Subgroups — C₂×#22559101 #30825567

Order 17152.

746 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863526	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#11761617	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863475	C₂	1	1	yes	maximal, characteristic
4	#22559101	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863128	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863125	C₂	1	1	yes	maximal, characteristic
8	C₂×C₈²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11761617	C₄	1	1	yes	characteristic
10	C₂²×#11761611	—	2	1	no	—
11	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
13	#16863526	—	2	2	no	—
14	#16863526	C₂²	1	4	yes	complemented
15	C₄×#11761617	C₄	1	4	yes	—
16	C₄×#11761617	C₂²	1	4	yes	—
17	#16863475	—	2	2	no	—
18	#16863475	C₂²	1	4	yes	—
19	C₂×#14523975	C₄	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×Dic₆₇⋊C₈	—	2	1	no	—
23	C₂×#14523968	C₄	1	1	yes	characteristic
24	C₂×#14523965	C₄	1	1	yes	characteristic
25	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
26	C₂×#14523953	—	2	1	no	—
27	#16863147	C₂²	1	4	yes	complemented
28	#16863128	C₂²	1	4	yes	complemented
29	#16863125	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₈²×C₆₇	C₂²	1	4	yes	complemented
34	C₂²×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₆₇	—	2	1	no	—
37	C₂×#11761617	—	2	4	no	—
38	C₂×#11761617	C₂×C₄	1	4	yes	—
39	C₂×#11761611	—	2	4	no	—
40	C₂×#11761611	—	4	4	no	—
41	C₂²×C₆₇⋊C₈	—	2	1	no	—
42	C₂²×C₆₇⋊C₈	—	2	1	no	—
43	C₄×Dic₁₃₄	—	2	1	no	—
44	C₄×Dic₁₃₄	—	2	1	no	—
45	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
46	C₄×Dic₁₃₄	C₂³	1	2	yes	—
47	C₄×D₂₆₈	—	2	1	no	—
48	C₄×D₂₆₈	—	2	1	no	—
49	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
50	C₄×D₂₆₈	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×Dic₆₇⋊C₄	—	2	1	no	—
54	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
55	C₂×C₄×Dic₆₇	—	2	1	no	—
56	#14523975	C₂×C₄	1	4	yes	—
57	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
61	Dic₆₇⋊C₈	—	2	4	no	—
62	#14523968	C₂×C₄	1	4	yes	—
63	#14523965	C₂×C₄	1	4	yes	—
64	(C₂×D₆₇)⋊C₈	—	2	4	no	—
65	#14523953	—	2	4	no	—
66	C₂²×C₈×C₆₇	—	2	1	no	—
67	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₆₇	—	2	1	no	—
73	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₆₇	D₄	1	2	yes	—
75	C₄×C₈×C₆₇	C₂³	1	2	yes	—
76	C₄×C₈×C₆₇	C₂³	1	2	yes	—
77	C₄×C₈×C₆₇	C₂³	1	2	yes	—
78	C₂³×D₆₇	—	2	1	no	—
79	C₂×Dic₁₃₄	—	2	2	no	—
80	C₂×Dic₁₃₄	—	2	2	no	—
81	C₂×Dic₁₃₄	—	2	1	no	—
82	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
83	C₂×D₂₆₈	—	2	2	no	—
84	C₂×D₂₆₈	—	2	2	no	—
85	C₂×D₂₆₈	—	2	1	no	—
86	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
87	C₂²×Dic₆₇	—	2	1	no	—
88	C₂²×Dic₆₇	—	2	1	no	—
89	C₂²×Dic₆₇	—	2	1	no	—
90	C₂×C₄×D₆₇	—	2	2	no	—
91	C₂×C₄×D₆₇	—	2	2	no	—
92	C₂×C₄×D₆₇	—	4	2	no	—
93	C₂×C₄×D₆₇	—	4	2	no	—
94	#11761617	—	2	8	no	—
95	#11761611	—	4	8	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	4	2	no	—
99	C₂×C₆₇⋊C₈	—	4	2	no	—
100	C₄⋊Dic₆₇	—	2	1	no	—
101	C₄⋊Dic₆₇	—	2	1	no	—
102	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
103	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
104	Dic₆₇⋊C₄	—	2	2	no	—
105	Dic₆₇⋊C₄	—	2	2	no	—
106	(C₂×D₆₇)⋊C₄	—	2	2	no	—
107	(C₂×D₆₇)⋊C₄	—	2	2	no	—
108	C₄×Dic₆₇	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
113	C₂×C₈×C₆₇	—	2	4	no	—
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	M₁₆	1	4	yes	complemented
118	C₂×C₈×C₆₇	SD₁₆	1	4	yes	complemented
119	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
123	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₆₇	#41	1	1	yes	characteristic
126	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
128	C₂²×D₆₇	—	2	2	no	—
129	C₂²×D₆₇	—	4	2	no	—
130	C₂²×D₆₇	—	4	2	no	—
131	C₂²×D₆₇	—	4	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
137	C₂×C₄×C₆₇	#131	1	2	yes	—
138	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
139	C₂×C₄×C₆₇	#135	1	2	yes	—
140	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
143	C₂×Dic₆₇	—	2	2	no	—
144	C₂×Dic₆₇	—	2	2	no	—
145	C₂×Dic₆₇	—	2	2	no	—
146	C₂×Dic₆₇	—	4	2	no	—
147	C₂×Dic₆₇	—	4	2	no	—
148	C₂×Dic₆₇	—	4	2	no	—
149	D₂₆₈	—	2	2	no	—
150	D₂₆₈	—	2	2	no	—
151	D₂₆₈	—	4	2	no	—
152	C₄×D₆₇	—	4	2	no	—
153	C₄×D₆₇	—	4	2	no	—
154	C₄×D₆₇	—	4	4	no	—
155	Dic₁₃₄	—	2	2	no	—
156	Dic₁₃₄	—	2	2	no	—
157	Dic₁₃₄	—	4	2	no	—
158	C₈×C₆₇	—	2	4	no	—
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	—	2	2	no	—
161	C₈×C₆₇	C₂×M₁₆	1	4	yes	complemented
162	C₈×C₆₇	C₂×SD₁₆	1	4	yes	complemented
163	C₆₇⋊C₈	—	4	2	no	—
164	C₆₇⋊C₈	—	4	2	no	—
165	C₂²×C₆₇	#436	1	2	yes	—
166	C₂²×C₆₇	C₄×SD₁₆	1	2	yes	—
167	C₂²×C₆₇	#443	1	2	yes	—
168	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂×D₆₇	—	4	2	no	—
170	C₂×D₆₇	—	4	2	no	—
171	C₂×D₆₇	—	4	2	no	—
172	C₂×D₆₇	—	8	4	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	#436	1	2	yes	—
176	C₄×C₆₇	C₄×SD₁₆	1	2	yes	—
177	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
179	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
180	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
181	Dic₆₇	—	4	2	no	—
182	Dic₆₇	—	4	2	no	—
183	Dic₆₇	—	4	2	no	—
184	C₂×#1590	—	67	1	no	maximal, Sylow
185	C₂×C₆₇	#1590	1	4	yes	complemented
186	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
187	C₂×C₆₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
188	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
189	D₆₇	—	8	2	no	—
190	C₂×#446	—	67	1	no	—
191	C₂×C₄×SD₁₆	—	67	1	no	—
192	C₂×#436	—	67	1	no	—
193	#1590	—	67	8	no	—
194	C₂×#334	—	67	1	no	—
195	C₂×Q₈⋊C₈	—	67	1	no	—
196	C₂×D₄⋊C₈	—	67	1	no	—
197	C₂×C₈²	D₆₇	1	1	yes	characteristic, complemented
198	C₆₇	C₂×#1590	1	1	yes	characteristic, complemented, Sylow
199	C₂²×SD₁₆	—	67	1	no	—
200	C₂²×M₁₆	—	134	1	no	—
201	C₂×C₄×Q₈	—	67	1	no	—
202	C₂×C₄×D₄	—	67	1	no	—
203	#446	—	67	4	no	—
204	#446	—	134	2	no	—
205	C₄×SD₁₆	—	67	4	no	—
206	C₄×SD₁₆	—	67	4	no	—
207	#436	—	67	4	no	—
208	#436	—	134	2	no	—
209	C₂×#106	—	67	1	no	—
210	C₂×C₄⋊C₈	—	67	1	no	—
211	C₂×C₄⋊C₈	—	67	1	no	—
212	C₂×C₄⋊C₈	—	134	1	no	—
213	C₂×#103	—	67	1	no	—
214	C₂×#102	—	67	1	no	—
215	C₂×C₂²⋊C₈	—	134	1	no	—
216	C₂×#97	—	134	1	no	—
217	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
220	#334	—	67	4	no	—
221	Q₈⋊C₈	—	67	4	no	—
222	D₄⋊C₈	—	67	4	no	—
223	C₈²	C₂×D₆₇	1	4	yes	complemented
224	C₂²×Q₈	—	67	1	no	—
225	C₂²×D₄	—	67	1	no	—
226	C₂³×C₄	—	134	1	no	—
227	C₂×SD₁₆	—	67	4	no	—
228	C₂×SD₁₆	—	134	4	no	—
229	C₂×M₁₆	—	268	4	no	—
230	C₂×M₁₆	—	134	4	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	134	1	no	—
233	C₂²×C₈	—	134	1	no	—
234	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
235	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
236	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
237	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
238	C₄×Q₈	—	67	2	no	—
239	C₄×Q₈	—	67	2	no	—
240	C₄×Q₈	—	134	1	no	—
241	C₄×Q₈	—	134	1	no	—
242	C₄×D₄	—	67	2	no	—
243	C₄×D₄	—	67	2	no	—
244	C₄×D₄	—	134	1	no	—
245	C₄×D₄	—	134	1	no	—
246	C₂×C₄⋊C₄	—	67	1	no	—
247	C₂×C₄⋊C₄	—	67	1	no	—
248	C₂×C₄⋊C₄	—	134	1	no	—
249	C₂×C₂²⋊C₄	—	134	1	no	—
250	C₂×C₄²	—	134	1	no	—
251	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
252	#106	—	67	4	no	—
253	C₄⋊C₈	—	67	2	no	—
254	C₄⋊C₈	—	67	2	no	—
255	C₄⋊C₈	—	134	4	no	—
256	C₄⋊C₈	—	134	1	no	—
257	C₄⋊C₈	—	134	1	no	—
258	#103	—	67	4	no	—
259	#102	—	67	4	no	—
260	C₂²⋊C₈	—	134	4	no	—
261	#97	—	134	4	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	C₄×D₆₇	1	2	yes	—
264	C₄×C₈	D₂₆₈	1	2	yes	—
265	C₄×C₈	C₂²×D₆₇	1	2	yes	—
266	C₄×C₈	C₂²×D₆₇	1	2	yes	—
267	C₄×C₈	C₂²×D₆₇	1	2	yes	—
268	C₂⁴	—	134	1	no	—
269	C₂×Q₈	—	67	2	no	—
270	C₂×Q₈	—	134	2	no	—
271	C₂×Q₈	—	134	2	no	—
272	C₂×Q₈	—	134	1	no	—
273	C₂×D₄	—	67	2	no	—
274	C₂×D₄	—	134	1	no	—
275	C₂×D₄	—	134	2	no	—
276	C₂×D₄	—	134	2	no	—
277	C₂²×C₄	—	268	2	no	—
278	C₂²×C₄	—	268	2	no	—
279	C₂²×C₄	—	134	1	no	—
280	C₂²×C₄	—	134	1	no	—
281	C₂²×C₄	—	134	1	no	—
282	C₂²×C₄	—	134	2	no	—
283	C₂²×C₄	—	134	2	no	—
284	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
286	C₂²×C₄	#11761628	1	1	yes	characteristic
287	SD₁₆	—	134	8	no	—
288	M₁₆	—	268	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	268	2	no	—
294	C₂×C₈	—	268	2	no	—
295	C₂×C₈	—	134	2	no	—
296	C₂×C₈	—	134	2	no	—
297	C₂×C₈	#11761611	1	4	yes	complemented
298	C₂×C₈	#11761617	1	4	yes	complemented
299	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
300	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
301	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
302	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
303	C₄⋊C₄	—	67	2	no	—
304	C₄⋊C₄	—	67	2	no	—
305	C₄⋊C₄	—	134	1	no	—
306	C₄⋊C₄	—	134	1	no	—
307	C₄⋊C₄	—	134	2	no	—
308	C₄⋊C₄	—	134	2	no	—
309	C₂²⋊C₄	—	134	2	no	—
310	C₂²⋊C₄	—	134	2	no	—
311	C₄²	—	134	2	no	—
312	C₄²	—	134	2	no	—
313	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
314	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
315	C₄²	#11761628	1	1	yes	characteristic
316	C₄²	C₂³×D₆₇	1	1	yes	characteristic
317	C₂³	—	268	2	no	—
318	C₂³	—	268	2	no	—
319	C₂³	—	268	2	no	—
320	C₂³	—	134	2	no	—
321	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
322	Q₈	—	268	2	no	—
323	Q₈	—	134	2	no	—
324	Q₈	—	134	2	no	—
325	D₄	—	268	2	no	—
326	D₄	—	134	2	no	—
327	D₄	—	134	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	268	2	no	—
330	C₂×C₄	—	268	2	no	—
331	C₂×C₄	—	268	2	no	—
332	C₂×C₄	—	268	2	no	—
333	C₂×C₄	—	268	2	no	—
334	C₂×C₄	—	268	4	no	—
335	C₂×C₄	—	134	2	no	—
336	C₂×C₄	—	134	2	no	—
337	C₂×C₄	—	134	2	no	—
338	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
339	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
340	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
341	C₂×C₄	C₂×#11761611	1	2	yes	—
342	C₂×C₄	#14524049	1	2	yes	—
343	C₂×C₄	C₂×#11761617	1	2	yes	—
344	C₂×C₄	#14524065	1	2	yes	—
345	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
347	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	268	2	no	—
352	C₈	—	268	2	no	—
353	C₈	C₂×#11761611	1	4	yes	complemented
354	C₈	C₂×#11761617	1	4	yes	complemented
355	C₂²	—	268	2	no	—
356	C₂²	—	268	2	no	—
357	C₂²	—	268	2	no	—
358	C₂²	—	536	4	no	—
359	C₂²	#16863475	1	2	yes	—
360	C₂²	C₄×#11761617	1	2	yes	—
361	C₂²	#16863514	1	2	yes	—
362	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	268	2	no	—
366	C₄	—	268	2	no	—
367	C₄	—	268	2	no	—
368	C₄	#16863475	1	2	yes	—
369	C₄	C₄×#11761617	1	2	yes	—
370	C₄	C₂²×#11761611	1	1	yes	characteristic
371	C₄	C₂×#14524049	1	1	yes	characteristic
372	C₄	C₂²×#11761617	1	1	yes	characteristic
373	C₄	C₂×#14524065	1	1	yes	characteristic
374	C₂	—	536	2	no	—
375	C₂	#22559101	1	4	yes	direct product factor
376	C₂	C₂×#16863475	1	1	yes	characteristic
377	C₂	C₂×C₄×#11761617	1	1	yes	characteristic
378	C₂	C₂×#16863514	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×C₈²×C₆₇	C₂
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×D₂₆₈	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₂×C₈²	D₆₇
hypocenter	C₆₇	C₂×#1590
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
1. C₂×#16863526	C₂	semidirect
4. #22559101	C₂	direct (N × H)
5. C₂×#16863147	C₂	semidirect
6. C₂×#16863128	C₂	semidirect
8. C₂×C₈²×C₆₇	C₂	semidirect
14. #16863526	C₂²	semidirect
27. #16863147	C₂²	semidirect
28. #16863128	C₂²	semidirect
33. C₈²×C₆₇	C₂²	semidirect
117. C₂×C₈×C₆₇	M₁₆	semidirect
118. C₂×C₈×C₆₇	SD₁₆	semidirect
161. C₈×C₆₇	C₂×M₁₆	semidirect
162. C₈×C₆₇	C₂×SD₁₆	semidirect
185. C₂×C₆₇	#1590	semidirect
197. C₂×C₈²	D₆₇	semidirect
198. C₆₇	C₂×#1590	semidirect
223. C₈²	C₂×D₆₇	semidirect
297. C₂×C₈	#11761611	semidirect
298. C₂×C₈	#11761617	semidirect
353. C₈	C₂×#11761611	semidirect
354. C₈	C₂×#11761617	semidirect
375. C₂	#22559101	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×#16863526	2
C₂×C₄×#11761617	2
C₂×#16863475	2
#22559101	2
C₂×#16863147	2
C₂×#16863128	2
C₂×#16863125	2
C₂×C₈²×C₆₇	2
C₂×#1590	67

Subgroups — C2×#22559101 #30825567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559101 #30825567