Subgroups — C₂×C₆₇×#3006 #30739608

Order 17152.

5422 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3006	C₂	1	16	yes	maximal, direct product factor
5	C₂×#449×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#448×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#447×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#417×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#407×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₇	—	2	16	no	—
11	C₂²×#41×C₆₇	—	2	1	no	—
12	C₂²×#41×C₆₇	—	2	1	no	—
13	C₂²×#41×C₆₇	—	2	4	no	—
14	C₂²×#41×C₆₇	C₂²	1	2	yes	—
15	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
16	C₂²×#41×C₆₇	C₂²	1	8	yes	complemented
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₄×C₆₇	—	2	1	no	—
19	C₂³×D₄×C₆₇	—	2	1	no	—
20	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×C₄×C₆₇	—	2	1	no	—
23	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	16	yes	complemented
26	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
27	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
28	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#121×C₆₇	—	2	1	no	—
30	C₂×#121×C₆₇	—	2	4	no	—
31	C₂×#121×C₆₇	—	2	1	no	—
32	C₂×#121×C₆₇	C₂²	1	2	yes	—
33	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#121×C₆₇	C₂²	1	8	yes	complemented
35	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
37	#449×C₆₇	C₂²	1	32	yes	complemented
38	#448×C₆₇	C₂²	1	16	yes	complemented
39	#447×C₆₇	C₂²	1	16	yes	complemented
40	#417×C₆₇	C₂²	1	16	yes	complemented
41	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
42	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
43	#407×C₆₇	C₂²	1	8	yes	complemented
44	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
45	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
46	C₂⁵×C₆₇	—	2	1	no	—
47	C₂⁵×C₆₇	—	2	1	no	—
48	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
49	C₂×#41×C₆₇	—	2	16	no	—
50	C₂×#41×C₆₇	—	2	64	no	—
51	C₂×#41×C₆₇	—	2	16	no	—
52	C₂×#41×C₆₇	—	2	64	no	—
53	C₂×#41×C₆₇	—	2	8	no	—
54	C₂×#41×C₆₇	—	2	8	no	—
55	C₂×#41×C₆₇	—	2	8	no	—
56	C₂×#41×C₆₇	—	2	4	no	—
57	C₂×#41×C₆₇	—	2	8	no	—
58	C₂×#41×C₆₇	—	2	8	no	—
59	C₂×#41×C₆₇	—	2	4	no	—
60	C₂×#41×C₆₇	D₄	1	16	yes	complemented
61	C₂×#41×C₆₇	C₂³	1	8	yes	—
62	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
63	C₂²×Q₈×C₆₇	—	2	8	no	—
64	C₂²×Q₈×C₆₇	—	2	2	no	—
65	C₂²×Q₈×C₆₇	—	2	1	no	—
66	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
67	C₂²×Q₈×C₆₇	C₂³	1	4	yes	complemented
68	C₂²×D₄×C₆₇	—	2	16	no	—
69	C₂²×D₄×C₆₇	—	2	2	no	—
70	C₂²×D₄×C₆₇	—	2	8	no	—
71	C₂²×D₄×C₆₇	—	2	2	no	—
72	C₂²×D₄×C₆₇	—	2	8	no	—
73	C₂²×D₄×C₆₇	—	2	2	no	—
74	C₂²×D₄×C₆₇	—	2	8	no	—
75	C₂²×D₄×C₆₇	—	2	2	no	—
76	C₂²×D₄×C₆₇	—	2	2	no	—
77	C₂²×D₄×C₆₇	—	2	1	no	—
78	C₂²×D₄×C₆₇	—	2	8	no	—
79	C₂²×D₄×C₆₇	—	2	2	no	—
80	C₂²×D₄×C₆₇	—	2	1	no	—
81	C₂²×D₄×C₆₇	—	4	8	no	—
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
85	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
86	C₂³×C₄×C₆₇	—	2	16	no	—
87	C₂³×C₄×C₆₇	—	2	1	no	—
88	C₂³×C₄×C₆₇	—	2	2	no	—
89	C₂³×C₄×C₆₇	—	2	8	no	—
90	C₂³×C₄×C₆₇	—	2	2	no	—
91	C₂³×C₄×C₆₇	—	2	8	no	—
92	C₂³×C₄×C₆₇	—	2	1	no	—
93	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	D₄	1	4	yes	—
96	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	AGL(1,ℤ/8)×C₆₇	—	2	64	no	—
102	C₂×SD₁₆×C₆₇	—	2	16	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	16	yes	complemented
104	C₂×D₈×C₆₇	—	2	16	no	—
105	C₂×D₈×C₆₇	C₂³	1	16	yes	complemented
106	C₂×M₁₆×C₆₇	—	2	8	no	—
107	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
108	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
109	#121×C₆₇	—	2	4	no	—
110	#121×C₆₇	—	2	8	no	—
111	#121×C₆₇	—	2	4	no	—
112	#121×C₆₇	—	2	8	no	—
113	#121×C₆₇	C₂³	1	8	yes	—
114	#121×C₆₇	C₂³	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
119	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
122	#103×C₆₇	C₂³	1	16	yes	complemented
123	#102×C₆₇	C₂³	1	16	yes	complemented
124	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
125	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
126	C₂⁴×C₆₇	—	2	8	no	—
127	C₂⁴×C₆₇	—	2	4	no	—
128	C₂⁴×C₆₇	—	2	4	no	—
129	C₂⁴×C₆₇	—	2	4	no	—
130	C₂⁴×C₆₇	—	2	2	no	—
131	C₂⁴×C₆₇	—	2	4	no	—
132	C₂⁴×C₆₇	—	2	2	no	—
133	C₂⁴×C₆₇	—	4	2	no	—
134	C₂⁴×C₆₇	—	4	4	no	—
135	C₂⁴×C₆₇	—	4	4	no	—
136	C₂⁴×C₆₇	—	4	4	no	—
137	C₂⁴×C₆₇	—	4	4	no	—
138	C₂⁴×C₆₇	—	4	4	no	—
139	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
141	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
143	#41×C₆₇	—	2	64	no	—
144	#41×C₆₇	—	2	32	no	—
145	#41×C₆₇	—	2	64	no	—
146	#41×C₆₇	—	2	16	no	—
147	#41×C₆₇	—	2	16	no	—
148	#41×C₆₇	—	2	32	no	—
149	#41×C₆₇	—	2	16	no	—
150	#41×C₆₇	C₂×D₄	1	32	yes	complemented
151	C₂×Q₈×C₆₇	—	2	16	no	—
152	C₂×Q₈×C₆₇	—	2	8	no	—
153	C₂×Q₈×C₆₇	—	2	16	no	—
154	C₂×Q₈×C₆₇	—	2	4	no	—
155	C₂×Q₈×C₆₇	—	2	2	no	—
156	C₂×Q₈×C₆₇	—	2	4	no	—
157	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	complemented
158	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
159	C₂×D₄×C₆₇	—	2	64	no	—
160	C₂×D₄×C₆₇	—	2	16	no	—
161	C₂×D₄×C₆₇	—	2	8	no	—
162	C₂×D₄×C₆₇	—	2	16	no	—
163	C₂×D₄×C₆₇	—	2	16	no	—
164	C₂×D₄×C₆₇	—	2	8	no	—
165	C₂×D₄×C₆₇	—	2	8	no	—
166	C₂×D₄×C₆₇	—	2	16	no	—
167	C₂×D₄×C₆₇	—	2	8	no	—
168	C₂×D₄×C₆₇	—	2	8	no	—
169	C₂×D₄×C₆₇	—	2	2	no	—
170	C₂×D₄×C₆₇	—	2	4	no	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	8	no	—
173	C₂×D₄×C₆₇	—	2	16	no	—
174	C₂×D₄×C₆₇	—	2	2	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	4	32	no	—
177	C₂×D₄×C₆₇	—	4	8	no	—
178	C₂×D₄×C₆₇	—	4	8	no	—
179	C₂×D₄×C₆₇	—	4	4	no	—
180	C₂×D₄×C₆₇	—	4	8	no	—
181	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
182	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
183	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₆₇	—	2	8	no	—
185	C₂²×C₄×C₆₇	—	2	64	no	—
186	C₂²×C₄×C₆₇	—	2	16	no	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	—	2	4	no	—
189	C₂²×C₄×C₆₇	—	2	2	no	—
190	C₂²×C₄×C₆₇	—	2	4	no	—
191	C₂²×C₄×C₆₇	—	2	16	no	—
192	C₂²×C₄×C₆₇	—	2	4	no	—
193	C₂²×C₄×C₆₇	—	2	16	no	—
194	C₂²×C₄×C₆₇	—	2	8	no	—
195	C₂²×C₄×C₆₇	—	2	8	no	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	2	4	no	—
198	C₂²×C₄×C₆₇	—	2	16	no	—
199	C₂²×C₄×C₆₇	—	2	4	no	—
200	C₂²×C₄×C₆₇	—	2	2	no	—
201	C₂²×C₄×C₆₇	—	4	4	no	—
202	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
216	SD₁₆×C₆₇	—	2	32	no	—
217	D₈×C₆₇	—	2	32	no	—
218	M₁₆×C₆₇	—	2	16	no	—
219	C₂×C₈×C₆₇	—	2	8	no	—
220	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
221	C₄⋊C₄×C₆₇	—	2	2	no	—
222	C₄⋊C₄×C₆₇	—	2	4	no	—
223	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
224	C₂²⋊C₄×C₆₇	—	2	8	no	—
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂³×C₆₇	—	2	2	no	—
227	C₂³×C₆₇	—	2	2	no	—
228	C₂³×C₆₇	—	2	2	no	—
229	C₂³×C₆₇	—	2	2	no	—
230	C₂³×C₆₇	—	2	16	no	—
231	C₂³×C₆₇	—	2	8	no	—
232	C₂³×C₆₇	—	2	2	no	—
233	C₂³×C₆₇	—	2	8	no	—
234	C₂³×C₆₇	—	2	2	no	—
235	C₂³×C₆₇	—	2	8	no	—
236	C₂³×C₆₇	—	2	2	no	—
237	C₂³×C₆₇	—	2	4	no	—
238	C₂³×C₆₇	—	2	4	no	—
239	C₂³×C₆₇	—	4	4	no	—
240	C₂³×C₆₇	—	4	16	no	—
241	C₂³×C₆₇	—	4	32	no	—
242	C₂³×C₆₇	—	4	8	no	—
243	C₂³×C₆₇	—	4	8	no	—
244	C₂³×C₆₇	—	4	8	no	—
245	C₂³×C₆₇	—	4	4	no	—
246	C₂³×C₆₇	—	4	8	no	—
247	C₂³×C₆₇	—	4	4	no	—
248	C₂³×C₆₇	—	4	8	no	—
249	C₂³×C₆₇	—	4	4	no	—
250	C₂³×C₆₇	—	4	4	no	—
251	C₂³×C₆₇	—	4	4	no	—
252	C₂³×C₆₇	—	8	16	no	—
253	C₂³×C₆₇	#120	1	4	yes	—
254	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
255	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
256	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
257	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
258	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₆₇	—	2	16	no	—
260	Q₈×C₆₇	—	2	8	no	—
261	Q₈×C₆₇	—	2	4	no	—
262	Q₈×C₆₇	C₂²×D₄	1	8	yes	complemented
263	D₄×C₆₇	—	2	32	no	—
264	D₄×C₆₇	—	2	16	no	—
265	D₄×C₆₇	—	2	32	no	—
266	D₄×C₆₇	—	2	8	no	—
267	D₄×C₆₇	—	2	4	no	—
268	D₄×C₆₇	—	2	8	no	—
269	D₄×C₆₇	—	4	16	no	—
270	D₄×C₆₇	—	4	16	no	—
271	D₄×C₆₇	—	4	8	no	—
272	D₄×C₆₇	—	4	4	no	—
273	D₄×C₆₇	C₂²×D₄	1	8	yes	complemented
274	C₂×C₄×C₆₇	—	2	16	no	—
275	C₂×C₄×C₆₇	—	2	32	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	8	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	8	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	8	no	—
282	C₂×C₄×C₆₇	—	2	32	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	8	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	4	8	no	—
290	C₂×C₄×C₆₇	—	4	4	no	—
291	C₂×C₄×C₆₇	#120	1	4	yes	—
292	C₂×C₄×C₆₇	#120	1	8	yes	—
293	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
299	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
300	C₈×C₆₇	—	2	8	no	—
301	C₂²×C₆₇	—	2	2	no	—
302	C₂²×C₆₇	—	2	8	no	—
303	C₂²×C₆₇	—	2	8	no	—
304	C₂²×C₆₇	—	2	2	no	—
305	C₂²×C₆₇	—	2	2	no	—
306	C₂²×C₆₇	—	2	2	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	8	no	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	4	16	no	—
312	C₂²×C₆₇	—	4	32	no	—
313	C₂²×C₆₇	—	4	4	no	—
314	C₂²×C₆₇	—	4	16	no	—
315	C₂²×C₆₇	—	4	4	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	—	4	4	no	—
318	C₂²×C₆₇	—	4	4	no	—
319	C₂²×C₆₇	—	4	4	no	—
320	C₂²×C₆₇	—	8	16	no	—
321	C₂²×C₆₇	—	8	8	no	—
322	C₂²×C₆₇	C₂×#120	1	4	yes	—
323	C₂²×C₆₇	C₂×#120	1	2	yes	—
324	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
325	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
326	C₂²×C₆₇	#575	1	2	yes	—
327	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	8	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	4	4	no	—
332	C₄×C₆₇	C₂×#120	1	4	yes	—
333	C₄×C₆₇	C₂×#120	1	2	yes	—
334	C₄×C₆₇	C₂³×D₄	1	2	yes	—
335	C₂×#3006	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂×C₆₇	—	2	4	no	—
337	C₂×C₆₇	—	2	4	no	—
338	C₂×C₆₇	—	4	2	no	—
339	C₂×C₆₇	—	4	8	no	—
340	C₂×C₆₇	—	8	4	no	—
341	C₂×C₆₇	#3006	1	4	yes	direct product factor
342	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
343	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
345	C₂³×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
346	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	2	yes	complemented
347	C₂²×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
348	#3006	C₂×C₆₇	1	16	yes	direct product factor
349	C₂×#449	C₂×C₆₇	1	4	yes	complemented
350	C₂×#448	C₂×C₆₇	1	2	yes	complemented
351	C₂×#447	C₂×C₆₇	1	2	yes	complemented
352	C₂×#417	C₂×C₆₇	1	2	yes	complemented
353	C₂×#407	C₂×C₆₇	1	1	yes	characteristic, complemented
354	C₆₇	C₂×#3006	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²×#41	—	2	16	no	—
356	C₂²×#41	—	2	1	no	—
357	C₂²×#41	—	2	1	no	—
358	C₂²×#41	—	2	4	no	—
359	C₂²×#41	C₂²×C₆₇	1	2	yes	—
360	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
361	C₂²×#41	C₂²×C₆₇	1	8	yes	complemented
362	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
363	C₂³×D₄	—	2	1	no	—
364	C₂³×D₄	—	2	1	no	—
365	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
366	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
367	C₂⁴×C₄	—	2	1	no	—
368	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
369	C₂×AGL(1,ℤ/8)	—	2	16	no	—
370	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	16	yes	complemented
371	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
372	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
373	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
374	C₂×#121	—	2	1	no	—
375	C₂×#121	—	2	4	no	—
376	C₂×#121	—	2	1	no	—
377	C₂×#121	C₂²×C₆₇	1	2	yes	—
378	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
379	C₂×#121	C₂²×C₆₇	1	8	yes	complemented
380	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
381	C₂²×C₂²⋊C₄	—	2	1	no	—
382	#449	C₂²×C₆₇	1	32	yes	complemented
383	#448	C₂²×C₆₇	1	16	yes	complemented
384	#447	C₂²×C₆₇	1	16	yes	complemented
385	#417	C₂²×C₆₇	1	16	yes	complemented
386	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
387	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
388	#407	C₂²×C₆₇	1	8	yes	complemented
389	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
390	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
391	C₂⁵	—	2	1	no	—
392	C₂⁵	—	2	1	no	—
393	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
394	C₂×#41	—	2	16	no	—
395	C₂×#41	—	2	64	no	—
396	C₂×#41	—	2	16	no	—
397	C₂×#41	—	2	64	no	—
398	C₂×#41	—	2	8	no	—
399	C₂×#41	—	2	8	no	—
400	C₂×#41	—	2	8	no	—
401	C₂×#41	—	2	4	no	—
402	C₂×#41	—	2	8	no	—
403	C₂×#41	—	2	8	no	—
404	C₂×#41	—	2	4	no	—
405	C₂×#41	D₄×C₆₇	1	16	yes	complemented
406	C₂×#41	C₂³×C₆₇	1	8	yes	—
407	C₂×#41	C₂³×C₆₇	1	8	yes	complemented
408	C₂²×Q₈	—	2	8	no	—
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×Q₈	—	2	2	no	—
411	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
412	C₂²×Q₈	C₂³×C₆₇	1	4	yes	complemented
413	C₂²×D₄	—	2	16	no	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	8	no	—
417	C₂²×D₄	—	2	8	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	—	2	2	no	—
420	C₂²×D₄	—	2	8	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	2	no	—
423	C₂²×D₄	—	2	8	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	2	no	—
426	C₂²×D₄	—	4	8	no	—
427	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
428	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
429	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
430	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
431	C₂³×C₄	—	2	16	no	—
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	—	2	2	no	—
434	C₂³×C₄	—	2	2	no	—
435	C₂³×C₄	—	2	8	no	—
436	C₂³×C₄	—	2	8	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
439	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
440	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
441	C₂³×C₄	D₄×C₆₇	1	4	yes	—
442	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
445	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
446	AGL(1,ℤ/8)	—	2	64	no	—
447	C₂×SD₁₆	—	2	16	no	—
448	C₂×SD₁₆	C₂³×C₆₇	1	16	yes	complemented
449	C₂×D₈	—	2	16	no	—
450	C₂×D₈	C₂³×C₆₇	1	16	yes	complemented
451	C₂×M₁₆	—	2	8	no	—
452	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
453	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
454	#121	—	2	4	no	—
455	#121	—	2	8	no	—
456	#121	—	2	4	no	—
457	#121	—	2	8	no	—
458	#121	C₂³×C₆₇	1	8	yes	—
459	#121	C₂³×C₆₇	1	8	yes	complemented
460	C₂×C₄⋊C₄	—	2	2	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	2	8	no	—
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	#103	C₂³×C₆₇	1	16	yes	complemented
468	#102	C₂³×C₆₇	1	16	yes	complemented
469	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
470	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
471	C₂⁴	—	2	8	no	—
472	C₂⁴	—	2	4	no	—
473	C₂⁴	—	2	4	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	4	no	—
476	C₂⁴	—	2	2	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	4	2	no	—
479	C₂⁴	—	4	4	no	—
480	C₂⁴	—	4	4	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	—	4	4	no	—
483	C₂⁴	—	4	4	no	—
484	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
485	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
486	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
487	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
488	#41	—	2	64	no	—
489	#41	—	2	32	no	—
490	#41	—	2	64	no	—
491	#41	—	2	16	no	—
492	#41	—	2	16	no	—
493	#41	—	2	32	no	—
494	#41	—	2	16	no	—
495	#41	C₂×D₄×C₆₇	1	32	yes	complemented
496	C₂×Q₈	—	2	16	no	—
497	C₂×Q₈	—	2	8	no	—
498	C₂×Q₈	—	2	16	no	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	complemented
503	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
504	C₂×D₄	—	2	64	no	—
505	C₂×D₄	—	2	16	no	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	2	16	no	—
508	C₂×D₄	—	2	16	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	16	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	16	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	4	32	no	—
522	C₂×D₄	—	4	8	no	—
523	C₂×D₄	—	4	8	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
527	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
528	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	64	no	—
531	C₂²×C₄	—	2	16	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	16	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	16	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	16	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
553	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
554	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
561	SD₁₆	—	2	32	no	—
562	D₈	—	2	32	no	—
563	M₁₆	—	2	16	no	—
564	C₂×C₈	—	2	8	no	—
565	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	8	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	16	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	8	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	8	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	4	4	no	—
585	C₂³	—	4	16	no	—
586	C₂³	—	4	8	no	—
587	C₂³	—	4	32	no	—
588	C₂³	—	4	8	no	—
589	C₂³	—	4	8	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	4	no	—
593	C₂³	—	4	8	no	—
594	C₂³	—	4	4	no	—
595	C₂³	—	4	4	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	8	16	no	—
598	C₂³	#120×C₆₇	1	4	yes	—
599	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
600	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
601	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
602	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
603	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
604	Q₈	—	2	16	no	—
605	Q₈	—	2	8	no	—
606	Q₈	—	2	4	no	—
607	Q₈	C₂²×D₄×C₆₇	1	8	yes	complemented
608	D₄	—	2	32	no	—
609	D₄	—	2	16	no	—
610	D₄	—	2	32	no	—
611	D₄	—	2	8	no	—
612	D₄	—	2	4	no	—
613	D₄	—	2	8	no	—
614	D₄	—	4	16	no	—
615	D₄	—	4	16	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	4	no	—
618	D₄	C₂²×D₄×C₆₇	1	8	yes	complemented
619	C₂×C₄	—	2	16	no	—
620	C₂×C₄	—	2	32	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	32	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	4	8	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	#120×C₆₇	1	4	yes	—
637	C₂×C₄	#120×C₆₇	1	8	yes	—
638	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
641	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
642	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
643	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
644	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
645	C₈	—	2	8	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	8	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	8	no	—
656	C₂²	—	4	16	no	—
657	C₂²	—	4	32	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	16	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	8	16	no	—
666	C₂²	—	8	8	no	—
667	C₂²	C₂×#120×C₆₇	1	4	yes	—
668	C₂²	C₂×#120×C₆₇	1	2	yes	—
669	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
670	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
671	C₂²	#575×C₆₇	1	2	yes	—
672	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	8	no	—
675	C₄	—	2	2	no	—
676	C₄	—	4	4	no	—
677	C₄	C₂×#120×C₆₇	1	4	yes	—
678	C₄	C₂×#120×C₆₇	1	2	yes	—
679	C₄	C₂³×D₄×C₆₇	1	2	yes	—
680	C₂	—	2	4	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	8	no	—
684	C₂	—	8	4	no	—
685	C₂	C₆₇×#3006	1	4	yes	direct product factor
686	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
687	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
688	C₂	C₂×#575×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 ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₂²×#121×C₆₇	C₂	semidirect
4. C₆₇×#3006	C₂	direct (N × H)
5. C₂×#449×C₆₇	C₂	semidirect
6. C₂×#448×C₆₇	C₂	semidirect
7. C₂×#447×C₆₇	C₂	semidirect
8. C₂×#417×C₆₇	C₂	semidirect
9. C₂×#407×C₆₇	C₂	semidirect
15. C₂²×#41×C₆₇	C₂²	semidirect
16. C₂²×#41×C₆₇	C₂²	semidirect
17. C₂³×Q₈×C₆₇	C₂²	semidirect
20. C₂³×D₄×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂²×SD₁₆×C₆₇	C₂²	semidirect
27. C₂²×D₈×C₆₇	C₂²	semidirect
28. C₂²×M₁₆×C₆₇	C₂²	semidirect
33. C₂×#121×C₆₇	C₂²	semidirect
34. C₂×#121×C₆₇	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
37. #449×C₆₇	C₂²	semidirect
38. #448×C₆₇	C₂²	semidirect
39. #447×C₆₇	C₂²	semidirect
40. #417×C₆₇	C₂²	semidirect
41. C₂×#103×C₆₇	C₂²	semidirect
42. C₂×#102×C₆₇	C₂²	semidirect
43. #407×C₆₇	C₂²	semidirect
44. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
45. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
60. C₂×#41×C₆₇	D₄	semidirect
62. C₂×#41×C₆₇	C₂³	semidirect
67. C₂²×Q₈×C₆₇	C₂³	semidirect
84. C₂²×D₄×C₆₇	C₂³	semidirect
85. C₂²×D₄×C₆₇	C₂³	semidirect
103. C₂×SD₁₆×C₆₇	C₂³	semidirect
105. C₂×D₈×C₆₇	C₂³	semidirect
107. C₂×M₁₆×C₆₇	C₂³	semidirect
114. #121×C₆₇	C₂³	semidirect
118. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
122. #103×C₆₇	C₂³	semidirect
123. #102×C₆₇	C₂³	semidirect
124. C₂²⋊C₈×C₆₇	C₂³	semidirect
125. C₂²⋊C₈×C₆₇	C₂³	semidirect
150. #41×C₆₇	C₂×D₄	semidirect
157. C₂×Q₈×C₆₇	C₂×D₄	semidirect
181. C₂×D₄×C₆₇	C₂×D₄	semidirect
254. C₂³×C₆₇	AGL(1,ℤ/8)	semidirect
262. Q₈×C₆₇	C₂²×D₄	semidirect
273. D₄×C₆₇	C₂²×D₄	semidirect
325. C₂²×C₆₇	C₂×AGL(1,ℤ/8)	semidirect
335. C₂×#3006	C₆₇	direct (N × H)
341. C₂×C₆₇	#3006	direct (N × H)
345. C₂³×#41	C₂×C₆₇	semidirect
346. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
347. C₂²×#121	C₂×C₆₇	semidirect
348. #3006	C₂×C₆₇	direct (N × H)
349. C₂×#449	C₂×C₆₇	semidirect
350. C₂×#448	C₂×C₆₇	semidirect
351. C₂×#447	C₂×C₆₇	semidirect
352. C₂×#417	C₂×C₆₇	semidirect
353. C₂×#407	C₂×C₆₇	semidirect
354. C₆₇	C₂×#3006	direct (N × H)
360. C₂²×#41	C₂²×C₆₇	semidirect
361. C₂²×#41	C₂²×C₆₇	semidirect
362. C₂³×Q₈	C₂²×C₆₇	semidirect
365. C₂³×D₄	C₂²×C₆₇	semidirect
366. C₂³×D₄	C₂²×C₆₇	semidirect
370. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
371. C₂²×SD₁₆	C₂²×C₆₇	semidirect
372. C₂²×D₈	C₂²×C₆₇	semidirect
373. C₂²×M₁₆	C₂²×C₆₇	semidirect
378. C₂×#121	C₂²×C₆₇	semidirect
379. C₂×#121	C₂²×C₆₇	semidirect
380. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
382. #449	C₂²×C₆₇	semidirect
383. #448	C₂²×C₆₇	semidirect
384. #447	C₂²×C₆₇	semidirect
385. #417	C₂²×C₆₇	semidirect
386. C₂×#103	C₂²×C₆₇	semidirect
387. C₂×#102	C₂²×C₆₇	semidirect
388. #407	C₂²×C₆₇	semidirect
389. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
390. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
405. C₂×#41	D₄×C₆₇	semidirect
407. C₂×#41	C₂³×C₆₇	semidirect
412. C₂²×Q₈	C₂³×C₆₇	semidirect
429. C₂²×D₄	C₂³×C₆₇	semidirect
430. C₂²×D₄	C₂³×C₆₇	semidirect
448. C₂×SD₁₆	C₂³×C₆₇	semidirect
450. C₂×D₈	C₂³×C₆₇	semidirect
452. C₂×M₁₆	C₂³×C₆₇	semidirect
459. #121	C₂³×C₆₇	semidirect
463. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
467. #103	C₂³×C₆₇	semidirect
468. #102	C₂³×C₆₇	semidirect
469. C₂²⋊C₈	C₂³×C₆₇	semidirect
470. C₂²⋊C₈	C₂³×C₆₇	semidirect
495. #41	C₂×D₄×C₆₇	semidirect
502. C₂×Q₈	C₂×D₄×C₆₇	semidirect
526. C₂×D₄	C₂×D₄×C₆₇	semidirect
599. C₂³	AGL(1,ℤ/8)×C₆₇	semidirect
607. Q₈	C₂²×D₄×C₆₇	semidirect
618. D₄	C₂²×D₄×C₆₇	semidirect
670. C₂²	C₂×AGL(1,ℤ/8)×C₆₇	semidirect
685. C₂	C₆₇×#3006	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×#41×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂²×#121×C₆₇	2
C₆₇×#3006	2
C₂×#449×C₆₇	2
C₂×#448×C₆₇	2
C₂×#447×C₆₇	2
C₂×#417×C₆₇	2
C₂×#407×C₆₇	2
C₂×#3006	67

Subgroups — C2×C67×#3006 #30739608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3006 #30739608