Subgroups — #19143241

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10621898	C₂	1	1	yes	maximal, characteristic
2	#14582959	C₂	1	2	yes	maximal, complemented
3	#14582957	C₂	1	2	yes	maximal, complemented
4	#14582956	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582954	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582954	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582924	C₂	1	2	yes	maximal, complemented
8	#14582864	C₂	1	2	yes	maximal
9	#14582851	C₂	1	1	yes	maximal, characteristic, complemented
10	#97×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10621898	C₂²	1	1	yes	characteristic
13	C₂×#10621872	C₂²	1	2	yes	—
14	C₂×C₈×D₄₃	C₂²	1	2	yes	—
15	C₄×Dic₈₆	C₄	1	2	yes	—
16	C₄×D₁₇₂	C₄	1	2	yes	—
17	C₄×C₂²⋊D₄₃	C₄	1	2	yes	—
18	C₄×C₂²⋊D₄₃	C₄	1	2	yes	—
19	#13063284	C₂²	1	1	yes	characteristic
20	#13063282	C₂²	1	1	yes	characteristic
21	#13063282	C₂²	1	1	yes	characteristic
22	C₄²×D₄₃	C₂²	1	1	yes	characteristic
23	C₄²×D₄₃	C₂²	1	1	yes	characteristic
24	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
25	Dic₄₃⋊C₈	C₂²	1	2	yes	—
26	Dic₄₃⋊C₈	C₂²	1	2	yes	—
27	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
28	(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
29	(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
30	#13063236	C₂²	1	1	yes	characteristic
31	#13063236	C₂²	1	1	yes	characteristic
32	#13063235	C₂²	1	2	yes	—
33	C₈×Dic₄₃	C₂²	1	2	yes	—
34	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
36	C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	#97×C₄₃	C₂²	1	1	yes	characteristic
38	#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
43	#10621898	—	2	4	no	—
44	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
47	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
49	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂×C₈×C₄₃	C₂³	1	2	yes	—
52	C₄²×C₄₃	C₂×C₄	1	2	yes	—
53	C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
56	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
57	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
58	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
59	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
60	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
61	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
62	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
63	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
64	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
67	#10621872	—	2	4	no	—
68	C₈×D₄₃	—	2	4	no	—
69	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₄₃	—	2	2	no	—
73	C₂×C₄×C₄₃	—	4	2	no	—
74	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂²⋊D₄₃	—	2	2	no	—
79	C₂²⋊D₄₃	—	2	2	no	—
80	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
82	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
83	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
84	D₁₇₂	—	2	2	no	—
85	C₄×D₄₃	—	2	2	no	—
86	C₄×D₄₃	—	4	2	no	—
87	C₄×D₄₃	—	4	2	no	—
88	C₄×D₄₃	#41	1	4	yes	—
89	Dic₈₆	—	2	2	no	—
90	C₈×C₄₃	—	2	2	no	—
91	C₈×C₄₃	—	2	2	no	—
92	C₄₃⋊C₈	—	2	2	no	—
93	C₄₃⋊C₈	—	2	2	no	—
94	C₂²×C₄₃	—	2	1	no	—
95	C₂²×C₄₃	—	2	2	no	—
96	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
97	C₂×D₄₃	—	2	2	no	—
98	C₂×D₄₃	—	2	1	no	—
99	C₂×D₄₃	—	2	2	no	—
100	C₂×D₄₃	#117	1	2	yes	—
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	2	no	—
103	C₄×C₄₃	—	2	2	no	—
104	C₄×C₄₃	C₂×#41	1	2	yes	—
105	Dic₄₃	—	2	1	no	—
106	Dic₄₃	—	2	2	no	—
107	Dic₄₃	—	2	2	no	—
108	Dic₄₃	#117	1	2	yes	—
109	#2923	—	43	1	no	maximal, Sylow
110	C₂×C₄₃	—	4	1	no	—
111	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
112	C₂×C₄₃	#568	1	2	yes	—
113	D₄₃	—	2	2	no	—
114	D₄₃	—	4	1	no	—
115	C₄×#41	—	43	1	no	—
116	#433	—	43	2	no	—
117	#433	—	43	2	no	—
118	#432	—	43	1	no	—
119	#432	—	43	1	no	—
120	#432	—	43	1	no	—
121	#432	D₄₃	1	1	yes	characteristic, complemented
122	#424	—	43	2	no	—
123	#408	—	43	2	no	—
124	C₄×M₁₆	—	43	1	no	—
125	C₂×#97	—	43	1	no	—
126	C₄₃	#2923	1	1	yes	characteristic, complemented, Sylow
127	C₂×#41	—	43	1	no	—
128	C₂×M₁₆	—	43	2	no	—
129	C₂²×C₈	—	43	2	no	—
130	C₄×Q₈	—	43	2	no	—
131	C₄×D₄	—	43	2	no	—
132	C₄×D₄	—	43	2	no	—
133	C₄×D₄	—	43	2	no	—
134	#117	—	43	1	no	—
135	#117	—	43	1	no	—
136	#117	—	43	1	no	—
137	C₂×C₄²	—	43	1	no	—
138	C₂×C₄²	—	43	1	no	—
139	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
140	C₄⋊C₈	—	43	2	no	—
141	C₄⋊C₈	—	43	2	no	—
142	C₄⋊C₈	—	43	2	no	—
143	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
144	C₂²⋊C₈	—	43	2	no	—
145	C₂²⋊C₈	—	43	2	no	—
146	C₂²⋊C₈	—	43	2	no	—
147	C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
148	#97	—	43	2	no	—
149	#97	—	43	1	no	—
150	#97	—	43	1	no	—
151	#97	C₂×D₄₃	1	1	yes	characteristic
152	#97	C₂×D₄₃	1	1	yes	characteristic
153	C₄×C₈	—	43	2	no	—
154	#41	—	86	4	no	—
155	C₂×Q₈	—	43	1	no	—
156	C₂×D₄	—	43	1	no	—
157	C₂×D₄	—	43	1	no	—
158	C₂×D₄	—	43	1	no	—
159	C₂²×C₄	—	43	1	no	—
160	C₂²×C₄	—	43	1	no	—
161	C₂²×C₄	—	43	2	no	—
162	C₂²×C₄	—	43	2	no	—
163	C₂²×C₄	C₄×D₄₃	1	2	yes	—
164	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
165	M₁₆	—	86	4	no	—
166	C₂×C₈	—	43	2	no	—
167	C₂×C₈	—	43	2	no	—
168	C₂×C₈	—	86	4	no	—
169	C₂×C₈	C₂²×D₄₃	1	2	yes	—
170	C₂×C₈	C₂²×D₄₃	1	2	yes	—
171	C₄⋊C₄	—	43	2	no	—
172	C₄⋊C₄	—	43	2	no	—
173	C₄⋊C₄	—	43	2	no	—
174	C₂²⋊C₄	—	43	2	no	—
175	C₂²⋊C₄	—	43	2	no	—
176	C₂²⋊C₄	—	43	2	no	—
177	C₄²	—	43	2	no	—
178	C₄²	—	43	2	no	—
179	C₄²	—	43	1	no	—
180	C₄²	—	43	1	no	—
181	C₄²	C₄×D₄₃	1	2	yes	—
182	C₄²	C₂²×D₄₃	1	1	yes	characteristic
183	C₄²	C₂²×D₄₃	1	1	yes	characteristic
184	C₂³	—	43	1	no	—
185	C₂³	—	43	1	no	—
186	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
187	Q₈	—	86	2	no	—
188	D₄	—	86	2	no	—
189	D₄	—	86	2	no	—
190	D₄	—	86	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	43	1	no	—
194	C₂×C₄	—	43	4	no	—
195	C₂×C₄	—	43	2	no	—
196	C₂×C₄	—	43	2	no	—
197	C₂×C₄	—	43	1	no	—
198	C₂×C₄	—	86	2	no	—
199	C₂×C₄	—	172	2	no	—
200	C₂×C₄	—	172	2	no	—
201	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
202	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
203	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
204	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
205	C₈	—	2	2	no	—
206	C₈	—	2	2	no	—
207	C₈	—	86	2	no	—
208	C₈	—	86	2	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	43	2	no	—
212	C₂²	—	86	2	no	—
213	C₂²	—	86	1	no	—
214	C₂²	—	86	2	no	—
215	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	43	2	no	—
220	C₄	—	86	1	no	—
221	C₄	—	86	2	no	—
222	C₄	—	86	2	no	—
223	C₄	#41×D₄₃	1	2	yes	—
224	C₂	—	4	1	no	—
225	C₂	—	86	2	no	—
226	C₂	—	172	1	no	—
227	C₂	#117×D₄₃	1	1	yes	characteristic
228	C₂	#14583665	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#432	C₂
hypercenter	#432	D₄₃
hypocenter	C₄₃	#2923
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
2. #14582959	C₂	semidirect
3. #14582957	C₂	semidirect
4. #14582956	C₂	semidirect
5. #14582954	C₂	semidirect
6. #14582954	C₂	semidirect
7. #14582924	C₂	semidirect
9. #14582851	C₂	semidirect
10. #97×D₄₃	C₂	semidirect
11. C₄₃×#432	C₂	semidirect
121. #432	D₄₃	semidirect
126. C₄₃	#2923	semidirect