Subgroups — C₂×#19132666 #25008174

Order 11008.

262 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582652	C₂	1	1	yes	maximal, characteristic
3	#19132666	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄×C₄₃⋊C₁₆	C₄	1	2	yes	—
9	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	#14582652	—	2	1	no	—
11	#14582652	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
13	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#335	—	2	1	no	—
15	C₄₃×#335	C₂²	1	2	yes	—
16	C₂²×C₄₃⋊C₈	—	4	1	no	—
17	C₂×C₄₃⋊C₁₆	—	2	2	no	—
18	C₂×C₄₃⋊C₁₆	C₈	1	4	yes	complemented
19	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
21	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
22	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
23	C₂²×C₈×C₄₃	—	4	1	no	—
24	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
26	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
27	C₄⋊C₈×C₄₃	—	2	2	no	—
28	C₄⋊C₈×C₄₃	—	4	1	no	—
29	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₄×C₈×C₄₃	Q₈	1	1	yes	characteristic
32	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
36	C₂×C₈×C₄₃	—	2	2	no	—
37	C₂×C₈×C₄₃	—	4	2	no	—
38	C₂×C₈×C₄₃	—	8	2	no	—
39	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
43	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₄₃	D₈	1	1	yes	characteristic
47	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
48	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄₃⋊C₈	—	4	2	no	—
50	C₂×C₄₃⋊C₈	—	8	2	no	—
51	C₄₃⋊C₁₆	—	2	2	no	—
52	C₄₃⋊C₁₆	C₂×C₈	1	4	yes	complemented
53	C₂³×C₄₃	#107	1	1	yes	characteristic
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	C₄⋊C₈	1	2	yes	—
56	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
57	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
59	C₂×C₄×C₄₃	#108	1	2	yes	—
60	C₂×C₄×C₄₃	D₁₆	1	2	yes	—
61	C₂×C₄×C₄₃	Q₃₂	1	2	yes	—
62	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
65	C₈×C₄₃	—	2	1	no	—
66	C₈×C₄₃	—	2	1	no	—
67	C₈×C₄₃	—	8	2	no	—
68	C₈×C₄₃	C₄⋊C₈	1	2	yes	—
69	C₈×C₄₃	C₂²×C₈	1	1	yes	characteristic
70	C₈×C₄₃	C₂×M₁₆	1	1	yes	characteristic
71	C₄₃⋊C₈	—	8	2	no	—
72	C₂×#1371	—	43	1	no	maximal, Sylow
73	C₂²×C₄₃	#335	1	2	yes	—
74	C₂²×C₄₃	#366	1	2	yes	—
75	C₂²×C₄₃	#368	1	2	yes	—
76	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
77	C₄×C₄₃	—	2	1	no	—
78	C₄×C₄₃	—	2	1	no	—
79	C₄×C₄₃	#335	1	2	yes	—
80	C₄×C₄₃	#366	1	2	yes	—
81	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₄×C₄₃	C₂×#108	1	1	yes	characteristic
83	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
84	C₄×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
85	C₂×C₄×C₁₆	—	43	1	no	—
86	C₂×#335	—	43	1	no	—
87	C₂×#335	D₄₃	1	1	yes	characteristic
88	#1371	—	43	4	no	—
89	C₂×C₄₃	#1371	1	4	yes	complemented
90	C₂×C₄₃	C₂×#335	1	1	yes	characteristic
91	C₂×C₄₃	C₂×#366	1	1	yes	characteristic
92	C₂×C₄₃	C₂×#368	1	1	yes	characteristic
93	C₂²×C₁₆	—	43	1	no	—
94	C₂²×C₁₆	—	43	1	no	—
95	C₂×C₄⋊C₈	—	2	1	no	—
96	C₂×C₄⋊C₈	—	86	1	no	—
97	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
98	C₄×C₁₆	—	43	2	no	—
99	C₄×C₁₆	—	43	2	no	—
100	#335	—	2	1	no	—
101	#335	—	43	2	no	—
102	#335	—	86	1	no	—
103	#335	C₂×D₄₃	1	2	yes	—
104	C₄₃	C₂×#1371	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₈	—	4	1	no	—
106	C₂²×C₈	—	172	1	no	—
107	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
108	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
109	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
110	C₂×C₁₆	—	43	4	no	—
111	C₂×C₁₆	—	43	2	no	—
112	C₂×C₁₆	—	43	2	no	—
113	C₂×C₁₆	—	86	2	no	—
114	C₄⋊C₈	—	2	2	no	—
115	C₄⋊C₈	—	4	1	no	—
116	C₄⋊C₈	—	86	2	no	—
117	C₄⋊C₈	—	172	1	no	—
118	C₄×C₈	Dic₈₆	1	1	yes	characteristic
119	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
120	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
121	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
122	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
123	C₂²×C₄	#10621882	1	1	yes	characteristic
124	C₂²×C₄	#10621885	1	1	yes	characteristic
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	4	2	no	—
127	C₂×C₈	—	8	2	no	—
128	C₂×C₈	—	344	2	no	—
129	C₂×C₈	—	172	2	no	—
130	C₂×C₈	C₈×D₄₃	1	2	yes	—
131	C₂×C₈	#10621872	1	2	yes	—
132	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
133	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
134	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
136	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
137	C₄²	#10621882	1	1	yes	characteristic
138	C₄²	#10621885	1	1	yes	characteristic
139	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
140	C₁₆	—	43	4	no	—
141	C₁₆	—	86	2	no	—
142	C₂³	#13063258	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	Dic₄₃⋊C₈	1	2	yes	—
145	C₂×C₄	#13063258	1	1	yes	characteristic
146	C₂×C₄	#13063258	1	1	yes	characteristic
147	C₂×C₄	#13063258	1	1	yes	characteristic
148	C₂×C₄	#13063260	1	2	yes	—
149	C₂×C₄	#13063266	1	2	yes	—
150	C₂×C₄	#13063271	1	2	yes	—
151	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
152	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
153	C₂×C₄	C₂×#10621885	1	1	yes	characteristic
154	C₈	—	2	1	no	—
155	C₈	—	2	1	no	—
156	C₈	—	8	2	no	—
157	C₈	—	344	2	no	—
158	C₈	Dic₄₃⋊C₈	1	2	yes	—
159	C₈	C₂×C₈×D₄₃	1	1	yes	characteristic
160	C₈	C₂×#10621872	1	1	yes	characteristic
161	C₂²	#14582651	1	2	yes	—
162	C₂²	#14582724	1	2	yes	—
163	C₂²	#14582728	1	2	yes	—
164	C₂²	C₂×#13063258	1	1	yes	characteristic
165	C₄	—	2	1	no	—
166	C₄	—	2	1	no	—
167	C₄	#14582651	1	2	yes	—
168	C₄	#14582724	1	2	yes	—
169	C₄	C₂×Dic₄₃⋊C₈	1	1	yes	characteristic
170	C₄	C₂×#13063260	1	1	yes	characteristic
171	C₄	C₂×#13063266	1	1	yes	characteristic
172	C₄	C₂×#13063271	1	1	yes	characteristic
173	C₂	#19132666	1	4	yes	direct product factor
174	C₂	C₂×#14582651	1	1	yes	characteristic
175	C₂	C₂×#14582724	1	1	yes	characteristic
176	C₂	C₂×#14582728	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#10621882
commutator	C₈×C₄₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle, prime radical	C₂³×C₄₃	#107
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	C₂×#1371
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. #19132666	C₂	direct (N × H)
18. C₂×C₄₃⋊C₁₆	C₈	semidirect
52. C₄₃⋊C₁₆	C₂×C₈	semidirect
89. C₂×C₄₃	#1371	semidirect
104. C₄₃	C₂×#1371	semidirect
173. C₂	#19132666	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄₃⋊C₁₆	2
C₂×#14582652	2
#19132666	2
C₂×C₄₃×#335	2
C₂×#1371	43

Subgroups — C2×#19132666 #25008174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19132666 #25008174