Subgroups — C₂×#19134344 #25094063

Order 11008.

1310 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	C₂²×#13063236	C₂	1	2	yes	maximal
2	#19134344	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14582654	C₂	1	4	yes	maximal
4	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	—
6	C₂×#13063236	C₄	1	16	yes	complemented
7	C₂×#13063236	C₂²	1	8	yes	—
8	#14582654	C₂²	1	16	yes	—
9	C₂²×C₄²×C₄₃	C₄	1	4	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄³×C₄₃	C₄	1	4	yes	—
13	C₄³×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄₃⋊C₈	—	2	16	no	—
15	C₂²×C₄₃⋊C₈	C₂×C₄	1	16	yes	—
16	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
17	#13063236	C₂×C₄	1	32	yes	complemented
18	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₄₃	—	2	16	no	—
22	C₂×C₄²×C₄₃	—	2	8	no	—
23	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
24	C₂×C₄²×C₄₃	C₂×C₄	1	16	yes	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
28	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
29	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	—	2	8	no	—
31	C₂²×C₄×C₄₃	—	2	8	no	—
32	C₂²×C₄×C₄₃	—	2	8	no	—
33	C₂²×C₄×C₄₃	C₄²	1	8	yes	—
34	C₂²×C₄×C₄₃	M₁₆	1	16	yes	—
35	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
36	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
37	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
38	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	#41	1	8	yes	—
40	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₄²×C₄₃	—	2	8	no	—
42	C₄²×C₄₃	—	2	32	no	—
43	C₄²×C₄₃	—	2	8	no	—
44	C₄²×C₄₃	C₄²	1	8	yes	—
45	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
46	C₂×C₄₃⋊C₈	—	2	32	no	—
47	C₂×C₄₃⋊C₈	—	2	16	no	—
48	C₂×C₄₃⋊C₈	C₂²×C₄	1	16	yes	—
49	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
50	C₂³×C₄₃	#117	1	4	yes	—
51	C₂³×C₄₃	C₂×M₁₆	1	8	yes	—
52	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	—	2	8	no	—
54	C₂×C₄×C₄₃	—	2	8	no	—
55	C₂×C₄×C₄₃	—	2	8	no	—
56	C₂×C₄×C₄₃	—	2	16	no	—
57	C₂×C₄×C₄₃	—	2	32	no	—
58	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
59	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
60	C₂×C₄×C₄₃	#117	1	16	yes	—
61	C₂×C₄×C₄₃	#117	1	4	yes	—
62	C₂×C₄×C₄₃	C₂×M₁₆	1	16	yes	—
63	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
64	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
65	C₄₃⋊C₈	—	2	16	no	—
66	C₂×#1745	—	43	1	no	maximal, Sylow
67	C₂²×C₄₃	#376	1	4	yes	—
68	C₂²×C₄₃	C₄×M₁₆	1	8	yes	—
69	C₂²×C₄₃	#432	1	16	yes	—
70	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
71	C₂²×C₄₃	C₂×#117	1	2	yes	—
72	C₂²×C₄₃	C₂²×M₁₆	1	4	yes	—
73	C₄×C₄₃	—	2	8	no	—
74	C₄×C₄₃	—	2	16	no	—
75	C₄×C₄₃	#376	1	4	yes	—
76	C₄×C₄₃	C₂×#117	1	4	yes	—
77	C₂²×#97	—	43	2	no	—
78	C₂×C₄³	D₄₃	1	1	yes	characteristic
79	#1745	—	43	8	no	—
80	C₂×#336	—	43	4	no	—
81	C₂×C₄₃	#1745	1	8	yes	complemented
82	C₂×C₄₃	C₂×#376	1	1	yes	characteristic
83	C₂×C₄₃	C₂×C₄×M₁₆	1	2	yes	—
84	C₂×C₄₃	C₂×#432	1	4	yes	—
85	C₂³×C₈	—	43	4	no	—
86	C₂²×C₄²	Dic₄₃	1	4	yes	—
87	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
88	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
89	C₂×#97	—	43	8	no	—
90	C₂×#97	—	43	16	no	—
91	C₄³	Dic₄₃	1	4	yes	—
92	C₄³	C₂×D₄₃	1	4	yes	—
93	#336	—	43	16	no	—
94	C₄₃	C₂×#1745	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₄	C₂×Dic₄₃	1	4	yes	—
96	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
97	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
98	C₂²×C₈	—	43	16	no	—
99	C₂²×C₈	—	43	8	no	—
100	C₂²×C₈	—	86	16	no	—
101	C₂×C₄²	—	2	16	no	—
102	C₂×C₄²	—	2	8	no	—
103	C₂×C₄²	C₄×D₄₃	1	8	yes	—
104	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
105	C₂×C₄²	C₂×Dic₄₃	1	16	yes	—
106	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
107	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
108	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
109	#97	—	43	32	no	—
110	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
111	C₂²×C₄	—	2	8	no	—
112	C₂²×C₄	—	2	8	no	—
113	C₂²×C₄	—	2	8	no	—
114	C₂²×C₄	#10621877	1	16	yes	—
115	C₂²×C₄	C₄×Dic₄₃	1	8	yes	—
116	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
117	C₂²×C₄	#10621898	1	8	yes	—
118	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
119	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
120	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
121	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
122	C₂×C₈	—	43	16	no	—
123	C₂×C₈	—	86	32	no	—
124	C₂×C₈	—	86	16	no	—
125	C₄²	—	2	8	no	—
126	C₄²	—	2	32	no	—
127	C₄²	—	2	8	no	—
128	C₄²	C₄×Dic₄₃	1	8	yes	—
129	C₄²	C₂×C₄×D₄₃	1	8	yes	—
130	C₂³	C₂×C₄×Dic₄₃	1	2	yes	—
131	C₂³	#13063284	1	4	yes	—
132	C₂³	C₂×#10621877	1	8	yes	—
133	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
134	C₂×C₄	—	2	8	no	—
135	C₂×C₄	—	2	16	no	—
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	8	no	—
138	C₂×C₄	—	2	32	no	—
139	C₂×C₄	C₂×C₄×Dic₄₃	1	8	yes	—
140	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
141	C₂×C₄	#13063282	1	16	yes	—
142	C₂×C₄	#13063284	1	4	yes	—
143	C₂×C₄	C₂×#10621877	1	16	yes	—
144	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
145	C₂×C₄	C₂×#10621898	1	4	yes	—
146	C₈	—	86	16	no	—
147	C₂²	#14582745	1	4	yes	—
148	C₂²	C₄×#10621877	1	8	yes	—
149	C₂²	#14582956	1	16	yes	—
150	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
151	C₂²	C₂×#13063284	1	2	yes	—
152	C₂²	C₂²×#10621877	1	4	yes	—
153	C₄	—	2	16	no	—
154	C₄	—	2	8	no	—
155	C₄	#14582745	1	4	yes	—
156	C₄	C₂×#13063282	1	4	yes	—
157	C₂	#19134344	1	8	yes	direct product factor
158	C₂	C₂×#14582745	1	1	yes	characteristic
159	C₂	C₂×C₄×#10621877	1	2	yes	—
160	C₂	C₂×#14582956	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄³×C₄₃	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄³	D₄₃
hypocenter	C₄₃	C₂×#1745
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
2. #19134344	C₂	direct (N × H)
6. C₂×#13063236	C₄	semidirect
17. #13063236	C₂×C₄	semidirect
81. C₂×C₄₃	#1745	semidirect
94. C₄₃	C₂×#1745	semidirect
157. C₂	#19134344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063236	2
#19134344	2
C₂×#14582654	2
C₂×C₄³×C₄₃	2
C₂×#1745	43

Subgroups — C2×#19134344 #25094063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19134344 #25094063