Subgroups — C₂×#22569061 #31719959

Order 17152.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863871	C₂	1	2	yes	maximal, complemented
2	#22569061	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16863508	C₂	1	4	yes	maximal, complemented
4	C₂×D₈×Dic₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#16863434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863401	C₂	1	2	yes	maximal, complemented
7	C₂×#16863351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	#16863871	—	2	8	no	—
11	#16863871	C₂²	1	16	yes	complemented
12	C₂×D₄×Dic₆₇	—	2	4	no	—
13	C₂×D₄×Dic₆₇	C₂²	1	8	yes	complemented
14	C₂×#14524002	C₂²	1	2	yes	—
15	C₂×#14524002	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊Dic₆₇	—	2	4	no	—
17	#16863508	C₂²	1	32	yes	complemented
18	D₈×Dic₆₇	C₂²	1	32	yes	complemented
19	#16863434	C₂²	1	8	yes	complemented
20	C₂×#14523977	C₂²	1	2	yes	complemented
21	C₂×#14523975	C₂²	1	2	yes	complemented
22	#16863401	C₂²	1	16	yes	complemented
23	C₂×#14523964	C₂²	1	8	yes	complemented
24	#16863351	C₂²	1	8	yes	complemented
25	C₂×#14523953	C₂²	1	2	yes	complemented
26	C₂×C₈×Dic₆₇	C₂²	1	2	yes	complemented
27	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂²×D₈×C₆₇	C₄	1	16	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
30	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
31	C₂²×D₈×C₆₇	C₂²	1	8	yes	—
32	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂³×Dic₆₇	—	2	8	no	—
34	C₂×#11761612	—	2	4	no	—
35	C₂×#11761612	C₂³	1	4	yes	—
36	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
37	D₄×Dic₆₇	—	2	32	no	—
38	D₄×Dic₆₇	—	2	16	no	—
39	D₄×Dic₆₇	C₂³	1	32	yes	complemented
40	#14524002	—	2	4	no	—
41	#14524002	D₄	1	4	yes	—
42	#14524002	C₂³	1	8	yes	—
43	#14524002	C₂³	1	4	yes	—
44	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
46	C₂×C₂²⋊Dic₆₇	—	2	8	no	—
47	C₂×C₂²⋊Dic₆₇	—	2	32	no	—
48	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
49	C₂×C₂²⋊Dic₆₇	D₄	1	2	yes	—
50	C₂×C₄×Dic₆₇	—	2	2	no	—
51	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
52	#14523977	C₂³	1	8	yes	complemented
53	#14523975	C₂³	1	8	yes	complemented
54	#14523964	C₂³	1	32	yes	complemented
55	#14523953	C₂³	1	8	yes	complemented
56	C₈×Dic₆₇	C₂³	1	8	yes	complemented
57	C₂⁵×C₆₇	—	2	2	no	—
58	C₂²×D₄×C₆₇	—	2	2	no	—
59	C₂²×D₄×C₆₇	—	2	4	no	—
60	C₂²×D₄×C₆₇	—	2	8	no	—
61	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
62	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
63	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
64	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×D₈×C₆₇	C₂×C₄	1	16	yes	complemented
66	C₂×D₈×C₆₇	C₂×C₄	1	16	yes	complemented
67	C₂×D₈×C₆₇	C₂×C₄	1	64	yes	complemented
68	C₂×D₈×C₆₇	C₂³	1	8	yes	—
69	C₂×D₈×C₆₇	C₂³	1	8	yes	—
70	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
71	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
74	C₂²×Dic₆₇	—	2	4	no	—
75	C₂²×Dic₆₇	—	2	32	no	—
76	C₂²×Dic₆₇	—	8	16	no	—
77	C₂²×Dic₆₇	C₂×D₄	1	4	yes	—
78	#11761612	—	2	8	no	—
79	C₂×C₆₇⋊C₈	—	2	4	no	—
80	C₂×C₆₇⋊C₈	C₂⁴	1	4	yes	—
81	C₄⋊Dic₆₇	—	2	4	no	—
82	C₄⋊Dic₆₇	C₂×D₄	1	8	yes	—
83	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
84	C₂²⋊Dic₆₇	—	2	8	no	—
85	C₂²⋊Dic₆₇	—	2	32	no	—
86	C₂²⋊Dic₆₇	C₂×D₄	1	8	yes	—
87	C₄×Dic₆₇	—	2	8	no	—
88	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
89	C₄×Dic₆₇	C₂⁴	1	4	yes	—
90	C₂⁴×C₆₇	—	2	4	no	—
91	C₂⁴×C₆₇	—	2	16	no	—
92	C₂⁴×C₆₇	—	2	8	no	—
93	C₂⁴×C₆₇	—	8	8	no	—
94	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₆₇	—	2	32	no	—
96	C₂×D₄×C₆₇	—	2	16	no	—
97	C₂×D₄×C₆₇	—	2	8	no	—
98	C₂×D₄×C₆₇	—	2	4	no	—
99	C₂×D₄×C₆₇	—	2	8	no	—
100	C₂×D₄×C₆₇	—	2	16	no	—
101	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
102	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	complemented
103	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
104	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₆₇	#41	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
110	D₈×C₆₇	C₂²×C₄	1	32	yes	complemented
111	D₈×C₆₇	C₂²×C₄	1	32	yes	complemented
112	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₆₇	C₂²×C₄	1	16	yes	complemented
115	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
116	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
117	C₂³×C₆₇	—	2	4	no	—
118	C₂³×C₆₇	—	2	16	no	—
119	C₂³×C₆₇	—	2	8	no	—
120	C₂³×C₆₇	—	2	32	no	—
121	C₂³×C₆₇	—	4	16	no	—
122	C₂³×C₆₇	—	8	32	no	—
123	C₂³×C₆₇	—	8	16	no	—
124	C₂³×C₆₇	C₄×D₄	1	4	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
126	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
127	D₄×C₆₇	—	2	16	no	—
128	D₄×C₆₇	—	2	32	no	—
129	D₄×C₆₇	—	2	8	no	—
130	D₄×C₆₇	C₂³×C₄	1	16	yes	—
131	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
132	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
133	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
134	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
135	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
136	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
138	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
139	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
140	C₂×Dic₆₇	—	2	8	no	—
141	C₂×Dic₆₇	—	2	8	no	—
142	C₂×Dic₆₇	—	4	8	no	—
143	C₂×Dic₆₇	—	8	32	no	—
144	C₂×Dic₆₇	C₂²×D₄	1	8	yes	—
145	C₈×C₆₇	C₂³×C₄	1	4	yes	—
146	C₈×C₆₇	C₂³×C₄	1	4	yes	—
147	C₆₇⋊C₈	—	2	4	no	—
148	C₂²×C₆₇	—	2	8	no	—
149	C₂²×C₆₇	—	2	4	no	—
150	C₂²×C₆₇	—	2	16	no	—
151	C₂²×C₆₇	—	4	32	no	—
152	C₂²×C₆₇	—	4	16	no	—
153	C₂²×C₆₇	—	8	32	no	—
154	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
155	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
156	C₂²×C₆₇	#576	1	4	yes	—
157	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
158	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
159	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
160	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
161	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
162	Dic₆₇	—	2	8	no	—
163	Dic₆₇	—	4	8	no	—
164	C₂×#2948	—	67	1	no	maximal, Sylow
165	C₂×C₆₇	—	2	4	no	—
166	C₂×C₆₇	—	4	16	no	—
167	C₂×C₆₇	#2948	1	4	yes	complemented
168	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#576	1	2	yes	—
170	C₂³×D₈	D₆₇	1	1	yes	characteristic
171	C₂×#518	—	67	2	no	—
172	#2948	—	67	16	no	—
173	C₂×#442	—	67	4	no	—
174	C₂×C₄×D₈	—	67	4	no	—
175	C₂×#427	—	67	1	no	—
176	C₂×#418	—	67	2	no	—
177	C₂×#405	—	67	1	no	—
178	C₆₇	C₂×#2948	1	1	yes	characteristic, complemented, Sylow
179	C₂³×D₄	C₂×D₆₇	1	2	yes	—
180	C₂²×D₈	Dic₆₇	1	16	yes	complemented
181	C₂²×D₈	C₂×D₆₇	1	2	yes	—
182	C₂²×D₈	C₂×D₆₇	1	2	yes	—
183	C₂²×D₈	C₂×D₆₇	1	8	yes	—
184	C₂²×M₁₆	—	67	1	no	—
185	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
186	#518	—	67	16	no	—
187	#518	—	134	8	no	—
188	C₂×C₄×D₄	—	67	8	no	—
189	C₂×C₄×D₄	—	134	4	no	—
190	C₂×#117	—	67	1	no	—
191	C₂×#117	—	67	2	no	—
192	C₂²×C₂²⋊C₄	—	134	4	no	—
193	#442	—	67	32	no	—
194	C₄×D₈	—	67	32	no	—
195	#427	—	67	8	no	—
196	C₂×#107	—	67	2	no	—
197	C₂×#106	—	67	2	no	—
198	#418	—	67	16	no	—
199	C₂×#102	—	67	8	no	—
200	#405	—	67	8	no	—
201	C₂×#97	—	67	2	no	—
202	C₂×C₄×C₈	—	67	2	no	—
203	C₂⁵	—	2	2	no	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	C₂×Dic₆₇	1	16	yes	complemented
208	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
209	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
210	C₂³×C₄	—	134	8	no	—
211	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
212	C₂×D₈	C₂×Dic₆₇	1	16	yes	complemented
213	C₂×D₈	C₂×Dic₆₇	1	16	yes	complemented
214	C₂×D₈	C₂×Dic₆₇	1	64	yes	complemented
215	C₂×D₈	C₂²×D₆₇	1	8	yes	—
216	C₂×D₈	C₂²×D₆₇	1	8	yes	—
217	C₂×M₁₆	—	67	4	no	—
218	C₂×M₁₆	—	134	4	no	—
219	C₂²×C₈	—	67	2	no	—
220	C₂²×C₈	C₂×Dic₆₇	1	8	yes	complemented
221	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
223	C₂²×C₈	C₂²×D₆₇	1	4	yes	—
224	C₄×D₄	—	67	32	no	—
225	C₄×D₄	—	134	16	no	—
226	C₄×D₄	—	134	32	no	—
227	#117	—	67	4	no	—
228	#117	—	67	4	no	—
229	#117	—	67	8	no	—
230	#117	—	134	4	no	—
231	C₂×C₄⋊C₄	—	67	2	no	—
232	C₂×C₄⋊C₄	—	67	4	no	—
233	C₂×C₂²⋊C₄	—	67	2	no	—
234	C₂×C₂²⋊C₄	—	134	32	no	—
235	C₂×C₂²⋊C₄	—	134	8	no	—
236	C₂×C₂²⋊C₄	—	134	2	no	—
237	C₂×C₄²	—	67	2	no	—
238	C₂×C₄²	—	134	2	no	—
239	#107	—	67	8	no	—
240	#106	—	67	8	no	—
241	#102	—	67	32	no	—
242	#97	—	67	8	no	—
243	C₄×C₈	—	67	8	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	8	8	no	—
248	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
249	C₂×D₄	—	2	32	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	C₂²×Dic₆₇	1	16	yes	—
256	C₂×D₄	C₂²×Dic₆₇	1	32	yes	complemented
257	C₂×D₄	C₂³×D₆₇	1	8	yes	—
258	C₂²×C₄	—	536	16	no	—
259	C₂²×C₄	—	67	4	no	—
260	C₂²×C₄	—	134	4	no	—
261	C₂²×C₄	—	134	32	no	—
262	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
263	C₂²×C₄	D₄×D₆₇	1	2	yes	—
264	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
265	C₂²×C₄	#11761627	1	4	yes	—
266	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
267	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
268	D₈	C₂²×Dic₆₇	1	32	yes	complemented
269	D₈	C₂²×Dic₆₇	1	32	yes	complemented
270	M₁₆	—	134	8	no	—
271	C₂×C₈	—	67	4	no	—
272	C₂×C₈	—	134	4	no	—
273	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
274	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
275	C₂×C₈	C₂²×Dic₆₇	1	16	yes	complemented
276	C₂×C₈	C₂³×D₆₇	1	2	yes	—
277	C₂×C₈	C₂³×D₆₇	1	2	yes	—
278	C₄⋊C₄	—	67	8	no	—
279	C₄⋊C₄	—	67	8	no	—
280	C₄⋊C₄	—	134	4	no	—
281	C₂²⋊C₄	—	67	8	no	—
282	C₂²⋊C₄	—	134	32	no	—
283	C₂²⋊C₄	—	134	8	no	—
284	C₄²	—	67	4	no	—
285	C₄²	—	67	4	no	—
286	C₄²	—	134	8	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	16	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	8	32	no	—
293	C₂³	—	8	16	no	—
294	C₂³	D₄×Dic₆₇	1	4	yes	—
295	C₂³	C₂×D₄×D₆₇	1	2	yes	—
296	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
297	D₄	—	2	16	no	—
298	D₄	—	2	32	no	—
299	D₄	—	2	8	no	—
300	D₄	C₂³×Dic₆₇	1	16	yes	—
301	C₂×C₄	—	268	8	no	—
302	C₂×C₄	—	536	32	no	—
303	C₂×C₄	—	67	8	no	—
304	C₂×C₄	—	134	8	no	—
305	C₂×C₄	—	134	8	no	—
306	C₂×C₄	D₄×Dic₆₇	1	8	yes	—
307	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
308	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
309	C₂×C₄	C₂³×Dic₆₇	1	4	yes	—
310	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
312	C₂×C₄	C₂×#11761627	1	2	yes	—
313	C₂×C₄	C₂×#11761627	1	4	yes	—
314	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
315	C₈	—	134	4	no	—
316	C₈	C₂³×Dic₆₇	1	4	yes	—
317	C₈	C₂³×Dic₆₇	1	4	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	4	32	no	—
322	C₂²	—	4	16	no	—
323	C₂²	—	8	32	no	—
324	C₂²	C₂×D₄×Dic₆₇	1	4	yes	—
325	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
326	C₂²	#16864197	1	4	yes	—
327	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
328	C₄	—	268	8	no	—
329	C₄	—	134	8	no	—
330	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
331	C₄	C₂×D₄×Dic₆₇	1	4	yes	—
332	C₄	C₂⁴×Dic₆₇	1	1	yes	characteristic
333	C₄	C₂²×#11761627	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	16	no	—
336	C₂	#22569061	1	4	yes	direct product factor
337	C₂	C₂²×D₄×Dic₆₇	1	1	yes	characteristic
338	C₂	C₂×#16864197	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting, prime radical	C₂³×D₈×C₆₇	C₂
socle	C₂³×C₆₇	C₂²×D₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂³×D₈	D₆₇
hypocenter	C₆₇	C₂×#2948
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#16863871	C₂	semidirect
2. #22569061	C₂	direct (N × H)
3. C₂×#16863508	C₂	semidirect
4. C₂×D₈×Dic₆₇	C₂	semidirect
5. C₂×#16863434	C₂	semidirect
6. C₂×#16863401	C₂	semidirect
7. C₂×#16863351	C₂	semidirect
11. #16863871	C₂²	semidirect
13. C₂×D₄×Dic₆₇	C₂²	semidirect
17. #16863508	C₂²	semidirect
18. D₈×Dic₆₇	C₂²	semidirect
19. #16863434	C₂²	semidirect
20. C₂×#14523977	C₂²	semidirect
21. C₂×#14523975	C₂²	semidirect
22. #16863401	C₂²	semidirect
23. C₂×#14523964	C₂²	semidirect
24. #16863351	C₂²	semidirect
25. C₂×#14523953	C₂²	semidirect
26. C₂×C₈×Dic₆₇	C₂²	semidirect
28. C₂²×D₈×C₆₇	C₄	semidirect
39. D₄×Dic₆₇	C₂³	semidirect
52. #14523977	C₂³	semidirect
53. #14523975	C₂³	semidirect
54. #14523964	C₂³	semidirect
55. #14523953	C₂³	semidirect
56. C₈×Dic₆₇	C₂³	semidirect
61. C₂²×D₄×C₆₇	C₂×C₄	semidirect
65. C₂×D₈×C₆₇	C₂×C₄	semidirect
66. C₂×D₈×C₆₇	C₂×C₄	semidirect
67. C₂×D₈×C₆₇	C₂×C₄	semidirect
70. C₂²×C₈×C₆₇	C₂×C₄	semidirect
102. C₂×D₄×C₆₇	C₂²×C₄	semidirect
110. D₈×C₆₇	C₂²×C₄	semidirect
111. D₈×C₆₇	C₂²×C₄	semidirect
114. C₂×C₈×C₆₇	C₂²×C₄	semidirect
167. C₂×C₆₇	#2948	semidirect
178. C₆₇	C₂×#2948	semidirect
180. C₂²×D₈	Dic₆₇	semidirect
207. C₂²×D₄	C₂×Dic₆₇	semidirect
212. C₂×D₈	C₂×Dic₆₇	semidirect
213. C₂×D₈	C₂×Dic₆₇	semidirect
214. C₂×D₈	C₂×Dic₆₇	semidirect
220. C₂²×C₈	C₂×Dic₆₇	semidirect
256. C₂×D₄	C₂²×Dic₆₇	semidirect
268. D₈	C₂²×Dic₆₇	semidirect
269. D₈	C₂²×Dic₆₇	semidirect
275. C₂×C₈	C₂²×Dic₆₇	semidirect
336. C₂	#22569061	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×#16863871	2
#22569061	2
C₂×#16863508	2
C₂×D₈×Dic₆₇	2
C₂×#16863434	2
C₂×#16863401	2
C₂×#16863351	2
C₂³×D₈×C₆₇	2
C₂×#2948	67

Subgroups — C2×#22569061 #31719959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22569061 #31719959