Subgroups — C₂×#22569062 #31719960

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	C₂³×D₅₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863870	C₂	1	2	yes	maximal, complemented
3	#22569062	C₂	1	16	yes	maximal, direct product factor
4	C₂×#16863509	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×D₅₃₆	C₂	1	4	yes	maximal, complemented
6	C₂×#16863434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863402	C₂	1	2	yes	maximal, complemented
8	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₂₆₈	C₂²	1	2	yes	—
10	C₂²×D₅₃₆	C₄	1	16	yes	complemented
11	C₂²×D₅₃₆	C₂²	1	2	yes	—
12	C₂²×D₅₃₆	C₂²	1	2	yes	—
13	C₂²×D₅₃₆	C₂²	1	8	yes	—
14	#16863870	—	2	8	no	—
15	#16863870	C₂²	1	16	yes	complemented
16	C₂×C₄×D₂₆₈	C₂²	1	8	yes	complemented
17	C₂×#14524005	—	2	4	no	—
18	C₂×#14524002	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₄×D₆₇	—	2	4	no	—
20	#16863509	C₂²	1	32	yes	complemented
21	C₄×D₅₃₆	C₂²	1	32	yes	complemented
22	#16863434	C₂²	1	8	yes	complemented
23	C₂×#14523977	C₂²	1	2	yes	complemented
24	C₂×#14523975	C₂²	1	2	yes	complemented
25	#16863402	C₂²	1	16	yes	complemented
26	C₂×#14523965	C₂²	1	8	yes	complemented
27	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	#405×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
33	C₂⁴×D₆₇	—	2	2	no	—
34	C₂²×D₂₆₈	—	2	2	no	—
35	C₂²×D₂₆₈	—	2	4	no	—
36	C₂²×D₂₆₈	—	2	8	no	—
37	C₂²×D₂₆₈	C₂×C₄	1	16	yes	complemented
38	C₂²×D₂₆₈	C₂³	1	4	yes	—
39	C₂²×D₂₆₈	C₂³	1	8	yes	—
40	C₂²×C₄×D₆₇	—	2	8	no	—
41	C₂×D₅₃₆	C₂×C₄	1	16	yes	complemented
42	C₂×D₅₃₆	C₂×C₄	1	16	yes	complemented
43	C₂×D₅₃₆	C₂×C₄	1	64	yes	complemented
44	C₂×D₅₃₆	C₂³	1	8	yes	—
45	C₂×D₅₃₆	C₂³	1	8	yes	—
46	C₄×D₂₆₈	—	2	16	no	—
47	C₄×D₂₆₈	C₂³	1	32	yes	complemented
48	#14524005	—	2	32	no	—
49	#14524002	—	2	4	no	—
50	#14524002	C₂³	1	8	yes	—
51	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
52	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
53	C₂×(C₂×D₆₇)⋊C₄	—	2	8	no	—
54	C₂²⋊C₄×D₆₇	—	2	32	no	—
55	C₂×C₄×Dic₆₇	—	2	2	no	—
56	#14523977	C₂³	1	8	yes	complemented
57	#14523975	C₂³	1	8	yes	complemented
58	#14523965	C₂³	1	32	yes	complemented
59	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₆₇	—	2	4	no	—
61	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
62	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
63	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
67	#117×C₆₇	D₄	1	4	yes	—
68	#117×C₆₇	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
71	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
72	#97×C₆₇	C₂³	1	8	yes	complemented
73	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
74	C₂³×D₆₇	—	2	4	no	—
75	C₂³×D₆₇	—	2	16	no	—
76	C₂³×D₆₇	—	2	8	no	—
77	C₂³×D₆₇	—	8	8	no	—
78	C₂×D₂₆₈	—	2	32	no	—
79	C₂×D₂₆₈	—	2	16	no	—
80	C₂×D₂₆₈	—	2	8	no	—
81	C₂×D₂₆₈	—	2	4	no	—
82	C₂×D₂₆₈	—	2	8	no	—
83	C₂×D₂₆₈	—	2	16	no	—
84	C₂×D₂₆₈	C₂²×C₄	1	16	yes	—
85	C₂×D₂₆₈	C₂²×C₄	1	32	yes	complemented
86	C₂×D₂₆₈	C₂⁴	1	8	yes	—
87	C₂²×Dic₆₇	—	2	4	no	—
88	C₂×C₄×D₆₇	—	2	32	no	—
89	C₂×C₄×D₆₇	—	8	16	no	—
90	D₅₃₆	C₂²×C₄	1	32	yes	complemented
91	D₅₃₆	C₂²×C₄	1	32	yes	complemented
92	C₄⋊Dic₆₇	—	2	4	no	—
93	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
94	C₂²⋊Dic₆₇	—	2	8	no	—
95	(C₂×D₆₇)⋊C₄	—	2	32	no	—
96	C₄×Dic₆₇	—	2	8	no	—
97	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₇	#41	1	4	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
105	M₁₆×C₆₇	—	2	8	no	—
106	C₂×C₈×C₆₇	—	2	4	no	—
107	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₆₇	C₂²×C₄	1	16	yes	complemented
110	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
111	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
112	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
113	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
114	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
115	C₄²×C₆₇	C₂×D₄	1	4	yes	—
116	C₄²×C₆₇	C₂⁴	1	4	yes	—
117	C₂³×C₆₇	—	2	4	no	—
118	C₂³×C₆₇	C₄×D₄	1	4	yes	—
119	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
120	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
121	C₂²×D₆₇	—	2	16	no	—
122	C₂²×D₆₇	—	2	8	no	—
123	C₂²×D₆₇	—	2	32	no	—
124	C₂²×D₆₇	—	4	16	no	—
125	C₂²×D₆₇	—	8	32	no	—
126	C₂²×D₆₇	—	8	16	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
129	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
130	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
132	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
133	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
135	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
136	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
137	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
138	C₂×Dic₆₇	—	2	8	no	—
139	C₂×Dic₆₇	—	4	8	no	—
140	D₂₆₈	—	2	16	no	—
141	D₂₆₈	—	2	32	no	—
142	D₂₆₈	—	2	8	no	—
143	D₂₆₈	C₂³×C₄	1	16	yes	—
144	C₄×D₆₇	—	8	32	no	—
145	C₈×C₆₇	—	2	4	no	—
146	C₈×C₆₇	C₂³×C₄	1	4	yes	—
147	C₈×C₆₇	C₂³×C₄	1	4	yes	—
148	C₂²×C₆₇	—	2	8	no	—
149	C₂²×C₆₇	—	2	4	no	—
150	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
151	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
152	C₂²×C₆₇	#576	1	4	yes	—
153	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
154	C₂×D₆₇	—	2	16	no	—
155	C₂×D₆₇	—	4	32	no	—
156	C₂×D₆₇	—	4	16	no	—
157	C₂×D₆₇	—	8	32	no	—
158	C₄×C₆₇	—	2	8	no	—
159	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
160	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
161	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
162	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
163	Dic₆₇	—	4	8	no	—
164	C₂×#2948	—	67	1	no	maximal, Sylow
165	C₂×C₆₇	—	2	4	no	—
166	C₂×C₆₇	#2948	1	4	yes	complemented
167	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
168	C₂×C₆₇	C₂×#576	1	2	yes	—
169	D₆₇	—	4	16	no	—
170	C₂³×D₈	—	67	1	no	—
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	D₆₇	1	1	yes	characteristic, complemented
178	C₆₇	C₂×#2948	1	1	yes	characteristic, complemented, Sylow
179	C₂³×D₄	—	67	2	no	—
180	C₂²×D₈	—	67	16	no	—
181	C₂²×D₈	—	67	2	no	—
182	C₂²×D₈	—	67	2	no	—
183	C₂²×D₈	—	67	8	no	—
184	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
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	2	no	—
191	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
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	C₂×D₆₇	1	8	yes	complemented
201	C₂×#97	C₂×D₆₇	1	2	yes	complemented
202	C₂×C₄×C₈	C₂×D₆₇	1	2	yes	complemented
203	C₂⁵	—	134	2	no	—
204	C₂²×D₄	—	67	16	no	—
205	C₂²×D₄	—	67	4	no	—
206	C₂²×D₄	—	67	8	no	—
207	C₂²×D₄	—	134	2	no	—
208	C₂²×D₄	—	134	4	no	—
209	C₂²×D₄	—	134	8	no	—
210	C₂³×C₄	—	134	8	no	—
211	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
212	C₂×D₈	—	67	16	no	—
213	C₂×D₈	—	67	16	no	—
214	C₂×D₈	—	67	64	no	—
215	C₂×D₈	—	67	8	no	—
216	C₂×D₈	—	67	8	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	C₂²×D₆₇	1	4	yes	—
219	C₂²×C₈	C₄×D₆₇	1	8	yes	complemented
220	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
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	32	no	—
226	C₄×D₄	—	134	16	no	—
227	#117	—	67	8	no	—
228	#117	—	134	4	no	—
229	#117	D₂₆₈	1	4	yes	—
230	#117	C₂²×D₆₇	1	4	yes	—
231	C₂×C₄⋊C₄	—	67	4	no	—
232	C₂×C₄⋊C₄	D₂₆₈	1	2	yes	—
233	C₂×C₂²⋊C₄	—	134	2	no	—
234	C₂×C₂²⋊C₄	—	134	8	no	—
235	C₂×C₂²⋊C₄	—	134	32	no	—
236	C₂×C₂²⋊C₄	D₂₆₈	1	2	yes	—
237	C₂×C₄²	—	134	2	no	—
238	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
239	#107	—	67	8	no	—
240	#106	—	67	8	no	—
241	#102	—	67	32	no	—
242	#97	C₂²×D₆₇	1	8	yes	complemented
243	C₄×C₈	C₂²×D₆₇	1	8	yes	complemented
244	C₂⁴	—	536	8	no	—
245	C₂⁴	—	134	4	no	—
246	C₂⁴	—	134	16	no	—
247	C₂⁴	—	134	8	no	—
248	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
249	C₂×D₄	—	67	16	no	—
250	C₂×D₄	—	67	32	no	—
251	C₂×D₄	—	67	8	no	—
252	C₂×D₄	—	134	16	no	—
253	C₂×D₄	—	134	32	no	—
254	C₂×D₄	—	134	8	no	—
255	C₂×D₄	—	134	4	no	—
256	C₂×D₄	—	134	8	no	—
257	C₂×D₄	—	134	16	no	—
258	C₂²×C₄	—	536	16	no	—
259	C₂²×C₄	—	134	4	no	—
260	C₂²×C₄	—	134	32	no	—
261	C₂²×C₄	C₂×C₄×D₆₇	1	4	yes	—
262	C₂²×C₄	C₂×D₂₆₈	1	4	yes	—
263	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
264	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
265	C₂²×C₄	#11761628	1	4	yes	—
266	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
267	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
268	D₈	—	67	32	no	—
269	D₈	—	67	32	no	—
270	M₁₆	—	2	8	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	C₂×C₄×D₆₇	1	4	yes	—
273	C₂×C₈	C₂×C₄×D₆₇	1	4	yes	—
274	C₂×C₈	C₂×C₄×D₆₇	1	16	yes	complemented
275	C₂×C₈	C₂³×D₆₇	1	4	yes	—
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	—	134	4	no	—
280	C₄⋊C₄	C₂×D₂₆₈	1	8	yes	—
281	C₂²⋊C₄	—	134	8	no	—
282	C₂²⋊C₄	—	134	32	no	—
283	C₂²⋊C₄	C₂×D₂₆₈	1	8	yes	—
284	C₄²	—	134	8	no	—
285	C₄²	C₂×D₂₆₈	1	4	yes	—
286	C₄²	C₂³×D₆₇	1	4	yes	—
287	C₂³	—	2	4	no	—
288	C₂³	—	268	16	no	—
289	C₂³	—	536	32	no	—
290	C₂³	—	536	16	no	—
291	C₂³	—	134	16	no	—
292	C₂³	—	134	8	no	—
293	C₂³	—	134	32	no	—
294	C₂³	C₄×D₂₆₈	1	4	yes	—
295	C₂³	C₂²×D₂₆₈	1	2	yes	—
296	C₂³	C₂²×D₂₆₈	1	1	yes	characteristic
297	D₄	—	67	16	no	—
298	D₄	—	134	16	no	—
299	D₄	—	134	32	no	—
300	D₄	—	134	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	268	8	no	—
303	C₂×C₄	—	536	32	no	—
304	C₂×C₄	—	134	8	no	—
305	C₂×C₄	C₄×D₂₆₈	1	8	yes	—
306	C₂×C₄	C₄×D₂₆₈	1	4	yes	—
307	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
308	C₂×C₄	C₂²×C₄×D₆₇	1	4	yes	—
309	C₂×C₄	C₂²×D₂₆₈	1	8	yes	—
310	C₂×C₄	C₂²×D₂₆₈	1	2	yes	—
311	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
312	C₂×C₄	C₂×#11761628	1	2	yes	—
313	C₂×C₄	C₂×#11761628	1	4	yes	—
314	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
315	C₈	—	2	4	no	—
316	C₈	C₂²×C₄×D₆₇	1	4	yes	—
317	C₈	C₂²×C₄×D₆₇	1	4	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	268	32	no	—
321	C₂²	—	268	16	no	—
322	C₂²	—	536	32	no	—
323	C₂²	—	134	16	no	—
324	C₂²	C₂×C₄×D₂₆₈	1	4	yes	—
325	C₂²	C₂×C₄×D₂₆₈	1	2	yes	—
326	C₂²	#16864201	1	4	yes	—
327	C₂²	C₂³×D₂₆₈	1	1	yes	characteristic
328	C₄	—	2	8	no	—
329	C₄	—	268	8	no	—
330	C₄	C₂×C₄×D₂₆₈	1	2	yes	—
331	C₄	C₂×C₄×D₂₆₈	1	4	yes	—
332	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
333	C₄	C₂²×#11761628	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	268	16	no	—
336	C₂	#22569062	1	4	yes	direct product factor
337	C₂	C₂²×C₄×D₂₆₈	1	1	yes	characteristic
338	C₂	C₂×#16864201	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₆₈
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₂×#405×C₆₇	C₂
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂³×D₅₃₆	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂×#405	D₆₇
hypocenter	C₆₇	C₂×#2948
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#16863870	C₂	semidirect
3. #22569062	C₂	direct (N × H)
4. C₂×#16863509	C₂	semidirect
5. C₂×C₄×D₅₃₆	C₂	semidirect
6. C₂×#16863434	C₂	semidirect
7. C₂×#16863402	C₂	semidirect
8. C₂×#405×C₆₇	C₂	semidirect
10. C₂²×D₅₃₆	C₄	semidirect
15. #16863870	C₂²	semidirect
16. C₂×C₄×D₂₆₈	C₂²	semidirect
20. #16863509	C₂²	semidirect
21. C₄×D₅₃₆	C₂²	semidirect
22. #16863434	C₂²	semidirect
23. C₂×#14523977	C₂²	semidirect
24. C₂×#14523975	C₂²	semidirect
25. #16863402	C₂²	semidirect
26. C₂×#14523965	C₂²	semidirect
30. #405×C₆₇	C₂²	semidirect
31. C₂×#97×C₆₇	C₂²	semidirect
32. C₂×C₄×C₈×C₆₇	C₂²	semidirect
37. C₂²×D₂₆₈	C₂×C₄	semidirect
41. C₂×D₅₃₆	C₂×C₄	semidirect
42. C₂×D₅₃₆	C₂×C₄	semidirect
43. C₂×D₅₃₆	C₂×C₄	semidirect
47. C₄×D₂₆₈	C₂³	semidirect
56. #14523977	C₂³	semidirect
57. #14523975	C₂³	semidirect
58. #14523965	C₂³	semidirect
62. C₂²×C₈×C₆₇	C₂×C₄	semidirect
72. #97×C₆₇	C₂³	semidirect
73. C₄×C₈×C₆₇	C₂³	semidirect
85. C₂×D₂₆₈	C₂²×C₄	semidirect
90. D₅₃₆	C₂²×C₄	semidirect
91. D₅₃₆	C₂²×C₄	semidirect
109. C₂×C₈×C₆₇	C₂²×C₄	semidirect
166. C₂×C₆₇	#2948	semidirect
177. C₂×#405	D₆₇	semidirect
178. C₆₇	C₂×#2948	semidirect
200. #405	C₂×D₆₇	semidirect
201. C₂×#97	C₂×D₆₇	semidirect
202. C₂×C₄×C₈	C₂×D₆₇	semidirect
219. C₂²×C₈	C₄×D₆₇	semidirect
242. #97	C₂²×D₆₇	semidirect
243. C₄×C₈	C₂²×D₆₇	semidirect
274. C₂×C₈	C₂×C₄×D₆₇	semidirect
336. C₂	#22569062	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×D₅₃₆	2
C₂×#16863870	2
#22569062	2
C₂×#16863509	2
C₂×C₄×D₅₃₆	2
C₂×#16863434	2
C₂×#16863402	2
C₂×#405×C₆₇	2
C₂×#2948	67

Subgroups — C2×#22569062 #31719960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22569062 #31719960