Subgroups — #19143537

Order 5504.

356 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583453	C₂	1	1	yes	maximal, characteristic
2	#14583030	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583029	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583029	C₂	1	2	yes	maximal, complemented
5	#14583028	C₂	1	2	yes	maximal, complemented
6	#14583023	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582924	C₂	1	2	yes	maximal
8	C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
9	#14582853	C₂	1	2	yes	maximal
10	C₄×#10621872	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10621872	C₂²	1	1	yes	characteristic
13	C₂×#10621872	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₄₃	C₂²	1	2	yes	—
15	#13063324	C₄	1	1	yes	characteristic
16	#13063323	C₄	1	1	yes	characteristic
17	#13063315	C₄	1	2	yes	—
18	#13063305	C₄	1	1	yes	characteristic
19	#13063303	C₄	1	2	yes	—
20	#13063301	C₄	1	1	yes	characteristic
21	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
22	C₄×Dic₈₆	C₂²	1	2	yes	—
23	#13063282	C₂²	1	2	yes	—
24	C₄²×D₄₃	C₂²	1	1	yes	characteristic
25	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
27	Dic₄₃⋊C₈	C₂²	1	2	yes	—
28	Dic₄₃⋊C₈	C₂²	1	2	yes	—
29	Dic₄₃⋊C₈	C₂²	1	2	yes	—
30	#13063236	C₂²	1	2	yes	—
31	#13063235	C₂²	1	1	yes	characteristic
32	#13063235	C₂²	1	1	yes	characteristic
33	#13063235	C₂²	1	2	yes	—
34	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₈×Dic₄₃	C₂²	1	2	yes	—
36	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
39	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₄₃	C₂²	1	2	yes	—
41	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
45	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
47	C₂×C₈×C₄₃	C₂³	1	2	yes	—
48	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
51	C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×C₄₃	C₂³	1	1	yes	characteristic
53	C₄²×C₄₃	C₂³	1	2	yes	—
54	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
55	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
56	C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
58	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
59	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
60	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
61	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
62	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
63	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₄₃	C₂³	1	2	yes	—
66	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
69	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	#10621872	—	2	2	no	—
71	#10621872	Q₈	1	4	yes	complemented
72	C₈×D₄₃	—	2	4	no	—
73	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
74	Q₈×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
80	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
83	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
84	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₄×D₄₃	—	2	2	no	—
86	C₄×D₄₃	—	4	1	no	—
87	C₄×D₄₃	C₂×Q₈	1	2	yes	—
88	C₄×D₄₃	#41	1	2	yes	—
89	Dic₈₆	—	2	2	no	—
90	Dic₈₆	—	4	2	no	—
91	C₈×C₄₃	—	2	2	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	C₂×Q₈	1	2	yes	—
94	C₄₃⋊C₈	—	2	2	no	—
95	C₄₃⋊C₈	—	2	1	no	—
96	C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
97	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
98	C₂×D₄₃	—	2	1	no	—
99	C₂×D₄₃	—	2	1	no	—
100	C₂×D₄₃	C₄×Q₈	1	2	yes	—
101	C₄×C₄₃	—	2	2	no	—
102	C₄×C₄₃	—	2	2	no	—
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	#131	1	2	yes	—
105	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
107	Dic₄₃	—	2	2	no	—
108	Dic₄₃	—	2	1	no	—
109	Dic₄₃	—	2	1	no	—
110	Dic₄₃	—	2	2	no	—
111	Dic₄₃	C₄×Q₈	1	2	yes	—
112	#2962	—	43	1	no	maximal, Sylow
113	C₂×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
114	C₂×C₄₃	C₂×#131	1	1	yes	characteristic
115	C₂×C₄₃	#568	1	1	yes	characteristic
116	D₄₃	—	2	2	no	—
117	#533	—	43	1	no	—
118	#446	—	43	1	no	—
119	#446	—	43	2	no	—
120	#446	—	43	1	no	—
121	#446	—	43	2	no	—
122	C₈×Q₈	—	43	1	no	—
123	C₈×Q₈	D₄₃	1	1	yes	characteristic, complemented
124	#424	—	43	2	no	—
125	C₂×C₄⋊C₈	—	43	1	no	—
126	#405	—	43	2	no	—
127	C₄×M₁₆	—	43	1	no	—
128	C₄₃	#2962	1	1	yes	characteristic, complemented, Sylow
129	C₂×M₁₆	—	43	1	no	—
130	C₂×M₁₆	—	43	1	no	—
131	C₂²×C₈	—	43	2	no	—
132	C₄⋊Q₈	—	43	1	no	—
133	C₄⋊Q₈	—	43	1	no	—
134	#125	—	43	2	no	—
135	C₂²⋊Q₈	—	43	1	no	—
136	C₂²⋊Q₈	—	43	2	no	—
137	C₂²⋊Q₈	—	43	1	no	—
138	C₄×Q₈	—	43	1	no	—
139	C₄×Q₈	—	43	2	no	—
140	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
141	#117	—	43	2	no	—
142	C₂×C₄²	—	43	1	no	—
143	C₄⋊C₈	—	43	2	no	—
144	C₄⋊C₈	—	43	2	no	—
145	C₄⋊C₈	—	43	2	no	—
146	C₄⋊C₈	—	43	1	no	—
147	C₄⋊C₈	—	43	2	no	—
148	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
149	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
150	#97	—	43	1	no	—
151	#97	—	43	1	no	—
152	#97	—	43	2	no	—
153	#97	—	43	2	no	—
154	C₄×C₈	—	43	2	no	—
155	C₄×C₈	—	43	1	no	—
156	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
157	C₄×C₈	C₂×D₄₃	1	2	yes	—
158	C₂×Q₈	—	43	1	no	—
159	C₂×Q₈	—	43	2	no	—
160	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
161	C₂²×C₄	—	43	1	no	—
162	C₂²×C₄	—	43	1	no	—
163	C₂²×C₄	—	43	1	no	—
164	M₁₆	—	43	4	no	—
165	M₁₆	—	86	2	no	—
166	C₂×C₈	—	43	1	no	—
167	C₂×C₈	—	43	1	no	—
168	C₂×C₈	—	43	2	no	—
169	C₂×C₈	—	86	4	no	—
170	C₂×C₈	C₂²×D₄₃	1	2	yes	—
171	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
172	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
173	C₄⋊C₄	—	43	2	no	—
174	C₄⋊C₄	—	43	2	no	—
175	C₄⋊C₄	—	43	2	no	—
176	C₄⋊C₄	—	43	2	no	—
177	C₄⋊C₄	—	43	2	no	—
178	C₄⋊C₄	—	43	2	no	—
179	C₄⋊C₄	—	43	1	no	—
180	C₄⋊C₄	C₄×D₄₃	1	2	yes	—
181	C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
182	C₂²⋊C₄	—	43	2	no	—
183	C₂²⋊C₄	—	43	2	no	—
184	C₄²	—	43	1	no	—
185	C₄²	—	43	1	no	—
186	C₄²	—	43	2	no	—
187	C₄²	—	43	1	no	—
188	C₄²	C₂²×D₄₃	1	1	yes	characteristic
189	C₄²	C₂²×D₄₃	1	2	yes	—
190	C₂³	—	43	1	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	86	2	no	—
193	Q₈	—	172	2	no	—
194	C₂×C₄	—	43	1	no	—
195	C₂×C₄	—	43	2	no	—
196	C₂×C₄	—	43	2	no	—
197	C₂×C₄	—	43	1	no	—
198	C₂×C₄	—	43	1	no	—
199	C₂×C₄	—	43	2	no	—
200	C₂×C₄	—	43	2	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	—	172	1	no	—
203	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
204	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
205	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
206	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
207	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
208	C₈	—	2	2	no	—
209	C₈	—	2	1	no	—
210	C₈	—	43	2	no	—
211	C₈	—	86	2	no	—
212	C₈	—	86	1	no	—
213	C₈	Q₈×D₄₃	1	2	yes	—
214	C₂²	—	43	2	no	—
215	C₂²	—	86	1	no	—
216	C₂²	—	86	1	no	—
217	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
218	C₄	—	2	2	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	43	2	no	—
222	C₄	—	86	1	no	—
223	C₄	—	86	2	no	—
224	C₄	—	86	1	no	—
225	C₄	—	86	2	no	—
226	C₄	#13063331	1	2	yes	—
227	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
228	C₄	#41×D₄₃	1	1	yes	characteristic
229	C₂	—	86	2	no	—
230	C₂	C₄×Q₈×D₄₃	1	1	yes	characteristic
231	C₂	C₂×#13063331	1	1	yes	characteristic
232	C₂	#14583664	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₈×Q₈×C₄₃	C₂
hypercenter	C₈×Q₈	D₄₃
hypocenter	C₄₃	#2962
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. #14583030	C₂	semidirect
3. #14583029	C₂	semidirect
4. #14583029	C₂	semidirect
5. #14583028	C₂	semidirect
6. #14583023	C₂	semidirect
11. C₈×Q₈×C₄₃	C₂	semidirect
71. #10621872	Q₈	semidirect
123. C₈×Q₈	D₄₃	semidirect
128. C₄₃	#2962	semidirect