Subgroups — C₄×#13063323 #19137163

Order 5504.

588 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063323	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#14582806	C₂	1	1	yes	maximal, characteristic
4	#14582804	C₂	1	1	yes	maximal, characteristic
5	#14582794	C₂	1	4	yes	maximal
6	#14582768	C₂	1	1	yes	maximal, characteristic
7	C₄×Dic₄₃⋊C₄	C₂	1	4	yes	maximal
8	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
11	#13063323	C₄	1	8	yes	direct product factor
12	C₄×Dic₈₆	—	2	4	no	—
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
15	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
16	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
18	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
20	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
22	C₄₃⋊#95	C₂²	1	4	yes	—
23	C₄₃⋊#95	C₂²	1	4	yes	—
24	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₄×Q₈×C₄₃	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
29	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×Q₈×C₄₃	—	2	2	no	—
31	C₂×Q₈×C₄₃	—	2	2	no	—
32	C₂×Q₈×C₄₃	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂²×Dic₄₃	C₂³	1	2	yes	—
39	C₂²×Dic₄₃	C₂³	1	2	yes	—
40	C₂²×Dic₄₃	C₂³	1	2	yes	—
41	C₂²×Dic₄₃	C₂³	1	2	yes	—
42	C₂×Dic₈₆	—	2	2	no	—
43	C₂×Dic₈₆	—	2	2	no	—
44	C₂×Dic₈₆	C₂×C₄	1	4	yes	—
45	C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₄²×C₄₃	—	2	4	no	—
48	C₄²×C₄₃	D₄	1	4	yes	—
49	C₄⋊Dic₄₃	—	2	2	no	—
50	Dic₄₃⋊C₄	—	2	4	no	—
51	Dic₄₃⋊C₄	—	2	8	no	—
52	Dic₄₃⋊C₄	C₂×C₄	1	16	yes	—
53	C₄×Dic₄₃	—	2	4	no	—
54	C₄×Dic₄₃	—	2	2	no	—
55	C₄×Dic₄₃	—	2	4	no	—
56	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
57	C₄×Dic₄₃	Q₈	1	8	yes	complemented
58	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
59	Q₈×C₄₃	—	2	8	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	2	no	—
63	C₂×C₄×C₄₃	—	2	2	no	—
64	C₂×C₄×C₄₃	—	2	4	no	—
65	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
66	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
67	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
71	C₂×C₄×C₄₃	#41	1	2	yes	—
72	C₂×Dic₄₃	—	2	2	no	—
73	C₂×Dic₄₃	—	2	2	no	—
74	C₂×Dic₄₃	—	2	2	no	—
75	C₂×Dic₄₃	—	2	2	no	—
76	C₂×Dic₄₃	—	2	2	no	—
77	C₂×Dic₄₃	—	2	4	no	—
78	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
79	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
80	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
81	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
82	C₂×Dic₄₃	#41	1	4	yes	—
83	Dic₈₆	—	2	8	no	—
84	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
85	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
86	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
87	C₂²×C₄₃	C₂×#41	1	2	yes	—
88	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
89	C₄×C₄₃	—	2	4	no	—
90	C₄×C₄₃	—	2	2	no	—
91	C₄×C₄₃	—	4	2	no	—
92	C₄×C₄₃	C₄×D₄	1	4	yes	—
93	C₄×C₄₃	C₄⋊Q₈	1	4	yes	complemented
94	Dic₄₃	—	2	4	no	—
95	Dic₄₃	—	2	4	no	—
96	Dic₄₃	—	4	2	no	—
97	Dic₄₃	C₄×Q₈	1	8	yes	complemented
98	C₄×C₄⋊Q₈	—	43	1	no	maximal, Sylow
99	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
100	C₂×C₄₃	C₂×C₄×Q₈	1	2	yes	—
101	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
102	C₂×C₄₃	#532	1	1	yes	characteristic
103	C₂×C₄₃	#533	1	2	yes	—
104	C₂×C₄⋊Q₈	—	43	1	no	—
105	C₂×C₄×Q₈	—	43	1	no	—
106	C₂×C₄×Q₈	D₄₃	1	1	yes	characteristic
107	#391	—	43	1	no	—
108	#391	—	43	1	no	—
109	#389	—	43	4	no	—
110	#384	—	43	1	no	—
111	C₄×C₄⋊C₄	—	43	4	no	—
112	C₄³	—	43	1	no	—
113	C₄₃	C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
114	C₂²×Q₈	—	43	1	no	—
115	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
116	C₄⋊Q₈	—	43	8	no	—
117	C₄×Q₈	—	2	4	no	—
118	C₄×Q₈	—	86	4	no	—
119	C₂×C₄⋊C₄	—	43	4	no	—
120	C₂×C₄⋊C₄	—	43	2	no	—
121	C₂×C₄⋊C₄	—	43	1	no	—
122	C₂×C₄⋊C₄	—	43	4	no	—
123	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
124	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
125	C₂×C₄²	—	43	1	no	—
126	C₂×C₄²	—	43	2	no	—
127	C₂×C₄²	—	43	2	no	—
128	C₂×C₄²	—	43	1	no	—
129	C₂×C₄²	—	43	2	no	—
130	C₂×C₄²	C₂×D₄₃	1	2	yes	—
131	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
132	#95	—	43	4	no	—
133	#95	—	43	4	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	2	2	no	—
136	C₂×Q₈	—	43	4	no	—
137	C₂×Q₈	—	86	2	no	—
138	C₂×Q₈	—	86	2	no	—
139	C₂×Q₈	C₄×D₄₃	1	4	yes	—
140	C₂²×C₄	—	43	2	no	—
141	C₂²×C₄	—	43	2	no	—
142	C₂²×C₄	—	43	2	no	—
143	C₂²×C₄	—	43	2	no	—
144	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
145	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
146	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
147	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
148	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	2	2	no	—
151	C₄⋊C₄	—	43	16	no	—
152	C₄⋊C₄	—	86	8	no	—
153	C₄⋊C₄	—	86	4	no	—
154	C₄⋊C₄	—	86	2	no	—
155	C₄²	—	2	4	no	—
156	C₄²	—	43	4	no	—
157	C₄²	—	43	8	no	—
158	C₄²	—	86	4	no	—
159	C₄²	—	86	2	no	—
160	C₄²	—	86	4	no	—
161	C₄²	C₂²⋊D₄₃	1	4	yes	—
162	C₂³	C₂³×D₄₃	1	1	yes	characteristic
163	Q₈	—	2	8	no	—
164	Q₈	—	86	8	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	43	4	no	—
171	C₂×C₄	—	43	4	no	—
172	C₂×C₄	—	43	4	no	—
173	C₂×C₄	—	43	4	no	—
174	C₂×C₄	—	43	4	no	—
175	C₂×C₄	—	86	2	no	—
176	C₂×C₄	—	86	2	no	—
177	C₂×C₄	—	86	2	no	—
178	C₂×C₄	—	86	2	no	—
179	C₂×C₄	—	86	2	no	—
180	C₂×C₄	—	86	4	no	—
181	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
182	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
183	C₂×C₄	#10621898	1	2	yes	—
184	C₂×C₄	Q₈×D₄₃	1	4	yes	—
185	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
186	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
187	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
188	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
189	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
190	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
191	C₂²	#41×D₄₃	1	2	yes	—
192	C₂²	C₂×#10621898	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	2	2	no	—
195	C₄	—	4	2	no	—
196	C₄	—	43	8	no	—
197	C₄	—	86	4	no	—
198	C₄	—	86	4	no	—
199	C₄	—	172	2	no	—
200	C₄	C₄×C₂²⋊D₄₃	1	4	yes	—
201	C₄	#13063323	1	4	yes	direct product factor
202	C₂	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
203	C₂	C₄×Q₈×D₄₃	1	2	yes	—
204	C₂	C₂×#13063323	1	1	yes	characteristic
205	C₂	#14583445	1	1	yes	characteristic
206	C₂	#14583453	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₂×C₄×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₃
hypocenter	C₄₃	C₄×C₄⋊Q₈
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
11. #13063323	C₄	direct (N × H)
57. C₄×Dic₄₃	Q₈	semidirect
93. C₄×C₄₃	C₄⋊Q₈	semidirect
97. Dic₄₃	C₄×Q₈	semidirect
113. C₄₃	C₄×C₄⋊Q₈	semidirect
201. C₄	#13063323	direct (N × H)

Subgroups — C4×#13063323 #19137163

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063323 #19137163