Subgroups — #333×Dic₄₃ #24987543

Order 11008.

540 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₄₃	C₂	1	2	yes	maximal
3	C₂×#14582648	C₂	1	1	yes	maximal, characteristic
4	#19132479	C₂	1	2	yes	maximal
5	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₄₃	C₄	1	2	yes	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₈×Dic₄₃	—	2	2	no	—
9	#14582806	C₄	1	2	yes	—
10	#14582798	—	2	2	no	—
11	#14582769	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₄₃	—	2	2	no	—
13	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
14	#14582653	—	2	2	no	—
15	#14582648	C₄	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₄₃×#333	C₄	1	4	yes	complemented
19	C₂²×C₄₃⋊C₈	—	2	2	no	—
20	Q₈×Dic₄₃	—	4	4	no	—
21	C₂×C₄⋊Dic₄₃	—	2	2	no	—
22	C₂×C₄⋊Dic₄₃	—	2	2	no	—
23	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₄₃	—	2	2	no	—
25	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
28	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
29	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
31	C₈×Dic₄₃	—	4	4	no	—
32	C₄₃⋊#95	—	2	4	no	—
33	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₄₃	—	2	2	no	—
35	C₄⋊Q₈×C₄₃	—	2	2	no	—
36	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
37	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₃	—	2	2	no	—
41	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
42	C₂×Q₈×C₄₃	—	2	2	no	—
43	C₂×Q₈×C₄₃	—	4	2	no	—
44	C₂×Q₈×C₄₃	—	4	2	no	—
45	C₂×Q₈×C₄₃	C₄²	1	4	yes	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
49	C₂²×Dic₄₃	—	2	2	no	—
50	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
52	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₄₃	—	2	4	no	—
54	C₂×C₈×C₄₃	—	4	2	no	—
55	C₂×C₈×C₄₃	—	4	2	no	—
56	C₄⋊C₄×C₄₃	—	2	4	no	—
57	C₄⋊C₄×C₄₃	—	2	4	no	—
58	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₄₃	#41	1	2	yes	—
61	C₄⋊Dic₄₃	—	4	4	no	—
62	C₄⋊Dic₄₃	—	4	2	no	—
63	C₄⋊Dic₄₃	—	4	2	no	—
64	C₄⋊Dic₄₃	—	4	2	no	—
65	C₄×Dic₄₃	—	2	2	no	—
66	C₄×Dic₄₃	—	2	2	no	—
67	C₄×Dic₄₃	—	2	2	no	—
68	C₄×Dic₄₃	—	4	1	no	—
69	C₄×Dic₄₃	—	4	4	no	—
70	C₄×Dic₄₃	SD₁₆	1	4	yes	—
71	C₄×Dic₄₃	Q₁₆	1	4	yes	—
72	C₂×C₄₃⋊C₈	—	2	4	no	—
73	C₂×C₄₃⋊C₈	—	4	2	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₄₃	—	4	4	no	—
77	Q₈×C₄₃	—	4	4	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	—	2	4	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₄₃	#135	1	2	yes	—
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₂×Dic₄₃	—	2	2	no	—
92	C₂×Dic₄₃	—	2	2	no	—
93	C₂×Dic₄₃	—	2	1	no	—
94	C₂×Dic₄₃	—	2	2	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	C₂×Dic₄₃	—	4	4	no	—
97	C₂×Dic₄₃	#100	1	2	yes	—
98	C₂×Dic₄₃	#103	1	4	yes	—
99	C₂×Dic₄₃	#103	1	4	yes	—
100	C₈×C₄₃	—	4	4	no	—
101	C₄₃⋊C₈	—	4	4	no	—
102	C₄×#333	—	43	1	no	maximal, Sylow
103	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
105	C₂²×C₄₃	#413	1	1	yes	characteristic
106	C₂²×C₄₃	C₂×#103	1	2	yes	—
107	C₂²×C₄₃	#416	1	2	yes	—
108	C₄×C₄₃	—	2	1	no	—
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	—	4	4	no	—
111	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
112	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
113	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
114	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
115	Dic₄₃	—	2	4	no	—
116	Dic₄₃	—	4	1	no	—
117	Dic₄₃	—	8	2	no	—
118	Dic₄₃	#333	1	4	yes	direct product factor
119	C₄×C₄⋊Q₈	—	43	1	no	—
120	C₄×C₄⋊C₈	—	43	2	no	—
121	C₂×#333	—	43	1	no	—
122	C₂×#333	D₄₃	1	1	yes	characteristic
123	#1296	—	43	2	no	—
124	C₂×C₄₃	C₂×#333	1	1	yes	characteristic
125	C₂×C₄₃	#1542	1	2	yes	—
126	C₂×C₄₃	#1543	1	1	yes	characteristic
127	C₂×C₄₃	C₄×#100	1	1	yes	characteristic
128	C₂×C₄₃	C₄×#103	1	2	yes	—
129	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
130	C₂×C₄×Q₈	—	43	2	no	—
131	C₂×C₄⋊C₈	—	43	2	no	—
132	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
133	C₂×C₄×C₈	—	86	2	no	—
134	#391	—	43	2	no	—
135	#389	—	86	2	no	—
136	#384	—	43	1	no	—
137	C₄×C₄⋊C₄	—	86	2	no	—
138	C₄³	—	43	1	no	—
139	#336	—	86	2	no	—
140	#333	—	43	4	no	—
141	#333	Dic₄₃	1	4	yes	direct product factor
142	C₄₃	C₄×#333	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	C₄×D₄₃	1	2	yes	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	86	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
148	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
149	C₄×Q₈	—	172	4	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	43	2	no	—
152	C₂×C₄⋊C₄	—	86	2	no	—
153	C₂×C₄⋊C₄	—	86	2	no	—
154	C₂×C₄²	—	43	2	no	—
155	C₂×C₄²	—	43	1	no	—
156	C₂×C₄²	—	43	2	no	—
157	C₂×C₄²	—	43	1	no	—
158	C₂×C₄²	—	86	2	no	—
159	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	43	4	no	—
162	C₄⋊C₈	—	86	2	no	—
163	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	—
164	C₄×C₈	—	172	4	no	—
165	#95	—	86	4	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	C₄×Dic₄₃	1	4	yes	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	43	1	no	—
172	C₂²×C₄	—	43	2	no	—
173	C₂²×C₄	—	43	1	no	—
174	C₂²×C₄	—	86	2	no	—
175	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₄₃	1	2	yes	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	2	no	—
180	C₂×C₈	—	86	4	no	—
181	C₂×C₈	—	172	2	no	—
182	C₂×C₈	—	172	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	172	2	no	—
186	C₄⋊C₄	—	172	4	no	—
187	C₄⋊C₄	—	172	2	no	—
188	C₄⋊C₄	—	172	2	no	—
189	C₄²	—	43	4	no	—
190	C₄²	—	43	4	no	—
191	C₄²	—	86	2	no	—
192	C₄²	—	86	2	no	—
193	C₄²	—	86	2	no	—
194	C₄²	—	172	1	no	—
195	C₄²	—	172	4	no	—
196	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
197	C₄²	#10621900	1	2	yes	—
198	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
199	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
200	Q₈	—	4	4	no	—
201	Q₈	—	4	4	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	43	2	no	—
208	C₂×C₄	—	43	4	no	—
209	C₂×C₄	—	43	4	no	—
210	C₂×C₄	—	86	2	no	—
211	C₂×C₄	—	86	2	no	—
212	C₂×C₄	—	86	1	no	—
213	C₂×C₄	—	86	2	no	—
214	C₂×C₄	—	172	2	no	—
215	C₂×C₄	—	172	4	no	—
216	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
217	C₂×C₄	#13063281	1	1	yes	characteristic
218	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
219	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
220	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
221	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
222	C₂×C₄	#13063346	1	2	yes	—
223	C₂×C₄	#13063348	1	2	yes	—
224	C₈	—	4	4	no	—
225	C₈	—	172	4	no	—
226	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
227	C₂²	#100×D₄₃	1	1	yes	characteristic
228	C₂²	#14582880	1	1	yes	characteristic
229	C₂²	#103×D₄₃	1	2	yes	—
230	C₂²	#14582894	1	2	yes	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	4	4	no	—
234	C₄	—	43	4	no	—
235	C₄	—	86	4	no	—
236	C₄	—	344	2	no	—
237	C₄	—	172	1	no	—
238	C₄	#14582984	1	2	yes	—
239	C₄	SD₁₆×Dic₄₃	1	2	yes	—
240	C₄	#14582991	1	2	yes	—
241	C₄	Q₁₆×Dic₄₃	1	2	yes	—
242	C₂	#333×D₄₃	1	1	yes	characteristic
243	C₂	#19133249	1	2	yes	—
244	C₂	#19133256	1	1	yes	characteristic
245	C₂	#100×Dic₄₃	1	1	yes	characteristic
246	C₂	#103×Dic₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#333	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#333	D₄₃
hypocenter	C₄₃	C₄×#333
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
15. #14582648	C₄	semidirect
18. C₄₃×#333	C₄	semidirect
118. Dic₄₃	#333	direct (N × H)
141. #333	Dic₄₃	direct (N × H)
142. C₄₃	C₄×#333	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×Dic₄₃	2
C₄⋊C₈×Dic₄₃	2
C₂×#14582648	2
#19132479	2
C₂×C₄₃×#333	2
C₄×#333	43

Subgroups — #333×Dic43 #24987543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #333×Dic₄₃ #24987543