Subgroups — C₄₃×#17075 #24937092

Order 11008.

1314 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#398	C₂	1	4	yes	maximal
2	C₂×C₄₃×#389	C₂	1	2	yes	maximal
3	C₄₃×#1445	C₂	1	4	yes	maximal
4	C₄₃×#1444	C₂	1	4	yes	maximal
5	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
7	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#398	—	2	16	no	—
13	C₄₃×#389	—	2	8	no	—
14	C₂×#95×C₄₃	C₂²	1	8	yes	—
15	C₂×#95×C₄₃	C₂²	1	4	yes	—
16	C₂×#95×C₄₃	C₂²	1	4	yes	—
17	C₂×#95×C₄₃	C₂²	1	4	yes	—
18	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
19	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
20	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
21	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
23	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
24	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
25	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
27	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
28	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
29	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
30	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
31	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
32	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
33	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
34	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
35	C₂×C₄⋊C₄×C₄₃	Q₈	1	8	yes	—
36	C₂×C₄²×C₄₃	—	4	2	no	—
37	C₂×C₄²×C₄₃	D₄	1	4	yes	—
38	#95×C₄₃	—	2	8	no	—
39	#95×C₄₃	—	2	8	no	—
40	#95×C₄₃	—	2	16	no	—
41	#95×C₄₃	—	2	8	no	—
42	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	—	2	8	no	—
44	C₂²×C₄×C₄₃	—	2	4	no	—
45	C₂²×C₄×C₄₃	—	2	4	no	—
46	C₂²×C₄×C₄₃	—	2	8	no	—
47	C₂²×C₄×C₄₃	—	2	8	no	—
48	C₂²×C₄×C₄₃	—	2	4	no	—
49	C₂²×C₄×C₄₃	—	2	4	no	—
50	C₂²×C₄×C₄₃	—	2	2	no	—
51	C₂²×C₄×C₄₃	—	2	1	no	—
52	C₂²×C₄×C₄₃	—	2	4	no	—
53	C₂²×C₄×C₄₃	—	2	4	no	—
54	C₂²×C₄×C₄₃	—	2	8	no	—
55	C₂²×C₄×C₄₃	—	2	4	no	—
56	C₂²×C₄×C₄₃	—	2	4	no	—
57	C₂²×C₄×C₄₃	—	2	1	no	—
58	C₂²×C₄×C₄₃	—	2	8	no	—
59	C₂²×C₄×C₄₃	—	2	8	no	—
60	C₂²×C₄×C₄₃	—	2	4	no	—
61	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
62	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
63	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
65	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
66	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
67	C₂²×C₄×C₄₃	#41	1	4	yes	—
68	C₄⋊C₄×C₄₃	—	2	16	no	—
69	C₄⋊C₄×C₄₃	—	4	8	no	—
70	C₄⋊C₄×C₄₃	—	4	8	no	—
71	C₄⋊C₄×C₄₃	—	4	16	no	—
72	C₄⋊C₄×C₄₃	—	4	16	no	—
73	C₄²×C₄₃	—	4	4	no	—
74	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
75	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
76	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
77	C₂³×C₄₃	C₂×#41	1	2	yes	—
78	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
79	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
80	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
81	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
82	C₂×C₄×C₄₃	—	2	4	no	—
83	C₂×C₄×C₄₃	—	2	2	no	—
84	C₂×C₄×C₄₃	—	2	4	no	—
85	C₂×C₄×C₄₃	—	2	4	no	—
86	C₂×C₄×C₄₃	—	2	2	no	—
87	C₂×C₄×C₄₃	—	2	4	no	—
88	C₂×C₄×C₄₃	—	2	8	no	—
89	C₂×C₄×C₄₃	—	2	8	no	—
90	C₂×C₄×C₄₃	—	2	8	no	—
91	C₂×C₄×C₄₃	—	2	8	no	—
92	C₂×C₄×C₄₃	—	2	16	no	—
93	C₂×C₄×C₄₃	—	2	16	no	—
94	C₂×C₄×C₄₃	—	4	4	no	—
95	C₂×C₄×C₄₃	—	4	4	no	—
96	C₂×C₄×C₄₃	—	4	8	no	—
97	C₂×C₄×C₄₃	—	4	8	no	—
98	C₂×C₄×C₄₃	—	4	4	no	—
99	C₂×C₄×C₄₃	—	4	4	no	—
100	C₂×C₄×C₄₃	—	4	4	no	—
101	C₂×C₄×C₄₃	—	4	4	no	—
102	C₂×C₄×C₄₃	—	4	8	no	—
103	C₂×C₄×C₄₃	—	4	4	no	—
104	C₂×C₄×C₄₃	—	4	8	no	—
105	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
106	C₂×C₄×C₄₃	#127	1	4	yes	—
107	#17075	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
109	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
110	C₂²×C₄₃	#534	1	1	yes	characteristic
111	C₂²×C₄₃	#534	1	2	yes	—
112	C₂²×C₄₃	#536	1	2	yes	—
113	C₂²×C₄₃	#537	1	1	yes	characteristic
114	C₂²×C₄₃	#537	1	2	yes	—
115	C₂²×C₄₃	#539	1	4	yes	—
116	C₂²×C₄₃	#544	1	4	yes	—
117	C₂²×C₄₃	#547	1	4	yes	—
118	C₂²×C₄₃	D₄×Q₈	1	4	yes	—
119	C₂²×C₄₃	#557	1	2	yes	—
120	C₂²×C₄₃	Q₈²	1	1	yes	characteristic
121	C₂²×C₄₃	#559	1	1	yes	characteristic
122	C₂²×C₄₃	#563	1	2	yes	—
123	C₂²×C₄₃	#564	1	2	yes	—
124	C₄×C₄₃	—	2	8	no	—
125	C₄×C₄₃	—	2	4	no	—
126	C₄×C₄₃	—	4	8	no	—
127	C₄×C₄₃	—	4	8	no	—
128	C₄×C₄₃	—	8	4	no	—
129	C₂×#398	C₂×C₄₃	1	4	yes	—
130	C₂×#389	C₂×C₄₃	1	2	yes	—
131	#1445	C₂×C₄₃	1	4	yes	—
132	#1444	C₂×C₄₃	1	4	yes	—
133	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
134	C₂×C₄₃	#2542	1	2	yes	—
135	C₂×C₄₃	#2582	1	1	yes	characteristic
136	C₂×C₄₃	#2627	1	2	yes	—
137	C₂×C₄₃	#2656	1	1	yes	characteristic
138	C₂×C₄₃	#2724	1	2	yes	—
139	C₂×C₄₃	#2726	1	4	yes	—
140	C₂×C₄₃	#2734	1	2	yes	—
141	C₂×C₄₃	#2822	1	1	yes	characteristic
142	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
143	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
144	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
145	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
146	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
147	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
148	#398	—	2	16	no	—
149	#389	—	2	8	no	—
150	C₂×#95	C₂²×C₄₃	1	8	yes	—
151	C₂×#95	C₂²×C₄₃	1	4	yes	—
152	C₂×#95	C₂²×C₄₃	1	4	yes	—
153	C₂×#95	C₂²×C₄₃	1	4	yes	—
154	C₄₃	#17075	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
156	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
157	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
158	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
159	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
160	C₂×C₄⋊C₄	—	2	4	no	—
161	C₂×C₄⋊C₄	—	2	4	no	—
162	C₂×C₄⋊C₄	—	2	4	no	—
163	C₂×C₄⋊C₄	—	2	8	no	—
164	C₂×C₄⋊C₄	—	2	8	no	—
165	C₂×C₄⋊C₄	—	2	16	no	—
166	C₂×C₄⋊C₄	—	4	2	no	—
167	C₂×C₄⋊C₄	—	4	2	no	—
168	C₂×C₄⋊C₄	—	4	4	no	—
169	C₂×C₄⋊C₄	—	4	4	no	—
170	C₂×C₄⋊C₄	—	4	4	no	—
171	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
172	C₂×C₄⋊C₄	Q₈×C₄₃	1	8	yes	—
173	C₂×C₄²	—	4	2	no	—
174	C₂×C₄²	D₄×C₄₃	1	4	yes	—
175	#95	—	2	8	no	—
176	#95	—	2	8	no	—
177	#95	—	2	16	no	—
178	#95	—	2	8	no	—
179	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
180	C₂²×C₄	—	2	4	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	8	no	—
186	C₂²×C₄	—	2	4	no	—
187	C₂²×C₄	—	2	8	no	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	4	no	—
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	—	2	8	no	—
192	C₂²×C₄	—	2	8	no	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	8	no	—
195	C₂²×C₄	—	2	8	no	—
196	C₂²×C₄	—	2	4	no	—
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
199	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
200	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
201	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
202	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
203	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
204	C₂²×C₄	#41×C₄₃	1	4	yes	—
205	C₄⋊C₄	—	2	16	no	—
206	C₄⋊C₄	—	4	8	no	—
207	C₄⋊C₄	—	4	8	no	—
208	C₄⋊C₄	—	4	16	no	—
209	C₄⋊C₄	—	4	16	no	—
210	C₄²	—	4	4	no	—
211	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
212	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
213	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
214	C₂³	C₂×#41×C₄₃	1	2	yes	—
215	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
216	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
217	C₂³	2₋¹⁺⁴×C₄₃	1	4	yes	—
218	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	2	8	no	—
226	C₂×C₄	—	2	8	no	—
227	C₂×C₄	—	2	8	no	—
228	C₂×C₄	—	2	8	no	—
229	C₂×C₄	—	2	16	no	—
230	C₂×C₄	—	2	16	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	4	4	no	—
233	C₂×C₄	—	4	8	no	—
234	C₂×C₄	—	4	8	no	—
235	C₂×C₄	—	4	4	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	8	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	8	no	—
242	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
243	C₂×C₄	#127×C₄₃	1	4	yes	—
244	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
245	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
246	C₂²	C₄₃×#534	1	1	yes	characteristic
247	C₂²	C₄₃×#534	1	2	yes	—
248	C₂²	C₄₃×#536	1	2	yes	—
249	C₂²	C₄₃×#537	1	1	yes	characteristic
250	C₂²	C₄₃×#537	1	2	yes	—
251	C₂²	C₄₃×#539	1	4	yes	—
252	C₂²	C₄₃×#544	1	4	yes	—
253	C₂²	C₄₃×#547	1	4	yes	—
254	C₂²	D₄×Q₈×C₄₃	1	4	yes	—
255	C₂²	C₄₃×#557	1	2	yes	—
256	C₂²	Q₈²×C₄₃	1	1	yes	characteristic
257	C₂²	C₄₃×#559	1	1	yes	characteristic
258	C₂²	C₄₃×#563	1	2	yes	—
259	C₂²	C₄₃×#564	1	2	yes	—
260	C₄	—	2	8	no	—
261	C₄	—	2	4	no	—
262	C₄	—	4	8	no	—
263	C₄	—	4	8	no	—
264	C₄	—	8	4	no	—
265	C₂	C₄₃×#2542	1	2	yes	—
266	C₂	C₄₃×#2582	1	1	yes	characteristic
267	C₂	C₄₃×#2627	1	2	yes	—
268	C₂	C₄₃×#2656	1	1	yes	characteristic
269	C₂	C₄₃×#2724	1	2	yes	—
270	C₂	C₄₃×#2726	1	4	yes	—
271	C₂	C₄₃×#2734	1	2	yes	—
272	C₂	C₄₃×#2822	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
107. #17075	C₄₃	direct (N × H)
154. C₄₃	#17075	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#398	2
C₂×C₄₃×#389	2
C₄₃×#1445	2
C₄₃×#1444	2
C₄₃×C₄⋊#95	2
#17075	43

Subgroups — C43×#17075 #24937092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17075 #24937092