Subgroups — C₂×M₁₆×#10596842 #34034487

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989700	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#10596842	C₂	1	1	yes	maximal, characteristic
3	M₁₆×#10596842	C₂	1	8	yes	maximal, direct product factor
4	C₂×#17989671	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×#10596842	C₂	1	2	yes	maximal, complemented
6	C₂×M₁₆×#64408	C₂	1	1	yes	maximal, characteristic
7	C₂³×#10596842	C₄	1	2	yes	—
8	#17989700	C₄	1	4	yes	—
9	#17989700	C₂²	1	4	yes	—
10	C₂×C₄⋊#10596842	C₄	1	2	yes	—
11	C₂×C₂²⋊#10596842	C₄	1	2	yes	—
12	C₂×C₄×#10596842	C₄	1	4	yes	—
13	C₂×C₄×#10596842	C₄	1	2	yes	—
14	C₂×C₄×#10596842	C₂²	1	1	yes	characteristic
15	C₂×C₄×#10596842	C₂²	1	1	yes	characteristic
16	C₂×C₄×#10596842	C₂²	1	4	yes	—
17	C₂×C₄×#10596842	C₂²	1	2	yes	—
18	#17989671	C₂²	1	8	yes	complemented
19	C₈×#10596842	C₂²	1	8	yes	complemented
20	C₂×D₇₃⋊M₁₆	C₄	1	1	yes	characteristic
21	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
22	M₁₆×#64408	C₄	1	4	yes	—
23	M₁₆×#64408	C₂²	1	4	yes	—
24	C₂×#14556645	C₄	1	2	yes	—
25	C₂×C₈×#64408	C₂²	1	2	yes	—
26	C₂×M₁₆×D₇₃	C₄	1	1	yes	characteristic
27	C₂²×#10596842	—	2	8	no	—
28	C₂²×#10596842	C₂×C₄	1	8	yes	—
29	C₂²×#10596842	C₂×C₄	1	2	yes	—
30	C₂²×#10596842	C₂×C₄	1	4	yes	—
31	C₂²×#10596842	C₂×C₄	1	2	yes	—
32	C₄⋊#10596842	C₂×C₄	1	8	yes	—
33	C₂²⋊#10596842	C₂×C₄	1	8	yes	—
34	C₄×#10596842	C₂×C₄	1	2	yes	—
35	C₄×#10596842	C₂×C₄	1	8	yes	—
36	C₄×#10596842	C₂×C₄	1	2	yes	—
37	C₄×#10596842	C₂×C₄	1	4	yes	—
38	C₄×#10596842	C₂³	1	2	yes	—
39	C₄×#10596842	C₂³	1	4	yes	—
40	C₄×#10596842	C₂³	1	2	yes	—
41	C₂³×#64408	C₂×C₄	1	1	yes	characteristic
42	C₂³×#64408	C₂×C₄	1	1	yes	characteristic
43	C₂×#11924038	C₈	1	2	yes	complemented
44	D₇₃⋊M₁₆	C₈	1	4	yes	complemented
45	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
46	C₂×#11924037	C₈	1	2	yes	complemented
47	C₂×#11924036	C₂×C₄	1	2	yes	—
48	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
49	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
52	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
54	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
55	C₂×C₄×#64408	C₂³	1	2	yes	—
56	#14556645	C₂×C₄	1	8	yes	—
57	C₈×#64408	C₂×C₄	1	4	yes	—
58	C₈×#64408	C₂³	1	4	yes	—
59	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#11924012	C₈	1	1	yes	characteristic, complemented
61	C₂×#11924011	C₈	1	2	yes	complemented
62	M₁₆×D₇₃	C₈	1	4	yes	complemented
63	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
64	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
66	C₂×#10596842	—	2	4	no	—
67	C₂×#10596842	—	2	8	no	—
68	C₂×#10596842	—	2	16	no	—
69	C₂×#10596842	M₁₆	1	8	yes	direct product factor
70	C₂×#10596842	C₂²×C₄	1	4	yes	—
71	C₂×#10596842	C₂²×C₄	1	8	yes	—
72	C₂×#10596842	C₂²×C₄	1	4	yes	—
73	C₂²×#64408	—	2	4	no	—
74	C₂²×#64408	—	2	4	no	—
75	C₂²×#64408	C₄²	1	1	yes	characteristic
76	C₂²×#64408	C₄²	1	1	yes	characteristic
77	C₂²×#64408	C₄²	1	2	yes	—
78	C₂²×#64408	C₄²	1	2	yes	—
79	C₂²×#64408	C₂²×C₄	1	2	yes	—
80	C₂²×#64408	C₂²×C₄	1	2	yes	—
81	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
82	C₂²×#64408	C₂²×C₄	1	1	yes	characteristic
83	#11924038	C₂×C₈	1	8	yes	complemented
84	#11924037	C₂×C₈	1	8	yes	complemented
85	#11924036	C₂×C₈	1	4	yes	complemented
86	#11924036	C₂²×C₄	1	4	yes	—
87	C₂×#10596833	C₂×C₈	1	4	yes	complemented
88	C₄×#64408	C₄²	1	2	yes	—
89	C₄×#64408	C₄²	1	2	yes	—
90	C₄×#64408	C₄²	1	2	yes	—
91	C₄×#64408	C₂²×C₄	1	2	yes	—
92	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
93	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
94	C₄×#64408	C₂²×C₄	1	2	yes	—
95	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
96	C₄×#64408	C₂²×C₄	1	2	yes	—
97	C₄×#64408	C₂⁴	1	1	yes	characteristic
98	C₂³×D₇₃	C₄²	1	1	yes	characteristic
99	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₄²	1	2	yes	—
101	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
103	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
105	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
108	#11924012	C₂×C₈	1	4	yes	complemented
109	#11924011	C₂×C₈	1	8	yes	complemented
110	C₂×#10596831	C₂×C₈	1	2	yes	complemented
111	C₈×D₇₃	C₂×C₈	1	4	yes	complemented
112	C₈×D₇₃	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
114	M₁₆×C₇₃	C₂×C₈	1	4	yes	complemented
115	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	complemented
116	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
117	C₂²×D₇₃	—	2	2	no	—
118	C₂²×D₇₃	—	2	2	no	—
119	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
120	C₂²×D₇₃	C₄×C₈	1	2	yes	—
121	C₂²×D₇₃	C₂×C₄²	1	2	yes	—
122	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
123	C₂×#64408	—	2	2	no	—
124	C₂×#64408	—	2	2	no	—
125	C₂×#64408	—	2	4	no	—
126	C₂×#64408	—	2	4	no	—
127	C₂×#64408	—	2	4	no	—
128	C₂×#64408	—	2	4	no	—
129	C₂×#64408	C₂×C₄²	1	2	yes	—
130	C₂×#64408	C₂×C₄²	1	2	yes	—
131	C₂×#64408	C₂×C₄²	1	1	yes	characteristic
132	C₂×#64408	C₂×C₄²	1	1	yes	characteristic
133	C₂×#64408	C₂×M₁₆	1	4	yes	—
134	C₂×#64408	#131	1	4	yes	—
135	C₂×#64408	C₂³×C₄	1	1	yes	characteristic
136	C₂×#64408	C₂³×C₄	1	1	yes	characteristic
137	#10596842	—	2	4	no	—
138	#10596842	—	2	8	no	—
139	#10596842	C₂×M₁₆	1	8	yes	direct product factor
140	C₂×C₄×C₇₃	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
142	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
143	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×Dic₇₃	C₄×C₈	1	2	yes	—
145	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
146	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
148	C₄×D₇₃	C₄×C₈	1	2	yes	—
149	C₄×D₇₃	C₄×C₈	1	2	yes	—
150	C₄×D₇₃	C₄×C₈	1	2	yes	—
151	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
152	C₄×D₇₃	C₂×C₄²	1	2	yes	—
153	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
154	C₄×D₇₃	C₂²×C₈	1	2	yes	—
155	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
156	C₄×D₇₃	C₂²×C₈	1	2	yes	—
157	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
158	#10596833	C₂²×C₈	1	8	yes	complemented
159	C₈×C₇₃	C₂²×C₈	1	4	yes	complemented
160	#10596831	C₂²×C₈	1	4	yes	complemented
161	C₂²×C₇₃	—	2	2	no	—
162	C₂²×C₇₃	C₂×C₄×C₈	1	2	yes	—
163	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
164	C₂×D₇₃	—	2	2	no	—
165	C₂×D₇₃	—	2	2	no	—
166	C₂×D₇₃	—	2	2	no	—
167	C₂×D₇₃	—	2	4	no	—
168	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
169	C₂×D₇₃	C₂×C₄×C₈	1	1	yes	characteristic
170	C₂×D₇₃	C₄×M₁₆	1	2	yes	—
171	C₂×D₇₃	#405	1	2	yes	—
172	C₂×D₇₃	C₂²×C₄²	1	1	yes	characteristic
173	#64408	—	2	2	no	—
174	#64408	—	2	2	no	—
175	#64408	C₄×M₁₆	1	2	yes	—
176	#64408	#405	1	2	yes	—
177	#64408	C₂²×M₁₆	1	2	yes	—
178	#64408	C₂×#131	1	2	yes	—
179	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
180	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
181	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
182	Dic₇₃	C₂×C₄×C₈	1	1	yes	characteristic
183	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
184	Dic₇₃	C₂³×C₈	1	1	yes	characteristic
185	C₂×C₈×M₁₆	—	73	1	no	maximal, Sylow
186	C₂×C₇₃	—	2	2	no	—
187	C₂×C₇₃	C₈×M₁₆	1	2	yes	complemented
188	C₂×C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic
189	D₇₃	—	2	2	no	—
190	D₇₃	C₈×M₁₆	1	2	yes	complemented
191	D₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
192	D₇₃	C₂×#405	1	1	yes	characteristic
193	C₂×#431	—	73	1	no	—
194	C₂×C₄×M₁₆	—	73	1	no	—
195	C₂²×C₄×C₈	—	73	1	no	—
196	C₈×M₁₆	—	73	8	no	—
197	C₂×#322	—	73	2	no	—
198	C₂×C₈²	—	73	2	no	—
199	C₇₃	C₂×C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
200	C₂²×M₁₆	—	73	1	no	—
201	C₂²×M₁₆	—	73	1	no	—
202	C₂³×C₈	—	73	2	no	—
203	C₂²×C₄²	—	73	1	no	—
204	#431	—	73	4	no	—
205	#431	—	73	4	no	—
206	C₂×C₄⋊C₈	—	73	2	no	—
207	C₂×C₂²⋊C₈	—	73	2	no	—
208	C₄×M₁₆	—	73	4	no	—
209	C₄×M₁₆	—	73	4	no	—
210	C₂×#97	—	73	2	no	—
211	C₂×C₄×C₈	—	73	2	no	—
212	C₂×C₄×C₈	—	73	4	no	—
213	C₂×C₄×C₈	—	73	1	no	—
214	C₂×C₄×C₈	—	73	1	no	—
215	C₂×C₄×C₈	—	73	4	no	—
216	C₂×C₄×C₈	—	73	2	no	—
217	C₂×C₄×C₈	—	73	2	no	—
218	#322	—	73	8	no	—
219	C₈²	—	73	8	no	—
220	C₂³×C₄	—	73	1	no	—
221	C₂³×C₄	—	73	1	no	—
222	C₂³×C₄	—	73	1	no	—
223	C₂×M₁₆	—	73	2	no	—
224	C₂×M₁₆	—	73	4	no	—
225	C₂×M₁₆	—	73	4	no	—
226	C₂×M₁₆	—	73	2	no	—
227	C₂×M₁₆	—	73	1	no	—
228	C₂×M₁₆	—	73	4	no	—
229	C₂×M₁₆	—	73	4	no	—
230	C₂×M₁₆	—	73	2	no	—
231	C₂×M₁₆	#10596842	1	1	yes	characteristic, direct product factor
232	C₂²×C₈	—	73	2	no	—
233	C₂²×C₈	—	73	2	no	—
234	C₂²×C₈	—	73	2	no	—
235	C₂²×C₈	—	73	8	no	—
236	C₂²×C₈	—	73	2	no	—
237	C₂²×C₈	—	73	4	no	—
238	C₂²×C₈	—	146	8	no	—
239	C₂×C₄²	—	73	1	no	—
240	C₂×C₄²	—	73	2	no	—
241	C₂×C₄²	—	73	1	no	—
242	C₂×C₄²	—	73	2	no	—
243	C₂×C₄²	—	73	1	no	—
244	C₂×C₄²	—	73	2	no	—
245	C₂×C₄²	—	73	1	no	—
246	C₂×C₄²	—	73	2	no	—
247	C₄⋊C₈	—	73	8	no	—
248	C₂²⋊C₈	—	73	8	no	—
249	#97	—	73	8	no	—
250	C₄×C₈	—	73	2	no	—
251	C₄×C₈	—	73	8	no	—
252	C₄×C₈	—	73	2	no	—
253	C₄×C₈	—	73	4	no	—
254	C₄×C₈	—	73	2	no	—
255	C₄×C₈	—	73	4	no	—
256	C₄×C₈	—	73	2	no	—
257	C₄×C₈	—	73	4	no	—
258	C₄×C₈	—	73	4	no	—
259	C₂⁴	—	73	1	no	—
260	C₂²×C₄	—	73	1	no	—
261	C₂²×C₄	—	73	1	no	—
262	C₂²×C₄	—	73	1	no	—
263	C₂²×C₄	—	73	1	no	—
264	C₂²×C₄	—	73	2	no	—
265	C₂²×C₄	—	73	1	no	—
266	C₂²×C₄	—	73	2	no	—
267	C₂²×C₄	—	73	2	no	—
268	C₂²×C₄	—	73	2	no	—
269	C₂²×C₄	—	73	1	no	—
270	C₂²×C₄	—	73	1	no	—
271	C₂²×C₄	—	73	2	no	—
272	C₂²×C₄	—	73	2	no	—
273	C₂²×C₄	—	73	1	no	—
274	C₂²×C₄	—	73	1	no	—
275	C₂²×C₄	—	73	2	no	—
276	C₂²×C₄	—	73	2	no	—
277	C₂²×C₄	—	146	4	no	—
278	C₂²×C₄	—	146	4	no	—
279	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
280	M₁₆	—	73	8	no	—
281	M₁₆	—	73	8	no	—
282	M₁₆	—	73	4	no	—
283	M₁₆	—	73	8	no	—
284	M₁₆	C₂×#10596842	1	4	yes	direct product factor
285	C₂×C₈	—	73	4	no	—
286	C₂×C₈	—	73	4	no	—
287	C₂×C₈	—	73	4	no	—
288	C₂×C₈	—	73	8	no	—
289	C₂×C₈	—	73	4	no	—
290	C₂×C₈	—	73	2	no	—
291	C₂×C₈	—	73	4	no	—
292	C₂×C₈	—	73	4	no	—
293	C₂×C₈	—	73	4	no	—
294	C₂×C₈	—	73	8	no	—
295	C₂×C₈	—	146	16	no	—
296	C₂×C₈	—	146	8	no	—
297	C₂×C₈	—	146	4	no	—
298	C₂×C₈	C₂×#10596842	1	2	yes	complemented
299	C₄²	—	73	2	no	—
300	C₄²	—	73	2	no	—
301	C₄²	—	73	2	no	—
302	C₄²	—	73	1	no	—
303	C₄²	—	73	1	no	—
304	C₄²	—	73	2	no	—
305	C₄²	—	73	1	no	—
306	C₄²	—	73	2	no	—
307	C₄²	—	73	2	no	—
308	C₄²	—	73	1	no	—
309	C₂³	—	73	1	no	—
310	C₂³	—	73	2	no	—
311	C₂³	—	73	2	no	—
312	C₂³	—	73	1	no	—
313	C₂³	—	146	2	no	—
314	C₂³	—	146	2	no	—
315	C₂³	C₄×#10596842	1	1	yes	characteristic
316	C₂×C₄	—	73	1	no	—
317	C₂×C₄	—	73	1	no	—
318	C₂×C₄	—	73	1	no	—
319	C₂×C₄	—	73	1	no	—
320	C₂×C₄	—	73	4	no	—
321	C₂×C₄	—	73	4	no	—
322	C₂×C₄	—	73	1	no	—
323	C₂×C₄	—	73	2	no	—
324	C₂×C₄	—	73	2	no	—
325	C₂×C₄	—	73	1	no	—
326	C₂×C₄	—	73	2	no	—
327	C₂×C₄	—	73	1	no	—
328	C₂×C₄	—	73	1	no	—
329	C₂×C₄	—	73	2	no	—
330	C₂×C₄	—	73	2	no	—
331	C₂×C₄	—	73	2	no	—
332	C₂×C₄	—	73	2	no	—
333	C₂×C₄	—	73	1	no	—
334	C₂×C₄	—	73	1	no	—
335	C₂×C₄	—	73	2	no	—
336	C₂×C₄	—	73	2	no	—
337	C₂×C₄	—	73	2	no	—
338	C₂×C₄	—	146	4	no	—
339	C₂×C₄	—	146	4	no	—
340	C₂×C₄	—	146	4	no	—
341	C₂×C₄	—	146	4	no	—
342	C₂×C₄	—	146	2	no	—
343	C₂×C₄	—	146	2	no	—
344	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
345	C₂×C₄	C₄×#10596842	1	2	yes	—
346	C₂×C₄	C₂²×#10596842	1	2	yes	—
347	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
348	C₈	—	73	8	no	—
349	C₈	—	73	8	no	—
350	C₈	—	73	4	no	—
351	C₈	—	146	4	no	—
352	C₈	—	146	8	no	—
353	C₈	C₂²×#10596842	1	4	yes	complemented
354	C₂²	—	2	2	no	—
355	C₂²	—	73	1	no	—
356	C₂²	—	73	1	no	—
357	C₂²	—	73	2	no	—
358	C₂²	—	73	2	no	—
359	C₂²	—	73	2	no	—
360	C₂²	—	146	2	no	—
361	C₂²	—	146	2	no	—
362	C₂²	—	146	4	no	—
363	C₂²	—	146	2	no	—
364	C₂²	C₂×C₄×#10596842	1	2	yes	—
365	C₂²	C₂×C₄×#10596842	1	1	yes	characteristic
366	C₄	—	73	2	no	—
367	C₄	—	73	2	no	—
368	C₄	—	73	2	no	—
369	C₄	—	73	2	no	—
370	C₄	—	73	1	no	—
371	C₄	—	73	1	no	—
372	C₄	—	73	2	no	—
373	C₄	—	146	2	no	—
374	C₄	—	146	2	no	—
375	C₄	C₂×C₄×#10596842	1	2	yes	—
376	C₄	C₂×C₄×#10596842	1	1	yes	characteristic
377	C₄	C₂³×#10596842	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	73	1	no	—
380	C₂	—	73	1	no	—
381	C₂	—	73	2	no	—
382	C₂	—	146	2	no	—
383	C₂	M₁₆×#10596842	1	2	yes	direct product factor
384	C₂	C₂²×C₄×#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#10596842
commutator	C₂×C₇₃	C₂²×C₄×C₈
Frattini	C₄	C₂³×#10596842
Fitting	C₂×M₁₆×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₄×C₈
prime radical	C₂³×D₇₃	C₄²
cosocle	C₄×#64408	C₂⁴
hypercenter	C₂×M₁₆	#10596842
hypocenter	C₇₃	C₂×C₈×M₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. M₁₆×#10596842	C₂	direct (N × H)
4. C₂×#17989671	C₂	semidirect
5. C₂×C₈×#10596842	C₂	semidirect
18. #17989671	C₂²	semidirect
19. C₈×#10596842	C₂²	semidirect
43. C₂×#11924038	C₈	semidirect
44. D₇₃⋊M₁₆	C₈	semidirect
46. C₂×#11924037	C₈	semidirect
60. C₂×#11924012	C₈	semidirect
61. C₂×#11924011	C₈	semidirect
62. M₁₆×D₇₃	C₈	semidirect
65. C₂×M₁₆×C₇₃	C₈	semidirect
69. C₂×#10596842	M₁₆	direct (N × H)
83. #11924038	C₂×C₈	semidirect
84. #11924037	C₂×C₈	semidirect
85. #11924036	C₂×C₈	semidirect
87. C₂×#10596833	C₂×C₈	semidirect
108. #11924012	C₂×C₈	semidirect
109. #11924011	C₂×C₈	semidirect
110. C₂×#10596831	C₂×C₈	semidirect
111. C₈×D₇₃	C₂×C₈	semidirect
114. M₁₆×C₇₃	C₂×C₈	semidirect
115. C₂×C₈×C₇₃	C₂×C₈	semidirect
139. #10596842	C₂×M₁₆	direct (N × H)
158. #10596833	C₂²×C₈	semidirect
159. C₈×C₇₃	C₂²×C₈	semidirect
160. #10596831	C₂²×C₈	semidirect
187. C₂×C₇₃	C₈×M₁₆	semidirect
190. D₇₃	C₈×M₁₆	semidirect
199. C₇₃	C₂×C₈×M₁₆	semidirect
231. C₂×M₁₆	#10596842	direct (N × H)
284. M₁₆	C₂×#10596842	direct (N × H)
298. C₂×C₈	C₂×#10596842	semidirect
353. C₈	C₂²×#10596842	semidirect
383. C₂	M₁₆×#10596842	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×#17989700	2
C₂²×C₄×#10596842	2
M₁₆×#10596842	2
C₂×#17989671	2
C₂×C₈×#10596842	2
C₂×M₁₆×#64408	2
C₂×C₈×M₁₆	73

Subgroups — C2×M16×#10596842 #34034487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×M₁₆×#10596842 #34034487