Subgroups — #19148000

Order 5504.

996 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583530	C₂	1	4	yes	maximal, complemented
2	#14583527	C₂	1	8	yes	maximal, complemented
3	#14583525	C₂	1	4	yes	maximal
4	#14583456	C₂	1	4	yes	maximal, complemented
5	#14583452	C₂	1	8	yes	maximal, complemented
6	C₂×#13063284	C₂	1	2	yes	maximal
7	C₂×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
8	#13063325	C₂²	1	8	yes	complemented
9	#13063324	C₂²	1	16	yes	complemented
10	#13063317	C₂²	1	8	yes	complemented
11	#13063316	C₂²	1	16	yes	complemented
12	#13063304	C₂²	1	16	yes	—
13	#13063302	C₂²	1	32	yes	—
14	C₄×Dic₈₆	C₂²	1	16	yes	complemented
15	#13063284	C₂²	1	4	yes	—
16	#13063284	C₂²	1	4	yes	—
17	#13063284	C₂²	1	4	yes	—
18	#13063284	C₂²	1	4	yes	—
19	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
20	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
21	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
22	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
23	#117×C₄₃	C₂²	1	4	yes	—
24	#117×C₄₃	C₂²	1	4	yes	—
25	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
28	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	Q₈	1	8	yes	complemented
30	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
31	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂²×Dic₄₃	C₂³	1	8	yes	—
36	C₂×Dic₈₆	C₂³	1	16	yes	—
37	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
38	C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
39	C₄²×C₄₃	C₂³	1	4	yes	—
40	C₄²×C₄₃	C₂³	1	4	yes	—
41	C₂²⋊Dic₄₃	C₂³	1	8	yes	—
42	C₂²⋊Dic₄₃	C₂³	1	8	yes	—
43	C₄⋊Dic₄₃	C₂³	1	8	yes	—
44	C₄⋊Dic₄₃	C₂³	1	8	yes	—
45	C₄⋊Dic₄₃	C₂³	1	16	yes	—
46	Dic₄₃⋊C₄	C₂³	1	32	yes	—
47	C₄×Dic₄₃	C₂³	1	8	yes	—
48	C₄×Dic₄₃	C₂³	1	8	yes	—
49	C₂³×C₄₃	—	4	2	no	—
50	C₂³×C₄₃	C₂×Q₈	1	4	yes	—
51	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
52	C₂³×C₄₃	C₂⁴	1	2	yes	—
53	C₂×C₄×C₄₃	—	4	4	no	—
54	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
55	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
56	C₂×C₄×C₄₃	C₂×Q₈	1	8	yes	—
57	C₂×C₄×C₄₃	C₂×Q₈	1	8	yes	—
58	C₂×C₄×C₄₃	C₂⁴	1	8	yes	—
59	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
60	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
61	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
62	C₂×Dic₄₃	—	4	8	no	—
63	C₂×Dic₄₃	C₂⁴	1	16	yes	—
64	Dic₈₆	—	4	16	no	—
65	C₂²×C₄₃	—	2	4	no	—
66	C₂²×C₄₃	—	2	2	no	—
67	C₂²×C₄₃	—	4	4	no	—
68	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
69	C₂²×C₄₃	C₂²×Q₈	1	4	yes	—
70	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
71	C₄×C₄₃	—	2	8	no	—
72	C₄×C₄₃	C₂²×Q₈	1	4	yes	—
73	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
74	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
75	Dic₄₃	—	2	16	no	—
76	#3458	—	43	1	no	maximal, Sylow
77	C₂×C₄₃	—	2	4	no	—
78	C₂×C₄₃	—	2	2	no	—
79	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
80	C₂×C₄₃	#585	1	2	yes	—
81	#544	—	43	8	no	—
82	#544	—	43	4	no	—
83	#543	—	43	4	no	—
84	#533	—	43	8	no	—
85	#533	—	43	4	no	—
86	C₂×#117	—	43	2	no	—
87	C₂×#117	D₄₃	1	1	yes	characteristic
88	C₄₃	#3458	1	1	yes	characteristic, complemented, Sylow
89	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
90	C₄⋊Q₈	—	43	16	no	—
91	C₄⋊Q₈	—	43	8	no	—
92	#125	—	43	16	no	—
93	#125	—	43	8	no	—
94	C₂²⋊Q₈	—	43	16	no	—
95	C₂²⋊Q₈	—	43	32	no	—
96	C₄×Q₈	—	43	16	no	—
97	#117	—	43	4	no	—
98	#117	—	43	4	no	—
99	#117	—	43	4	no	—
100	#117	—	43	4	no	—
101	#117	C₂×D₄₃	1	4	yes	—
102	#117	C₂×D₄₃	1	4	yes	—
103	C₂×C₄⋊C₄	—	43	4	no	—
104	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
105	C₂×C₂²⋊C₄	—	43	4	no	—
106	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
107	C₂×C₄²	—	43	4	no	—
108	C₂×C₄²	C₂×D₄₃	1	2	yes	—
109	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
110	C₂×Q₈	—	43	16	no	—
111	C₂²×C₄	—	43	8	no	—
112	C₂²×C₄	Dic₈₆	1	8	yes	complemented
113	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
114	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
115	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
117	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
118	C₄⋊C₄	—	43	8	no	—
119	C₄⋊C₄	—	43	8	no	—
120	C₄⋊C₄	—	43	32	no	—
121	C₄⋊C₄	—	43	16	no	—
122	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
123	C₂²⋊C₄	—	43	8	no	—
124	C₂²⋊C₄	—	43	8	no	—
125	C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
126	C₄²	—	43	8	no	—
127	C₄²	—	43	8	no	—
128	C₄²	C₂²×D₄₃	1	4	yes	—
129	C₄²	C₂²×D₄₃	1	4	yes	—
130	C₂³	—	4	2	no	—
131	C₂³	C₂×Dic₈₆	1	4	yes	—
132	C₂³	C₂³×D₄₃	1	1	yes	characteristic
133	C₂³	C₂³×D₄₃	1	2	yes	—
134	Q₈	—	172	16	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	43	16	no	—
137	C₂×C₄	—	172	8	no	—
138	C₂×C₄	C₂×Dic₈₆	1	8	yes	—
139	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
140	C₂×C₄	C₂×Dic₈₆	1	8	yes	—
141	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
142	C₂×C₄	C₂³×D₄₃	1	8	yes	—
143	C₂×C₄	C₂³×D₄₃	1	2	yes	—
144	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
145	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
146	C₂²	—	2	2	no	—
147	C₂²	—	2	4	no	—
148	C₂²	—	4	4	no	—
149	C₂²	C₂²×Dic₈₆	1	2	yes	—
150	C₂²	C₂²×Dic₈₆	1	4	yes	—
151	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
152	C₄	—	2	8	no	—
153	C₄	—	86	16	no	—
154	C₄	C₂²×Dic₈₆	1	4	yes	—
155	C₄	C₂²×Dic₈₆	1	2	yes	—
156	C₄	C₂²×Dic₈₆	1	2	yes	—
157	C₂	—	2	2	no	—
158	C₂	—	2	4	no	—
159	C₂	C₂³×Dic₈₆	1	1	yes	characteristic
160	C₂	#14583735	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×#117×C₄₃	C₂
hypercenter	C₂×#117	D₄₃
hypocenter	C₄₃	#3458
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #14583530	C₂	semidirect
2. #14583527	C₂	semidirect
4. #14583456	C₂	semidirect
5. #14583452	C₂	semidirect
8. #13063325	C₂²	semidirect
9. #13063324	C₂²	semidirect
10. #13063317	C₂²	semidirect
11. #13063316	C₂²	semidirect
14. C₄×Dic₈₆	C₂²	semidirect
29. C₂²×C₄×C₄₃	Q₈	semidirect
88. C₄₃	#3458	semidirect
112. C₂²×C₄	Dic₈₆	semidirect