Subgroups — C₆₇×#60294 #30739545

Order 17152.

1808 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2990	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2988	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2985	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2981	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2977	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2966	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2925	C₂	1	4	yes	maximal, complemented
11	C₂×#432×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#533×C₆₇	C₄	1	1	yes	characteristic
14	#533×C₆₇	C₄	1	1	yes	characteristic
15	#533×C₆₇	C₂²	1	1	yes	characteristic
16	#532×C₆₇	C₄	1	1	yes	characteristic
17	#532×C₆₇	C₄	1	1	yes	characteristic
18	#532×C₆₇	C₂²	1	1	yes	characteristic
19	#529×C₆₇	C₄	1	2	yes	—
20	#529×C₆₇	C₄	1	2	yes	—
21	#529×C₆₇	C₄	1	2	yes	—
22	#529×C₆₇	C₄	1	2	yes	—
23	#529×C₆₇	C₂²	1	2	yes	—
24	#529×C₆₇	C₂²	1	2	yes	—
25	#525×C₆₇	C₄	1	2	yes	—
26	#525×C₆₇	C₄	1	2	yes	—
27	#525×C₆₇	C₂²	1	2	yes	—
28	C₄×#41×C₆₇	C₂²	1	2	yes	—
29	C₄×#41×C₆₇	C₂²	1	2	yes	—
30	C₄×#41×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
32	#446×C₆₇	C₂²	1	4	yes	complemented
33	#446×C₆₇	C₂²	1	8	yes	complemented
34	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
35	#436×C₆₇	C₂²	1	4	yes	complemented
36	#435×C₆₇	C₂²	1	8	yes	—
37	#435×C₆₇	C₂²	1	8	yes	—
38	#435×C₆₇	C₂²	1	8	yes	complemented
39	C₈×D₄×C₆₇	C₂²	1	8	yes	—
40	C₈×D₄×C₆₇	C₂²	1	8	yes	—
41	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
42	#433×C₆₇	C₂²	1	8	yes	—
43	#433×C₆₇	C₂²	1	8	yes	complemented
44	#432×C₆₇	C₂²	1	2	yes	—
45	#432×C₆₇	C₂²	1	2	yes	—
46	#432×C₆₇	C₂²	1	2	yes	—
47	#432×C₆₇	C₂²	1	2	yes	—
48	#432×C₆₇	C₂²	1	4	yes	complemented
49	#431×C₆₇	C₂²	1	2	yes	—
50	#431×C₆₇	C₂²	1	2	yes	—
51	#431×C₆₇	C₂²	1	2	yes	—
52	#431×C₆₇	C₂²	1	1	yes	characteristic
53	#431×C₆₇	C₂²	1	1	yes	characteristic
54	#431×C₆₇	C₂²	1	4	yes	complemented
55	#423×C₆₇	C₂²	1	4	yes	complemented
56	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
57	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
58	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
59	#408×C₆₇	C₂²	1	8	yes	—
60	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
61	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
62	#405×C₆₇	C₂²	1	8	yes	complemented
63	C₂×#97×C₆₇	C₂²	1	2	yes	—
64	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
65	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
66	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
67	C₂×#41×C₆₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
72	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
73	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
74	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
75	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
78	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
79	#126×C₆₇	C₂×C₄	1	4	yes	—
80	#126×C₆₇	C₂×C₄	1	4	yes	—
81	#125×C₆₇	C₂×C₄	1	2	yes	—
82	#125×C₆₇	C₂×C₄	1	2	yes	—
83	#125×C₆₇	C₂×C₄	1	2	yes	—
84	#124×C₆₇	C₂×C₄	1	2	yes	—
85	#124×C₆₇	C₂×C₄	1	2	yes	—
86	#124×C₆₇	C₂×C₄	1	2	yes	—
87	#123×C₆₇	C₂×C₄	1	4	yes	—
88	#123×C₆₇	C₂×C₄	1	4	yes	—
89	#123×C₆₇	C₂×C₄	1	4	yes	—
90	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
92	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
93	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
94	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
95	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
96	#121×C₆₇	C₂×C₄	1	2	yes	—
97	#121×C₆₇	C₂×C₄	1	2	yes	—
98	#121×C₆₇	C₂×C₄	1	2	yes	—
99	#121×C₆₇	C₂×C₄	1	2	yes	—
100	#121×C₆₇	C₂×C₄	1	2	yes	—
101	#121×C₆₇	C₂×C₄	1	2	yes	—
102	#120×C₆₇	C₂×C₄	1	4	yes	—
103	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
104	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
105	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
106	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
107	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
108	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
110	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
111	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
112	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
113	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
114	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
115	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
116	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
117	C₄×D₄×C₆₇	C₂³	1	4	yes	—
118	C₄×D₄×C₆₇	C₂³	1	4	yes	—
119	C₄×D₄×C₆₇	C₂³	1	2	yes	—
120	C₄×D₄×C₆₇	C₂³	1	2	yes	—
121	#117×C₆₇	C₂×C₄	1	2	yes	—
122	#117×C₆₇	C₂×C₄	1	2	yes	—
123	#117×C₆₇	C₂×C₄	1	4	yes	—
124	#117×C₆₇	C₂×C₄	1	4	yes	—
125	#117×C₆₇	C₂³	1	2	yes	—
126	#117×C₆₇	C₂³	1	4	yes	—
127	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂×C₄	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	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
140	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
141	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
142	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
143	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
144	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
145	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
146	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
147	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
148	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
150	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
152	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
153	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
154	#97×C₆₇	C₂³	1	4	yes	—
155	#97×C₆₇	C₂³	1	4	yes	—
156	#97×C₆₇	C₂³	1	8	yes	—
157	C₄×C₈×C₆₇	C₂³	1	4	yes	—
158	C₄×C₈×C₆₇	C₂³	1	2	yes	—
159	C₄×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄×C₈×C₆₇	C₂³	1	8	yes	—
161	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
162	#41×C₆₇	—	2	8	no	—
163	#41×C₆₇	—	4	4	no	—
164	#41×C₆₇	—	4	4	no	—
165	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
167	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
168	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
169	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
171	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₆₇	—	2	4	no	—
175	C₂²×C₄×C₆₇	—	4	2	no	—
176	C₂²×C₄×C₆₇	—	4	2	no	—
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	4	yes	—
185	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
198	M₁₆×C₆₇	—	4	8	no	—
199	C₂×C₈×C₆₇	—	4	8	no	—
200	C₂×C₈×C₆₇	—	4	4	no	—
201	C₂×C₈×C₆₇	—	4	4	no	—
202	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
203	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
204	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
205	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
206	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
211	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
216	C₄⋊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	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
222	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
223	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
224	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
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	1	yes	characteristic
233	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
235	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
239	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
240	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₄²×C₆₇	C₂⁴	1	4	yes	—
244	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	4	1	no	—
248	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
249	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
250	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
251	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
252	Q₈×C₆₇	—	2	4	no	—
253	Q₈×C₆₇	—	4	2	no	—
254	Q₈×C₆₇	—	4	2	no	—
255	D₄×C₆₇	—	2	8	no	—
256	D₄×C₆₇	—	2	8	no	—
257	D₄×C₆₇	—	2	4	no	—
258	D₄×C₆₇	—	4	2	no	—
259	D₄×C₆₇	—	4	4	no	—
260	D₄×C₆₇	—	4	2	no	—
261	C₂×C₄×C₆₇	—	2	2	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	8	no	—
269	C₂×C₄×C₆₇	—	2	2	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	2	no	—
274	C₂×C₄×C₆₇	—	4	1	no	—
275	C₂×C₄×C₆₇	—	4	1	no	—
276	C₂×C₄×C₆₇	—	4	1	no	—
277	C₂×C₄×C₆₇	—	4	1	no	—
278	C₂×C₄×C₆₇	—	4	1	no	—
279	C₂×C₄×C₆₇	—	4	1	no	—
280	C₂×C₄×C₆₇	—	4	1	no	—
281	C₂×C₄×C₆₇	—	4	4	no	—
282	C₂×C₄×C₆₇	#131	1	4	yes	—
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	1	yes	characteristic
289	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
298	C₈×C₆₇	—	2	4	no	—
299	C₈×C₆₇	—	2	8	no	—
300	C₈×C₆₇	—	2	4	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	—	2	1	no	—
303	C₂²×C₆₇	—	2	1	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	2	1	no	—
306	C₂²×C₆₇	—	2	4	no	—
307	C₂²×C₆₇	—	2	1	no	—
308	C₂²×C₆₇	—	2	4	no	—
309	C₂²×C₆₇	—	2	1	no	—
310	C₂²×C₆₇	—	2	4	no	—
311	C₂²×C₆₇	—	4	4	no	—
312	C₂²×C₆₇	C₂×#131	1	2	yes	—
313	C₂²×C₆₇	#568	1	2	yes	—
314	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
315	C₄×C₆₇	—	2	1	no	—
316	C₄×C₆₇	—	2	1	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	4	no	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	—	2	1	no	—
323	C₄×C₆₇	—	2	1	no	—
324	C₄×C₆₇	—	2	1	no	—
325	C₄×C₆₇	—	2	1	no	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	C₂×#131	1	2	yes	—
328	C₄×C₆₇	C₂×#131	1	2	yes	—
329	C₄×C₆₇	#585	1	2	yes	—
330	#60294	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂×C₆₇	—	2	2	no	—
332	C₂×C₆₇	—	2	2	no	—
333	C₂×C₆₇	—	4	4	no	—
334	C₂×C₆₇	—	4	1	no	—
335	C₂×C₆₇	#3428	1	1	yes	characteristic
336	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
337	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
338	#3444	C₂×C₆₇	1	1	yes	characteristic
339	#2990	C₂×C₆₇	1	4	yes	complemented
340	#2989	C₂×C₆₇	1	2	yes	complemented
341	#2988	C₂×C₆₇	1	2	yes	complemented
342	#2985	C₂×C₆₇	1	2	yes	complemented
343	#2981	C₂×C₆₇	1	2	yes	complemented
344	#2977	C₂×C₆₇	1	4	yes	complemented
345	#2968	C₂×C₆₇	1	4	yes	complemented
346	#2966	C₂×C₆₇	1	4	yes	complemented
347	#2925	C₂×C₆₇	1	4	yes	complemented
348	C₂×#432	C₂×C₆₇	1	1	yes	characteristic, complemented
349	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
350	C₆₇	#60294	1	1	yes	characteristic, direct product factor, Sylow
351	#533	C₄×C₆₇	1	1	yes	characteristic
352	#533	C₄×C₆₇	1	1	yes	characteristic
353	#533	C₂²×C₆₇	1	1	yes	characteristic
354	#532	C₄×C₆₇	1	1	yes	characteristic
355	#532	C₄×C₆₇	1	1	yes	characteristic
356	#532	C₂²×C₆₇	1	1	yes	characteristic
357	#529	C₄×C₆₇	1	2	yes	—
358	#529	C₄×C₆₇	1	2	yes	—
359	#529	C₄×C₆₇	1	2	yes	—
360	#529	C₄×C₆₇	1	2	yes	—
361	#529	C₂²×C₆₇	1	2	yes	—
362	#529	C₂²×C₆₇	1	2	yes	—
363	#525	C₄×C₆₇	1	2	yes	—
364	#525	C₄×C₆₇	1	2	yes	—
365	#525	C₂²×C₆₇	1	2	yes	—
366	C₄×#41	C₂²×C₆₇	1	2	yes	—
367	C₄×#41	C₂²×C₆₇	1	2	yes	—
368	C₄×#41	C₂²×C₆₇	1	2	yes	—
369	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
370	#446	C₂²×C₆₇	1	4	yes	complemented
371	#446	C₂²×C₆₇	1	8	yes	complemented
372	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
373	#436	C₂²×C₆₇	1	4	yes	complemented
374	#435	C₂²×C₆₇	1	8	yes	—
375	#435	C₂²×C₆₇	1	8	yes	—
376	#435	C₂²×C₆₇	1	8	yes	complemented
377	C₈×D₄	C₂²×C₆₇	1	8	yes	—
378	C₈×D₄	C₂²×C₆₇	1	8	yes	—
379	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
380	#433	C₂²×C₆₇	1	8	yes	—
381	#433	C₂²×C₆₇	1	8	yes	complemented
382	#432	C₂²×C₆₇	1	2	yes	—
383	#432	C₂²×C₆₇	1	2	yes	—
384	#432	C₂²×C₆₇	1	2	yes	—
385	#432	C₂²×C₆₇	1	2	yes	—
386	#432	C₂²×C₆₇	1	4	yes	complemented
387	#431	C₂²×C₆₇	1	2	yes	—
388	#431	C₂²×C₆₇	1	2	yes	—
389	#431	C₂²×C₆₇	1	2	yes	—
390	#431	C₂²×C₆₇	1	1	yes	characteristic
391	#431	C₂²×C₆₇	1	1	yes	characteristic
392	#431	C₂²×C₆₇	1	4	yes	complemented
393	#423	C₂²×C₆₇	1	4	yes	complemented
394	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
395	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
396	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
397	#408	C₂²×C₆₇	1	8	yes	—
398	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
399	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
400	#405	C₂²×C₆₇	1	8	yes	complemented
401	C₂×#97	C₂²×C₆₇	1	2	yes	—
402	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
403	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
404	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
405	C₂×#41	C₂³×C₆₇	1	2	yes	—
406	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
407	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
409	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
410	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
411	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
412	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
413	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
414	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
415	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
416	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
417	#126	C₂×C₄×C₆₇	1	4	yes	—
418	#126	C₂×C₄×C₆₇	1	4	yes	—
419	#125	C₂×C₄×C₆₇	1	2	yes	—
420	#125	C₂×C₄×C₆₇	1	2	yes	—
421	#125	C₂×C₄×C₆₇	1	2	yes	—
422	#124	C₂×C₄×C₆₇	1	2	yes	—
423	#124	C₂×C₄×C₆₇	1	2	yes	—
424	#124	C₂×C₄×C₆₇	1	2	yes	—
425	#123	C₂×C₄×C₆₇	1	4	yes	—
426	#123	C₂×C₄×C₆₇	1	4	yes	—
427	#123	C₂×C₄×C₆₇	1	4	yes	—
428	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
429	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
430	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
431	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
432	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
433	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
434	#121	C₂×C₄×C₆₇	1	2	yes	—
435	#121	C₂×C₄×C₆₇	1	2	yes	—
436	#121	C₂×C₄×C₆₇	1	2	yes	—
437	#121	C₂×C₄×C₆₇	1	2	yes	—
438	#121	C₂×C₄×C₆₇	1	2	yes	—
439	#121	C₂×C₄×C₆₇	1	2	yes	—
440	#120	C₂×C₄×C₆₇	1	4	yes	—
441	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
442	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
443	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
444	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
445	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
446	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
447	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
448	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
449	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
450	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
451	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
452	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
453	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
454	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
455	C₄×D₄	C₂³×C₆₇	1	4	yes	—
456	C₄×D₄	C₂³×C₆₇	1	4	yes	—
457	C₄×D₄	C₂³×C₆₇	1	2	yes	—
458	C₄×D₄	C₂³×C₆₇	1	2	yes	—
459	#117	C₂×C₄×C₆₇	1	2	yes	—
460	#117	C₂×C₄×C₆₇	1	2	yes	—
461	#117	C₂×C₄×C₆₇	1	4	yes	—
462	#117	C₂×C₄×C₆₇	1	4	yes	—
463	#117	C₂³×C₆₇	1	2	yes	—
464	#117	C₂³×C₆₇	1	4	yes	—
465	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
466	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
467	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
468	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
469	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
470	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
472	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
478	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
479	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
480	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
481	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
482	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
483	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
484	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
485	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
488	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
489	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
491	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
492	#97	C₂³×C₆₇	1	4	yes	—
493	#97	C₂³×C₆₇	1	4	yes	—
494	#97	C₂³×C₆₇	1	8	yes	—
495	C₄×C₈	C₂³×C₆₇	1	4	yes	—
496	C₄×C₈	C₂³×C₆₇	1	2	yes	—
497	C₄×C₈	C₂³×C₆₇	1	2	yes	—
498	C₄×C₈	C₂³×C₆₇	1	8	yes	—
499	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
500	#41	—	2	8	no	—
501	#41	—	4	4	no	—
502	#41	—	4	4	no	—
503	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
504	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
505	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
506	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
507	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
508	C₂×D₄	C₂²×C₄×C₆₇	1	2	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	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
527	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
531	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
536	M₁₆	—	4	8	no	—
537	C₂×C₈	—	4	8	no	—
538	C₂×C₈	—	4	4	no	—
539	C₂×C₈	—	4	4	no	—
540	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
541	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
542	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
543	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
544	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
546	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
547	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
549	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
552	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
553	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
556	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
557	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
558	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
564	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
565	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
566	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
567	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
568	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
569	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
570	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
571	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
572	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
573	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
576	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
577	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
578	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
580	C₄²	C₂⁴×C₆₇	1	4	yes	—
581	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	4	1	no	—
586	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
587	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
588	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
589	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
590	Q₈	—	2	4	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	2	no	—
593	D₄	—	2	8	no	—
594	D₄	—	2	8	no	—
595	D₄	—	2	4	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	#131×C₆₇	1	4	yes	—
621	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
633	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
635	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
636	C₈	—	2	4	no	—
637	C₈	—	2	8	no	—
638	C₈	—	2	4	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	4	no	—
650	C₂²	C₂×#131×C₆₇	1	2	yes	—
651	C₂²	#568×C₆₇	1	2	yes	—
652	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	4	no	—
665	C₄	C₂×#131×C₆₇	1	2	yes	—
666	C₄	C₂×#131×C₆₇	1	2	yes	—
667	C₄	#585×C₆₇	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	2	no	—
670	C₂	—	4	1	no	—
671	C₂	—	4	4	no	—
672	C₂	C₆₇×#3428	1	1	yes	characteristic
673	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
674	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	C₆₇×#3444	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
2. C₆₇×#2990	C₂	semidirect
3. C₆₇×#2989	C₂	semidirect
4. C₆₇×#2988	C₂	semidirect
5. C₆₇×#2985	C₂	semidirect
6. C₆₇×#2981	C₂	semidirect
7. C₆₇×#2977	C₂	semidirect
8. C₆₇×#2968	C₂	semidirect
9. C₆₇×#2966	C₂	semidirect
10. C₆₇×#2925	C₂	semidirect
11. C₂×#432×C₆₇	C₂	semidirect
12. C₂×#431×C₆₇	C₂	semidirect
32. #446×C₆₇	C₂²	semidirect
33. #446×C₆₇	C₂²	semidirect
34. C₈×Q₈×C₆₇	C₂²	semidirect
35. #436×C₆₇	C₂²	semidirect
38. #435×C₆₇	C₂²	semidirect
41. C₈×D₄×C₆₇	C₂²	semidirect
43. #433×C₆₇	C₂²	semidirect
48. #432×C₆₇	C₂²	semidirect
54. #431×C₆₇	C₂²	semidirect
55. #423×C₆₇	C₂²	semidirect
58. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
62. #405×C₆₇	C₂²	semidirect
330. #60294	C₆₇	direct (N × H)
339. #2990	C₂×C₆₇	semidirect
340. #2989	C₂×C₆₇	semidirect
341. #2988	C₂×C₆₇	semidirect
342. #2985	C₂×C₆₇	semidirect
343. #2981	C₂×C₆₇	semidirect
344. #2977	C₂×C₆₇	semidirect
345. #2968	C₂×C₆₇	semidirect
346. #2966	C₂×C₆₇	semidirect
347. #2925	C₂×C₆₇	semidirect
348. C₂×#432	C₂×C₆₇	semidirect
349. C₂×#431	C₂×C₆₇	semidirect
350. C₆₇	#60294	direct (N × H)
370. #446	C₂²×C₆₇	semidirect
371. #446	C₂²×C₆₇	semidirect
372. C₈×Q₈	C₂²×C₆₇	semidirect
373. #436	C₂²×C₆₇	semidirect
376. #435	C₂²×C₆₇	semidirect
379. C₈×D₄	C₂²×C₆₇	semidirect
381. #433	C₂²×C₆₇	semidirect
386. #432	C₂²×C₆₇	semidirect
392. #431	C₂²×C₆₇	semidirect
393. #423	C₂²×C₆₇	semidirect
396. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
400. #405	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3444	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2988	2
C₆₇×#2985	2
C₆₇×#2981	2
C₆₇×#2977	2
C₆₇×#2968	2
C₆₇×#2966	2
C₆₇×#2925	2
C₂×#432×C₆₇	2
C₂×#431×C₆₇	2
#60294	67

Subgroups — C67×#60294 #30739545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60294 #30739545