Subgroups — C₆₇×#60291 #30739542

Order 17152.

1772 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2992	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2983	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2974	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2973	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2967	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2924	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#432×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#529×C₆₇	C₄	1	2	yes	—
13	#529×C₆₇	C₄	1	2	yes	—
14	#529×C₆₇	C₄	1	2	yes	—
15	#529×C₆₇	C₄	1	2	yes	—
16	#529×C₆₇	C₂²	1	2	yes	—
17	#529×C₆₇	C₂²	1	2	yes	—
18	#529×C₆₇	C₂²	1	2	yes	—
19	#529×C₆₇	C₂²	1	2	yes	—
20	C₂×#126×C₆₇	C₄	1	2	yes	—
21	C₂×#125×C₆₇	C₄	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₄	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₄	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
31	#446×C₆₇	C₂²	1	8	yes	complemented
32	#446×C₆₇	C₂²	1	8	yes	complemented
33	#436×C₆₇	C₂²	1	8	yes	complemented
34	#435×C₆₇	C₂²	1	8	yes	complemented
35	#435×C₆₇	C₂²	1	8	yes	complemented
36	#435×C₆₇	C₂²	1	8	yes	complemented
37	#435×C₆₇	C₂²	1	8	yes	complemented
38	C₈×D₄×C₆₇	C₂²	1	8	yes	complemented
39	#433×C₆₇	C₂²	1	8	yes	complemented
40	#433×C₆₇	C₂²	1	8	yes	complemented
41	#432×C₆₇	C₂²	1	2	yes	—
42	#432×C₆₇	C₂²	1	2	yes	—
43	#432×C₆₇	C₂²	1	2	yes	—
44	#432×C₆₇	C₂²	1	4	yes	—
45	#432×C₆₇	C₂²	1	2	yes	complemented
46	#432×C₆₇	C₂²	1	2	yes	complemented
47	#432×C₆₇	C₂²	1	2	yes	complemented
48	#431×C₆₇	C₂²	1	2	yes	—
49	#431×C₆₇	C₂²	1	4	yes	—
50	#431×C₆₇	C₂²	1	2	yes	complemented
51	#424×C₆₇	C₂²	1	8	yes	complemented
52	#423×C₆₇	C₂²	1	2	yes	complemented
53	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
54	#407×C₆₇	C₂²	1	2	yes	—
55	#407×C₆₇	C₂²	1	4	yes	—
56	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
57	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
58	#405×C₆₇	C₂²	1	8	yes	complemented
59	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
60	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
61	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
68	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
69	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
70	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
71	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
72	#126×C₆₇	C₂×C₄	1	4	yes	—
73	#126×C₆₇	C₂×C₄	1	4	yes	—
74	#126×C₆₇	C₂×C₄	1	4	yes	—
75	#126×C₆₇	C₂×C₄	1	4	yes	—
76	#125×C₆₇	C₂×C₄	1	2	yes	—
77	#125×C₆₇	C₂×C₄	1	2	yes	—
78	#125×C₆₇	C₂×C₄	1	2	yes	—
79	#125×C₆₇	C₂×C₄	1	2	yes	—
80	#124×C₆₇	C₂×C₄	1	2	yes	—
81	#124×C₆₇	C₂×C₄	1	2	yes	—
82	#124×C₆₇	C₂×C₄	1	2	yes	—
83	#124×C₆₇	C₂×C₄	1	2	yes	—
84	#123×C₆₇	C₂×C₄	1	4	yes	—
85	#123×C₆₇	C₂×C₄	1	4	yes	—
86	#123×C₆₇	C₂×C₄	1	4	yes	—
87	#123×C₆₇	C₂×C₄	1	4	yes	—
88	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
89	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
90	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
92	#121×C₆₇	C₂×C₄	1	2	yes	—
93	#121×C₆₇	C₂×C₄	1	2	yes	—
94	#121×C₆₇	C₂×C₄	1	2	yes	—
95	#121×C₆₇	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
99	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
100	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
101	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
102	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
103	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
104	C₄×D₄×C₆₇	C₂³	1	4	yes	—
105	C₄×D₄×C₆₇	C₂³	1	2	yes	—
106	C₄×D₄×C₆₇	C₂³	1	2	yes	—
107	C₄×D₄×C₆₇	C₂³	1	4	yes	—
108	#117×C₆₇	C₂×C₄	1	4	yes	—
109	#117×C₆₇	C₂×C₄	1	4	yes	—
110	#117×C₆₇	C₂³	1	4	yes	—
111	#117×C₆₇	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
123	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
136	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
137	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
138	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
139	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
140	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
141	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
142	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
143	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
144	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
145	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
146	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
147	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
148	#97×C₆₇	C₂³	1	4	yes	—
149	#97×C₆₇	C₂³	1	4	yes	—
150	#97×C₆₇	C₂³	1	4	yes	—
151	#97×C₆₇	C₂³	1	8	yes	—
152	C₄×C₈×C₆₇	C₂³	1	4	yes	—
153	C₄×C₈×C₆₇	C₂³	1	8	yes	—
154	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
156	C₂×Q₈×C₆₇	—	4	2	no	—
157	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
158	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
159	C₂×D₄×C₆₇	—	4	2	no	—
160	C₂×D₄×C₆₇	—	4	4	no	—
161	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
163	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₆₇	—	4	2	no	—
166	C₂²×C₄×C₆₇	—	4	4	no	—
167	C₂²×C₄×C₆₇	—	4	2	no	—
168	C₂²×C₄×C₆₇	—	4	2	no	—
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
192	M₁₆×C₆₇	—	4	8	no	—
193	M₁₆×C₆₇	—	4	4	no	—
194	C₂×C₈×C₆₇	—	4	4	no	—
195	C₂×C₈×C₆₇	—	4	8	no	—
196	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
197	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
198	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
199	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
200	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
201	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
202	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
203	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
205	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
206	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
208	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
210	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
211	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
212	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
213	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
214	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
215	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
216	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
217	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
218	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
219	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
220	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
223	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
225	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
226	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
227	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
230	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
233	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₄²×C₆₇	C₂⁴	1	4	yes	—
237	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂³×C₆₇	—	2	2	no	—
239	C₂³×C₆₇	—	2	2	no	—
240	C₂³×C₆₇	—	2	4	no	—
241	C₂³×C₆₇	—	4	1	no	—
242	C₂³×C₆₇	—	4	2	no	—
243	C₂³×C₆₇	—	4	2	no	—
244	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
245	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
246	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
247	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
248	Q₈×C₆₇	—	4	2	no	—
249	Q₈×C₆₇	—	4	2	no	—
250	D₄×C₆₇	—	2	8	no	—
251	D₄×C₆₇	—	4	2	no	—
252	D₄×C₆₇	—	4	2	no	—
253	D₄×C₆₇	—	4	4	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	2	2	no	—
257	C₂×C₄×C₆₇	—	2	2	no	—
258	C₂×C₄×C₆₇	—	2	4	no	—
259	C₂×C₄×C₆₇	—	2	2	no	—
260	C₂×C₄×C₆₇	—	2	8	no	—
261	C₂×C₄×C₆₇	—	2	2	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	4	1	no	—
264	C₂×C₄×C₆₇	—	4	1	no	—
265	C₂×C₄×C₆₇	—	4	4	no	—
266	C₂×C₄×C₆₇	—	4	1	no	—
267	C₂×C₄×C₆₇	—	4	2	no	—
268	C₂×C₄×C₆₇	—	4	1	no	—
269	C₂×C₄×C₆₇	—	4	1	no	—
270	C₂×C₄×C₆₇	—	4	1	no	—
271	C₂×C₄×C₆₇	—	4	1	no	—
272	C₂×C₄×C₆₇	—	4	1	no	—
273	C₂×C₄×C₆₇	—	4	1	no	—
274	C₂×C₄×C₆₇	—	4	1	no	—
275	C₂×C₄×C₆₇	—	4	1	no	—
276	C₂×C₄×C₆₇	—	4	2	no	—
277	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
283	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
292	C₈×C₆₇	—	2	8	no	—
293	C₈×C₆₇	—	2	8	no	—
294	C₂²×C₆₇	—	2	1	no	—
295	C₂²×C₆₇	—	2	1	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	1	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	—	2	4	no	—
300	C₂²×C₆₇	—	2	1	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	—	2	4	no	—
303	C₂²×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	4	4	no	—
305	C₂²×C₆₇	—	8	4	no	—
306	C₂²×C₆₇	#568	1	2	yes	—
307	C₂²×C₆₇	#568	1	2	yes	—
308	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
309	C₄×C₆₇	—	2	1	no	—
310	C₄×C₆₇	—	2	1	no	—
311	C₄×C₆₇	—	2	4	no	—
312	C₄×C₆₇	—	2	1	no	—
313	C₄×C₆₇	—	2	1	no	—
314	C₄×C₆₇	—	2	1	no	—
315	C₄×C₆₇	—	2	1	no	—
316	C₄×C₆₇	—	2	1	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	1	no	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	—	2	4	no	—
323	C₄×C₆₇	#585	1	2	yes	—
324	#60291	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂×C₆₇	—	2	2	no	—
326	C₂×C₆₇	—	2	2	no	—
327	C₂×C₆₇	—	4	1	no	—
328	C₂×C₆₇	—	4	4	no	—
329	C₂×C₆₇	#3428	1	1	yes	characteristic
330	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
331	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
332	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
333	#2995	C₂×C₆₇	1	4	yes	complemented
334	#2992	C₂×C₆₇	1	4	yes	complemented
335	#2983	C₂×C₆₇	1	2	yes	complemented
336	#2974	C₂×C₆₇	1	4	yes	complemented
337	#2973	C₂×C₆₇	1	2	yes	complemented
338	#2968	C₂×C₆₇	1	4	yes	complemented
339	#2967	C₂×C₆₇	1	4	yes	complemented
340	#2924	C₂×C₆₇	1	4	yes	complemented
341	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
342	C₂×#432	C₂×C₆₇	1	1	yes	characteristic, complemented
343	C₆₇	#60291	1	1	yes	characteristic, direct product factor, Sylow
344	#529	C₄×C₆₇	1	2	yes	—
345	#529	C₄×C₆₇	1	2	yes	—
346	#529	C₄×C₆₇	1	2	yes	—
347	#529	C₄×C₆₇	1	2	yes	—
348	#529	C₂²×C₆₇	1	2	yes	—
349	#529	C₂²×C₆₇	1	2	yes	—
350	#529	C₂²×C₆₇	1	2	yes	—
351	#529	C₂²×C₆₇	1	2	yes	—
352	C₂×#126	C₄×C₆₇	1	2	yes	—
353	C₂×#125	C₄×C₆₇	1	1	yes	characteristic
354	C₂×#124	C₄×C₆₇	1	1	yes	characteristic
355	C₂×#123	C₄×C₆₇	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
357	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
361	C₂×#117	C₂²×C₆₇	1	2	yes	—
362	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
363	#446	C₂²×C₆₇	1	8	yes	complemented
364	#446	C₂²×C₆₇	1	8	yes	complemented
365	#436	C₂²×C₆₇	1	8	yes	complemented
366	#435	C₂²×C₆₇	1	8	yes	complemented
367	#435	C₂²×C₆₇	1	8	yes	complemented
368	#435	C₂²×C₆₇	1	8	yes	complemented
369	#435	C₂²×C₆₇	1	8	yes	complemented
370	C₈×D₄	C₂²×C₆₇	1	8	yes	complemented
371	#433	C₂²×C₆₇	1	8	yes	complemented
372	#433	C₂²×C₆₇	1	8	yes	complemented
373	#432	C₂²×C₆₇	1	2	yes	—
374	#432	C₂²×C₆₇	1	2	yes	—
375	#432	C₂²×C₆₇	1	2	yes	—
376	#432	C₂²×C₆₇	1	4	yes	—
377	#432	C₂²×C₆₇	1	2	yes	complemented
378	#432	C₂²×C₆₇	1	2	yes	complemented
379	#432	C₂²×C₆₇	1	2	yes	complemented
380	#431	C₂²×C₆₇	1	2	yes	—
381	#431	C₂²×C₆₇	1	4	yes	—
382	#431	C₂²×C₆₇	1	2	yes	complemented
383	#424	C₂²×C₆₇	1	8	yes	complemented
384	#423	C₂²×C₆₇	1	2	yes	complemented
385	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
386	#407	C₂²×C₆₇	1	2	yes	—
387	#407	C₂²×C₆₇	1	4	yes	—
388	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
389	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
390	#405	C₂²×C₆₇	1	8	yes	complemented
391	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
392	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
393	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
394	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
395	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
396	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
397	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
401	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
402	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
403	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
404	#126	C₂×C₄×C₆₇	1	4	yes	—
405	#126	C₂×C₄×C₆₇	1	4	yes	—
406	#126	C₂×C₄×C₆₇	1	4	yes	—
407	#126	C₂×C₄×C₆₇	1	4	yes	—
408	#125	C₂×C₄×C₆₇	1	2	yes	—
409	#125	C₂×C₄×C₆₇	1	2	yes	—
410	#125	C₂×C₄×C₆₇	1	2	yes	—
411	#125	C₂×C₄×C₆₇	1	2	yes	—
412	#124	C₂×C₄×C₆₇	1	2	yes	—
413	#124	C₂×C₄×C₆₇	1	2	yes	—
414	#124	C₂×C₄×C₆₇	1	2	yes	—
415	#124	C₂×C₄×C₆₇	1	2	yes	—
416	#123	C₂×C₄×C₆₇	1	4	yes	—
417	#123	C₂×C₄×C₆₇	1	4	yes	—
418	#123	C₂×C₄×C₆₇	1	4	yes	—
419	#123	C₂×C₄×C₆₇	1	4	yes	—
420	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
421	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
422	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
423	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
424	#121	C₂×C₄×C₆₇	1	2	yes	—
425	#121	C₂×C₄×C₆₇	1	2	yes	—
426	#121	C₂×C₄×C₆₇	1	2	yes	—
427	#121	C₂×C₄×C₆₇	1	2	yes	—
428	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
429	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
430	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
431	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
432	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
433	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
434	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
435	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
436	C₄×D₄	C₂³×C₆₇	1	4	yes	—
437	C₄×D₄	C₂³×C₆₇	1	2	yes	—
438	C₄×D₄	C₂³×C₆₇	1	2	yes	—
439	C₄×D₄	C₂³×C₆₇	1	4	yes	—
440	#117	C₂×C₄×C₆₇	1	4	yes	—
441	#117	C₂×C₄×C₆₇	1	4	yes	—
442	#117	C₂³×C₆₇	1	4	yes	—
443	#117	C₂³×C₆₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
445	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
446	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
448	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
455	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
456	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
457	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
458	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
459	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
460	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
463	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
468	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
469	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
470	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
471	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
472	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
473	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
474	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
475	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
476	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
477	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
478	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
479	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
480	#97	C₂³×C₆₇	1	4	yes	—
481	#97	C₂³×C₆₇	1	4	yes	—
482	#97	C₂³×C₆₇	1	4	yes	—
483	#97	C₂³×C₆₇	1	8	yes	—
484	C₄×C₈	C₂³×C₆₇	1	4	yes	—
485	C₄×C₈	C₂³×C₆₇	1	8	yes	—
486	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
487	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
488	C₂×Q₈	—	4	2	no	—
489	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
490	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	4	no	—
493	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
494	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
495	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
496	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
506	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
507	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
515	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
518	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
519	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
524	M₁₆	—	4	8	no	—
525	M₁₆	—	4	4	no	—
526	C₂×C₈	—	4	4	no	—
527	C₂×C₈	—	4	8	no	—
528	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
529	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
530	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
531	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
532	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
533	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
534	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
535	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
536	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
537	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
538	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
539	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
540	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
541	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
542	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
543	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
544	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
545	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
546	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
547	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
548	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
549	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
551	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
552	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
553	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
554	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
555	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
556	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
557	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
558	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
559	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
560	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
561	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
562	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
563	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
564	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
565	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
566	C₄²	C₂⁴×C₆₇	1	4	yes	—
567	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
568	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
569	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
577	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
578	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
579	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
580	Q₈	—	4	2	no	—
581	Q₈	—	4	2	no	—
582	D₄	—	2	8	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
610	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
615	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
616	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
617	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
621	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
622	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
623	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
624	C₈	—	2	8	no	—
625	C₈	—	2	8	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	8	4	no	—
638	C₂²	#568×C₆₇	1	2	yes	—
639	C₂²	#568×C₆₇	1	2	yes	—
640	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	4	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	1	no	—
655	C₄	#585×C₆₇	1	2	yes	—
656	C₂	—	2	2	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	4	no	—
660	C₂	C₆₇×#3428	1	1	yes	characteristic
661	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
662	C₂	C₂×#568×C₆₇	1	1	yes	characteristic

	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×#121×C₆₇	C₄
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
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2992	C₂	semidirect
4. C₆₇×#2983	C₂	semidirect
5. C₆₇×#2974	C₂	semidirect
6. C₆₇×#2973	C₂	semidirect
7. C₆₇×#2968	C₂	semidirect
8. C₆₇×#2967	C₂	semidirect
9. C₆₇×#2924	C₂	semidirect
10. C₆₇×#2920	C₂	semidirect
11. C₂×#432×C₆₇	C₂	semidirect
31. #446×C₆₇	C₂²	semidirect
32. #446×C₆₇	C₂²	semidirect
33. #436×C₆₇	C₂²	semidirect
34. #435×C₆₇	C₂²	semidirect
35. #435×C₆₇	C₂²	semidirect
36. #435×C₆₇	C₂²	semidirect
37. #435×C₆₇	C₂²	semidirect
38. C₈×D₄×C₆₇	C₂²	semidirect
39. #433×C₆₇	C₂²	semidirect
40. #433×C₆₇	C₂²	semidirect
45. #432×C₆₇	C₂²	semidirect
46. #432×C₆₇	C₂²	semidirect
47. #432×C₆₇	C₂²	semidirect
50. #431×C₆₇	C₂²	semidirect
51. #424×C₆₇	C₂²	semidirect
52. #423×C₆₇	C₂²	semidirect
53. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
58. #405×C₆₇	C₂²	semidirect
59. C₄×M₁₆×C₆₇	C₂²	semidirect
60. C₂×#97×C₆₇	C₂²	semidirect
324. #60291	C₆₇	direct (N × H)
333. #2995	C₂×C₆₇	semidirect
334. #2992	C₂×C₆₇	semidirect
335. #2983	C₂×C₆₇	semidirect
336. #2974	C₂×C₆₇	semidirect
337. #2973	C₂×C₆₇	semidirect
338. #2968	C₂×C₆₇	semidirect
339. #2967	C₂×C₆₇	semidirect
340. #2924	C₂×C₆₇	semidirect
341. #2920	C₂×C₆₇	semidirect
342. C₂×#432	C₂×C₆₇	semidirect
343. C₆₇	#60291	direct (N × H)
363. #446	C₂²×C₆₇	semidirect
364. #446	C₂²×C₆₇	semidirect
365. #436	C₂²×C₆₇	semidirect
366. #435	C₂²×C₆₇	semidirect
367. #435	C₂²×C₆₇	semidirect
368. #435	C₂²×C₆₇	semidirect
369. #435	C₂²×C₆₇	semidirect
370. C₈×D₄	C₂²×C₆₇	semidirect
371. #433	C₂²×C₆₇	semidirect
372. #433	C₂²×C₆₇	semidirect
377. #432	C₂²×C₆₇	semidirect
378. #432	C₂²×C₆₇	semidirect
379. #432	C₂²×C₆₇	semidirect
382. #431	C₂²×C₆₇	semidirect
383. #424	C₂²×C₆₇	semidirect
384. #423	C₂²×C₆₇	semidirect
385. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
390. #405	C₂²×C₆₇	semidirect
391. C₄×M₁₆	C₂²×C₆₇	semidirect
392. C₂×#97	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2995	2
C₆₇×#2992	2
C₆₇×#2983	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2924	2
C₆₇×#2920	2
C₂×#432×C₆₇	2
#60291	67

Subgroups — C67×#60291 #30739542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60291 #30739542