Subgroups — C₆₇×#60141 #30739392

Order 17152.

2862 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic
4	D₄×M₁₆×C₆₇	C₂	1	8	yes	maximal, complemented
5	C₆₇×#2933	C₂	1	8	yes	maximal, complemented
6	C₆₇×#2930	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2929	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#407×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	#568×C₆₇	—	2	8	no	—
15	C₂×#131×C₆₇	C₂²	1	4	yes	complemented
16	C₂×#131×C₆₇	C₂²	1	4	yes	complemented
17	C₂²×M₁₆×C₆₇	—	2	8	no	—
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	—
20	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
24	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	complemented
25	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	complemented
26	C₂³×C₈×C₆₇	C₂²	1	2	yes	complemented
27	#525×C₆₇	C₄	1	2	yes	—
28	#525×C₆₇	C₄	1	4	yes	—
29	#525×C₆₇	C₄	1	2	yes	—
30	#525×C₆₇	C₂²	1	2	yes	—
31	#525×C₆₇	C₂²	1	2	yes	—
32	#525×C₆₇	C₂²	1	4	yes	—
33	C₂×#123×C₆₇	C₄	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₆₇	C₄	1	2	yes	—
35	C₂×#121×C₆₇	C₄	1	2	yes	—
36	C₂×#120×C₆₇	C₄	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	#436×C₆₇	C₂²	1	16	yes	complemented
40	#435×C₆₇	C₂²	1	16	yes	complemented
41	#435×C₆₇	C₂²	1	16	yes	complemented
42	C₈×D₄×C₆₇	C₂²	1	16	yes	complemented
43	#424×C₆₇	C₂²	1	4	yes	complemented
44	#424×C₆₇	C₂²	1	4	yes	complemented
45	#423×C₆₇	C₂²	1	4	yes	complemented
46	#408×C₆₇	C₂²	1	4	yes	complemented
47	#408×C₆₇	C₂²	1	4	yes	complemented
48	#407×C₆₇	C₂²	1	4	yes	—
49	#407×C₆₇	C₂²	1	2	yes	complemented
50	#407×C₆₇	C₂²	1	2	yes	complemented
51	#407×C₆₇	C₂²	1	4	yes	complemented
52	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
53	#405×C₆₇	C₂²	1	4	yes	complemented
54	#405×C₆₇	C₂²	1	4	yes	complemented
55	C₄×M₁₆×C₆₇	C₂²	1	4	yes	complemented
56	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×#41×C₆₇	—	2	4	no	—
58	C₂×#41×C₆₇	—	2	4	no	—
59	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
60	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
61	C₂×#41×C₆₇	C₂³	1	2	yes	—
62	C₂×#41×C₆₇	C₂³	1	2	yes	—
63	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
67	C₂³×C₄×C₆₇	—	2	4	no	—
68	C₂³×C₄×C₆₇	—	2	4	no	—
69	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
70	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
73	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	#131×C₆₇	—	2	16	no	—
81	#131×C₆₇	—	2	16	no	—
82	C₂×M₁₆×C₆₇	—	2	4	no	—
83	C₂×M₁₆×C₆₇	—	2	4	no	—
84	C₂×M₁₆×C₆₇	—	2	4	no	—
85	C₂×M₁₆×C₆₇	—	2	16	no	—
86	C₂×M₁₆×C₆₇	—	2	16	no	—
87	C₂×M₁₆×C₆₇	—	2	16	no	—
88	C₂×M₁₆×C₆₇	—	2	8	no	—
89	C₂×M₁₆×C₆₇	D₄	1	8	yes	complemented
90	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
92	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
93	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
94	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
95	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
96	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₆₇	C₂³	1	8	yes	complemented
100	C₂²×C₈×C₆₇	—	2	8	no	—
101	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
103	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	8	yes	complemented
107	#123×C₆₇	C₂×C₄	1	4	yes	—
108	#123×C₆₇	C₂×C₄	1	4	yes	—
109	#123×C₆₇	C₂×C₄	1	8	yes	—
110	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
111	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
112	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
113	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
114	#121×C₆₇	C₂×C₄	1	4	yes	—
115	#121×C₆₇	C₂×C₄	1	4	yes	—
116	#121×C₆₇	C₂×C₄	1	4	yes	—
117	#121×C₆₇	C₂×C₄	1	4	yes	—
118	#120×C₆₇	C₂×C₄	1	4	yes	—
119	#120×C₆₇	C₂×C₄	1	8	yes	—
120	#120×C₆₇	C₂×C₄	1	4	yes	—
121	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
122	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
123	C₄×D₄×C₆₇	C₂³	1	8	yes	—
124	C₄×D₄×C₆₇	C₂³	1	8	yes	—
125	#117×C₆₇	C₂×C₄	1	2	yes	—
126	#117×C₆₇	C₂×C₄	1	2	yes	—
127	#117×C₆₇	C₂³	1	2	yes	—
128	#117×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
135	C₄⋊C₈×C₆₇	C₂³	1	16	yes	complemented
136	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
137	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
138	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
139	#97×C₆₇	C₂³	1	8	yes	complemented
140	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
141	C₂⁴×C₆₇	—	2	4	no	—
142	C₂⁴×C₆₇	—	4	4	no	—
143	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
145	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
147	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	#41×C₆₇	—	2	8	no	—
150	#41×C₆₇	—	2	8	no	—
151	#41×C₆₇	—	2	4	no	—
152	#41×C₆₇	—	2	4	no	—
153	#41×C₆₇	—	2	4	no	—
154	#41×C₆₇	—	2	4	no	—
155	C₂×Q₈×C₆₇	—	2	4	no	—
156	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
157	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
158	C₂×D₄×C₆₇	—	2	8	no	—
159	C₂×D₄×C₆₇	—	2	4	no	—
160	C₂×D₄×C₆₇	—	4	8	no	—
161	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
162	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
163	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
164	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
166	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
167	C₂²×C₄×C₆₇	—	2	4	no	—
168	C₂²×C₄×C₆₇	—	2	8	no	—
169	C₂²×C₄×C₆₇	—	2	4	no	—
170	C₂²×C₄×C₆₇	—	2	4	no	—
171	C₂²×C₄×C₆₇	—	2	8	no	—
172	C₂²×C₄×C₆₇	—	2	2	no	—
173	C₂²×C₄×C₆₇	—	2	4	no	—
174	C₂²×C₄×C₆₇	—	2	4	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	4	no	—
177	C₂²×C₄×C₆₇	—	2	4	no	—
178	C₂²×C₄×C₆₇	—	2	4	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
184	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
188	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₆₇	#41	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	M₁₆×C₆₇	—	2	4	no	—
207	M₁₆×C₆₇	—	2	4	no	—
208	M₁₆×C₆₇	—	2	4	no	—
209	M₁₆×C₆₇	—	2	4	no	—
210	M₁₆×C₆₇	—	2	4	no	—
211	M₁₆×C₆₇	—	2	4	no	—
212	M₁₆×C₆₇	—	2	16	no	—
213	M₁₆×C₆₇	—	2	16	no	—
214	M₁₆×C₆₇	C₂×D₄	1	8	yes	—
215	M₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
216	C₂×C₈×C₆₇	—	2	4	no	—
217	C₂×C₈×C₆₇	—	2	4	no	—
218	C₂×C₈×C₆₇	—	2	4	no	—
219	C₂×C₈×C₆₇	—	2	16	no	—
220	C₂×C₈×C₆₇	—	2	16	no	—
221	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	complemented
222	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
223	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
224	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
225	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
229	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
236	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
237	C₄²×C₆₇	C₂⁴	1	4	yes	—
238	C₂³×C₆₇	—	2	2	no	—
239	C₂³×C₆₇	—	2	4	no	—
240	C₂³×C₆₇	—	2	4	no	—
241	C₂³×C₆₇	—	2	4	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	4	no	—
244	C₂³×C₆₇	—	2	4	no	—
245	C₂³×C₆₇	—	2	4	no	—
246	C₂³×C₆₇	—	4	2	no	—
247	C₂³×C₆₇	—	4	2	no	—
248	C₂³×C₆₇	—	4	2	no	—
249	C₂³×C₆₇	—	4	2	no	—
250	C₂³×C₆₇	—	4	4	no	—
251	C₂³×C₆₇	—	4	16	no	—
252	C₂³×C₆₇	C₄×D₄	1	4	yes	—
253	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
254	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
255	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
256	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
257	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
258	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
259	Q₈×C₆₇	—	2	4	no	—
260	Q₈×C₆₇	—	2	4	no	—
261	D₄×C₆₇	—	2	8	no	—
262	D₄×C₆₇	—	2	8	no	—
263	D₄×C₆₇	—	2	16	no	—
264	D₄×C₆₇	—	2	4	no	—
265	D₄×C₆₇	—	2	4	no	—
266	D₄×C₆₇	—	4	8	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	4	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	4	no	—
272	C₂×C₄×C₆₇	—	2	4	no	—
273	C₂×C₄×C₆₇	—	2	4	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	4	no	—
277	C₂×C₄×C₆₇	—	2	4	no	—
278	C₂×C₄×C₆₇	—	2	8	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	4	4	no	—
286	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
287	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
288	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
300	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
301	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
302	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
303	C₈×C₆₇	—	2	4	no	—
304	C₈×C₆₇	—	2	4	no	—
305	C₈×C₆₇	—	2	4	no	—
306	C₈×C₆₇	C₂²×D₄	1	8	yes	—
307	C₂²×C₆₇	—	2	8	no	—
308	C₂²×C₆₇	—	2	2	no	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	2	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	4	no	—
315	C₂²×C₆₇	—	2	8	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	2	no	—
318	C₂²×C₆₇	—	4	4	no	—
319	C₂²×C₆₇	—	4	8	no	—
320	C₂²×C₆₇	—	4	8	no	—
321	C₂²×C₆₇	—	4	4	no	—
322	C₂²×C₆₇	—	8	4	no	—
323	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
324	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
325	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
326	C₂²×C₆₇	#568	1	4	yes	complemented
327	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	4	no	—
331	C₄×C₆₇	—	2	8	no	—
332	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
333	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
334	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
335	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
337	#60141	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂×C₆₇	—	2	2	no	—
339	C₂×C₆₇	—	2	4	no	—
340	C₂×C₆₇	—	2	2	no	—
341	C₂×C₆₇	—	2	2	no	—
342	C₂×C₆₇	—	4	2	no	—
343	C₂×C₆₇	—	4	4	no	—
344	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
345	C₂×C₆₇	C₂×#568	1	2	yes	—
346	C₂×#568	C₂×C₆₇	1	1	yes	characteristic, complemented
347	C₂³×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
348	C₂×#525	C₂×C₆₇	1	1	yes	characteristic
349	D₄×M₁₆	C₂×C₆₇	1	8	yes	complemented
350	#2933	C₂×C₆₇	1	8	yes	complemented
351	#2930	C₂×C₆₇	1	4	yes	complemented
352	#2929	C₂×C₆₇	1	4	yes	complemented
353	#2905	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2879	C₂×C₆₇	1	1	yes	characteristic, complemented
355	C₂×#407	C₂×C₆₇	1	1	yes	characteristic, complemented
356	#2873	C₂×C₆₇	1	1	yes	characteristic, complemented
357	C₆₇	#60141	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
359	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
360	#568	—	2	8	no	—
361	C₂×#131	C₂²×C₆₇	1	4	yes	complemented
362	C₂×#131	C₂²×C₆₇	1	4	yes	complemented
363	C₂²×M₁₆	—	2	8	no	—
364	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
365	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
366	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
367	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	—
368	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
369	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
370	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	complemented
371	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	complemented
372	C₂³×C₈	C₂²×C₆₇	1	2	yes	complemented
373	#525	C₄×C₆₇	1	2	yes	—
374	#525	C₄×C₆₇	1	4	yes	—
375	#525	C₄×C₆₇	1	2	yes	—
376	#525	C₂²×C₆₇	1	2	yes	—
377	#525	C₂²×C₆₇	1	2	yes	—
378	#525	C₂²×C₆₇	1	4	yes	—
379	C₂×#123	C₄×C₆₇	1	2	yes	—
380	C₂×C₂²⋊Q₈	C₄×C₆₇	1	2	yes	—
381	C₂×#121	C₄×C₆₇	1	2	yes	—
382	C₂×#120	C₄×C₆₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
384	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
385	#436	C₂²×C₆₇	1	16	yes	complemented
386	#435	C₂²×C₆₇	1	16	yes	complemented
387	#435	C₂²×C₆₇	1	16	yes	complemented
388	C₈×D₄	C₂²×C₆₇	1	16	yes	complemented
389	#424	C₂²×C₆₇	1	4	yes	complemented
390	#424	C₂²×C₆₇	1	4	yes	complemented
391	#423	C₂²×C₆₇	1	4	yes	complemented
392	#408	C₂²×C₆₇	1	4	yes	complemented
393	#408	C₂²×C₆₇	1	4	yes	complemented
394	#407	C₂²×C₆₇	1	4	yes	—
395	#407	C₂²×C₆₇	1	2	yes	complemented
396	#407	C₂²×C₆₇	1	2	yes	complemented
397	#407	C₂²×C₆₇	1	4	yes	complemented
398	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
399	#405	C₂²×C₆₇	1	4	yes	complemented
400	#405	C₂²×C₆₇	1	4	yes	complemented
401	C₄×M₁₆	C₂²×C₆₇	1	4	yes	complemented
402	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
403	C₂×#41	—	2	4	no	—
404	C₂×#41	—	2	4	no	—
405	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
406	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
407	C₂×#41	C₂³×C₆₇	1	2	yes	—
408	C₂×#41	C₂³×C₆₇	1	2	yes	—
409	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
410	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
411	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
412	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
413	C₂³×C₄	—	2	4	no	—
414	C₂³×C₄	—	2	4	no	—
415	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
416	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
417	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
418	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
419	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
421	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
422	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
424	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
426	#131	—	2	16	no	—
427	#131	—	2	16	no	—
428	C₂×M₁₆	—	2	4	no	—
429	C₂×M₁₆	—	2	4	no	—
430	C₂×M₁₆	—	2	4	no	—
431	C₂×M₁₆	—	2	16	no	—
432	C₂×M₁₆	—	2	16	no	—
433	C₂×M₁₆	—	2	16	no	—
434	C₂×M₁₆	—	2	8	no	—
435	C₂×M₁₆	D₄×C₆₇	1	8	yes	complemented
436	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
437	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
438	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
439	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
440	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
441	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
442	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
443	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
444	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
445	C₂×M₁₆	C₂³×C₆₇	1	8	yes	complemented
446	C₂²×C₈	—	2	8	no	—
447	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
448	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
449	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
450	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
451	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
452	C₂²×C₈	C₂³×C₆₇	1	8	yes	complemented
453	#123	C₂×C₄×C₆₇	1	4	yes	—
454	#123	C₂×C₄×C₆₇	1	4	yes	—
455	#123	C₂×C₄×C₆₇	1	8	yes	—
456	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
457	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
458	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
459	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
460	#121	C₂×C₄×C₆₇	1	4	yes	—
461	#121	C₂×C₄×C₆₇	1	4	yes	—
462	#121	C₂×C₄×C₆₇	1	4	yes	—
463	#121	C₂×C₄×C₆₇	1	4	yes	—
464	#120	C₂×C₄×C₆₇	1	4	yes	—
465	#120	C₂×C₄×C₆₇	1	8	yes	—
466	#120	C₂×C₄×C₆₇	1	4	yes	—
467	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
468	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
469	C₄×D₄	C₂³×C₆₇	1	8	yes	—
470	C₄×D₄	C₂³×C₆₇	1	8	yes	—
471	#117	C₂×C₄×C₆₇	1	2	yes	—
472	#117	C₂×C₄×C₆₇	1	2	yes	—
473	#117	C₂³×C₆₇	1	2	yes	—
474	#117	C₂³×C₆₇	1	2	yes	—
475	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
480	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
481	C₄⋊C₈	C₂³×C₆₇	1	16	yes	complemented
482	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
483	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
484	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
485	#97	C₂³×C₆₇	1	8	yes	complemented
486	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
487	C₂⁴	—	2	4	no	—
488	C₂⁴	—	4	4	no	—
489	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
490	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
491	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
492	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
493	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
494	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
495	#41	—	2	8	no	—
496	#41	—	2	8	no	—
497	#41	—	2	4	no	—
498	#41	—	2	4	no	—
499	#41	—	2	4	no	—
500	#41	—	2	4	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
503	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
504	C₂×D₄	—	2	8	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	4	8	no	—
507	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
508	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
509	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
510	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
511	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
512	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
529	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
530	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
531	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
532	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
534	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
535	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
536	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
537	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
539	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
541	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
545	C₂²×C₄	#41×C₆₇	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
552	M₁₆	—	2	4	no	—
553	M₁₆	—	2	4	no	—
554	M₁₆	—	2	4	no	—
555	M₁₆	—	2	4	no	—
556	M₁₆	—	2	4	no	—
557	M₁₆	—	2	4	no	—
558	M₁₆	—	2	16	no	—
559	M₁₆	—	2	16	no	—
560	M₁₆	C₂×D₄×C₆₇	1	8	yes	—
561	M₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	—	2	4	no	—
564	C₂×C₈	—	2	4	no	—
565	C₂×C₈	—	2	16	no	—
566	C₂×C₈	—	2	16	no	—
567	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	complemented
568	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
569	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
570	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
571	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
575	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
582	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
583	C₄²	C₂⁴×C₆₇	1	4	yes	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	4	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	16	no	—
598	C₂³	C₄×D₄×C₆₇	1	4	yes	—
599	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
600	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
601	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
602	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
603	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
604	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
605	Q₈	—	2	4	no	—
606	Q₈	—	2	4	no	—
607	D₄	—	2	8	no	—
608	D₄	—	2	8	no	—
609	D₄	—	2	16	no	—
610	D₄	—	2	4	no	—
611	D₄	—	2	4	no	—
612	D₄	—	4	8	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
633	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
634	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
636	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
637	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
639	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
640	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
641	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
642	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
644	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
645	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
646	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
647	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
648	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
649	C₈	—	2	4	no	—
650	C₈	—	2	4	no	—
651	C₈	—	2	4	no	—
652	C₈	C₂²×D₄×C₆₇	1	8	yes	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	8	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	8	no	—
666	C₂²	—	4	8	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	8	4	no	—
669	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
670	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
671	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
672	C₂²	#568×C₆₇	1	4	yes	complemented
673	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
674	C₄	—	2	8	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
679	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
680	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
681	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
682	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
683	C₂	—	2	2	no	—
684	C₂	—	2	4	no	—
685	C₂	—	2	2	no	—
686	C₂	—	2	2	no	—
687	C₂	—	4	2	no	—
688	C₂	—	4	4	no	—
689	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
690	C₂	C₂×#568×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₂×#525×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#568×C₆₇	C₂	semidirect
2. C₂³×M₁₆×C₆₇	C₂	semidirect
4. D₄×M₁₆×C₆₇	C₂	semidirect
5. C₆₇×#2933	C₂	semidirect
6. C₆₇×#2930	C₂	semidirect
7. C₆₇×#2929	C₂	semidirect
8. C₆₇×#2905	C₂	semidirect
9. C₆₇×#2879	C₂	semidirect
10. C₂×#407×C₆₇	C₂	semidirect
11. C₆₇×#2873	C₂	semidirect
15. C₂×#131×C₆₇	C₂²	semidirect
16. C₂×#131×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
24. C₂²×M₁₆×C₆₇	C₂²	semidirect
25. C₂²×M₁₆×C₆₇	C₂²	semidirect
26. C₂³×C₈×C₆₇	C₂²	semidirect
39. #436×C₆₇	C₂²	semidirect
40. #435×C₆₇	C₂²	semidirect
41. #435×C₆₇	C₂²	semidirect
42. C₈×D₄×C₆₇	C₂²	semidirect
43. #424×C₆₇	C₂²	semidirect
44. #424×C₆₇	C₂²	semidirect
45. #423×C₆₇	C₂²	semidirect
46. #408×C₆₇	C₂²	semidirect
47. #408×C₆₇	C₂²	semidirect
49. #407×C₆₇	C₂²	semidirect
50. #407×C₆₇	C₂²	semidirect
51. #407×C₆₇	C₂²	semidirect
52. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
53. #405×C₆₇	C₂²	semidirect
54. #405×C₆₇	C₂²	semidirect
55. C₄×M₁₆×C₆₇	C₂²	semidirect
89. C₂×M₁₆×C₆₇	D₄	semidirect
99. C₂×M₁₆×C₆₇	C₂³	semidirect
106. C₂²×C₈×C₆₇	C₂³	semidirect
135. C₄⋊C₈×C₆₇	C₂³	semidirect
138. C₂²⋊C₈×C₆₇	C₂³	semidirect
139. #97×C₆₇	C₂³	semidirect
140. C₄×C₈×C₆₇	C₂³	semidirect
215. M₁₆×C₆₇	C₂×D₄	semidirect
221. C₂×C₈×C₆₇	C₂×D₄	semidirect
326. C₂²×C₆₇	#568	semidirect
337. #60141	C₆₇	direct (N × H)
346. C₂×#568	C₂×C₆₇	semidirect
347. C₂³×M₁₆	C₂×C₆₇	semidirect
349. D₄×M₁₆	C₂×C₆₇	semidirect
350. #2933	C₂×C₆₇	semidirect
351. #2930	C₂×C₆₇	semidirect
352. #2929	C₂×C₆₇	semidirect
353. #2905	C₂×C₆₇	semidirect
354. #2879	C₂×C₆₇	semidirect
355. C₂×#407	C₂×C₆₇	semidirect
356. #2873	C₂×C₆₇	semidirect
357. C₆₇	#60141	direct (N × H)
361. C₂×#131	C₂²×C₆₇	semidirect
362. C₂×#131	C₂²×C₆₇	semidirect
369. C₂²×M₁₆	C₂²×C₆₇	semidirect
370. C₂²×M₁₆	C₂²×C₆₇	semidirect
371. C₂²×M₁₆	C₂²×C₆₇	semidirect
372. C₂³×C₈	C₂²×C₆₇	semidirect
385. #436	C₂²×C₆₇	semidirect
386. #435	C₂²×C₆₇	semidirect
387. #435	C₂²×C₆₇	semidirect
388. C₈×D₄	C₂²×C₆₇	semidirect
389. #424	C₂²×C₆₇	semidirect
390. #424	C₂²×C₆₇	semidirect
391. #423	C₂²×C₆₇	semidirect
392. #408	C₂²×C₆₇	semidirect
393. #408	C₂²×C₆₇	semidirect
395. #407	C₂²×C₆₇	semidirect
396. #407	C₂²×C₆₇	semidirect
397. #407	C₂²×C₆₇	semidirect
398. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
399. #405	C₂²×C₆₇	semidirect
400. #405	C₂²×C₆₇	semidirect
401. C₄×M₁₆	C₂²×C₆₇	semidirect
435. C₂×M₁₆	D₄×C₆₇	semidirect
445. C₂×M₁₆	C₂³×C₆₇	semidirect
452. C₂²×C₈	C₂³×C₆₇	semidirect
481. C₄⋊C₈	C₂³×C₆₇	semidirect
484. C₂²⋊C₈	C₂³×C₆₇	semidirect
485. #97	C₂³×C₆₇	semidirect
486. C₄×C₈	C₂³×C₆₇	semidirect
561. M₁₆	C₂×D₄×C₆₇	semidirect
567. C₂×C₈	C₂×D₄×C₆₇	semidirect
672. C₂²	#568×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#568×C₆₇	2
C₂³×M₁₆×C₆₇	2
C₂×#525×C₆₇	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2930	2
C₆₇×#2929	2
C₆₇×#2905	2
C₆₇×#2879	2
C₂×#407×C₆₇	2
C₆₇×#2873	2
#60141	67

Subgroups — C67×#60141 #30739392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60141 #30739392