Subgroups — C₂×#22627056 #34034515

Order 18688.

834 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×#17989700	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊#10596842	C₂	1	1	yes	maximal, characteristic
3	#22627056	C₂	1	8	yes	maximal, direct product factor
4	C₂×#17989677	C₂	1	2	yes	maximal, complemented
5	C₂×#17989676	C₂	1	2	yes	maximal, complemented
6	C₂×M₁₆×#64408	C₂	1	1	yes	maximal, characteristic
7	C₂³×#10596842	—	2	1	no	—
8	#17989700	—	2	2	no	—
9	#17989700	C₂²	1	4	yes	—
10	C₂×C₄⋊#10596842	—	2	1	no	—
11	C₂×C₄⋊#10596842	—	2	2	no	—
12	C₂×C₄⋊#10596842	C₂²	1	2	yes	—
13	C₂×C₄⋊#10596842	C₂²	1	4	yes	—
14	C₂×C₄⋊#10596842	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10596842	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊#10596842	—	2	1	no	—
17	C₂×C₄×#10596842	—	2	1	no	—
18	#17989677	C₂²	1	8	yes	complemented
19	#17989676	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	1	no	—
28	C₂²×#10596842	—	2	1	no	—
29	C₂²×#10596842	—	2	4	no	—
30	C₂²×#10596842	—	2	2	no	—
31	C₂²×#10596842	—	4	4	no	—
32	C₄⋊#10596842	—	2	4	no	—
33	C₄⋊#10596842	—	2	2	no	—
34	C₄⋊#10596842	—	2	1	no	—
35	C₄⋊#10596842	—	2	1	no	—
36	C₄⋊#10596842	C₂³	1	2	yes	—
37	C₄⋊#10596842	C₂³	1	4	yes	—
38	C₄⋊#10596842	C₂³	1	2	yes	—
39	C₂²⋊#10596842	—	2	4	no	—
40	C₄×#10596842	—	2	4	no	—
41	C₂³×#64408	D₄	1	1	yes	characteristic
42	C₂³×#64408	Q₈	1	1	yes	characteristic
43	C₂×#11924038	—	2	1	no	—
44	D₇₃⋊M₁₆	—	2	2	no	—
45	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
46	C₂×#11924037	—	2	1	no	—
47	C₂×#11924036	C₂×C₄	1	2	yes	—
48	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
50	C₂×C₄×#64408	D₄	1	1	yes	characteristic
51	C₂×C₄×#64408	D₄	1	2	yes	—
52	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
53	C₂×C₄×#64408	Q₈	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	2	no	—
67	C₂×#10596842	—	2	2	no	—
68	C₂×#10596842	—	2	4	no	—
69	C₂×#10596842	—	4	8	no	—
70	C₂×#10596842	—	4	2	no	—
71	C₂×#10596842	—	4	4	no	—
72	C₂×#10596842	—	4	2	no	—
73	C₂²×#64408	—	2	2	no	—
74	C₂²×#64408	—	2	2	no	—
75	C₂²×#64408	—	4	2	no	—
76	C₂²×#64408	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×#64408	C₄⋊C₄	1	2	yes	—
78	C₂²×#64408	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×#64408	C₄⋊C₄	1	2	yes	—
80	C₂²×#64408	C₂×D₄	1	2	yes	—
81	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
82	C₂²×#64408	C₂×Q₈	1	1	yes	characteristic
83	C₂²×#64408	C₂×Q₈	1	2	yes	—
84	#11924038	—	2	4	no	—
85	#11924037	—	2	4	no	—
86	#11924036	—	2	2	no	—
87	#11924036	C₂²×C₄	1	4	yes	—
88	C₂×#10596833	—	2	2	no	—
89	C₄×#64408	C₄⋊C₄	1	2	yes	—
90	C₄×#64408	C₄⋊C₄	1	2	yes	—
91	C₄×#64408	C₄⋊C₄	1	2	yes	—
92	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
93	C₄×#64408	C₂²×C₄	1	2	yes	—
94	C₄×#64408	C₂×D₄	1	2	yes	—
95	C₄×#64408	C₂×D₄	1	1	yes	characteristic
96	C₄×#64408	C₂×Q₈	1	2	yes	—
97	C₄×#64408	C₂×Q₈	1	1	yes	characteristic
98	C₄×#64408	C₂⁴	1	1	yes	characteristic
99	C₂³×D₇₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
102	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
104	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	M₁₆	1	2	yes	—
106	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
109	#11924012	C₂×C₈	1	4	yes	complemented
110	#11924011	C₂×C₈	1	8	yes	complemented
111	C₂×#10596831	C₂×C₈	1	2	yes	complemented
112	C₈×D₇₃	C₂×C₈	1	4	yes	complemented
113	C₈×D₇₃	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
115	M₁₆×C₇₃	C₂×C₈	1	4	yes	complemented
116	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	complemented
117	C₂³×C₇₃	C₄⋊C₈	1	1	yes	characteristic
118	C₂²×D₇₃	—	2	2	no	—
119	C₂²×D₇₃	—	2	2	no	—
120	C₂²×D₇₃	C₄⋊C₈	1	2	yes	—
121	C₂²×D₇₃	C₄⋊C₈	1	1	yes	characteristic
122	C₂²×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
123	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×#64408	—	2	2	no	—
125	C₂×#64408	—	2	2	no	—
126	C₂×#64408	—	2	2	no	—
127	C₂×#64408	—	2	2	no	—
128	C₂×#64408	—	2	2	no	—
129	C₂×#64408	—	2	4	no	—
130	C₂×#64408	—	4	2	no	—
131	C₂×#64408	—	4	2	no	—
132	C₂×#64408	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×#64408	C₂×C₄⋊C₄	1	2	yes	—
134	C₂×#64408	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×#64408	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×#64408	AGL(1,ℤ/8)	1	2	yes	—
137	C₂×#64408	#137	1	2	yes	—
138	C₂×#64408	C₂²×D₄	1	1	yes	characteristic
139	C₂×#64408	C₂²×Q₈	1	1	yes	characteristic
140	#10596842	—	4	2	no	—
141	#10596842	—	4	4	no	—
142	#10596842	—	4	2	no	—
143	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
144	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
145	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
147	C₂×Dic₇₃	C₄⋊C₈	1	2	yes	—
148	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
149	C₂×Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂×Dic₇₃	C₂×M₁₆	1	2	yes	—
151	C₄×D₇₃	C₄⋊C₈	1	2	yes	—
152	C₄×D₇₃	C₄⋊C₈	1	2	yes	—
153	C₄×D₇₃	C₄⋊C₈	1	2	yes	—
154	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
156	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
157	C₄×D₇₃	C₂²×C₈	1	2	yes	—
158	C₄×D₇₃	C₂×M₁₆	1	1	yes	characteristic
159	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
160	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
161	#10596833	—	2	4	no	—
162	C₈×C₇₃	C₂²×C₈	1	4	yes	complemented
163	#10596831	C₂²×C₈	1	4	yes	complemented
164	C₂²×C₇₃	—	2	2	no	—
165	C₂²×C₇₃	C₂×C₄⋊C₈	1	2	yes	—
166	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
167	C₂×D₇₃	—	2	2	no	—
168	C₂×D₇₃	—	2	4	no	—
169	C₂×D₇₃	—	2	2	no	—
170	C₂×D₇₃	—	2	2	no	—
171	C₂×D₇₃	C₂×C₄⋊C₈	1	2	yes	—
172	C₂×D₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
173	C₂×D₇₃	#428	1	2	yes	—
174	C₂×D₇₃	#430	1	2	yes	—
175	C₂×D₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	#64408	—	2	2	no	—
177	#64408	—	2	2	no	—
178	#64408	—	2	1	no	—
179	#64408	—	2	1	no	—
180	#64408	#428	1	2	yes	—
181	#64408	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	#64408	C₂×#137	1	1	yes	characteristic
183	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
184	C₄×C₇₃	C₂×C₄⋊C₈	1	2	yes	—
185	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
186	Dic₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
187	Dic₇₃	C₂×C₄⋊C₈	1	2	yes	—
188	Dic₇₃	C₂²×M₁₆	1	1	yes	characteristic
189	C₂×#1565	—	73	1	no	maximal, Sylow
190	C₂×C₇₃	—	2	2	no	—
191	C₂×C₇₃	#1565	1	2	yes	complemented
192	C₂×C₇₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
193	D₇₃	—	2	2	no	—
194	D₇₃	#1565	1	2	yes	complemented
195	D₇₃	C₂×#428	1	1	yes	characteristic
196	D₇₃	C₂×#430	1	1	yes	characteristic
197	C₂×#431	—	73	1	no	—
198	C₂²×C₄⋊C₈	—	73	1	no	—
199	C₂×C₄×M₁₆	—	73	1	no	—
200	#1565	—	73	8	no	—
201	C₂×#335	—	73	2	no	—
202	C₂×#334	—	73	2	no	—
203	C₇₃	C₂×#1565	1	1	yes	characteristic, complemented, Sylow
204	C₂²×M₁₆	—	73	1	no	—
205	C₂²×M₁₆	—	73	1	no	—
206	C₂³×C₈	—	146	1	no	—
207	C₂²×C₄²	—	73	1	no	—
208	#431	—	73	4	no	—
209	#431	—	146	2	no	—
210	C₂×C₄⋊C₈	—	73	1	no	—
211	C₂×C₄⋊C₈	—	73	2	no	—
212	C₂×C₄⋊C₈	—	73	1	no	—
213	C₂×C₄⋊C₈	—	73	4	no	—
214	C₂×C₄⋊C₈	—	146	1	no	—
215	C₂×C₄⋊C₈	—	146	2	no	—
216	C₂×C₂²⋊C₈	—	146	1	no	—
217	C₄×M₁₆	—	73	4	no	—
218	C₄×M₁₆	—	73	4	no	—
219	C₂×#97	—	73	2	no	—
220	C₂×C₄×C₈	—	73	2	no	—
221	C₂×C₄×C₈	—	146	1	no	—
222	#335	—	73	8	no	—
223	#334	—	73	8	no	—
224	C₂³×C₄	—	73	1	no	—
225	C₂³×C₄	—	73	1	no	—
226	C₂³×C₄	—	73	1	no	—
227	C₂×M₁₆	—	73	1	no	—
228	C₂×M₁₆	—	73	4	no	—
229	C₂×M₁₆	—	73	4	no	—
230	C₂×M₁₆	—	73	4	no	—
231	C₂×M₁₆	—	73	2	no	—
232	C₂×M₁₆	—	146	1	no	—
233	C₂×M₁₆	—	146	2	no	—
234	C₂×M₁₆	—	146	1	no	—
235	C₂×M₁₆	#10596842	1	1	yes	characteristic, complemented
236	C₂²×C₈	—	292	4	no	—
237	C₂²×C₈	—	73	2	no	—
238	C₂²×C₈	—	73	2	no	—
239	C₂²×C₈	—	146	2	no	—
240	C₂²×C₈	—	146	4	no	—
241	C₂²×C₈	—	146	1	no	—
242	C₂²×C₈	—	146	1	no	—
243	C₂×C₄²	—	73	1	no	—
244	C₂×C₄²	—	73	1	no	—
245	C₂×C₄²	—	73	1	no	—
246	C₂×C₄²	—	73	2	no	—
247	C₂×C₄²	—	73	2	no	—
248	C₂×C₄²	—	73	2	no	—
249	C₂×C₄²	—	73	2	no	—
250	C₂×C₄²	—	73	1	no	—
251	C₄⋊C₈	—	73	2	no	—
252	C₄⋊C₈	—	73	4	no	—
253	C₄⋊C₈	—	73	2	no	—
254	C₄⋊C₈	—	146	4	no	—
255	C₄⋊C₈	—	146	2	no	—
256	C₄⋊C₈	—	146	1	no	—
257	C₄⋊C₈	—	146	1	no	—
258	C₂²⋊C₈	—	146	4	no	—
259	#97	—	73	8	no	—
260	C₄×C₈	—	73	4	no	—
261	C₄×C₈	—	73	4	no	—
262	C₄×C₈	—	146	4	no	—
263	C₂⁴	—	73	1	no	—
264	C₂²×C₄	—	292	2	no	—
265	C₂²×C₄	—	73	2	no	—
266	C₂²×C₄	—	73	2	no	—
267	C₂²×C₄	—	73	1	no	—
268	C₂²×C₄	—	73	1	no	—
269	C₂²×C₄	—	73	2	no	—
270	C₂²×C₄	—	73	1	no	—
271	C₂²×C₄	—	73	2	no	—
272	C₂²×C₄	—	73	1	no	—
273	C₂²×C₄	—	73	2	no	—
274	C₂²×C₄	—	73	1	no	—
275	C₂²×C₄	—	73	1	no	—
276	C₂²×C₄	—	73	2	no	—
277	C₂²×C₄	—	73	2	no	—
278	C₂²×C₄	—	73	1	no	—
279	C₂²×C₄	—	73	1	no	—
280	C₂²×C₄	—	73	2	no	—
281	C₂²×C₄	—	73	1	no	—
282	C₂²×C₄	—	146	2	no	—
283	C₂²×C₄	—	146	2	no	—
284	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
285	M₁₆	—	73	4	no	—
286	M₁₆	—	73	8	no	—
287	M₁₆	—	146	4	no	—
288	M₁₆	—	146	4	no	—
289	M₁₆	C₂×#10596842	1	4	yes	complemented
290	C₂×C₈	—	292	4	no	—
291	C₂×C₈	—	292	2	no	—
292	C₂×C₈	—	292	2	no	—
293	C₂×C₈	—	292	8	no	—
294	C₂×C₈	—	73	2	no	—
295	C₂×C₈	—	73	4	no	—
296	C₂×C₈	—	73	4	no	—
297	C₂×C₈	—	73	4	no	—
298	C₂×C₈	—	146	2	no	—
299	C₂×C₈	—	146	2	no	—
300	C₂×C₈	—	146	4	no	—
301	C₂×C₈	—	146	2	no	—
302	C₂×C₈	—	146	2	no	—
303	C₂×C₈	C₂×#10596842	1	2	yes	complemented
304	C₄²	—	73	2	no	—
305	C₄²	—	73	2	no	—
306	C₄²	—	73	2	no	—
307	C₄²	—	73	1	no	—
308	C₄²	—	73	2	no	—
309	C₄²	—	73	2	no	—
310	C₄²	—	73	1	no	—
311	C₄²	—	73	1	no	—
312	C₄²	—	73	2	no	—
313	C₄²	—	73	1	no	—
314	C₂³	—	73	1	no	—
315	C₂³	—	73	2	no	—
316	C₂³	—	73	2	no	—
317	C₂³	—	73	1	no	—
318	C₂³	—	146	2	no	—
319	C₂³	—	146	2	no	—
320	C₂³	C₄⋊#10596842	1	1	yes	characteristic
321	C₂×C₄	—	292	2	no	—
322	C₂×C₄	—	292	2	no	—
323	C₂×C₄	—	73	1	no	—
324	C₂×C₄	—	73	1	no	—
325	C₂×C₄	—	73	2	no	—
326	C₂×C₄	—	73	2	no	—
327	C₂×C₄	—	73	2	no	—
328	C₂×C₄	—	73	2	no	—
329	C₂×C₄	—	73	1	no	—
330	C₂×C₄	—	73	1	no	—
331	C₂×C₄	—	73	2	no	—
332	C₂×C₄	—	73	1	no	—
333	C₂×C₄	—	73	1	no	—
334	C₂×C₄	—	73	2	no	—
335	C₂×C₄	—	73	2	no	—
336	C₂×C₄	—	73	2	no	—
337	C₂×C₄	—	73	2	no	—
338	C₂×C₄	—	73	1	no	—
339	C₂×C₄	—	73	1	no	—
340	C₂×C₄	—	73	2	no	—
341	C₂×C₄	—	73	1	no	—
342	C₂×C₄	—	73	2	no	—
343	C₂×C₄	—	73	2	no	—
344	C₂×C₄	—	73	1	no	—
345	C₂×C₄	—	146	2	no	—
346	C₂×C₄	—	146	2	no	—
347	C₂×C₄	—	146	4	no	—
348	C₂×C₄	—	146	2	no	—
349	C₂×C₄	—	146	2	no	—
350	C₂×C₄	—	146	2	no	—
351	C₂×C₄	C₄⋊#10596842	1	2	yes	—
352	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
353	C₂×C₄	C₂²×#10596842	1	2	yes	—
354	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
355	C₈	—	292	4	no	—
356	C₈	—	292	2	no	—
357	C₈	—	292	2	no	—
358	C₈	—	73	4	no	—
359	C₈	—	146	4	no	—
360	C₈	C₂²×#10596842	1	4	yes	complemented
361	C₂²	—	2	2	no	—
362	C₂²	—	73	1	no	—
363	C₂²	—	73	1	no	—
364	C₂²	—	73	2	no	—
365	C₂²	—	73	2	no	—
366	C₂²	—	73	2	no	—
367	C₂²	—	146	2	no	—
368	C₂²	—	146	2	no	—
369	C₂²	—	146	4	no	—
370	C₂²	—	146	2	no	—
371	C₂²	C₂×C₄⋊#10596842	1	2	yes	—
372	C₂²	C₂×C₄⋊#10596842	1	1	yes	characteristic
373	C₄	—	73	1	no	—
374	C₄	—	73	1	no	—
375	C₄	—	73	2	no	—
376	C₄	—	73	1	no	—
377	C₄	—	73	2	no	—
378	C₄	—	73	1	no	—
379	C₄	—	146	1	no	—
380	C₄	—	146	2	no	—
381	C₄	—	146	1	no	—
382	C₄	—	146	2	no	—
383	C₄	C₂×C₄⋊#10596842	1	1	yes	characteristic
384	C₄	C₂×C₄⋊#10596842	1	2	yes	—
385	C₄	C₂³×#10596842	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	73	1	no	—
388	C₂	—	73	1	no	—
389	C₂	—	73	2	no	—
390	C₂	—	146	2	no	—
391	C₂	#22627056	1	2	yes	direct product factor
392	C₂	C₂²×C₄⋊#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10596842
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₄	C₂³×#10596842
Fitting	C₂×M₁₆×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₄⋊C₈
prime radical	C₂³×D₇₃	C₄⋊C₄
cosocle	C₄×#64408	C₂⁴
hypercenter	C₂×M₁₆	#10596842
hypocenter	C₇₃	C₂×#1565
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22627056	C₂	direct (N × H)
4. C₂×#17989677	C₂	semidirect
5. C₂×#17989676	C₂	semidirect
18. #17989677	C₂²	semidirect
19. #17989676	C₂²	semidirect
60. C₂×#11924012	C₈	semidirect
61. C₂×#11924011	C₈	semidirect
62. M₁₆×D₇₃	C₈	semidirect
65. C₂×M₁₆×C₇₃	C₈	semidirect
109. #11924012	C₂×C₈	semidirect
110. #11924011	C₂×C₈	semidirect
111. C₂×#10596831	C₂×C₈	semidirect
112. C₈×D₇₃	C₂×C₈	semidirect
115. M₁₆×C₇₃	C₂×C₈	semidirect
116. C₂×C₈×C₇₃	C₂×C₈	semidirect
162. C₈×C₇₃	C₂²×C₈	semidirect
163. #10596831	C₂²×C₈	semidirect
191. C₂×C₇₃	#1565	semidirect
194. D₇₃	#1565	semidirect
203. C₇₃	C₂×#1565	semidirect
235. C₂×M₁₆	#10596842	semidirect
289. M₁₆	C₂×#10596842	semidirect
303. C₂×C₈	C₂×#10596842	semidirect
360. C₈	C₂²×#10596842	semidirect
391. C₂	#22627056	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
#22627056	2
C₂×#17989677	2
C₂×#17989676	2
C₂×M₁₆×#64408	2
C₂×#1565	73

Subgroups — C2×#22627056 #34034515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22627056 #34034515