2	no	—
81	C₂²	—	556	1	no	—
82	C₂²	—	556	1	no	—
83	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	278	1	no	—
87	C₄	—	556	1	no	—
88	C₄	—	139	2	no	—
89	C₄	Q₈×D₁₃₉	1	1	yes	characteristic
90	C₄	#14555785	1	1	yes	characteristic
91	C₂	—	556	2	no	—
92	C₂	#17984820	1	1	yes	characteristic
93	C₂	D₈×D₁₃₉	1	1	yes	characteristic
94	C₂	#17984874	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#107×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#107	D₁₃₉
hypocenter	C₁₃₉	#474
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
1. #17984841	C₂	semidirect
3. #17984775	C₂	semidirect
4. Dic₁₃₉⋊C₈	C₂	semidirect
7. #107×C₁₃₉	C₂	semidirect
22. D₅₅₆	Q₈	semidirect
47. C₁₃₉	#474	semidirect
52. #107	D₁₃₉	semidirect