Subgroups — C₂×#22558960 #30824809

Order 17152.

834 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×D₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#11761611	C₂	1	1	yes	maximal, characteristic
4	#22558960	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863148	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863146	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#335×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11761611	C₄	1	1	yes	characteristic
10	C₂²×#11761611	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₆₇	—	2	1	no	—
12	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
13	#16863448	—	2	2	no	—
14	#16863448	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₆₇⋊C₈	—	2	1	no	—
18	C₄⋊C₈×D₆₇	—	2	2	no	—
19	C₄⋊C₈×D₆₇	C₂²	1	4	yes	—
20	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
21	C₄×#11761611	C₄	1	4	yes	—
22	C₄×#11761611	C₂²	1	4	yes	—
23	C₂×#14523953	C₄	1	1	yes	characteristic
24	C₂×#14523953	C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₆₇	—	2	1	no	—
27	#16863148	C₂²	1	4	yes	complemented
28	#16863147	C₂²	1	4	yes	complemented
29	#16863146	C₂²	1	4	yes	complemented
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	#335×C₆₇	C₂²	1	4	yes	complemented
34	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₆₇	Q₈	1	1	yes	characteristic
37	C₂×#11761611	—	2	4	no	—
38	C₂×#11761611	C₈	1	8	yes	complemented
39	C₂×#11761611	C₂×C₄	1	4	yes	—
40	C₂×#11761611	C₂×C₄	1	4	yes	—
41	C₂²×C₆₇⋊C₈	—	2	1	no	—
42	C₂²×C₆₇⋊C₈	—	2	1	no	—
43	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₇	—	2	4	no	—
46	C₂×C₈×D₆₇	—	4	4	no	—
47	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₆₇	Q₈	1	1	yes	characteristic
50	C₄²×D₆₇	C₂×C₄	1	2	yes	—
51	C₄²×D₆₇	D₄	1	2	yes	—
52	C₄²×D₆₇	Q₈	1	2	yes	—
53	C₄²×D₆₇	C₂³	1	2	yes	—
54	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
58	Dic₆₇⋊C₈	—	2	4	no	—
59	(C₂×D₆₇)⋊C₈	—	2	4	no	—
60	#14523953	C₂×C₄	1	4	yes	—
61	#14523953	C₂×C₄	1	4	yes	—
62	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
63	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
64	C₈×Dic₆₇	—	2	4	no	—
65	C₂²×C₈×C₆₇	—	2	1	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	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₆₇	—	2	1	no	—
71	C₄⋊C₈×C₆₇	—	2	1	no	—
72	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
74	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₆₇	C₂³	1	2	yes	—
76	C₂³×D₆₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₆₇	—	2	2	no	—
81	C₂×C₄×D₆₇	—	2	2	no	—
82	C₂×C₄×D₆₇	—	4	2	no	—
83	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
84	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
85	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
86	C₂×C₄×D₆₇	C₂×C₈	1	4	yes	—
87	C₂×C₄×D₆₇	M₁₆	1	4	yes	—
88	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
90	C₂×C₄×D₆₇	C₂×Q₈	1	2	yes	—
91	#11761611	—	2	8	no	—
92	#11761611	C₂×C₈	1	16	yes	complemented
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	—	4	2	no	—
97	C₂×C₆₇⋊C₈	—	4	2	no	—
98	C₂×C₆₇⋊C₈	C₂×C₈	1	4	yes	complemented
99	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
100	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
101	C₈×D₆₇	—	4	8	no	—
102	C₄×Dic₆₇	C₄⋊C₄	1	2	yes	—
103	C₄×Dic₆₇	C₄⋊C₄	1	2	yes	—
104	C₄×Dic₆₇	C₄⋊C₄	1	2	yes	—
105	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
106	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
107	C₄×Dic₆₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	—	2	2	no	—
113	C₂×C₈×C₆₇	—	2	2	no	—
114	C₂×C₈×C₆₇	—	4	2	no	—
115	C₂×C₈×C₆₇	—	4	2	no	—
116	C₂×C₈×C₆₇	C₂×C₈	1	4	yes	complemented
117	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
123	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₆₇	—	2	2	no	—
125	C₂²×D₆₇	—	2	2	no	—
126	C₂²×D₆₇	C₄⋊C₈	1	4	yes	—
127	C₂²×D₆₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
134	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₆₇	#137	1	2	yes	—
136	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
139	C₂×Dic₆₇	—	2	2	no	—
140	C₂×Dic₆₇	—	2	2	no	—
141	C₂×Dic₆₇	C₄⋊C₈	1	4	yes	—
142	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₄×D₆₇	—	2	2	no	—
146	C₄×D₆₇	—	2	2	no	—
147	C₄×D₆₇	—	2	4	no	—
148	C₄×D₆₇	—	4	2	no	—
149	C₄×D₆₇	—	4	2	no	—
150	C₄×D₆₇	C₄⋊C₈	1	8	yes	—
151	C₄×D₆₇	C₂²×C₈	1	4	yes	—
152	C₄×D₆₇	C₂×M₁₆	1	4	yes	—
153	C₈×C₆₇	—	2	2	no	—
154	C₈×C₆₇	—	4	2	no	—
155	C₈×C₆₇	—	4	2	no	—
156	C₈×C₆₇	C₂²×C₈	1	4	yes	complemented
157	C₆₇⋊C₈	—	2	2	no	—
158	C₆₇⋊C₈	—	4	2	no	—
159	C₆₇⋊C₈	—	4	2	no	—
160	C₆₇⋊C₈	C₂²×C₈	1	4	yes	complemented
161	C₂²×C₆₇	C₂×C₄⋊C₈	1	2	yes	—
162	C₂²×C₆₇	#428	1	2	yes	—
163	C₂²×C₆₇	#430	1	2	yes	—
164	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂×D₆₇	—	2	8	no	—
166	C₂×D₆₇	—	2	2	no	—
167	C₂×D₆₇	—	2	2	no	—
168	C₂×D₆₇	C₂×C₄⋊C₈	1	4	yes	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	C₂×C₄⋊C₈	1	2	yes	—
172	C₄×C₆₇	#428	1	2	yes	—
173	C₄×C₆₇	C₂³×C₈	1	1	yes	characteristic
174	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
175	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
177	Dic₆₇	—	2	2	no	—
178	Dic₆₇	—	2	2	no	—
179	Dic₆₇	C₂×C₄⋊C₈	1	4	yes	—
180	C₂×#1565	—	67	1	no	maximal, Sylow
181	C₂×C₆₇	#1565	1	4	yes	complemented
182	C₂×C₆₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
183	C₂×C₆₇	C₂×#428	1	1	yes	characteristic
184	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
185	D₆₇	—	2	4	no	—
186	C₂×#431	—	67	1	no	—
187	C₂²×C₄⋊C₈	—	67	1	no	—
188	C₂×C₄×M₁₆	—	67	1	no	—
189	#1565	—	67	8	no	—
190	C₂×#335	—	67	1	no	—
191	C₂×#335	D₆₇	1	1	yes	characteristic, complemented
192	C₂×#334	—	67	1	no	—
193	C₂×#334	—	67	1	no	—
194	C₆₇	C₂×#1565	1	1	yes	characteristic, complemented, Sylow
195	C₂²×M₁₆	—	67	1	no	—
196	C₂²×M₁₆	—	67	1	no	—
197	C₂³×C₈	—	134	1	no	—
198	C₂²×C₄²	—	67	1	no	—
199	#431	—	67	4	no	—
200	#431	—	134	2	no	—
201	C₂×C₄⋊C₈	—	67	1	no	—
202	C₂×C₄⋊C₈	—	67	1	no	—
203	C₂×C₄⋊C₈	—	67	4	no	—
204	C₂×C₄⋊C₈	—	134	2	no	—
205	C₂×C₄⋊C₈	—	134	1	no	—
206	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
208	C₂×C₂²⋊C₈	—	134	1	no	—
209	C₄×M₁₆	—	67	4	no	—
210	C₄×M₁₆	—	67	4	no	—
211	C₂×#97	—	67	1	no	—
212	C₂×#97	—	67	1	no	—
213	C₂×C₄×C₈	—	67	1	no	—
214	C₂×C₄×C₈	—	134	1	no	—
215	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
216	#335	—	67	4	no	—
217	#335	C₂×D₆₇	1	4	yes	complemented
218	#334	—	67	4	no	—
219	#334	—	67	4	no	—
220	C₂³×C₄	—	67	1	no	—
221	C₂³×C₄	—	67	1	no	—
222	C₂³×C₄	—	67	1	no	—
223	C₂×M₁₆	—	67	8	no	—
224	C₂×M₁₆	—	67	4	no	—
225	C₂×M₁₆	—	67	4	no	—
226	C₂×M₁₆	—	134	4	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	268	4	no	—
230	C₂²×C₈	—	67	1	no	—
231	C₂²×C₈	—	67	1	no	—
232	C₂²×C₈	—	134	4	no	—
233	C₂²×C₈	—	134	1	no	—
234	C₂²×C₈	—	134	1	no	—
235	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
237	C₂×C₄²	—	67	1	no	—
238	C₂×C₄²	—	67	1	no	—
239	C₂×C₄²	—	67	1	no	—
240	C₂×C₄²	—	67	2	no	—
241	C₂×C₄²	—	67	2	no	—
242	C₂×C₄²	—	67	2	no	—
243	C₂×C₄²	—	67	2	no	—
244	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	67	2	no	—
248	C₄⋊C₈	—	67	2	no	—
249	C₄⋊C₈	—	134	4	no	—
250	C₄⋊C₈	—	134	1	no	—
251	C₄⋊C₈	—	134	1	no	—
252	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
253	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
254	C₂²⋊C₈	—	134	4	no	—
255	#97	—	67	4	no	—
256	#97	—	67	4	no	—
257	C₄×C₈	—	67	2	no	—
258	C₄×C₈	—	67	2	no	—
259	C₄×C₈	—	134	4	no	—
260	C₄×C₈	C₄×D₆₇	1	2	yes	—
261	C₄×C₈	C₂²×D₆₇	1	2	yes	—
262	C₂⁴	—	67	1	no	—
263	C₂²×C₄	—	268	2	no	—
264	C₂²×C₄	—	67	2	no	—
265	C₂²×C₄	—	67	2	no	—
266	C₂²×C₄	—	67	1	no	—
267	C₂²×C₄	—	67	2	no	—
268	C₂²×C₄	—	67	4	no	—
269	C₂²×C₄	—	67	4	no	—
270	C₂²×C₄	—	67	2	no	—
271	C₂²×C₄	—	67	1	no	—
272	C₂²×C₄	—	67	1	no	—
273	C₂²×C₄	—	67	2	no	—
274	C₂²×C₄	—	67	2	no	—
275	C₂²×C₄	—	134	2	no	—
276	C₂²×C₄	—	134	2	no	—
277	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
278	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
280	M₁₆	—	67	16	no	—
281	M₁₆	—	134	8	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	268	8	no	—
288	C₂×C₈	—	268	2	no	—
289	C₂×C₈	—	268	2	no	—
290	C₂×C₈	—	67	4	no	—
291	C₂×C₈	—	67	2	no	—
292	C₂×C₈	—	67	2	no	—
293	C₂×C₈	—	134	2	no	—
294	C₂×C₈	—	134	2	no	—
295	C₂×C₈	—	134	2	no	—
296	C₂×C₈	C₈×D₆₇	1	4	yes	complemented
297	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
299	C₄²	—	67	2	no	—
300	C₄²	—	67	2	no	—
301	C₄²	—	67	2	no	—
302	C₄²	—	67	2	no	—
303	C₄²	—	67	2	no	—
304	C₄²	—	67	2	no	—
305	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
306	C₄²	D₄×D₆₇	1	1	yes	characteristic
307	C₄²	Q₈×D₆₇	1	1	yes	characteristic
308	C₄²	C₂³×D₆₇	1	1	yes	characteristic
309	C₂³	—	67	2	no	—
310	C₂³	—	67	4	no	—
311	C₂³	—	134	2	no	—
312	C₂³	—	134	2	no	—
313	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	268	2	no	—
316	C₂×C₄	—	268	2	no	—
317	C₂×C₄	—	67	2	no	—
318	C₂×C₄	—	67	4	no	—
319	C₂×C₄	—	67	4	no	—
320	C₂×C₄	—	67	4	no	—
321	C₂×C₄	—	67	8	no	—
322	C₂×C₄	—	67	2	no	—
323	C₂×C₄	—	67	2	no	—
324	C₂×C₄	—	134	2	no	—
325	C₂×C₄	—	134	2	no	—
326	C₂×C₄	—	134	2	no	—
327	C₂×C₄	—	134	2	no	—
328	C₂×C₄	—	134	4	no	—
329	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
331	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
332	C₂×C₄	C₂×C₈×D₆₇	1	2	yes	—
333	C₂×C₄	M₁₆×D₆₇	1	2	yes	—
334	C₂×C₄	#14524067	1	2	yes	—
335	C₂×C₄	#14524075	1	2	yes	—
336	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	268	2	no	—
343	C₈	—	268	2	no	—
344	C₈	—	67	4	no	—
345	C₈	—	134	2	no	—
346	C₈	C₂×C₈×D₆₇	1	4	yes	complemented
347	C₂²	—	67	4	no	—
348	C₂²	—	134	2	no	—
349	C₂²	—	134	2	no	—
350	C₂²	—	134	8	no	—
351	C₂²	C₄⋊C₈×D₆₇	1	2	yes	—
352	C₂²	#16863437	1	2	yes	—
353	C₂²	#16863443	1	2	yes	—
354	C₂²	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	67	4	no	—
358	C₄	—	134	2	no	—
359	C₄	—	134	2	no	—
360	C₄	C₄⋊C₈×D₆₇	1	2	yes	—
361	C₄	#16863437	1	2	yes	—
362	C₄	C₂²×C₈×D₆₇	1	1	yes	characteristic
363	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
364	C₄	C₂×#14524067	1	1	yes	characteristic
365	C₄	C₂×#14524075	1	1	yes	characteristic
366	C₂	—	134	4	no	—
367	C₂	#22558960	1	4	yes	direct product factor
368	C₂	C₂×C₄⋊C₈×D₆₇	1	1	yes	characteristic
369	C₂	C₂×#16863437	1	1	yes	characteristic
370	C₂	C₂×#16863443	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₇
commutator	C₄×C₆₇	C₂³×C₈
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#335×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₄⋊C₄
prime radical	C₂³×D₆₇	C₄⋊C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₂×#335	D₆₇
hypocenter	C₆₇	C₂×#1565
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
4. #22558960	C₂	direct (N × H)
5. C₂×#16863148	C₂	semidirect
6. C₂×#16863147	C₂	semidirect
7. C₂×#16863146	C₂	semidirect
8. C₂×#335×C₆₇	C₂	semidirect
27. #16863148	C₂²	semidirect
28. #16863147	C₂²	semidirect
29. #16863146	C₂²	semidirect
33. #335×C₆₇	C₂²	semidirect
38. C₂×#11761611	C₈	semidirect
92. #11761611	C₂×C₈	semidirect
98. C₂×C₆₇⋊C₈	C₂×C₈	semidirect
116. C₂×C₈×C₆₇	C₂×C₈	semidirect
156. C₈×C₆₇	C₂²×C₈	semidirect
160. C₆₇⋊C₈	C₂²×C₈	semidirect
181. C₂×C₆₇	#1565	semidirect
191. C₂×#335	D₆₇	semidirect
194. C₆₇	C₂×#1565	semidirect
217. #335	C₂×D₆₇	semidirect
296. C₂×C₈	C₈×D₆₇	semidirect
346. C₈	C₂×C₈×D₆₇	semidirect
367. C₂	#22558960	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×#16863448	2
C₂×C₄⋊C₈×D₆₇	2
C₂×C₄×#11761611	2
#22558960	2
C₂×#16863148	2
C₂×#16863147	2
C₂×#16863146	2
C₂×#335×C₆₇	2
C₂×#1565	67

Subgroups — C2×#22558960 #30824809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22558960 #30824809