Subgroups — #25253266

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₄₃	C₂	1	2	yes	maximal, complemented
2	Q₁₆×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146270	C₂	1	1	yes	maximal, characteristic
4	#19136850	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136690	C₂	1	2	yes	maximal, complemented
6	#19136641	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136525	C₂	1	2	yes	maximal, complemented
8	#19136510	C₂	1	2	yes	maximal, complemented
9	C₄×#13063268	C₂	1	1	yes	maximal, characteristic, complemented
10	#19136414	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₄₃	C₂²	1	2	yes	complemented
13	C₂×D₈×D₄₃	C₂²	1	2	yes	—
14	Q₈×D₁₇₂	—	2	1	no	—
15	#14583534	—	2	1	no	—
16	C₂×#13063270	C₂²	1	2	yes	—
17	C₂×#13063269	C₂²	1	2	yes	complemented
18	C₂×#13063269	C₂²	1	2	yes	complemented
19	C₂×#13063268	C₂²	1	1	yes	characteristic
20	SD₃₂×D₄₃	—	2	8	no	—
21	C₂×C₁₆×D₄₃	C₂²	1	2	yes	complemented
22	#14583279	C₂²	1	1	yes	characteristic, complemented
23	#14583141	C₂²	1	2	yes	complemented
24	#14583132	C₂²	1	2	yes	—
25	#14583109	—	2	1	no	—
26	#14583091	—	2	1	no	—
27	#14583056	—	2	2	no	—
28	#14583031	—	2	2	no	—
29	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
30	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
31	#14582726	C₂²	1	1	yes	characteristic, complemented
32	#14582704	C₂²	1	2	yes	complemented
33	#14582703	C₂²	1	1	yes	characteristic, complemented
34	#14582699	C₂²	1	1	yes	characteristic
35	(C₂×D₄₃)⋊C₁₆	C₂²	1	2	yes	complemented
36	C₄×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×SD₃₂×C₄₃	C₂²	1	2	yes	complemented
38	C₄₃×#493	C₂²	1	1	yes	characteristic
39	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#357	C₂²	1	2	yes	complemented
42	C₂×Q₈×D₄₃	—	2	2	no	—
43	C₂×D₄×D₄₃	—	2	2	no	—
44	C₂×D₄×D₄₃	—	4	1	no	—
45	C₂×Dic₁₇₂	—	2	1	no	—
46	C₂×Dic₁₇₂	C₂³	1	2	yes	—
47	C₂×#10621885	—	2	2	no	—
48	Q₁₆×D₄₃	—	2	4	no	—
49	Q₁₆×D₄₃	—	4	2	no	—
50	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
51	C₂×#10621882	—	2	2	no	—
52	D₈×D₄₃	—	2	4	no	—
53	D₈×D₄₃	—	4	2	no	—
54	C₂×C₈×D₄₃	C₂³	1	2	yes	—
55	#13063325	—	2	1	no	—
56	#13063325	—	4	1	no	—
57	#13063305	—	2	2	no	—
58	#13063305	—	4	2	no	—
59	#13063296	—	2	2	no	—
60	#13063296	—	4	1	no	—
61	#13063293	—	4	2	no	—
62	C₄×D₁₇₂	—	2	1	no	—
63	C₄×D₁₇₂	—	4	1	no	—
64	C₄×D₁₇₂	D₄	1	1	yes	characteristic
65	#13063270	—	2	4	no	—
66	#13063269	—	2	4	no	—
67	#13063269	—	4	2	no	—
68	#13063268	D₄	1	4	yes	complemented
69	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
71	C₁₆×D₄₃	—	2	4	no	—
72	#13063259	C₂³	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
74	#13063248	—	2	2	no	—
75	#13063247	—	2	1	no	—
76	#13063246	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
78	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×D₈×C₄₃	—	2	1	no	—
80	C₂×D₈×C₄₃	C₂³	1	2	yes	—
81	#127×C₄₃	—	2	1	no	—
82	C₄×Q₈×C₄₃	—	2	1	no	—
83	SD₃₂×C₄₃	—	2	4	no	—
84	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
85	#107×C₄₃	C₂³	1	1	yes	characteristic
86	#103×C₄₃	—	2	1	no	—
87	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂³×D₄₃	—	4	2	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	4	1	no	—
92	C₂×D₄×C₄₃	—	4	1	no	—
93	C₂×C₂²⋊D₄₃	—	4	2	no	—
94	C₂×C₂²⋊D₄₃	—	4	2	no	—
95	Q₈×D₄₃	—	4	4	no	—
96	Q₈×D₄₃	—	8	2	no	—
97	D₄×D₄₃	—	4	4	no	—
98	D₄×D₄₃	—	8	2	no	—
99	D₄×D₄₃	—	8	4	no	—
100	C₂×D₁₇₂	—	2	1	no	—
101	C₂×D₁₇₂	D₈	1	1	yes	characteristic
102	C₂×C₄×D₄₃	—	4	1	no	—
103	C₂×C₄×D₄₃	—	4	2	no	—
104	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
105	C₂×Dic₈₆	—	2	2	no	—
106	C₂×Dic₈₆	—	4	2	no	—
107	Q₁₆×C₄₃	—	2	1	no	—
108	Q₁₆×C₄₃	C₂×D₄	1	2	yes	complemented
109	D₈×C₄₃	—	2	2	no	—
110	D₈×C₄₃	—	2	2	no	—
111	D₈×C₄₃	—	8	1	no	—
112	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₄₃	—	2	1	no	—
115	C₄⋊C₄×C₄₃	—	4	1	no	—
116	C₄²×C₄₃	—	4	1	no	—
117	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²⋊Dic₄₃	—	4	2	no	—
119	#10621885	—	4	4	no	—
120	#10621882	—	4	4	no	—
121	(C₂×D₄₃)⋊C₄	—	4	1	no	—
122	(C₂×D₄₃)⋊C₄	—	4	2	no	—
123	(C₂×D₄₃)⋊C₄	D₈	1	2	yes	—
124	C₄⋊Dic₄₃	—	2	1	no	—
125	C₄⋊Dic₄₃	—	4	1	no	—
126	C₄⋊Dic₄₃	—	4	1	no	—
127	C₄⋊Dic₄₃	—	4	2	no	—
128	C₄⋊Dic₄₃	D₈	1	1	yes	characteristic
129	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
130	Dic₁₇₂	—	2	2	no	—
131	Dic₁₇₂	—	2	2	no	—
132	Dic₁₇₂	—	8	1	no	—
133	D₃₄₄	—	2	1	no	—
134	D₃₄₄	C₂×D₄	1	2	yes	—
135	C₈×D₄₃	—	2	2	no	—
136	C₈×D₄₃	—	2	2	no	—
137	C₁₆×C₄₃	—	2	2	no	—
138	C₄₃⋊C₁₆	—	2	1	no	—
139	C₄₃⋊C₁₆	C₂×D₄	1	2	yes	complemented
140	C₂³×C₄₃	—	4	2	no	—
141	C₂²×D₄₃	—	4	1	no	—
142	C₂²×D₄₃	—	8	4	no	—
143	C₂²×D₄₃	—	8	4	no	—
144	C₂²×D₄₃	—	16	2	no	—
145	C₂²×D₄₃	C₂×D₈	1	2	yes	—
146	Q₈×C₄₃	—	2	2	no	—
147	Q₈×C₄₃	—	4	1	no	—
148	D₄×C₄₃	—	4	2	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	8	2	no	—
151	D₄×C₄₃	—	16	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	1	no	—
154	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
157	C₂²⋊D₄₃	—	8	4	no	—
158	C₂²⋊D₄₃	—	8	4	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
162	D₁₇₂	—	2	2	no	—
163	D₁₇₂	—	4	1	no	—
164	D₁₇₂	SD₃₂	1	4	yes	complemented
165	C₄×D₄₃	—	2	2	no	—
166	C₄×D₄₃	—	2	2	no	—
167	C₄×D₄₃	—	8	4	no	—
168	C₄×D₄₃	—	8	2	no	—
169	Dic₈₆	—	4	2	no	—
170	Dic₈₆	—	4	2	no	—
171	Dic₈₆	—	8	4	no	—
172	C₈×C₄₃	—	2	1	no	—
173	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₄₃⋊C₈	—	2	2	no	—
176	D₄×SD₃₂	—	43	1	no	maximal, Sylow
177	C₂²×C₄₃	—	8	2	no	—
178	C₂²×C₄₃	—	8	2	no	—
179	C₂²×C₄₃	—	8	2	no	—
180	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
181	C₂×D₄₃	—	2	2	no	—
182	C₂×D₄₃	—	2	2	no	—
183	C₂×D₄₃	—	4	2	no	—
184	C₂×D₄₃	—	8	1	no	—
185	C₂×D₄₃	—	8	1	no	—
186	C₂×D₄₃	—	16	8	no	—
187	C₂×D₄₃	C₂×SD₃₂	1	4	yes	complemented
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	—	8	1	no	—
191	C₄×C₄₃	C₂×SD₃₂	1	2	yes	complemented
192	C₄×C₄₃	D₄²	1	1	yes	characteristic
193	C₄×C₄₃	#576	1	1	yes	characteristic
194	Dic₄₃	—	2	2	no	—
195	Dic₄₃	—	8	1	no	—
196	Dic₄₃	—	8	2	no	—
197	C₂²×SD₃₂	—	43	2	no	—
198	D₄×Q₁₆	—	43	1	no	—
199	D₄×D₈	—	43	1	no	—
200	#2248	—	43	1	no	—
201	#2217	—	43	2	no	—
202	#2208	—	43	1	no	—
203	#2207	D₄₃	1	1	yes	characteristic, complemented
204	#2187	—	43	2	no	—
205	#2185	—	43	2	no	—
206	C₄×SD₃₂	—	43	1	no	—
207	D₄×C₁₆	—	43	1	no	—
208	C₂×C₄₃	—	16	2	no	—
209	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
210	C₂×C₄₃	C₂²×SD₃₂	1	1	yes	characteristic
211	C₂×C₄₃	#3416	1	1	yes	characteristic
212	D₄₃	—	2	4	no	—
213	D₄₃	—	8	2	no	—
214	C₂²×Q₁₆	—	43	2	no	—
215	C₂²×D₈	—	43	2	no	—
216	D₄×Q₈	—	86	1	no	—
217	D₄²	—	86	1	no	—
218	C₂×SD₃₂	—	43	1	no	—
219	C₂×SD₃₂	—	43	2	no	—
220	C₂×SD₃₂	—	43	2	no	—
221	C₂×SD₃₂	—	43	2	no	—
222	C₂×SD₃₂	—	86	8	no	—
223	C₂×SD₃₂	C₂×D₄₃	1	2	yes	complemented
224	C₂²×C₁₆	—	43	2	no	—
225	#494	—	43	1	no	—
226	#493	C₂×D₄₃	1	1	yes	characteristic
227	#467	—	43	2	no	—
228	#466	—	43	2	no	—
229	#462	—	86	1	no	—
230	#459	—	86	1	no	—
231	#451	—	86	2	no	—
232	#447	—	86	2	no	—
233	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
234	C₄×D₈	—	43	1	no	—
235	C₈×D₄	—	43	1	no	—
236	#367	—	43	1	no	—
237	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
238	#358	—	43	1	no	—
239	#358	—	43	2	no	—
240	#357	—	43	1	no	—
241	#357	C₂×D₄₃	1	2	yes	complemented
242	C₂²⋊C₁₆	—	43	2	no	—
243	C₄×C₁₆	—	43	1	no	—
244	C₄₃	D₄×SD₃₂	1	1	yes	characteristic, complemented, Sylow
245	C₂²×Q₈	—	86	2	no	—
246	C₂²×D₄	—	86	2	no	—
247	C₂²×D₄	—	172	1	no	—
248	C₂×Q₁₆	—	43	2	no	—
249	C₂×Q₁₆	—	86	2	no	—
250	C₂×Q₁₆	—	86	4	no	—
251	C₂×Q₁₆	—	86	1	no	—
252	C₂×Q₁₆	—	172	2	no	—
253	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	43	1	no	—
256	C₂×D₈	—	86	2	no	—
257	C₂×D₈	—	86	4	no	—
258	C₂×D₈	—	172	2	no	—
259	C₂×D₈	C₂²×D₄₃	1	2	yes	—
260	C₂²×C₈	—	43	2	no	—
261	C₄⋊Q₈	—	86	1	no	—
262	C₄⋊Q₈	—	172	1	no	—
263	#127	—	2	1	no	—
264	C₂²⋊Q₈	—	86	2	no	—
265	C₂²⋊Q₈	—	172	2	no	—
266	#121	—	86	2	no	—
267	#121	—	172	1	no	—
268	#120	—	172	2	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×D₄	—	43	1	no	—
271	C₄×D₄	—	86	1	no	—
272	C₄×D₄	—	172	1	no	—
273	SD₃₂	—	2	4	no	—
274	SD₃₂	—	43	4	no	—
275	SD₃₂	—	86	4	no	—
276	SD₃₂	—	86	4	no	—
277	SD₃₂	—	172	2	no	—
278	C₂×C₁₆	—	43	1	no	—
279	C₂×C₁₆	—	43	1	no	—
280	C₂×C₁₆	—	86	4	no	—
281	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
282	#107	—	43	1	no	—
283	#107	C₂²×D₄₃	1	1	yes	characteristic
284	C₄⋊C₈	—	43	1	no	—
285	#103	—	2	1	no	—
286	#103	—	86	2	no	—
287	#102	—	86	2	no	—
288	#102	—	86	1	no	—
289	C₂²⋊C₈	—	43	2	no	—
290	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₂⁴	—	172	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	86	2	no	—
294	C₂×Q₈	—	344	2	no	—
295	C₂×Q₈	—	172	2	no	—
296	C₂×Q₈	—	172	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	43	1	no	—
301	C₂×D₄	—	86	1	no	—
302	C₂×D₄	—	344	2	no	—
303	C₂×D₄	—	344	4	no	—
304	C₂×D₄	—	172	2	no	—
305	C₂×D₄	—	172	4	no	—
306	C₂×D₄	—	172	2	no	—
307	C₂²×C₄	—	43	2	no	—
308	C₂²×C₄	—	172	2	no	—
309	C₂²×C₄	—	172	1	no	—
310	Q₁₆	—	2	1	no	—
311	Q₁₆	—	86	2	no	—
312	Q₁₆	—	86	2	no	—
313	Q₁₆	—	344	1	no	—
314	Q₁₆	—	172	4	no	—
315	Q₁₆	D₄×D₄₃	1	2	yes	complemented
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	8	1	no	—
319	D₈	—	43	2	no	—
320	D₈	—	86	1	no	—
321	D₈	—	172	4	no	—
322	C₂×C₈	—	43	2	no	—
323	C₂×C₈	—	86	2	no	—
324	C₂×C₈	—	86	2	no	—
325	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	43	1	no	—
330	C₄⋊C₄	—	86	1	no	—
331	C₄⋊C₄	—	172	2	no	—
332	C₄⋊C₄	—	172	1	no	—
333	C₄⋊C₄	—	172	1	no	—
334	C₂²⋊C₄	—	43	2	no	—
335	C₂²⋊C₄	—	172	2	no	—
336	C₂²⋊C₄	—	172	2	no	—
337	C₂²⋊C₄	—	172	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	D₄×D₄₃	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	43	2	no	—
342	C₁₆	—	86	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	43	2	no	—
345	C₂³	—	344	4	no	—
346	C₂³	—	344	4	no	—
347	C₂³	—	172	1	no	—
348	C₂³	—	688	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	344	4	no	—
352	Q₈	—	172	2	no	—
353	Q₈	—	172	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	8	2	no	—
357	D₄	—	16	1	no	—
358	D₄	—	43	4	no	—
359	D₄	—	86	2	no	—
360	D₄	—	344	4	no	—
361	D₄	—	344	4	no	—
362	D₄	—	172	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	43	2	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	344	4	no	—
369	C₂×C₄	—	344	2	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	2	no	—
372	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
373	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	86	2	no	—
377	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
378	C₈	#13063371	1	1	yes	characteristic
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	43	4	no	—
383	C₂²	—	86	2	no	—
384	C₂²	—	86	2	no	—
385	C₂²	—	344	1	no	—
386	C₂²	—	344	1	no	—
387	C₂²	—	172	2	no	—
388	C₂²	—	688	8	no	—
389	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	86	2	no	—
394	C₄	—	344	2	no	—
395	C₄	—	344	1	no	—
396	C₄	SD₃₂×D₄₃	1	2	yes	complemented
397	C₄	#14583533	1	1	yes	characteristic
398	C₄	#14583703	1	1	yes	characteristic
399	C₂	—	16	2	no	—
400	C₂	—	86	4	no	—
401	C₂	—	344	2	no	—
402	C₂	#19146267	1	1	yes	characteristic
403	C₂	C₂×SD₃₂×D₄₃	1	1	yes	characteristic
404	C₂	#19147741	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₃
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2207	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	#19146270	C₂
hypercenter	#2207	D₄₃
hypocenter	C₄₃	D₄×SD₃₂
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2207

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₄₃	C₂	semidirect
2. Q₁₆×D₁₇₂	C₂	semidirect
4. #19136850	C₂	semidirect
5. #19136690	C₂	semidirect
6. #19136641	C₂	semidirect
7. #19136525	C₂	semidirect
8. #19136510	C₂	semidirect
9. C₄×#13063268	C₂	semidirect
10. #19136414	C₂	semidirect
11. C₄₃×#2207	C₂	semidirect
12. C₂×Q₁₆×D₄₃	C₂²	semidirect
17. C₂×#13063269	C₂²	semidirect
18. C₂×#13063269	C₂²	semidirect
21. C₂×C₁₆×D₄₃	C₂²	semidirect
22. #14583279	C₂²	semidirect
23. #14583141	C₂²	semidirect
31. #14582726	C₂²	semidirect
32. #14582704	C₂²	semidirect
33. #14582703	C₂²	semidirect
35. (C₂×D₄₃)⋊C₁₆	C₂²	semidirect
36. C₄×C₄₃⋊C₁₆	C₂²	semidirect
37. C₂×SD₃₂×C₄₃	C₂²	semidirect
39. C₄×Q₁₆×C₄₃	C₂²	semidirect
40. C₄₃×C₄⋊C₁₆	C₂²	semidirect
41. C₄₃×#357	C₂²	semidirect
68. #13063268	D₄	semidirect
108. Q₁₆×C₄₃	C₂×D₄	semidirect
139. C₄₃⋊C₁₆	C₂×D₄	semidirect
164. D₁₇₂	SD₃₂	semidirect
187. C₂×D₄₃	C₂×SD₃₂	semidirect
191. C₄×C₄₃	C₂×SD₃₂	semidirect
203. #2207	D₄₃	semidirect
223. C₂×SD₃₂	C₂×D₄₃	semidirect
233. C₄×Q₁₆	C₂×D₄₃	semidirect
237. C₄⋊C₁₆	C₂×D₄₃	semidirect
241. #357	C₂×D₄₃	semidirect
244. C₄₃	D₄×SD₃₂	semidirect
315. Q₁₆	D₄×D₄₃	semidirect
396. C₄	SD₃₂×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₄₃	2
Q₁₆×D₁₇₂	2
#19146270	2
#19136850	2
#19136690	2
#19136641	2
#19136525	2
#19136510	2
C₄×#13063268	2
#19136414	2
C₄₃×#2207	2
D₄×SD₃₂	43