Subgroups — #25253262

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583331	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146282	C₂	1	2	yes	maximal, complemented
4	#19136856	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136686	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136681	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136651	C₂	1	2	yes	maximal, complemented
8	#19136526	C₂	1	2	yes	maximal, complemented
9	#19136520	C₂	1	2	yes	maximal, complemented
10	C₄×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	2	yes	complemented
13	C₂²×D₃₄₄	C₂²	1	2	yes	—
14	#14583545	—	2	2	no	—
15	#14583331	—	2	4	no	—
16	C₂×Dic₃₄₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×#13063270	C₂²	1	2	yes	complemented
18	C₂×#13063270	C₂²	1	2	yes	complemented
19	C₂×D₆₈₈	—	2	4	no	—
20	C₂×D₆₈₈	C₂²	1	2	yes	—
21	C₂×D₆₈₈	C₂²	1	1	yes	characteristic
22	C₂×D₆₈₈	C₂²	1	1	yes	characteristic
23	#14583283	C₂²	1	2	yes	complemented
24	#14583140	C₂²	1	2	yes	—
25	#14583135	C₂²	1	2	yes	complemented
26	#14583115	—	2	2	no	—
27	#14583052	—	2	2	no	—
28	#14583046	—	2	2	no	—
29	C₄×D₃₄₄	C₂²	1	2	yes	complemented
30	#14582725	C₂²	1	1	yes	characteristic, complemented
31	#14582704	C₂²	1	2	yes	complemented
32	#14582701	C₂²	1	2	yes	complemented
33	#14582701	C₂²	1	2	yes	complemented
34	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
36	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₄₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₄₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#10621898	—	2	2	no	—
42	C₂²×D₁₇₂	—	2	2	no	—
43	#13063347	—	2	4	no	—
44	#13063347	—	4	2	no	—
45	C₂×Dic₁₇₂	C₂³	1	2	yes	—
46	C₂×#10621873	—	2	2	no	—
47	C₂×#10621873	—	2	2	no	—
48	C₂×D₃₄₄	—	2	4	no	—
49	C₂×D₃₄₄	—	2	2	no	—
50	C₂×D₃₄₄	—	4	2	no	—
51	C₂×D₃₄₄	C₂³	1	2	yes	—
52	C₂×D₃₄₄	C₂³	1	2	yes	—
53	#13063313	—	2	2	no	—
54	#13063310	—	4	2	no	—
55	#13063304	—	2	2	no	—
56	#13063299	—	2	2	no	—
57	#13063298	—	4	2	no	—
58	#13063293	—	4	2	no	—
59	C₄×D₁₇₂	—	2	2	no	—
60	C₂²⋊C₄×D₄₃	—	4	2	no	—
61	Dic₃₄₄	—	2	2	no	—
62	#13063270	—	2	4	no	—
63	#13063270	—	4	2	no	—
64	D₆₈₈	—	2	4	no	—
65	D₆₈₈	—	2	2	no	—
66	D₆₈₈	D₄	1	4	yes	complemented
67	#13063259	C₂³	1	2	yes	—
68	#13063250	—	2	2	no	—
69	#13063247	—	2	2	no	—
70	#13063247	—	2	2	no	—
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₁₆×C₄₃	—	2	2	no	—
75	C₂×C₁₆×C₄₃	—	2	2	no	—
76	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
81	C₂²⋊C₈×C₄₃	D₄	1	1	yes	characteristic
82	C₂²⋊C₈×C₄₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂³×D₄₃	—	4	2	no	—
85	C₂×D₄×C₄₃	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₂²⋊D₄₃	—	4	2	no	—
89	C₂×C₂²⋊D₄₃	—	4	2	no	—
90	#10621898	—	4	4	no	—
91	#10621898	—	8	2	no	—
92	C₂×D₁₇₂	—	2	2	no	—
93	C₂×D₁₇₂	—	2	2	no	—
94	C₂×D₁₇₂	—	4	2	no	—
95	C₂×D₁₇₂	—	4	4	no	—
96	C₂×D₁₇₂	—	8	2	no	—
97	C₂×C₄×D₄₃	—	4	2	no	—
98	C₂×C₄×D₄₃	—	4	2	no	—
99	C₂×Dic₈₆	—	2	2	no	—
100	C₂×C₈×C₄₃	—	2	1	no	—
101	C₂×C₈×C₄₃	—	2	1	no	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	—	2	1	no	—
104	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₄₃	D₈	1	1	yes	characteristic
109	C₂²⋊C₄×C₄₃	D₈	1	1	yes	characteristic
110	C₂²⋊C₄×C₄₃	D₈	1	1	yes	characteristic
111	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²⋊Dic₄₃	—	4	2	no	—
113	(C₂×D₄₃)⋊C₄	—	4	2	no	—
114	(C₂×D₄₃)⋊C₄	—	4	2	no	—
115	(C₂×D₄₃)⋊C₄	—	4	2	no	—
116	(C₂×D₄₃)⋊C₄	—	4	2	no	—
117	C₄⋊Dic₄₃	—	2	2	no	—
118	Dic₄₃⋊C₄	—	4	2	no	—
119	Dic₁₇₂	—	2	2	no	—
120	Dic₁₇₂	—	2	2	no	—
121	D₃₄₄	—	2	2	no	—
122	D₃₄₄	—	2	2	no	—
123	D₃₄₄	—	2	2	no	—
124	D₃₄₄	—	4	4	no	—
125	D₃₄₄	C₂×D₄	1	4	yes	—
126	#10621873	—	4	4	no	—
127	#10621873	—	8	2	no	—
128	C₁₆×C₄₃	—	2	1	no	—
129	C₁₆×C₄₃	—	2	1	no	—
130	C₁₆×C₄₃	—	2	1	no	—
131	C₁₆×C₄₃	C₂×D₄	1	2	yes	—
132	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
133	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
134	C₂²×D₄₃	—	4	2	no	—
135	C₂²×D₄₃	—	4	2	no	—
136	C₂²×D₄₃	—	8	4	no	—
137	C₂²×D₄₃	—	8	4	no	—
138	C₂²×D₄₃	—	16	2	no	—
139	D₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₄₃	—	8	4	no	—
150	C₂²⋊D₄₃	—	16	2	no	—
151	C₂×Dic₄₃	—	4	2	no	—
152	C₂×Dic₄₃	—	4	2	no	—
153	D₁₇₂	—	2	4	no	—
154	D₁₇₂	—	4	2	no	—
155	D₁₇₂	—	4	2	no	—
156	D₁₇₂	—	4	2	no	—
157	D₁₇₂	—	8	4	no	—
158	C₄×D₄₃	—	8	4	no	—
159	C₄×D₄₃	—	16	2	no	—
160	Dic₈₆	—	4	2	no	—
161	Dic₈₆	—	4	2	no	—
162	C₈×C₄₃	—	2	1	no	—
163	C₈×C₄₃	—	2	1	no	—
164	C₈×C₄₃	—	2	1	no	—
165	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
167	#33846	—	43	1	no	maximal, Sylow
168	C₂²×C₄₃	—	2	1	no	—
169	C₂²×C₄₃	—	2	1	no	—
170	C₂²×C₄₃	—	2	1	no	—
171	C₂²×C₄₃	—	2	1	no	—
172	C₂²×C₄₃	—	2	1	no	—
173	C₂²×C₄₃	#508	1	2	yes	complemented
174	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
175	C₂×D₄₃	—	4	4	no	—
176	C₂×D₄₃	—	8	2	no	—
177	C₂×D₄₃	—	8	2	no	—
178	C₂×D₄₃	—	8	2	no	—
179	C₂×D₄₃	—	8	2	no	—
180	C₂×D₄₃	—	8	2	no	—
181	C₂×D₄₃	—	16	8	no	—
182	C₄×C₄₃	—	2	1	no	—
183	C₄×C₄₃	—	2	1	no	—
184	C₄×C₄₃	—	2	1	no	—
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	D₄²	1	1	yes	characteristic
187	C₄×C₄₃	#576	1	1	yes	characteristic
188	Dic₄₃	—	8	2	no	—
189	Dic₄₃	—	8	2	no	—
190	C₂×#508	—	43	1	no	—
191	C₂²×D₁₆	—	43	1	no	—
192	#3280	—	43	2	no	—
193	#2249	—	43	1	no	—
194	#2216	—	43	1	no	—
195	#2215	—	43	1	no	—
196	#2210	—	43	2	no	—
197	#2187	—	43	2	no	—
198	#2186	—	43	2	no	—
199	C₄×D₁₆	—	43	1	no	—
200	D₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
201	C₂×C₄₃	—	2	2	no	—
202	C₂×C₄₃	—	4	1	no	—
203	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
204	C₂×C₄₃	C₂×#508	1	1	yes	characteristic
205	C₂×C₄₃	#3415	1	1	yes	characteristic
206	D₄₃	—	8	4	no	—
207	D₄₃	—	16	2	no	—
208	C₂×#135	—	43	2	no	—
209	C₂²×D₈	—	43	2	no	—
210	#546	—	86	2	no	—
211	#508	—	86	4	no	—
212	C₂×Q₃₂	—	43	1	no	—
213	C₂×SD₃₂	—	43	2	no	—
214	C₂×SD₃₂	—	43	2	no	—
215	C₂×D₁₆	—	43	1	no	—
216	C₂×D₁₆	—	43	2	no	—
217	C₂×D₁₆	—	43	1	no	—
218	C₂×D₁₆	—	86	4	no	—
219	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
220	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
221	#495	—	43	2	no	—
222	#467	—	43	2	no	—
223	#466	—	43	2	no	—
224	#463	—	86	2	no	—
225	#450	—	86	2	no	—
226	#449	—	86	2	no	—
227	C₄×D₈	—	43	2	no	—
228	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
229	#366	—	43	1	no	—
230	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
231	#358	—	43	2	no	—
232	#357	—	43	2	no	—
233	#357	—	43	2	no	—
234	C₂²⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
235	C₂²⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
236	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
237	C₄₃	#33846	1	1	yes	characteristic, complemented, Sylow
238	C₂×#41	—	86	2	no	—
239	C₂²×D₄	—	86	2	no	—
240	#135	—	86	4	no	—
241	#135	—	172	2	no	—
242	C₂×Q₁₆	—	43	2	no	—
243	C₂×SD₁₆	—	86	2	no	—
244	C₂×SD₁₆	—	86	2	no	—
245	C₂×D₈	—	43	2	no	—
246	C₂×D₈	—	43	2	no	—
247	C₂×D₈	—	86	4	no	—
248	C₂×D₈	—	86	2	no	—
249	C₂×D₈	—	172	2	no	—
250	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
252	#124	—	86	2	no	—
253	#123	—	172	2	no	—
254	C₂²⋊Q₈	—	86	2	no	—
255	#121	—	86	2	no	—
256	#121	—	172	2	no	—
257	#120	—	172	2	no	—
258	C₄×D₄	—	86	2	no	—
259	C₄×D₄	D₁₇₂	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	172	2	no	—
261	Q₃₂	—	86	2	no	—
262	SD₃₂	—	86	4	no	—
263	SD₃₂	—	172	2	no	—
264	D₁₆	—	43	4	no	—
265	D₁₆	—	86	4	no	—
266	D₁₆	—	86	2	no	—
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	2	2	no	—
269	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
270	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
271	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
272	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
273	#107	—	43	2	no	—
274	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
275	#103	—	86	2	no	—
276	#102	—	86	2	no	—
277	#102	—	86	2	no	—
278	C₂²⋊C₈	D₁₇₂	1	1	yes	characteristic
279	C₂²⋊C₈	D₁₇₂	1	1	yes	characteristic
280	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
281	C₂⁴	—	172	2	no	—
282	#41	—	344	2	no	—
283	#41	—	172	4	no	—
284	C₂×Q₈	—	86	2	no	—
285	C₂×D₄	—	86	2	no	—
286	C₂×D₄	—	86	2	no	—
287	C₂×D₄	—	344	2	no	—
288	C₂×D₄	—	172	4	no	—
289	C₂×D₄	—	172	2	no	—
290	C₂×D₄	—	172	2	no	—
291	C₂×D₄	—	172	2	no	—
292	C₂×D₄	D₃₄₄	1	1	yes	characteristic
293	C₂²×C₄	—	172	2	no	—
294	C₂²×C₄	—	172	2	no	—
295	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
297	Q₁₆	—	86	2	no	—
298	Q₁₆	—	86	2	no	—
299	SD₁₆	—	344	2	no	—
300	SD₁₆	—	172	4	no	—
301	D₈	—	43	4	no	—
302	D₈	—	86	2	no	—
303	D₈	—	86	2	no	—
304	D₈	—	86	2	no	—
305	D₈	—	172	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
311	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
312	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
313	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
314	C₄⋊C₄	—	86	2	no	—
315	C₄⋊C₄	—	172	2	no	—
316	C₄⋊C₄	D₃₄₄	1	1	yes	characteristic
317	C₂²⋊C₄	—	172	2	no	—
318	C₂²⋊C₄	—	172	2	no	—
319	C₂²⋊C₄	—	172	2	no	—
320	C₂²⋊C₄	—	172	2	no	—
321	C₂²⋊C₄	—	172	2	no	—
322	C₂²⋊C₄	D₃₄₄	1	1	yes	characteristic
323	C₂²⋊C₄	D₃₄₄	1	1	yes	characteristic
324	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	1	no	—
328	C₁₆	D₄×D₄₃	1	2	yes	—
329	C₂³	—	344	4	no	—
330	C₂³	—	344	4	no	—
331	C₂³	—	172	2	no	—
332	C₂³	—	172	2	no	—
333	C₂³	—	688	2	no	—
334	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
335	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
336	Q₈	—	172	2	no	—
337	Q₈	—	172	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	86	4	no	—
340	D₄	—	344	4	no	—
341	D₄	—	344	4	no	—
342	D₄	—	172	2	no	—
343	D₄	—	172	2	no	—
344	D₄	—	172	2	no	—
345	D₄	—	688	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	344	4	no	—
351	C₂×C₄	—	172	2	no	—
352	C₂×C₄	—	172	2	no	—
353	C₂×C₄	—	688	2	no	—
354	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
355	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
356	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
357	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
363	C₈	#13063371	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	344	2	no	—
370	C₂²	—	344	2	no	—
371	C₂²	—	344	2	no	—
372	C₂²	—	344	2	no	—
373	C₂²	—	344	2	no	—
374	C₂²	—	172	4	no	—
375	C₂²	—	688	8	no	—
376	C₂²	#14583331	1	2	yes	complemented
377	C₂²	C₂²×D₃₄₄	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	344	2	no	—
383	C₄	—	344	2	no	—
384	C₄	D₄×D₁₇₂	1	1	yes	characteristic
385	C₄	#14583704	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	344	4	no	—
389	C₂	—	688	2	no	—
390	C₂	D₄×D₃₄₄	1	1	yes	characteristic
391	C₂	C₂×#14583331	1	1	yes	characteristic
392	C₂	#19147736	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃₄₄
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	D₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₈
hypercenter	D₄×C₁₆	D₄₃
hypocenter	C₄₃	#33846
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#14583331	C₂	semidirect
2. C₂²×D₆₈₈	C₂	semidirect
3. #19146282	C₂	semidirect
4. #19136856	C₂	semidirect
5. #19136686	C₂	semidirect
6. #19136681	C₂	semidirect
7. #19136651	C₂	semidirect
8. #19136526	C₂	semidirect
9. #19136520	C₂	semidirect
10. C₄×D₆₈₈	C₂	semidirect
11. D₄×C₁₆×C₄₃	C₂	semidirect
12. C₂×#13063347	C₂²	semidirect
16. C₂×Dic₃₄₄	C₂²	semidirect
17. C₂×#13063270	C₂²	semidirect
18. C₂×#13063270	C₂²	semidirect
23. #14583283	C₂²	semidirect
25. #14583135	C₂²	semidirect
29. C₄×D₃₄₄	C₂²	semidirect
30. #14582725	C₂²	semidirect
31. #14582704	C₂²	semidirect
32. #14582701	C₂²	semidirect
33. #14582701	C₂²	semidirect
35. C₂²×C₁₆×C₄₃	C₂²	semidirect
37. C₄₃×C₄⋊C₁₆	C₂²	semidirect
39. C₄₃×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₄₃	C₂²	semidirect
66. D₆₈₈	D₄	semidirect
173. C₂²×C₄₃	#508	semidirect
200. D₄×C₁₆	D₄₃	semidirect
220. C₂²×C₁₆	C₂×D₄₃	semidirect
230. C₄⋊C₁₆	C₂×D₄₃	semidirect
235. C₂²⋊C₁₆	C₂×D₄₃	semidirect
236. C₄×C₁₆	C₂×D₄₃	semidirect
237. C₄₃	#33846	semidirect
376. C₂²	#14583331	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583331	2
C₂²×D₆₈₈	2
#19146282	2
#19136856	2
#19136686	2
#19136681	2
#19136651	2
#19136526	2
#19136520	2
C₄×D₆₈₈	2
D₄×C₁₆×C₄₃	2
#33846	43