Subgroups — #24987201

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₄₃	C₄	1	2	yes	—
9	C₂²×C₄×Dic₄₃	—	2	1	no	—
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₄₃	—	2	1	no	—
13	C₄⋊C₄×Dic₄₃	C₄	1	2	yes	—
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂²⋊C₄×Dic₄₃	—	2	2	no	—
16	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
17	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
18	#14582653	—	2	2	no	—
19	#14582653	—	2	1	no	—
20	D₄⋊(C₄₃⋊C₈)	C₄	1	4	yes	complemented
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×D₄⋊C₈	C₄	1	4	yes	complemented
25	C₂³×Dic₄₃	—	2	2	no	—
26	C₂²×C₄₃⋊C₈	—	2	1	no	—
27	C₂²×C₄₃⋊C₈	—	2	1	no	—
28	D₄×Dic₄₃	—	2	4	no	—
29	D₄×Dic₄₃	C₈	1	8	yes	complemented
30	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
31	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
32	C₂×C₄×Dic₄₃	—	2	1	no	—
33	C₂×C₄×Dic₄₃	—	2	2	no	—
34	C₂×C₄×Dic₄₃	—	4	2	no	—
35	C₂×C₄×Dic₄₃	—	4	2	no	—
36	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
37	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
40	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
41	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	complemented
42	C₄×C₄₃⋊C₈	—	2	1	no	—
43	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	complemented
44	C₈×Dic₄₃	—	4	2	no	—
45	C₄₃⋊#95	—	2	1	no	—
46	C₄₃⋊#95	—	2	2	no	—
47	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	1	no	—
49	C₂²×C₈×C₄₃	—	2	1	no	—
50	C₂²×C₈×C₄₃	—	2	1	no	—
51	C₄×D₄×C₄₃	—	2	1	no	—
52	C₄×D₄×C₄₃	—	2	1	no	—
53	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₄₃	—	2	1	no	—
59	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	complemented
60	C₄×C₈×C₄₃	—	2	1	no	—
61	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	complemented
62	C₂⁴×C₄₃	—	2	1	no	—
63	C₂×D₄×C₄₃	—	2	1	no	—
64	C₂×D₄×C₄₃	—	2	2	no	—
65	C₂×D₄×C₄₃	C₄²	1	2	yes	—
66	C₂×D₄×C₄₃	C₂×C₈	1	4	yes	—
67	C₂²×C₄×C₄₃	—	2	2	no	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	4	1	no	—
71	C₂²×C₄×C₄₃	—	4	1	no	—
72	C₂²×C₄×C₄₃	—	4	1	no	—
73	C₂²×C₄×C₄₃	—	4	1	no	—
74	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₄₃	—	2	8	no	—
78	C₂²×Dic₄₃	—	2	2	no	—
79	C₂²×Dic₄₃	—	4	4	no	—
80	C₂²×Dic₄₃	—	4	4	no	—
81	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
82	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₄₃	—	2	2	no	—
84	C₂×C₈×C₄₃	—	2	2	no	—
85	C₂×C₈×C₄₃	—	4	2	no	—
86	C₂×C₈×C₄₃	—	4	1	no	—
87	C₂×C₈×C₄₃	—	4	1	no	—
88	C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₄⋊C₄×C₄₃	C₄²	1	2	yes	—
90	C₂²⋊C₄×C₄₃	—	2	2	no	—
91	C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₄₃	#41	1	1	yes	characteristic
95	C₄²×C₄₃	#41	1	1	yes	characteristic
96	C₂²⋊Dic₄₃	—	2	8	no	—
97	C₄⋊Dic₄₃	—	2	2	no	—
98	C₄⋊Dic₄₃	C₂×C₈	1	4	yes	—
99	C₄×Dic₄₃	—	2	1	no	—
100	C₄×Dic₄₃	—	2	1	no	—
101	C₄×Dic₄₃	—	2	1	no	—
102	C₄×Dic₄₃	—	2	1	no	—
103	C₄×Dic₄₃	—	4	2	no	—
104	C₄×Dic₄₃	—	4	4	no	—
105	C₄×Dic₄₃	—	4	1	no	—
106	C₄×Dic₄₃	—	4	1	no	—
107	C₄×Dic₄₃	C₂×C₈	1	4	yes	—
108	C₄×Dic₄₃	M₁₆	1	4	yes	—
109	C₂×C₄₃⋊C₈	—	2	2	no	—
110	C₂×C₄₃⋊C₈	—	2	2	no	—
111	C₂×C₄₃⋊C₈	—	4	2	no	—
112	C₂×C₄₃⋊C₈	—	4	1	no	—
113	C₂×C₄₃⋊C₈	—	4	1	no	—
114	C₂³×C₄₃	—	2	2	no	—
115	C₂³×C₄₃	—	2	4	no	—
116	C₂³×C₄₃	—	4	1	no	—
117	C₂³×C₄₃	—	4	1	no	—
118	C₂³×C₄₃	—	4	2	no	—
119	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	D₄×C₄₃	—	2	2	no	—
121	D₄×C₄₃	—	2	4	no	—
122	D₄×C₄₃	C₄×C₈	1	4	yes	complemented
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	4	1	no	—
126	C₂×C₄×C₄₃	—	4	1	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	—	4	2	no	—
129	C₂×C₄×C₄₃	—	4	2	no	—
130	C₂×C₄×C₄₃	—	4	2	no	—
131	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
132	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
133	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
140	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
143	C₂×Dic₄₃	—	2	2	no	—
144	C₂×Dic₄₃	—	2	2	no	—
145	C₂×Dic₄₃	—	2	2	no	—
146	C₂×Dic₄₃	—	2	2	no	—
147	C₂×Dic₄₃	—	2	4	no	—
148	C₂×Dic₄₃	—	4	16	no	—
149	C₂×Dic₄₃	—	4	2	no	—
150	C₂×Dic₄₃	—	4	2	no	—
151	C₂×Dic₄₃	C₂²⋊C₈	1	4	yes	—
152	C₂×Dic₄₃	C₂²⋊C₈	1	4	yes	—
153	C₈×C₄₃	—	4	2	no	—
154	C₈×C₄₃	—	4	2	no	—
155	C₄₃⋊C₈	—	4	2	no	—
156	C₄₃⋊C₈	—	4	2	no	—
157	#8170	—	43	1	no	maximal, Sylow
158	C₂²×C₄₃	—	2	4	no	—
159	C₂²×C₄₃	—	4	4	no	—
160	C₂²×C₄₃	—	4	4	no	—
161	C₂²×C₄₃	—	4	2	no	—
162	C₂²×C₄₃	—	4	2	no	—
163	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄₃	C₂×C₂²⋊C₈	1	2	yes	—
165	C₂²×C₄₃	#417	1	1	yes	characteristic
166	C₂²×C₄₃	#418	1	1	yes	characteristic
167	C₂²×C₄₃	#421	1	2	yes	—
168	C₄×C₄₃	—	2	1	no	—
169	C₄×C₄₃	—	2	1	no	—
170	C₄×C₄₃	—	4	2	no	—
171	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
172	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
173	C₄×C₄₃	#431	1	2	yes	—
174	C₄×C₄₃	#440	1	1	yes	characteristic
175	C₄×C₄₃	#440	1	1	yes	characteristic
176	C₄×C₄₃	#442	1	1	yes	characteristic
177	C₄×C₄₃	#442	1	1	yes	characteristic
178	Dic₄₃	—	2	4	no	—
179	Dic₄₃	—	2	4	no	—
180	Dic₄₃	—	4	4	no	—
181	C₄²×D₄	—	43	1	no	—
182	C₄×C₄⋊C₈	—	43	1	no	—
183	#1744	—	43	1	no	—
184	C₂×D₄⋊C₈	—	43	1	no	—
185	C₂×D₄⋊C₈	D₄₃	1	1	yes	characteristic
186	#1279	—	43	1	no	—
187	#1279	—	43	1	no	—
188	C₂×C₄₃	—	4	4	no	—
189	C₂×C₄₃	#1477	1	2	yes	—
190	C₂×C₄₃	#1478	1	2	yes	—
191	C₂×C₄₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
192	C₂×C₄₃	#1759	1	1	yes	characteristic
193	C₂×C₄₃	#1762	1	1	yes	characteristic
194	C₂×C₄×D₄	—	43	2	no	—
195	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
196	C₂²×C₄²	—	86	1	no	—
197	C₂×C₄⋊C₈	—	43	1	no	—
198	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
199	C₂×C₄×C₈	—	43	1	no	—
200	C₂×C₄×C₈	—	86	1	no	—
201	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
202	C₄×C₄⋊C₄	—	43	2	no	—
203	C₄×C₄⋊C₄	—	43	1	no	—
204	C₄×C₂²⋊C₄	—	86	2	no	—
205	C₄×C₂²⋊C₄	—	86	1	no	—
206	C₄³	—	43	1	no	—
207	#336	—	86	2	no	—
208	#336	—	86	1	no	—
209	D₄⋊C₈	—	43	4	no	—
210	D₄⋊C₈	Dic₄₃	1	4	yes	complemented
211	C₄₃	#8170	1	1	yes	characteristic, complemented, Sylow
212	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	86	2	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	86	1	no	—
218	C₂²×C₈	—	86	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	43	8	no	—
222	C₄×D₄	—	86	4	no	—
223	C₄×D₄	C₄×D₄₃	1	2	yes	—
224	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
225	C₂×C₄⋊C₄	—	43	2	no	—
226	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	86	2	no	—
229	C₂×C₄²	—	43	2	no	—
230	C₂×C₄²	—	43	1	no	—
231	C₂×C₄²	—	43	1	no	—
232	C₂×C₄²	—	43	2	no	—
233	C₂×C₄²	—	86	2	no	—
234	C₂×C₄²	—	86	1	no	—
235	C₂×C₄²	—	172	2	no	—
236	C₂×C₄²	—	172	2	no	—
237	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	43	2	no	—
240	C₄⋊C₈	—	86	1	no	—
241	C₄⋊C₈	C₂×Dic₄₃	1	2	yes	complemented
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	43	2	no	—
244	C₄×C₈	—	86	1	no	—
245	C₄×C₈	—	172	2	no	—
246	C₄×C₈	C₂×Dic₄₃	1	2	yes	complemented
247	#95	—	86	2	no	—
248	#95	—	86	1	no	—
249	C₂⁴	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	C₈×D₄₃	1	4	yes	—
253	C₂×D₄	C₄×Dic₄₃	1	2	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	43	2	no	—
262	C₂²×C₄	—	43	2	no	—
263	C₂²×C₄	—	86	8	no	—
264	C₂²×C₄	—	86	2	no	—
265	C₂²×C₄	—	172	4	no	—
266	C₂²×C₄	—	172	4	no	—
267	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
268	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
269	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	86	2	no	—
276	C₂×C₈	—	86	2	no	—
277	C₂×C₈	—	172	2	no	—
278	C₂×C₈	—	172	1	no	—
279	C₂×C₈	—	172	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	43	4	no	—
282	C₄⋊C₄	—	86	2	no	—
283	C₄⋊C₄	C₄×Dic₄₃	1	2	yes	—
284	C₂²⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	2	2	no	—
286	C₂²⋊C₄	—	86	8	no	—
287	C₄²	—	43	4	no	—
288	C₄²	—	43	4	no	—
289	C₄²	—	86	1	no	—
290	C₄²	—	86	1	no	—
291	C₄²	—	86	1	no	—
292	C₄²	—	86	1	no	—
293	C₄²	—	172	2	no	—
294	C₄²	—	172	4	no	—
295	C₄²	—	172	1	no	—
296	C₄²	—	172	1	no	—
297	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
298	C₄²	#10621900	1	1	yes	characteristic
299	C₄²	#10621900	1	1	yes	characteristic
300	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
301	C₂³	—	2	4	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	1	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
307	D₄	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	C₈×Dic₄₃	1	4	yes	complemented
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	43	4	no	—
319	C₂×C₄	—	43	4	no	—
320	C₂×C₄	—	86	2	no	—
321	C₂×C₄	—	86	2	no	—
322	C₂×C₄	—	86	2	no	—
323	C₂×C₄	—	86	2	no	—
324	C₂×C₄	—	86	4	no	—
325	C₂×C₄	—	172	16	no	—
326	C₂×C₄	—	172	2	no	—
327	C₂×C₄	—	172	2	no	—
328	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
329	C₂×C₄	#13063281	1	1	yes	characteristic
330	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
333	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
335	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
336	C₂×C₄	#13063349	1	1	yes	characteristic
337	C₂×C₄	#13063349	1	1	yes	characteristic
338	C₂×C₄	#13063352	1	1	yes	characteristic
339	C₂×C₄	#13063354	1	1	yes	characteristic
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	172	2	no	—
343	C₈	—	172	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
350	C₂²	C₂²⋊C₈×D₄₃	1	2	yes	—
351	C₂²	#14582897	1	1	yes	characteristic
352	C₂²	#14582902	1	1	yes	characteristic
353	C₂²	#14582914	1	2	yes	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	86	4	no	—
358	C₄	—	86	4	no	—
359	C₄	—	172	4	no	—
360	C₄	C₂×C₈×Dic₄₃	1	1	yes	characteristic
361	C₄	M₁₆×Dic₄₃	1	1	yes	characteristic
362	C₄	#14582949	1	2	yes	—
363	C₄	#14582996	1	1	yes	characteristic
364	C₄	#14583000	1	1	yes	characteristic
365	C₄	#14583008	1	1	yes	characteristic
366	C₄	#14583011	1	1	yes	characteristic
367	C₂	—	4	4	no	—
368	C₂	#19132979	1	2	yes	—
369	C₂	#19132984	1	2	yes	—
370	C₂	C₂²⋊C₈×Dic₄₃	1	1	yes	characteristic
371	C₂	#19134407	1	1	yes	characteristic
372	C₂	#19134422	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×D₄⋊C₈	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×D₄⋊C₈	D₄₃
hypocenter	C₄₃	#8170
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₈×Dic₄₃	C₂	semidirect
3. #19134340	C₂	semidirect
5. #19132435	C₂	semidirect
6. #19132434	C₂	semidirect
20. D₄⋊(C₄₃⋊C₈)	C₄	semidirect
24. C₄₃×D₄⋊C₈	C₄	semidirect
29. D₄×Dic₄₃	C₈	semidirect
41. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
43. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
59. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
61. C₄×C₈×C₄₃	C₂×C₄	semidirect
122. D₄×C₄₃	C₄×C₈	semidirect
210. D₄⋊C₈	Dic₄₃	semidirect
211. C₄₃	#8170	semidirect
241. C₄⋊C₈	C₂×Dic₄₃	semidirect
246. C₄×C₈	C₂×Dic₄₃	semidirect
309. D₄	C₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×Dic₄₃	2
C₄⋊C₈×Dic₄₃	2
#19134340	2
C₂×D₄⋊(C₄₃⋊C₈)	2
#19132435	2
#19132434	2
C₂×C₄₃×D₄⋊C₈	2
#8170	43