Subgroups — C₄×#14582652 #24987782

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
2	C₂×#14582652	C₂	1	2	yes	maximal
3	#19132430	C₂	1	2	yes	maximal
4	C₄²×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
6	C₂×C₄×C₄₃⋊C₈	—	2	2	no	—
7	#14582654	—	2	2	no	—
8	#14582652	C₄	1	8	yes	direct product factor
9	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄³×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄₃⋊C₈	—	2	4	no	—
15	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
16	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	8	yes	—
17	C₄×C₄₃⋊C₈	—	4	4	no	—
18	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
25	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
26	C₄×C₈×C₄₃	—	2	4	no	—
27	C₄×C₈×C₄₃	—	2	2	no	—
28	C₄×C₈×C₄₃	C₈	1	8	yes	complemented
29	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₄₃	—	2	2	no	—
36	C₂×C₈×C₄₃	—	2	2	no	—
37	C₂×C₈×C₄₃	—	2	2	no	—
38	C₂×C₈×C₄₃	C₄²	1	2	yes	—
39	C₂×C₈×C₄₃	C₄²	1	2	yes	—
40	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
41	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
42	C₄²×C₄₃	—	2	4	no	—
43	C₄²×C₄₃	—	2	2	no	—
44	C₄²×C₄₃	C₂×C₈	1	4	yes	—
45	C₄²×C₄₃	M₁₆	1	4	yes	—
46	C₄²×C₄₃	D₈	1	2	yes	—
47	C₄²×C₄₃	Q₁₆	1	2	yes	—
48	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
49	C₄²×C₄₃	#41	1	2	yes	—
50	C₂×C₄₃⋊C₈	—	2	8	no	—
51	C₂×C₄₃⋊C₈	—	4	4	no	—
52	C₂×C₄₃⋊C₈	—	4	4	no	—
53	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	—	2	2	no	—
56	C₂×C₄×C₄₃	—	2	2	no	—
57	C₂×C₄×C₄₃	C₄⋊C₈	1	4	yes	—
58	C₂×C₄×C₄₃	C₄⋊C₈	1	4	yes	—
59	C₂×C₄×C₄₃	#107	1	4	yes	—
60	C₂×C₄×C₄₃	#108	1	4	yes	—
61	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
62	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
64	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
65	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
66	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
67	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
69	C₂×C₄×C₄₃	#135	1	2	yes	—
70	C₈×C₄₃	—	2	2	no	—
71	C₈×C₄₃	—	2	4	no	—
72	C₈×C₄₃	C₄×C₈	1	4	yes	complemented
73	C₄₃⋊C₈	—	4	8	no	—
74	C₄×#335	—	43	1	no	maximal, Sylow
75	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄₃	C₂×C₄⋊C₈	1	2	yes	—
77	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
78	C₂²×C₄₃	#427	1	1	yes	characteristic
79	C₂²×C₄₃	C₂×#108	1	2	yes	—
80	C₄×C₄₃	—	2	4	no	—
81	C₄×C₄₃	—	2	2	no	—
82	C₄×C₄₃	#335	1	8	yes	complemented
83	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
84	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
85	C₄×C₄₃	#431	1	2	yes	—
86	C₄×C₄₃	C₄×D₈	1	2	yes	—
87	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
88	C₄×C₄⋊C₈	—	43	2	no	—
89	C₄²×C₈	D₄₃	1	1	yes	characteristic
90	C₂×#335	—	43	2	no	—
91	#1277	—	43	2	no	—
92	C₂×C₄₃	C₂×#335	1	2	yes	—
93	C₂×C₄₃	#1564	1	2	yes	—
94	C₂×C₄₃	C₄×C₄⋊C₈	1	1	yes	characteristic
95	C₂×C₄₃	C₄×#107	1	1	yes	characteristic
96	C₂×C₄₃	C₄×#108	1	1	yes	characteristic
97	C₂×C₄⋊C₈	—	43	4	no	—
98	C₂×C₄×C₈	—	86	2	no	—
99	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
100	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
101	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
102	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
103	C₄³	C₂×D₄₃	1	1	yes	characteristic
104	#336	—	86	2	no	—
105	#335	—	43	8	no	—
106	C₄₃	C₄×#335	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₈	—	86	4	no	—
108	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
109	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
110	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
111	C₂×C₄²	Dic₈₆	1	2	yes	—
112	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
113	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
114	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
115	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
116	C₄⋊C₈	—	43	8	no	—
117	C₄⋊C₈	—	86	4	no	—
118	C₄×C₈	—	2	4	no	—
119	C₄×C₈	—	2	2	no	—
120	C₄×C₈	—	172	4	no	—
121	C₄×C₈	C₄₃⋊C₈	1	8	yes	complemented
122	C₄×C₈	C₄×D₄₃	1	4	yes	—
123	C₂²×C₄	C₄⋊Dic₄₃	1	2	yes	—
124	C₂²×C₄	C₄⋊Dic₄₃	1	2	yes	—
125	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
126	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
127	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	86	8	no	—
132	C₂×C₈	—	172	4	no	—
133	C₂×C₈	—	172	4	no	—
134	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
135	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
136	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
137	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
138	C₄²	—	2	4	no	—
139	C₄²	—	2	2	no	—
140	C₄²	D₃₄₄	1	2	yes	—
141	C₄²	Dic₁₇₂	1	2	yes	—
142	C₄²	C₂×C₄₃⋊C₈	1	4	yes	—
143	C₄²	#10621877	1	4	yes	—
144	C₄²	C₂×C₄×D₄₃	1	2	yes	—
145	C₄²	#10621898	1	2	yes	—
146	C₂³	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	C₄⋊(C₄₃⋊C₈)	1	4	yes	—
151	C₂×C₄	C₄⋊(C₄₃⋊C₈)	1	4	yes	—
152	C₂×C₄	#13063259	1	4	yes	—
153	C₂×C₄	#13063261	1	4	yes	—
154	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
155	C₂×C₄	#13063284	1	1	yes	characteristic
156	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
157	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
158	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
159	C₂×C₄	C₂×#10621877	1	2	yes	—
160	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
161	C₂×C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
162	C₂×C₄	#13063347	1	2	yes	—
163	C₈	—	2	2	no	—
164	C₈	—	2	4	no	—
165	C₈	—	172	8	no	—
166	C₈	C₄×C₄₃⋊C₈	1	4	yes	complemented
167	C₂²	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
168	C₂²	C₂×C₄⋊(C₄₃⋊C₈)	1	2	yes	—
169	C₂²	C₂×#13063259	1	1	yes	characteristic
170	C₂²	#14582937	1	1	yes	characteristic
171	C₂²	C₂×#13063261	1	2	yes	—
172	C₄	—	2	2	no	—
173	C₄	—	2	4	no	—
174	C₄	#14582652	1	8	yes	direct product factor
175	C₄	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
176	C₄	C₄×#10621877	1	1	yes	characteristic
177	C₄	#14582952	1	2	yes	—
178	C₄	C₄×D₃₄₄	1	2	yes	—
179	C₄	C₄×Dic₁₇₂	1	2	yes	—
180	C₂	C₂×#14582652	1	2	yes	—
181	C₂	#19133343	1	2	yes	—
182	C₂	C₄×C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
183	C₂	C₄×#13063259	1	1	yes	characteristic
184	C₂	C₄×#13063261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	D₁₇₂
commutator	C₄×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄²×C₈×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄²×C₈	D₄₃
hypocenter	C₄₃	C₄×#335
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
8. #14582652	C₄	direct (N × H)
28. C₄×C₈×C₄₃	C₈	semidirect
72. C₈×C₄₃	C₄×C₈	semidirect
82. C₄×C₄₃	#335	semidirect
106. C₄₃	C₄×#335	semidirect
121. C₄×C₈	C₄₃⋊C₈	semidirect
166. C₈	C₄×C₄₃⋊C₈	semidirect
174. C₄	#14582652	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582652	2
#19132430	2
C₄²×C₈×C₄₃	2
C₄×#335	43

Subgroups — C4×#14582652 #24987782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14582652 #24987782