Subgroups — C₂²×#14583699 #26010403

Order 11008.

11294 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621898	C₂	1	2	yes	maximal, complemented
2	C₂×#14583699	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#13063358	C₂	1	4	yes	maximal, complemented
4	C₂²×#13063353	C₂	1	4	yes	maximal, complemented
5	C₂²×#13063347	C₂	1	4	yes	maximal, complemented
6	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10621898	—	2	2	no	—
8	C₂²×#10621898	—	2	2	no	—
9	C₂²×#10621898	—	2	24	no	—
10	C₂²×#10621898	C₂²	1	4	yes	—
11	C₂²×#10621898	C₂²	1	4	yes	complemented
12	C₂²×#10621898	C₂²	1	48	yes	complemented
13	C₂³×Dic₈₆	C₂²	1	2	yes	complemented
14	C₂³×D₁₇₂	C₂²	1	2	yes	complemented
15	C₂³×C₂²⋊D₄₃	—	2	2	no	—
16	C₂³×C₄×D₄₃	—	2	2	no	—
17	#14583699	C₂²	1	256	yes	direct product factor
18	C₂×#13063358	C₂²	1	96	yes	complemented
19	C₂×#13063353	C₂²	1	96	yes	complemented
20	C₂×#13063347	C₂²	1	96	yes	complemented
21	C₂²×Dic₁₇₂	C₂²	1	4	yes	complemented
22	C₂²×#10621873	C₂²	1	8	yes	complemented
23	C₂²×D₃₄₄	C₂²	1	4	yes	complemented
24	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₃	C₂²	1	4	yes	complemented
26	C₂²×M₁₆×C₄₃	C₂²	1	24	yes	complemented
27	C₂³×C₈×C₄₃	C₂²	1	2	yes	complemented
28	C₂⁴×D₄₃	—	2	2	no	—
29	C₂×#10621898	—	2	24	no	—
30	C₂×#10621898	—	2	24	no	—
31	C₂×#10621898	—	2	48	no	—
32	C₂×#10621898	—	2	192	no	—
33	C₂×#10621898	—	2	48	no	—
34	C₂×#10621898	C₂³	1	48	yes	—
35	C₂×#10621898	C₂³	1	48	yes	complemented
36	C₂×#10621898	C₂³	1	128	yes	complemented
37	C₂²×Dic₈₆	—	2	12	no	—
38	C₂²×Dic₈₆	—	2	2	no	—
39	C₂²×Dic₈₆	C₂³	1	4	yes	—
40	C₂²×Dic₈₆	C₂³	1	24	yes	complemented
41	C₂²×D₁₇₂	—	2	12	no	—
42	C₂²×D₁₇₂	—	2	2	no	—
43	C₂²×D₁₇₂	C₂³	1	4	yes	—
44	C₂²×D₁₇₂	C₂³	1	24	yes	complemented
45	C₂²×C₂²⋊D₄₃	—	2	4	no	—
46	C₂²×C₂²⋊D₄₃	—	2	4	no	—
47	C₂²×C₂²⋊D₄₃	—	2	48	no	—
48	C₂³×Dic₄₃	—	2	2	no	—
49	C₂²×C₄×D₄₃	—	2	4	no	—
50	C₂²×C₄×D₄₃	—	2	48	no	—
51	C₂²×C₄×D₄₃	—	2	4	no	—
52	#13063358	C₂³	1	256	yes	complemented
53	#13063353	C₂³	1	256	yes	complemented
54	#13063347	C₂³	1	256	yes	complemented
55	C₂×Dic₁₇₂	C₂³	1	48	yes	complemented
56	C₂×#10621873	C₂³	1	96	yes	complemented
57	C₂×D₃₄₄	C₂³	1	48	yes	complemented
58	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	D₄	1	2	yes	—
60	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	D₄	1	12	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₃	C₂³	1	12	yes	—
65	C₂×M₁₆×C₄₃	C₂³	1	48	yes	complemented
66	C₂×M₁₆×C₄₃	C₂³	1	64	yes	complemented
67	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
68	C₂²×C₈×C₄₃	C₂³	1	24	yes	complemented
69	C₂⁴×C₄₃	—	4	4	no	—
70	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
71	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂⁴×C₄₃	C₂×D₄	1	12	yes	—
73	C₂³×D₄₃	—	2	4	no	—
74	C₂³×D₄₃	—	2	24	no	—
75	C₂³×D₄₃	—	4	16	no	—
76	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₃	C₂×D₄	1	24	yes	—
78	C₂²×C₄×C₄₃	C₂×D₄	1	12	yes	—
79	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
80	C₂²×C₄×C₄₃	C₂×D₄	1	12	yes	—
81	C₂²×C₄×C₄₃	C₂×D₄	1	48	yes	—
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
85	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
86	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
87	C₂×C₂²⋊D₄₃	—	2	48	no	—
88	C₂×C₂²⋊D₄₃	—	2	48	no	—
89	C₂×C₂²⋊D₄₃	—	2	128	no	—
90	C₂²×Dic₄₃	—	2	4	no	—
91	C₂²×Dic₄₃	—	2	24	no	—
92	#10621898	—	2	96	no	—
93	#10621898	—	2	96	no	—
94	#10621898	—	2	128	no	—
95	#10621898	—	2	128	no	—
96	#10621898	C₂⁴	1	64	yes	—
97	#10621898	C₂⁴	1	64	yes	complemented
98	C₂×D₁₇₂	—	2	12	no	—
99	C₂×D₁₇₂	—	2	24	no	—
100	C₂×D₁₇₂	—	2	48	no	—
101	C₂×D₁₇₂	C₂⁴	1	24	yes	—
102	C₂×D₁₇₂	C₂⁴	1	32	yes	complemented
103	C₂×C₄×D₄₃	—	2	48	no	—
104	C₂×C₄×D₄₃	—	2	48	no	—
105	C₂×C₄×D₄₃	—	2	128	no	—
106	C₂×Dic₈₆	—	2	12	no	—
107	C₂×Dic₈₆	—	2	48	no	—
108	C₂×Dic₈₆	—	2	24	no	—
109	C₂×Dic₈₆	C₂⁴	1	24	yes	—
110	C₂×Dic₈₆	C₂⁴	1	32	yes	complemented
111	M₁₆×C₄₃	C₂⁴	1	64	yes	complemented
112	C₂×C₈×C₄₃	C₂⁴	1	24	yes	—
113	C₂×C₈×C₄₃	C₂⁴	1	32	yes	complemented
114	Dic₁₇₂	C₂⁴	1	64	yes	complemented
115	D₃₄₄	C₂⁴	1	64	yes	complemented
116	#10621873	C₂⁴	1	128	yes	complemented
117	C₂³×C₄₃	—	2	8	no	—
118	C₂³×C₄₃	—	2	4	no	—
119	C₂³×C₄₃	—	4	24	no	—
120	C₂³×C₄₃	C₂²×D₄	1	12	yes	—
121	C₂³×C₄₃	C₂²×D₄	1	6	yes	—
122	C₂³×C₄₃	C₂²×D₄	1	16	yes	—
123	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
124	C₂²×D₄₃	—	2	24	no	—
125	C₂²×D₄₃	—	2	32	no	—
126	C₂²×D₄₃	—	4	96	no	—
127	C₂²×D₄₃	—	4	16	no	—
128	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
129	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
130	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
131	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
132	C₂×C₄×C₄₃	C₂²×D₄	1	32	yes	—
133	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
134	C₂×C₄×C₄₃	C₂²×D₄	1	16	yes	—
135	C₂×C₄×C₄₃	C₂⁵	1	3	yes	—
136	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
137	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
138	C₂²⋊D₄₃	—	2	64	no	—
139	C₂²⋊D₄₃	—	2	64	no	—
140	C₂×Dic₄₃	—	2	24	no	—
141	C₂×Dic₄₃	—	2	32	no	—
142	D₁₇₂	—	2	24	no	—
143	D₁₇₂	—	2	32	no	—
144	D₁₇₂	C₂⁵	1	16	yes	—
145	C₄×D₄₃	—	2	64	no	—
146	C₄×D₄₃	—	2	64	no	—
147	Dic₈₆	—	2	24	no	—
148	Dic₈₆	—	2	32	no	—
149	Dic₈₆	C₂⁵	1	16	yes	—
150	C₈×C₄₃	C₂⁵	1	16	yes	—
151	C₂²×#575	—	43	1	no	maximal, Sylow
152	C₂²×C₄₃	—	2	24	no	—
153	C₂²×C₄₃	—	2	12	no	—
154	C₂²×C₄₃	—	4	16	no	—
155	C₂²×C₄₃	#575	1	4	yes	complemented
156	C₂²×C₄₃	C₂³×D₄	1	8	yes	—
157	C₂²×C₄₃	C₂³×D₄	1	4	yes	—
158	C₂²×C₄₃	C₂³×D₄	1	3	yes	—
159	C₂×D₄₃	—	2	16	no	—
160	C₂×D₄₃	—	4	64	no	—
161	C₂×D₄₃	—	4	48	no	—
162	C₄×C₄₃	C₂³×D₄	1	3	yes	—
163	C₄×C₄₃	C₂³×D₄	1	8	yes	—
164	C₄×C₄₃	C₂³×D₄	1	4	yes	—
165	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
166	Dic₄₃	—	2	16	no	—
167	C₂³×#41	—	43	2	no	—
168	C₂×#575	—	43	48	no	—
169	C₂²×#137	—	43	4	no	—
170	C₂²×AGL(1,ℤ/8)	—	43	4	no	—
171	C₂²×#135	—	43	4	no	—
172	C₂³×M₁₆	D₄₃	1	1	yes	characteristic, complemented
173	C₂×C₄₃	—	2	8	no	—
174	C₂×C₄₃	—	2	4	no	—
175	C₂×C₄₃	C₂×#575	1	6	yes	complemented
176	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
177	D₄₃	—	4	16	no	—
178	C₂²×#41	—	43	4	no	—
179	C₂²×#41	—	43	4	no	—
180	C₂²×#41	—	43	48	no	—
181	C₂²×#41	—	86	2	no	—
182	C₂²×#41	—	86	24	no	—
183	C₂²×#41	—	86	2	no	—
184	C₂³×Q₈	—	43	2	no	—
185	C₂³×D₄	—	43	2	no	—
186	C₂³×D₄	—	86	2	no	—
187	C₂⁴×C₄	—	86	2	no	—
188	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
189	#575	—	43	256	no	—
190	C₂×#137	—	43	96	no	—
191	C₂×AGL(1,ℤ/8)	—	43	96	no	—
192	C₂×#135	—	43	96	no	—
193	C₂²×Q₁₆	—	43	4	no	—
194	C₂²×SD₁₆	—	43	8	no	—
195	C₂²×D₈	—	43	4	no	—
196	C₂²×M₁₆	C₂×D₄₃	1	4	yes	complemented
197	C₂²×M₁₆	C₂×D₄₃	1	24	yes	complemented
198	C₂³×C₈	C₂×D₄₃	1	2	yes	complemented
199	C₄₃	C₂²×#575	1	1	yes	characteristic, complemented, Sylow
200	C₂⁵	—	86	2	no	—
201	C₂⁵	D₁₇₂	1	1	yes	characteristic
202	C₂×#41	—	43	48	no	—
203	C₂×#41	—	43	48	no	—
204	C₂×#41	—	43	128	no	—
205	C₂×#41	—	86	48	no	—
206	C₂×#41	—	86	24	no	—
207	C₂×#41	—	86	24	no	—
208	C₂×#41	—	86	48	no	—
209	C₂×#41	—	86	192	no	—
210	C₂²×Q₈	—	43	4	no	—
211	C₂²×Q₈	—	43	24	no	—
212	C₂²×Q₈	—	86	2	no	—
213	C₂²×Q₈	—	86	12	no	—
214	C₂²×D₄	—	43	4	no	—
215	C₂²×D₄	—	43	24	no	—
216	C₂²×D₄	—	86	4	no	—
217	C₂²×D₄	—	86	4	no	—
218	C₂²×D₄	—	86	48	no	—
219	C₂²×D₄	—	86	2	no	—
220	C₂²×D₄	—	86	12	no	—
221	C₂³×C₄	—	86	2	no	—
222	C₂³×C₄	—	86	4	no	—
223	C₂³×C₄	—	86	48	no	—
224	C₂³×C₄	—	86	4	no	—
225	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
226	C₂³×C₄	D₁₇₂	1	12	yes	—
227	C₂³×C₄	D₁₇₂	1	2	yes	—
228	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
229	C₂³×C₄	C₂²×D₄₃	1	12	yes	—
230	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
231	#137	—	43	256	no	—
232	AGL(1,ℤ/8)	—	43	256	no	—
233	#135	—	43	256	no	—
234	C₂×Q₁₆	—	43	48	no	—
235	C₂×SD₁₆	—	43	96	no	—
236	C₂×D₈	—	43	48	no	—
237	C₂×M₁₆	C₂²×D₄₃	1	48	yes	complemented
238	C₂×M₁₆	C₂²×D₄₃	1	64	yes	complemented
239	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
240	C₂²×C₈	C₂²×D₄₃	1	24	yes	complemented
241	C₂⁴	—	4	4	no	—
242	C₂⁴	—	86	24	no	—
243	C₂⁴	—	86	4	no	—
244	C₂⁴	—	172	16	no	—
245	C₂⁴	C₂×D₁₇₂	1	2	yes	—
246	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
247	C₂⁴	C₂×D₁₇₂	1	12	yes	—
248	#41	—	43	64	no	—
249	#41	—	43	64	no	—
250	#41	—	86	128	no	—
251	#41	—	86	96	no	—
252	#41	—	86	96	no	—
253	#41	—	86	128	no	—
254	C₂×Q₈	—	43	24	no	—
255	C₂×Q₈	—	43	32	no	—
256	C₂×Q₈	—	86	24	no	—
257	C₂×Q₈	—	86	12	no	—
258	C₂×Q₈	—	86	48	no	—
259	C₂×D₄	—	43	24	no	—
260	C₂×D₄	—	43	32	no	—
261	C₂×D₄	—	86	48	no	—
262	C₂×D₄	—	86	48	no	—
263	C₂×D₄	—	86	128	no	—
264	C₂×D₄	—	86	24	no	—
265	C₂×D₄	—	86	12	no	—
266	C₂×D₄	—	86	48	no	—
267	C₂²×C₄	—	86	24	no	—
268	C₂²×C₄	—	86	4	no	—
269	C₂²×C₄	—	86	48	no	—
270	C₂²×C₄	—	86	48	no	—
271	C₂²×C₄	—	86	128	no	—
272	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
273	C₂²×C₄	C₂×D₁₇₂	1	24	yes	—
274	C₂²×C₄	C₂×D₁₇₂	1	12	yes	—
275	C₂²×C₄	C₂×D₁₇₂	1	6	yes	—
276	C₂²×C₄	C₂×D₁₇₂	1	12	yes	—
277	C₂²×C₄	C₂×D₁₇₂	1	48	yes	—
278	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
279	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
280	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
281	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
282	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
283	Q₁₆	—	43	64	no	—
284	SD₁₆	—	43	128	no	—
285	D₈	—	43	64	no	—
286	M₁₆	C₂³×D₄₃	1	64	yes	complemented
287	C₂×C₈	C₂³×D₄₃	1	24	yes	—
288	C₂×C₈	C₂³×D₄₃	1	32	yes	complemented
289	C₂³	—	2	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	4	24	no	—
292	C₂³	—	86	32	no	—
293	C₂³	—	86	24	no	—
294	C₂³	—	172	96	no	—
295	C₂³	—	172	16	no	—
296	C₂³	C₂²×D₁₇₂	1	12	yes	—
297	C₂³	C₂²×D₁₇₂	1	6	yes	—
298	C₂³	C₂²×D₁₇₂	1	16	yes	—
299	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
300	Q₈	—	43	16	no	—
301	Q₈	—	86	32	no	—
302	Q₈	—	86	24	no	—
303	D₄	—	43	16	no	—
304	D₄	—	86	64	no	—
305	D₄	—	86	64	no	—
306	D₄	—	86	32	no	—
307	D₄	—	86	24	no	—
308	C₂×C₄	—	86	32	no	—
309	C₂×C₄	—	86	24	no	—
310	C₂×C₄	—	86	64	no	—
311	C₂×C₄	—	86	64	no	—
312	C₂×C₄	C₂²×D₁₇₂	1	6	yes	—
313	C₂×C₄	C₂²×D₁₇₂	1	12	yes	—
314	C₂×C₄	C₂²×D₁₇₂	1	32	yes	—
315	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
316	C₂×C₄	C₂²×D₁₇₂	1	24	yes	—
317	C₂×C₄	C₂²×D₁₇₂	1	12	yes	—
318	C₂×C₄	C₂²×D₁₇₂	1	16	yes	—
319	C₂×C₄	C₂⁴×D₄₃	1	3	yes	—
320	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
321	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
322	C₈	C₂⁴×D₄₃	1	16	yes	—
323	C₂²	—	2	24	no	—
324	C₂²	—	2	12	no	—
325	C₂²	—	4	16	no	—
326	C₂²	—	86	16	no	—
327	C₂²	—	172	64	no	—
328	C₂²	—	172	48	no	—
329	C₂²	#14583699	1	4	yes	direct product factor
330	C₂²	C₂³×D₁₇₂	1	8	yes	—
331	C₂²	C₂³×D₁₇₂	1	4	yes	—
332	C₂²	C₂³×D₁₇₂	1	3	yes	—
333	C₄	—	86	16	no	—
334	C₄	C₂³×D₁₇₂	1	4	yes	—
335	C₄	C₂³×D₁₇₂	1	8	yes	—
336	C₄	C₂³×D₁₇₂	1	3	yes	—
337	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
338	C₂	—	2	8	no	—
339	C₂	—	2	4	no	—
340	C₂	—	172	16	no	—
341	C₂	C₂×#14583699	1	6	yes	direct product factor
342	C₂	C₂⁴×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₂³×M₁₆×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
hypercenter	C₂³×M₁₆	D₄₃
hypocenter	C₄₃	C₂²×#575
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂³×#10621898	C₂	semidirect
2. C₂×#14583699	C₂	direct (N × H)
3. C₂²×#13063358	C₂	semidirect
4. C₂²×#13063353	C₂	semidirect
5. C₂²×#13063347	C₂	semidirect
6. C₂³×M₁₆×C₄₃	C₂	semidirect
11. C₂²×#10621898	C₂²	semidirect
12. C₂²×#10621898	C₂²	semidirect
13. C₂³×Dic₈₆	C₂²	semidirect
14. C₂³×D₁₇₂	C₂²	semidirect
17. #14583699	C₂²	direct (N × H)
18. C₂×#13063358	C₂²	semidirect
19. C₂×#13063353	C₂²	semidirect
20. C₂×#13063347	C₂²	semidirect
21. C₂²×Dic₁₇₂	C₂²	semidirect
22. C₂²×#10621873	C₂²	semidirect
23. C₂²×D₃₄₄	C₂²	semidirect
25. C₂²×M₁₆×C₄₃	C₂²	semidirect
26. C₂²×M₁₆×C₄₃	C₂²	semidirect
27. C₂³×C₈×C₄₃	C₂²	semidirect
35. C₂×#10621898	C₂³	semidirect
36. C₂×#10621898	C₂³	semidirect
40. C₂²×Dic₈₆	C₂³	semidirect
44. C₂²×D₁₇₂	C₂³	semidirect
52. #13063358	C₂³	semidirect
53. #13063353	C₂³	semidirect
54. #13063347	C₂³	semidirect
55. C₂×Dic₁₇₂	C₂³	semidirect
56. C₂×#10621873	C₂³	semidirect
57. C₂×D₃₄₄	C₂³	semidirect
65. C₂×M₁₆×C₄₃	C₂³	semidirect
66. C₂×M₁₆×C₄₃	C₂³	semidirect
68. C₂²×C₈×C₄₃	C₂³	semidirect
97. #10621898	C₂⁴	semidirect
102. C₂×D₁₇₂	C₂⁴	semidirect
110. C₂×Dic₈₆	C₂⁴	semidirect
111. M₁₆×C₄₃	C₂⁴	semidirect
113. C₂×C₈×C₄₃	C₂⁴	semidirect
114. Dic₁₇₂	C₂⁴	semidirect
115. D₃₄₄	C₂⁴	semidirect
116. #10621873	C₂⁴	semidirect
155. C₂²×C₄₃	#575	semidirect
172. C₂³×M₁₆	D₄₃	semidirect
175. C₂×C₄₃	C₂×#575	semidirect
196. C₂²×M₁₆	C₂×D₄₃	semidirect
197. C₂²×M₁₆	C₂×D₄₃	semidirect
198. C₂³×C₈	C₂×D₄₃	semidirect
199. C₄₃	C₂²×#575	semidirect
237. C₂×M₁₆	C₂²×D₄₃	semidirect
238. C₂×M₁₆	C₂²×D₄₃	semidirect
240. C₂²×C₈	C₂²×D₄₃	semidirect
286. M₁₆	C₂³×D₄₃	semidirect
288. C₂×C₈	C₂³×D₄₃	semidirect
329. C₂²	#14583699	direct (N × H)
341. C₂	C₂×#14583699	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10621898	2
C₂×#14583699	2
C₂²×#13063358	2
C₂²×#13063353	2
C₂²×#13063347	2
C₂³×M₁₆×C₄₃	2
C₂²×#575	43

Subgroups — C22×#14583699 #26010403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583699 #26010403