Subgroups — C₂×M₃₂×#64408 #34029781

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	M₃₂×#64408	C₂	1	8	yes	maximal, direct product factor
4	C₂×#17989474	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×#64408	C₂	1	2	yes	maximal, complemented
6	C₂×M₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11924036	C₄	1	1	yes	characteristic
8	C₂²×C₄×#64408	C₄	1	1	yes	characteristic
9	C₂×#14556666	C₄	1	2	yes	complemented
10	#17989643	C₄	1	4	yes	complemented
11	#17989643	C₂²	1	4	yes	—
12	C₂×#14556665	C₄	1	2	yes	complemented
13	C₂×#14556664	C₂²	1	2	yes	—
14	C₂×C₈×#64408	C₄	1	1	yes	characteristic
15	C₂×C₈×#64408	C₄	1	1	yes	characteristic
16	C₂×C₈×#64408	C₄	1	4	yes	—
17	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
18	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
19	C₂×C₈×#64408	C₂²	1	4	yes	—
20	#17989474	C₂²	1	8	yes	complemented
21	C₁₆×#64408	C₂²	1	8	yes	complemented
22	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×#14556531	C₄	1	1	yes	characteristic, complemented
24	C₂×#14556530	C₄	1	2	yes	complemented
25	M₃₂×D₇₃	C₄	1	4	yes	complemented
26	M₃₂×D₇₃	C₂²	1	4	yes	—
27	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
28	C₂×M₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
29	C₂³×#64408	C₈	1	2	yes	—
30	C₂×#11924036	C₈	1	2	yes	—
31	C₂×#11924036	C₈	1	4	yes	—
32	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
33	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
34	C₂×#11924036	C₂×C₄	1	4	yes	—
35	C₂²×#10596833	C₈	1	2	yes	—
36	C₂×C₄×#64408	C₈	1	4	yes	—
37	C₂×C₄×#64408	C₈	1	2	yes	—
38	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
40	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
41	#14556666	C₂×C₄	1	8	yes	complemented
42	#14556665	C₂×C₄	1	8	yes	complemented
43	#14556664	C₂×C₄	1	4	yes	complemented
44	#14556664	C₂³	1	4	yes	—
45	C₂×#11924031	C₂×C₄	1	4	yes	complemented
46	C₈×#64408	C₂×C₄	1	2	yes	—
47	C₈×#64408	C₂×C₄	1	2	yes	—
48	C₈×#64408	C₂×C₄	1	4	yes	—
49	C₈×#64408	C₂×C₄	1	4	yes	—
50	C₈×#64408	C₂³	1	2	yes	—
51	C₈×#64408	C₂³	1	2	yes	—
52	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂³	1	2	yes	—
62	#14556531	C₂×C₄	1	4	yes	complemented
63	#14556530	C₂×C₄	1	8	yes	complemented
64	C₂×#11924003	C₂×C₄	1	2	yes	complemented
65	C₁₆×D₇₃	C₂×C₄	1	4	yes	complemented
66	C₁₆×D₇₃	C₂³	1	4	yes	—
67	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
68	M₃₂×C₇₃	C₂×C₄	1	4	yes	complemented
69	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
70	C₂²×#64408	—	2	8	no	—
71	C₂²×#64408	C₂×C₈	1	2	yes	—
72	C₂²×#64408	C₂×C₈	1	8	yes	—
73	C₂²×#64408	C₂×C₈	1	2	yes	—
74	#11924036	C₂×C₈	1	8	yes	—
75	#11924036	C₂×C₈	1	2	yes	—
76	#11924036	C₂×C₈	1	2	yes	—
77	#11924036	C₂²×C₄	1	2	yes	—
78	#11924036	C₂²×C₄	1	2	yes	—
79	C₂×#10596833	C₂×C₈	1	8	yes	—
80	C₂×#10596833	C₂×C₈	1	2	yes	—
81	C₂×#10596833	C₂×C₈	1	2	yes	—
82	C₄×#64408	C₂×C₈	1	2	yes	—
83	C₄×#64408	C₂×C₈	1	8	yes	—
84	C₄×#64408	C₂×C₈	1	2	yes	—
85	C₄×#64408	C₂²×C₄	1	2	yes	—
86	C₄×#64408	C₂²×C₄	1	2	yes	—
87	#11924031	C₂²×C₄	1	8	yes	complemented
88	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
89	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₄²	1	2	yes	—
91	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
97	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×#10596831	C₄²	1	2	yes	—
99	C₂×#10596831	C₄²	1	1	yes	characteristic
100	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
101	C₂×#10596831	C₂²×C₄	1	2	yes	—
102	C₈×D₇₃	C₄²	1	2	yes	—
103	C₈×D₇₃	C₄²	1	2	yes	—
104	C₈×D₇₃	C₄²	1	2	yes	—
105	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₈×D₇₃	C₂²×C₄	1	2	yes	—
107	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₈×D₇₃	C₂²×C₄	1	2	yes	—
109	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
110	C₈×D₇₃	C₂²×C₄	1	2	yes	—
111	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
112	#11924003	C₂²×C₄	1	4	yes	complemented
113	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
114	C₂×C₈×C₇₃	C₄²	1	2	yes	—
115	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
116	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₁₆×C₇₃	C₂²×C₄	1	4	yes	complemented
119	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
120	C₂²×D₇₃	—	2	4	no	—
121	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
122	C₂²×D₇₃	C₄×C₈	1	2	yes	—
123	C₂²×D₇₃	C₂²×C₈	1	2	yes	—
124	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
125	C₂×#64408	—	2	4	no	—
126	C₂×#64408	—	2	16	no	—
127	C₂×#64408	M₃₂	1	8	yes	direct product factor
128	C₂×#64408	C₂²×C₈	1	4	yes	—
129	C₂×#64408	C₂²×C₈	1	4	yes	—
130	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
131	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
132	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
134	C₂×Dic₇₃	C₄×C₈	1	2	yes	—
135	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
136	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
137	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
138	C₄×D₇₃	C₄×C₈	1	2	yes	—
139	C₄×D₇₃	C₄×C₈	1	2	yes	—
140	C₄×D₇₃	C₄×C₈	1	2	yes	—
141	C₄×D₇₃	C₂×C₄²	1	2	yes	—
142	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
143	C₄×D₇₃	C₂²×C₈	1	2	yes	—
144	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
145	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
146	C₄×D₇₃	C₂²×C₈	1	2	yes	—
147	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
148	#10596833	C₂²×C₈	1	4	yes	—
149	#10596833	C₂²×C₈	1	4	yes	—
150	C₈×C₇₃	C₂×C₄²	1	2	yes	—
151	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
152	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
153	#10596831	C₂×C₄²	1	1	yes	characteristic
154	#10596831	C₂×C₄²	1	2	yes	—
155	#10596831	C₂³×C₄	1	1	yes	characteristic
156	C₂²×C₇₃	—	2	2	no	—
157	C₂²×C₇₃	C₂×C₄×C₈	1	2	yes	—
158	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
159	C₂×D₇₃	—	2	2	no	—
160	C₂×D₇₃	—	2	4	no	—
161	C₂×D₇₃	—	2	4	no	—
162	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
163	C₂×D₇₃	C₂×C₄×C₈	1	1	yes	characteristic
164	C₂×D₇₃	C₂×M₃₂	1	4	yes	—
165	C₂×D₇₃	C₂³×C₈	1	1	yes	characteristic
166	#64408	—	2	4	no	—
167	#64408	C₂×M₃₂	1	8	yes	direct product factor
168	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
169	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
170	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
171	Dic₇₃	C₂×C₄×C₈	1	1	yes	characteristic
172	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
173	Dic₇₃	C₂³×C₈	1	1	yes	characteristic
174	C₂×C₄×M₃₂	—	73	1	no	maximal, Sylow
175	C₂×C₇₃	—	2	2	no	—
176	C₂×C₇₃	C₄×M₃₂	1	2	yes	complemented
177	C₂×C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic
178	D₇₃	—	2	2	no	—
179	D₇₃	C₄×M₃₂	1	2	yes	complemented
180	D₇₃	C₂²×M₃₂	1	2	yes	—
181	C₂²×M₃₂	—	73	1	no	—
182	C₂²×M₃₂	—	73	1	no	—
183	C₂²×C₄×C₈	—	73	1	no	—
184	C₄×M₃₂	—	73	8	no	—
185	C₂×#346	—	73	2	no	—
186	C₂×C₄×C₁₆	—	73	2	no	—
187	C₇₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
188	C₂³×C₈	—	73	1	no	—
189	C₂³×C₈	—	73	1	no	—
190	C₂²×C₄²	—	73	1	no	—
191	C₂×M₃₂	—	73	2	no	—
192	C₂×M₃₂	—	73	4	no	—
193	C₂×M₃₂	—	73	4	no	—
194	C₂×M₃₂	—	73	2	no	—
195	C₂×M₃₂	—	73	1	no	—
196	C₂×M₃₂	—	73	4	no	—
197	C₂×M₃₂	—	73	4	no	—
198	C₂×M₃₂	—	73	2	no	—
199	C₂×M₃₂	#64408	1	1	yes	characteristic, direct product factor
200	C₂²×C₁₆	—	73	2	no	—
201	C₂²×C₁₆	—	73	2	no	—
202	C₂×C₄×C₈	—	73	1	no	—
203	C₂×C₄×C₈	—	73	1	no	—
204	C₂×C₄×C₈	—	73	4	no	—
205	C₂×C₄×C₈	—	73	4	no	—
206	C₂×C₄×C₈	—	73	1	no	—
207	C₂×C₄×C₈	—	73	1	no	—
208	#346	—	73	8	no	—
209	C₄×C₁₆	—	73	8	no	—
210	C₂³×C₄	—	73	1	no	—
211	C₂³×C₄	—	73	2	no	—
212	C₂²×C₈	—	73	2	no	—
213	C₂²×C₈	—	73	4	no	—
214	C₂²×C₈	—	73	2	no	—
215	C₂²×C₈	—	73	1	no	—
216	C₂²×C₈	—	73	1	no	—
217	C₂²×C₈	—	73	4	no	—
218	C₂²×C₈	—	73	1	no	—
219	C₂²×C₈	—	73	2	no	—
220	C₂²×C₈	—	73	1	no	—
221	C₂²×C₈	—	73	1	no	—
222	C₂²×C₈	—	73	2	no	—
223	C₂²×C₈	—	73	2	no	—
224	C₂²×C₈	—	73	2	no	—
225	C₂²×C₈	—	73	1	no	—
226	C₂²×C₈	—	73	1	no	—
227	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
228	C₂×C₄²	—	73	1	no	—
229	C₂×C₄²	—	73	1	no	—
230	C₂×C₄²	—	73	4	no	—
231	C₂×C₄²	—	73	2	no	—
232	C₂×C₄²	—	73	4	no	—
233	M₃₂	—	73	8	no	—
234	M₃₂	—	73	8	no	—
235	M₃₂	—	73	4	no	—
236	M₃₂	—	73	8	no	—
237	M₃₂	C₂×#64408	1	4	yes	direct product factor
238	C₂×C₁₆	—	73	4	no	—
239	C₂×C₁₆	—	73	4	no	—
240	C₂×C₁₆	—	73	4	no	—
241	C₂×C₁₆	—	73	2	no	—
242	C₂×C₁₆	—	73	4	no	—
243	C₂×C₁₆	—	73	4	no	—
244	C₂×C₁₆	C₂×#64408	1	2	yes	complemented
245	C₄×C₈	—	73	2	no	—
246	C₄×C₈	—	73	2	no	—
247	C₄×C₈	—	73	2	no	—
248	C₄×C₈	—	73	2	no	—
249	C₄×C₈	—	73	4	no	—
250	C₄×C₈	—	73	4	no	—
251	C₂⁴	—	73	1	no	—
252	C₂²×C₄	—	73	2	no	—
253	C₂²×C₄	—	73	1	no	—
254	C₂²×C₄	—	73	1	no	—
255	C₂²×C₄	—	73	2	no	—
256	C₂²×C₄	—	73	2	no	—
257	C₂²×C₄	—	73	1	no	—
258	C₂²×C₄	—	73	2	no	—
259	C₂²×C₄	—	73	1	no	—
260	C₂²×C₄	—	73	2	no	—
261	C₂²×C₄	—	73	1	no	—
262	C₂²×C₄	—	73	8	no	—
263	C₂²×C₄	—	73	2	no	—
264	C₂²×C₄	—	146	8	no	—
265	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
266	C₂×C₈	—	73	8	no	—
267	C₂×C₈	—	73	2	no	—
268	C₂×C₈	—	73	2	no	—
269	C₂×C₈	—	73	2	no	—
270	C₂×C₈	—	73	2	no	—
271	C₂×C₈	—	73	8	no	—
272	C₂×C₈	—	73	2	no	—
273	C₂×C₈	—	73	2	no	—
274	C₂×C₈	—	73	2	no	—
275	C₂×C₈	—	73	1	no	—
276	C₂×C₈	—	73	1	no	—
277	C₂×C₈	—	73	2	no	—
278	C₂×C₈	—	73	1	no	—
279	C₂×C₈	—	73	2	no	—
280	C₂×C₈	—	73	1	no	—
281	C₂×C₈	—	73	2	no	—
282	C₂×C₈	—	73	2	no	—
283	C₂×C₈	—	73	2	no	—
284	C₂×C₈	—	73	2	no	—
285	C₂×C₈	—	73	1	no	—
286	C₂×C₈	—	73	1	no	—
287	C₂×C₈	—	73	2	no	—
288	C₂×C₈	C₄×#64408	1	1	yes	characteristic
289	C₂×C₈	C₄×#64408	1	2	yes	—
290	C₂×C₈	C₂²×#64408	1	2	yes	—
291	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
292	C₄²	—	73	2	no	—
293	C₄²	—	73	8	no	—
294	C₄²	—	73	2	no	—
295	C₄²	—	73	2	no	—
296	C₄²	—	73	2	no	—
297	C₁₆	—	73	8	no	—
298	C₁₆	—	73	4	no	—
299	C₁₆	C₂²×#64408	1	4	yes	complemented
300	C₂³	—	73	1	no	—
301	C₂³	—	73	2	no	—
302	C₂³	—	73	2	no	—
303	C₂³	—	73	1	no	—
304	C₂³	—	146	4	no	—
305	C₂³	C₈×#64408	1	1	yes	characteristic
306	C₂×C₄	—	73	4	no	—
307	C₂×C₄	—	73	8	no	—
308	C₂×C₄	—	73	2	no	—
309	C₂×C₄	—	73	1	no	—
310	C₂×C₄	—	73	2	no	—
311	C₂×C₄	—	73	1	no	—
312	C₂×C₄	—	73	1	no	—
313	C₂×C₄	—	73	1	no	—
314	C₂×C₄	—	73	2	no	—
315	C₂×C₄	—	73	2	no	—
316	C₂×C₄	—	73	1	no	—
317	C₂×C₄	—	73	1	no	—
318	C₂×C₄	—	73	2	no	—
319	C₂×C₄	—	73	2	no	—
320	C₂×C₄	—	73	2	no	—
321	C₂×C₄	—	73	2	no	—
322	C₂×C₄	—	73	4	no	—
323	C₂×C₄	—	146	16	no	—
324	C₂×C₄	—	146	4	no	—
325	C₂×C₄	C₈×#64408	1	2	yes	—
326	C₂×C₄	C₈×#64408	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
328	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
329	C₈	—	73	4	no	—
330	C₈	—	73	4	no	—
331	C₈	—	73	1	no	—
332	C₈	—	73	1	no	—
333	C₈	—	73	2	no	—
334	C₈	C₂×C₄×#64408	1	2	yes	—
335	C₈	C₂×C₄×#64408	1	1	yes	characteristic
336	C₈	C₂³×#64408	1	1	yes	characteristic
337	C₂²	—	2	2	no	—
338	C₂²	—	73	4	no	—
339	C₂²	—	73	1	no	—
340	C₂²	—	73	1	no	—
341	C₂²	—	73	2	no	—
342	C₂²	—	146	4	no	—
343	C₂²	—	146	4	no	—
344	C₂²	—	146	2	no	—
345	C₂²	C₂×C₈×#64408	1	2	yes	—
346	C₂²	C₂×C₈×#64408	1	1	yes	characteristic
347	C₄	—	73	8	no	—
348	C₄	—	73	1	no	—
349	C₄	—	73	2	no	—
350	C₄	—	73	1	no	—
351	C₄	—	146	4	no	—
352	C₄	C₂×C₈×#64408	1	2	yes	—
353	C₄	C₂×C₈×#64408	1	1	yes	characteristic
354	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	73	2	no	—
357	C₂	—	73	2	no	—
358	C₂	—	146	2	no	—
359	C₂	M₃₂×#64408	1	2	yes	direct product factor
360	C₂	C₂²×C₈×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#64408
commutator	C₂×C₇₃	C₂²×C₄×C₈
Frattini	C₈	C₂³×#64408
Fitting	C₂×M₃₂×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄×C₈
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₈×D₇₃	C₂⁴
hypercenter	C₂×M₃₂	#64408
hypocenter	C₇₃	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. M₃₂×#64408	C₂	direct (N × H)
4. C₂×#17989474	C₂	semidirect
5. C₂×C₁₆×#64408	C₂	semidirect
9. C₂×#14556666	C₄	semidirect
10. #17989643	C₄	semidirect
12. C₂×#14556665	C₄	semidirect
20. #17989474	C₂²	semidirect
21. C₁₆×#64408	C₂²	semidirect
23. C₂×#14556531	C₄	semidirect
24. C₂×#14556530	C₄	semidirect
25. M₃₂×D₇₃	C₄	semidirect
28. C₂×M₃₂×C₇₃	C₄	semidirect
41. #14556666	C₂×C₄	semidirect
42. #14556665	C₂×C₄	semidirect
43. #14556664	C₂×C₄	semidirect
45. C₂×#11924031	C₂×C₄	semidirect
62. #14556531	C₂×C₄	semidirect
63. #14556530	C₂×C₄	semidirect
64. C₂×#11924003	C₂×C₄	semidirect
65. C₁₆×D₇₃	C₂×C₄	semidirect
68. M₃₂×C₇₃	C₂×C₄	semidirect
69. C₂×C₁₆×C₇₃	C₂×C₄	semidirect
87. #11924031	C₂²×C₄	semidirect
112. #11924003	C₂²×C₄	semidirect
118. C₁₆×C₇₃	C₂²×C₄	semidirect
127. C₂×#64408	M₃₂	direct (N × H)
167. #64408	C₂×M₃₂	direct (N × H)
176. C₂×C₇₃	C₄×M₃₂	semidirect
179. D₇₃	C₄×M₃₂	semidirect
187. C₇₃	C₂×C₄×M₃₂	semidirect
199. C₂×M₃₂	#64408	direct (N × H)
237. M₃₂	C₂×#64408	direct (N × H)
244. C₂×C₁₆	C₂×#64408	semidirect
299. C₁₆	C₂²×#64408	semidirect
359. C₂	M₃₂×#64408	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×#17989643	2
C₂²×C₈×#64408	2
M₃₂×#64408	2
C₂×#17989474	2
C₂×C₁₆×#64408	2
C₂×M₃₂×D₇₃	2
C₂×C₄×M₃₂	73

Subgroups — C2×M32×#64408 #34029781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×M₃₂×#64408 #34029781