Subgroups — C₂×C₆₇×#3272 #30740282

Order 17152.

3226 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3272	C₂	1	16	yes	maximal, direct product factor
5	C₂×#492×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#468×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#461×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#449×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#450×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₆₇	—	2	1	no	—
15	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	16	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
24	#547×C₆₇	—	2	4	no	—
25	#547×C₆₇	C₂²	1	8	yes	complemented
26	D₄²×C₆₇	—	2	4	no	—
27	D₄²×C₆₇	C₂²	1	8	yes	complemented
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#123×C₆₇	—	2	2	no	—
31	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#121×C₆₇	—	2	1	no	—
33	C₂×#121×C₆₇	—	2	1	no	—
34	C₂×#121×C₆₇	C₂²	1	2	yes	—
35	C₂×#120×C₆₇	—	2	2	no	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
40	#492×C₆₇	C₂²	1	8	yes	complemented
41	#468×C₆₇	C₂²	1	16	yes	complemented
42	#461×C₆₇	C₂²	1	8	yes	complemented
43	#459×C₆₇	C₂²	1	8	yes	complemented
44	#450×C₆₇	C₂²	1	16	yes	complemented
45	#449×C₆₇	C₂²	1	16	yes	complemented
46	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
47	#436×C₆₇	C₂²	1	8	yes	complemented
48	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
51	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₆₇	—	2	2	no	—
57	C₂×#41×C₆₇	—	2	4	no	—
58	C₂×#41×C₆₇	—	2	8	no	—
59	C₂×#41×C₆₇	—	4	4	no	—
60	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
61	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
62	C₂²×D₄×C₆₇	—	2	8	no	—
63	C₂²×D₄×C₆₇	—	2	2	no	—
64	C₂²×D₄×C₆₇	—	2	2	no	—
65	C₂²×D₄×C₆₇	—	2	8	no	—
66	C₂²×D₄×C₆₇	—	2	2	no	—
67	C₂²×D₄×C₆₇	—	2	1	no	—
68	C₂²×D₄×C₆₇	—	2	4	no	—
69	C₂²×D₄×C₆₇	—	2	1	no	—
70	C₂²×D₄×C₆₇	—	4	4	no	—
71	C₂²×D₄×C₆₇	—	4	8	no	—
72	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
75	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	—	2	1	no	—
78	C₂³×C₄×C₆₇	—	2	2	no	—
79	C₂³×C₄×C₆₇	—	2	1	no	—
80	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
81	AGL(1,ℤ/8)×C₆₇	—	2	64	no	—
82	C₂×SD₁₆×C₆₇	—	2	8	no	—
83	C₂×SD₁₆×C₆₇	—	2	8	no	—
84	C₂×SD₁₆×C₆₇	—	4	4	no	—
85	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
86	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
87	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
88	C₂×D₈×C₆₇	—	2	8	no	—
89	C₂×D₈×C₆₇	D₄	1	8	yes	complemented
90	C₂×D₈×C₆₇	C₂³	1	4	yes	—
91	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
92	C₂×M₁₆×C₆₇	—	2	8	no	—
93	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
94	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₇	—	2	2	no	—
98	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
99	#127×C₆₇	—	2	2	no	—
100	#127×C₆₇	C₂³	1	4	yes	—
101	#123×C₆₇	—	2	16	no	—
102	C₂²⋊Q₈×C₆₇	—	2	4	no	—
103	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
104	#121×C₆₇	—	2	8	no	—
105	#121×C₆₇	—	2	4	no	—
106	#121×C₆₇	—	2	8	no	—
107	#121×C₆₇	C₂³	1	8	yes	—
108	#120×C₆₇	—	2	16	no	—
109	C₄×D₄×C₆₇	—	2	2	no	—
110	C₄×D₄×C₆₇	—	2	2	no	—
111	C₄×D₄×C₆₇	D₄	1	4	yes	—
112	C₄×D₄×C₆₇	C₂³	1	4	yes	—
113	C₄×D₄×C₆₇	C₂³	1	4	yes	—
114	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
115	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
119	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
127	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
128	#107×C₆₇	C₂³	1	4	yes	complemented
129	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
130	#103×C₆₇	C₂³	1	8	yes	complemented
131	#102×C₆₇	C₂³	1	4	yes	—
132	#102×C₆₇	C₂³	1	4	yes	complemented
133	#102×C₆₇	C₂³	1	8	yes	complemented
134	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
135	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
136	C₂⁴×C₆₇	—	2	1	no	—
137	C₂⁴×C₆₇	—	2	1	no	—
138	C₂⁴×C₆₇	—	2	2	no	—
139	C₂⁴×C₆₇	—	2	8	no	—
140	C₂⁴×C₆₇	—	4	8	no	—
141	C₂⁴×C₆₇	—	4	8	no	—
142	C₂⁴×C₆₇	—	8	4	no	—
143	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
144	#41×C₆₇	—	2	16	no	—
145	#41×C₆₇	—	4	8	no	—
146	#41×C₆₇	—	4	16	no	—
147	C₂×Q₈×C₆₇	—	2	2	no	—
148	C₂×Q₈×C₆₇	—	2	4	no	—
149	C₂×Q₈×C₆₇	—	2	4	no	—
150	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
151	C₂×D₄×C₆₇	—	2	16	no	—
152	C₂×D₄×C₆₇	—	2	8	no	—
153	C₂×D₄×C₆₇	—	2	8	no	—
154	C₂×D₄×C₆₇	—	2	4	no	—
155	C₂×D₄×C₆₇	—	2	1	no	—
156	C₂×D₄×C₆₇	—	2	1	no	—
157	C₂×D₄×C₆₇	—	2	4	no	—
158	C₂×D₄×C₆₇	—	2	8	no	—
159	C₂×D₄×C₆₇	—	2	2	no	—
160	C₂×D₄×C₆₇	—	2	4	no	—
161	C₂×D₄×C₆₇	—	2	4	no	—
162	C₂×D₄×C₆₇	—	2	2	no	—
163	C₂×D₄×C₆₇	—	2	2	no	—
164	C₂×D₄×C₆₇	—	2	4	no	—
165	C₂×D₄×C₆₇	—	4	8	no	—
166	C₂×D₄×C₆₇	—	4	16	no	—
167	C₂×D₄×C₆₇	—	4	8	no	—
168	C₂×D₄×C₆₇	—	4	32	no	—
169	C₂×D₄×C₆₇	—	4	8	no	—
170	C₂×D₄×C₆₇	—	4	8	no	—
171	C₂×D₄×C₆₇	—	4	4	no	—
172	C₂×D₄×C₆₇	—	8	2	no	—
173	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
174	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
176	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
177	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
178	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	4	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	8	no	—
186	C₂²×C₄×C₆₇	—	2	4	no	—
187	C₂²×C₄×C₆₇	—	4	8	no	—
188	C₂²×C₄×C₆₇	—	4	4	no	—
189	C₂²×C₄×C₆₇	—	4	4	no	—
190	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	SD₁₆×C₆₇	—	2	16	no	—
197	SD₁₆×C₆₇	—	2	16	no	—
198	SD₁₆×C₆₇	—	4	8	no	—
199	D₈×C₆₇	—	2	16	no	—
200	D₈×C₆₇	C₂×D₄	1	16	yes	complemented
201	M₁₆×C₆₇	—	2	16	no	—
202	C₂×C₈×C₆₇	—	2	4	no	—
203	C₂×C₈×C₆₇	—	2	2	no	—
204	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
205	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
206	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
207	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	8	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	1	no	—
212	C₄⋊C₄×C₆₇	—	2	1	no	—
213	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²⋊C₄×C₆₇	—	2	8	no	—
217	C₂²⋊C₄×C₆₇	—	2	4	no	—
218	C₂²⋊C₄×C₆₇	—	2	4	no	—
219	C₂²⋊C₄×C₆₇	—	2	8	no	—
220	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
221	C₄²×C₆₇	C₂×D₄	1	2	yes	—
222	C₄²×C₆₇	C₂⁴	1	2	yes	—
223	C₂³×C₆₇	—	2	4	no	—
224	C₂³×C₆₇	—	2	4	no	—
225	C₂³×C₆₇	—	2	4	no	—
226	C₂³×C₆₇	—	2	4	no	—
227	C₂³×C₆₇	—	2	4	no	—
228	C₂³×C₆₇	—	2	2	no	—
229	C₂³×C₆₇	—	2	2	no	—
230	C₂³×C₆₇	—	2	4	no	—
231	C₂³×C₆₇	—	4	16	no	—
232	C₂³×C₆₇	—	4	16	no	—
233	C₂³×C₆₇	—	4	2	no	—
234	C₂³×C₆₇	—	4	2	no	—
235	C₂³×C₆₇	—	4	2	no	—
236	C₂³×C₆₇	—	4	2	no	—
237	C₂³×C₆₇	—	4	4	no	—
238	C₂³×C₆₇	—	4	4	no	—
239	C₂³×C₆₇	—	4	4	no	—
240	C₂³×C₆₇	—	8	8	no	—
241	C₂³×C₆₇	—	8	32	no	—
242	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
243	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₆₇	—	2	4	no	—
245	Q₈×C₆₇	—	2	4	no	—
246	Q₈×C₆₇	—	4	4	no	—
247	D₄×C₆₇	—	2	4	no	—
248	D₄×C₆₇	—	2	4	no	—
249	D₄×C₆₇	—	2	8	no	—
250	D₄×C₆₇	—	2	4	no	—
251	D₄×C₆₇	—	2	2	no	—
252	D₄×C₆₇	—	2	2	no	—
253	D₄×C₆₇	—	2	4	no	—
254	D₄×C₆₇	—	4	16	no	—
255	D₄×C₆₇	—	4	16	no	—
256	D₄×C₆₇	—	4	16	no	—
257	D₄×C₆₇	—	4	4	no	—
258	D₄×C₆₇	—	4	8	no	—
259	D₄×C₆₇	—	8	4	no	—
260	D₄×C₆₇	C₂²×D₄	1	4	yes	—
261	D₄×C₆₇	C₂²×D₄	1	4	yes	complemented
262	C₂×C₄×C₆₇	—	2	4	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	8	no	—
265	C₂×C₄×C₆₇	—	2	4	no	—
266	C₂×C₄×C₆₇	—	2	4	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	4	no	—
270	C₂×C₄×C₆₇	—	4	16	no	—
271	C₂×C₄×C₆₇	—	4	4	no	—
272	C₂×C₄×C₆₇	—	4	2	no	—
273	C₂×C₄×C₆₇	—	4	2	no	—
274	C₂×C₄×C₆₇	—	4	8	no	—
275	C₂×C₄×C₆₇	—	4	8	no	—
276	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
277	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
283	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
284	C₈×C₆₇	—	2	4	no	—
285	C₈×C₆₇	—	2	2	no	—
286	C₈×C₆₇	C₂²×D₄	1	4	yes	complemented
287	C₂²×C₆₇	—	2	4	no	—
288	C₂²×C₆₇	—	2	4	no	—
289	C₂²×C₆₇	—	2	4	no	—
290	C₂²×C₆₇	—	2	4	no	—
291	C₂²×C₆₇	—	2	4	no	—
292	C₂²×C₆₇	—	4	8	no	—
293	C₂²×C₆₇	—	4	8	no	—
294	C₂²×C₆₇	—	4	8	no	—
295	C₂²×C₆₇	—	4	2	no	—
296	C₂²×C₆₇	—	4	2	no	—
297	C₂²×C₆₇	—	4	2	no	—
298	C₂²×C₆₇	—	4	2	no	—
299	C₂²×C₆₇	—	4	4	no	—
300	C₂²×C₆₇	—	4	4	no	—
301	C₂²×C₆₇	—	4	4	no	—
302	C₂²×C₆₇	—	8	32	no	—
303	C₂²×C₆₇	—	8	8	no	—
304	C₂²×C₆₇	D₄²	1	2	yes	—
305	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
306	C₂²×C₆₇	#577	1	2	yes	—
307	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
308	C₄×C₆₇	—	2	4	no	—
309	C₄×C₆₇	—	2	2	no	—
310	C₄×C₆₇	—	4	4	no	—
311	C₄×C₆₇	—	4	2	no	—
312	C₄×C₆₇	—	4	2	no	—
313	C₄×C₆₇	D₄²	1	2	yes	—
314	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
315	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
316	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×#3272	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
318	C₂×C₆₇	—	4	4	no	—
319	C₂×C₆₇	—	4	4	no	—
320	C₂×C₆₇	—	4	4	no	—
321	C₂×C₆₇	—	8	4	no	—
322	C₂×C₆₇	#3272	1	4	yes	direct product factor
323	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
324	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
326	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	2	yes	complemented
327	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
328	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
329	#3272	C₂×C₆₇	1	16	yes	direct product factor
330	C₂×#492	C₂×C₆₇	1	1	yes	characteristic, complemented
331	C₂×#468	C₂×C₆₇	1	2	yes	complemented
332	C₂×#461	C₂×C₆₇	1	1	yes	characteristic, complemented
333	C₂×#459	C₂×C₆₇	1	1	yes	characteristic, complemented
334	C₂×#449	C₂×C₆₇	1	2	yes	complemented
335	C₂×#450	C₂×C₆₇	1	2	yes	complemented
336	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
337	C₂×#436	C₂×C₆₇	1	1	yes	characteristic, complemented
338	C₆₇	C₂×#3272	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
340	C₂³×D₄	—	2	1	no	—
341	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
342	C₂×AGL(1,ℤ/8)	—	2	16	no	—
343	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	16	yes	complemented
344	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
345	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
346	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
347	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
348	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
349	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
350	#547	—	2	4	no	—
351	#547	C₂²×C₆₇	1	8	yes	complemented
352	D₄²	—	2	4	no	—
353	D₄²	C₂²×C₆₇	1	8	yes	complemented
354	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
355	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
356	C₂×#123	—	2	2	no	—
357	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
358	C₂×#121	—	2	1	no	—
359	C₂×#121	—	2	1	no	—
360	C₂×#121	C₂²×C₆₇	1	2	yes	—
361	C₂×#120	—	2	2	no	—
362	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
365	C₂²×C₄⋊C₄	—	2	1	no	—
366	#492	C₂²×C₆₇	1	8	yes	complemented
367	#468	C₂²×C₆₇	1	16	yes	complemented
368	#461	C₂²×C₆₇	1	8	yes	complemented
369	#459	C₂²×C₆₇	1	8	yes	complemented
370	#450	C₂²×C₆₇	1	16	yes	complemented
371	#449	C₂²×C₆₇	1	16	yes	complemented
372	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
373	#436	C₂²×C₆₇	1	8	yes	complemented
374	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
375	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
376	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
377	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
379	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
380	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
381	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
382	C₂⁵	—	2	2	no	—
383	C₂×#41	—	2	4	no	—
384	C₂×#41	—	2	8	no	—
385	C₂×#41	—	4	4	no	—
386	C₂×#41	C₂³×C₆₇	1	8	yes	complemented
387	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
388	C₂²×D₄	—	2	8	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	8	no	—
392	C₂²×D₄	—	2	2	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	—	4	4	no	—
397	C₂²×D₄	—	4	8	no	—
398	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
400	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
401	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	—	2	2	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
407	AGL(1,ℤ/8)	—	2	64	no	—
408	C₂×SD₁₆	—	2	8	no	—
409	C₂×SD₁₆	—	2	8	no	—
410	C₂×SD₁₆	—	4	4	no	—
411	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
412	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
413	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
414	C₂×D₈	—	2	8	no	—
415	C₂×D₈	D₄×C₆₇	1	8	yes	complemented
416	C₂×D₈	C₂³×C₆₇	1	4	yes	—
417	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
418	C₂×M₁₆	—	2	8	no	—
419	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
420	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
421	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
423	C₄⋊Q₈	—	2	2	no	—
424	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
425	#127	—	2	2	no	—
426	#127	C₂³×C₆₇	1	4	yes	—
427	#123	—	2	16	no	—
428	C₂²⋊Q₈	—	2	4	no	—
429	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
430	#121	—	2	8	no	—
431	#121	—	2	4	no	—
432	#121	—	2	8	no	—
433	#121	C₂³×C₆₇	1	8	yes	—
434	#120	—	2	16	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	D₄×C₆₇	1	4	yes	—
438	C₄×D₄	C₂³×C₆₇	1	4	yes	—
439	C₄×D₄	C₂³×C₆₇	1	4	yes	—
440	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	2	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	8	no	—
445	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	2	no	—
452	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
453	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
454	#107	C₂³×C₆₇	1	4	yes	complemented
455	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
456	#103	C₂³×C₆₇	1	8	yes	complemented
457	#102	C₂³×C₆₇	1	4	yes	—
458	#102	C₂³×C₆₇	1	4	yes	complemented
459	#102	C₂³×C₆₇	1	8	yes	complemented
460	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
461	C₄×C₈	C₂³×C₆₇	1	4	yes	complemented
462	C₂⁴	—	2	1	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	—	2	8	no	—
466	C₂⁴	—	4	8	no	—
467	C₂⁴	—	4	8	no	—
468	C₂⁴	—	8	4	no	—
469	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
470	#41	—	2	16	no	—
471	#41	—	4	8	no	—
472	#41	—	4	16	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
477	C₂×D₄	—	2	16	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	4	8	no	—
492	C₂×D₄	—	4	16	no	—
493	C₂×D₄	—	4	8	no	—
494	C₂×D₄	—	4	32	no	—
495	C₂×D₄	—	4	8	no	—
496	C₂×D₄	—	4	8	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	8	2	no	—
499	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
500	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
501	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
502	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
503	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
504	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	8	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
518	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
519	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
522	SD₁₆	—	2	16	no	—
523	SD₁₆	—	2	16	no	—
524	SD₁₆	—	4	8	no	—
525	D₈	—	2	16	no	—
526	D₈	C₂×D₄×C₆₇	1	16	yes	complemented
527	M₁₆	—	2	16	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
531	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
532	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
533	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	8	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
540	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
541	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
547	C₄²	C₂×D₄×C₆₇	1	2	yes	—
548	C₄²	C₂⁴×C₆₇	1	2	yes	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	16	no	—
558	C₂³	—	4	16	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	4	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	4	no	—
566	C₂³	—	8	8	no	—
567	C₂³	—	8	32	no	—
568	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
569	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
570	Q₈	—	2	4	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	4	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	8	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	4	16	no	—
581	D₄	—	4	16	no	—
582	D₄	—	4	16	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	8	no	—
585	D₄	—	8	4	no	—
586	D₄	C₂²×D₄×C₆₇	1	4	yes	—
587	D₄	C₂²×D₄×C₆₇	1	4	yes	complemented
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	16	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
603	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
604	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
605	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
607	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
608	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
609	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	2	no	—
612	C₈	C₂²×D₄×C₆₇	1	4	yes	complemented
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	8	no	—
619	C₂²	—	4	8	no	—
620	C₂²	—	4	8	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	32	no	—
629	C₂²	—	8	8	no	—
630	C₂²	D₄²×C₆₇	1	2	yes	—
631	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
632	C₂²	#577×C₆₇	1	2	yes	—
633	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	4	no	—
639	C₄	D₄²×C₆₇	1	2	yes	—
640	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
641	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
642	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
643	C₂	—	4	4	no	—
644	C₂	—	4	4	no	—
645	C₂	—	4	4	no	—
646	C₂	—	8	4	no	—
647	C₂	C₆₇×#3272	1	4	yes	direct product factor
648	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
649	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
650	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₂×D₄²×C₆₇	C₂	semidirect
4. C₆₇×#3272	C₂	direct (N × H)
5. C₂×#492×C₆₇	C₂	semidirect
6. C₂×#468×C₆₇	C₂	semidirect
7. C₂×#461×C₆₇	C₂	semidirect
8. C₂×#459×C₆₇	C₂	semidirect
9. C₂×#449×C₆₇	C₂	semidirect
10. C₂×#450×C₆₇	C₂	semidirect
11. C₂×C₄×D₈×C₆₇	C₂	semidirect
12. C₂×#436×C₆₇	C₂	semidirect
13. C₂²×#41×C₆₇	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
19. C₂²×SD₁₆×C₆₇	C₂²	semidirect
20. C₂²×SD₁₆×C₆₇	C₂²	semidirect
22. C₂²×D₈×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
25. #547×C₆₇	C₂²	semidirect
27. D₄²×C₆₇	C₂²	semidirect
28. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
40. #492×C₆₇	C₂²	semidirect
41. #468×C₆₇	C₂²	semidirect
42. #461×C₆₇	C₂²	semidirect
43. #459×C₆₇	C₂²	semidirect
44. #450×C₆₇	C₂²	semidirect
45. #449×C₆₇	C₂²	semidirect
46. C₄×D₈×C₆₇	C₂²	semidirect
47. #436×C₆₇	C₂²	semidirect
48. C₂×#107×C₆₇	C₂²	semidirect
49. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
50. C₂×#103×C₆₇	C₂²	semidirect
52. C₂×#102×C₆₇	C₂²	semidirect
53. C₂×#102×C₆₇	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
55. C₂×C₄×C₈×C₆₇	C₂²	semidirect
60. C₂×#41×C₆₇	C₂³	semidirect
86. C₂×SD₁₆×C₆₇	C₂³	semidirect
87. C₂×SD₁₆×C₆₇	C₂³	semidirect
89. C₂×D₈×C₆₇	D₄	semidirect
91. C₂×D₈×C₆₇	C₂³	semidirect
93. C₂×M₁₆×C₆₇	C₂³	semidirect
98. C₄⋊Q₈×C₆₇	C₂³	semidirect
103. C₂²⋊Q₈×C₆₇	C₂³	semidirect
114. C₄×D₄×C₆₇	C₂³	semidirect
128. #107×C₆₇	C₂³	semidirect
129. C₄⋊C₈×C₆₇	C₂³	semidirect
130. #103×C₆₇	C₂³	semidirect
132. #102×C₆₇	C₂³	semidirect
133. #102×C₆₇	C₂³	semidirect
134. C₂²⋊C₈×C₆₇	C₂³	semidirect
135. C₄×C₈×C₆₇	C₂³	semidirect
175. C₂×D₄×C₆₇	C₂×D₄	semidirect
200. D₈×C₆₇	C₂×D₄	semidirect
204. C₂×C₈×C₆₇	C₂×D₄	semidirect
261. D₄×C₆₇	C₂²×D₄	semidirect
276. C₂×C₄×C₆₇	AGL(1,ℤ/8)	semidirect
286. C₈×C₆₇	C₂²×D₄	semidirect
314. C₄×C₆₇	C₂×AGL(1,ℤ/8)	semidirect
317. C₂×#3272	C₆₇	direct (N × H)
322. C₂×C₆₇	#3272	direct (N × H)
326. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
327. C₂×#547	C₂×C₆₇	semidirect
328. C₂×D₄²	C₂×C₆₇	semidirect
329. #3272	C₂×C₆₇	direct (N × H)
330. C₂×#492	C₂×C₆₇	semidirect
331. C₂×#468	C₂×C₆₇	semidirect
332. C₂×#461	C₂×C₆₇	semidirect
333. C₂×#459	C₂×C₆₇	semidirect
334. C₂×#449	C₂×C₆₇	semidirect
335. C₂×#450	C₂×C₆₇	semidirect
336. C₂×C₄×D₈	C₂×C₆₇	semidirect
337. C₂×#436	C₂×C₆₇	semidirect
338. C₆₇	C₂×#3272	direct (N × H)
339. C₂²×#41	C₂²×C₆₇	semidirect
343. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
345. C₂²×SD₁₆	C₂²×C₆₇	semidirect
346. C₂²×SD₁₆	C₂²×C₆₇	semidirect
348. C₂²×D₈	C₂²×C₆₇	semidirect
349. C₂²×M₁₆	C₂²×C₆₇	semidirect
351. #547	C₂²×C₆₇	semidirect
353. D₄²	C₂²×C₆₇	semidirect
354. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
357. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
364. C₂×C₄×D₄	C₂²×C₆₇	semidirect
366. #492	C₂²×C₆₇	semidirect
367. #468	C₂²×C₆₇	semidirect
368. #461	C₂²×C₆₇	semidirect
369. #459	C₂²×C₆₇	semidirect
370. #450	C₂²×C₆₇	semidirect
371. #449	C₂²×C₆₇	semidirect
372. C₄×D₈	C₂²×C₆₇	semidirect
373. #436	C₂²×C₆₇	semidirect
374. C₂×#107	C₂²×C₆₇	semidirect
375. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
376. C₂×#103	C₂²×C₆₇	semidirect
378. C₂×#102	C₂²×C₆₇	semidirect
379. C₂×#102	C₂²×C₆₇	semidirect
380. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
381. C₂×C₄×C₈	C₂²×C₆₇	semidirect
386. C₂×#41	C₂³×C₆₇	semidirect
412. C₂×SD₁₆	C₂³×C₆₇	semidirect
413. C₂×SD₁₆	C₂³×C₆₇	semidirect
415. C₂×D₈	D₄×C₆₇	semidirect
417. C₂×D₈	C₂³×C₆₇	semidirect
419. C₂×M₁₆	C₂³×C₆₇	semidirect
424. C₄⋊Q₈	C₂³×C₆₇	semidirect
429. C₂²⋊Q₈	C₂³×C₆₇	semidirect
440. C₄×D₄	C₂³×C₆₇	semidirect
454. #107	C₂³×C₆₇	semidirect
455. C₄⋊C₈	C₂³×C₆₇	semidirect
456. #103	C₂³×C₆₇	semidirect
458. #102	C₂³×C₆₇	semidirect
459. #102	C₂³×C₆₇	semidirect
460. C₂²⋊C₈	C₂³×C₆₇	semidirect
461. C₄×C₈	C₂³×C₆₇	semidirect
501. C₂×D₄	C₂×D₄×C₆₇	semidirect
526. D₈	C₂×D₄×C₆₇	semidirect
530. C₂×C₈	C₂×D₄×C₆₇	semidirect
587. D₄	C₂²×D₄×C₆₇	semidirect
602. C₂×C₄	AGL(1,ℤ/8)×C₆₇	semidirect
612. C₈	C₂²×D₄×C₆₇	semidirect
640. C₄	C₂×AGL(1,ℤ/8)×C₆₇	semidirect
647. C₂	C₆₇×#3272	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂×#547×C₆₇	2
C₂×D₄²×C₆₇	2
C₆₇×#3272	2
C₂×#492×C₆₇	2
C₂×#468×C₆₇	2
C₂×#461×C₆₇	2
C₂×#459×C₆₇	2
C₂×#449×C₆₇	2
C₂×#450×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#436×C₆₇	2
C₂×#3272	67

Subgroups — C2×C67×#3272 #30740282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3272 #30740282