Subgroups — C₆₇×#35145 #30714396

Order 17152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 732 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, complemented
2	C₂²×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2860	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2664	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2662	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2604	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2603	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2601	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2591	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2583	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2561	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2539	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2413	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2411	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
17	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₆₇	—	2	8	no	—
19	C₂×#126×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#126×C₆₇	C₂²	1	2	yes	—
24	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#123×C₆₇	C₂²	1	2	yes	—
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#120×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#117×C₆₇	C₂²	1	2	yes	—
36	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#400×C₆₇	C₂²	1	2	yes	complemented
45	#399×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	complemented
47	#398×C₆₇	C₂²	1	4	yes	complemented
48	#397×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	4	yes	—
50	#396×C₆₇	C₂²	1	4	yes	complemented
51	#395×C₆₇	C₂²	1	2	yes	complemented
52	#394×C₆₇	C₂²	1	4	yes	—
53	#394×C₆₇	C₂²	1	2	yes	complemented
54	#393×C₆₇	C₂²	1	2	yes	—
55	#392×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	4	yes	—
57	#390×C₆₇	C₂²	1	4	yes	—
58	#390×C₆₇	C₂²	1	4	yes	—
59	#389×C₆₇	C₂²	1	4	yes	complemented
60	#389×C₆₇	C₂²	1	4	yes	complemented
61	#389×C₆₇	C₂²	1	4	yes	complemented
62	#388×C₆₇	C₂²	1	4	yes	—
63	#388×C₆₇	C₂²	1	4	yes	—
64	#388×C₆₇	C₂²	1	4	yes	—
65	#388×C₆₇	C₂²	1	4	yes	—
66	#388×C₆₇	C₂²	1	4	yes	complemented
67	#388×C₆₇	C₂²	1	4	yes	complemented
68	#388×C₆₇	C₂²	1	4	yes	complemented
69	#387×C₆₇	C₂²	1	4	yes	complemented
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	4	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#385×C₆₇	C₂²	1	2	yes	—
74	#385×C₆₇	C₂²	1	2	yes	—
75	#385×C₆₇	C₂²	1	4	yes	complemented
76	#381×C₆₇	C₂²	1	2	yes	—
77	#379×C₆₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	#376×C₆₇	C₂²	1	2	yes	complemented
84	C₄³×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	#126×C₆₇	—	2	8	no	—
98	#126×C₆₇	—	2	8	no	—
99	#126×C₆₇	—	2	8	no	—
100	#126×C₆₇	—	2	8	no	—
101	#126×C₆₇	—	2	8	no	—
102	#125×C₆₇	—	2	4	no	—
103	#124×C₆₇	—	2	4	no	—
104	#123×C₆₇	—	2	8	no	—
105	#123×C₆₇	—	2	8	no	—
106	C₂²⋊Q₈×C₆₇	—	2	4	no	—
107	#121×C₆₇	—	2	4	no	—
108	#120×C₆₇	—	2	8	no	—
109	C₄×Q₈×C₆₇	—	2	4	no	—
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	2	4	no	—
112	#117×C₆₇	—	2	8	no	—
113	#117×C₆₇	—	2	8	no	—
114	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
156	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	4	yes	—
170	#95×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	C₂⁴×C₆₇	—	2	2	no	—
175	C₂⁴×C₆₇	—	2	4	no	—
176	C₂⁴×C₆₇	—	4	2	no	—
177	C₂⁴×C₆₇	—	4	2	no	—
178	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
179	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
180	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
181	C₂×Q₈×C₆₇	—	2	2	no	—
182	C₂×Q₈×C₆₇	—	4	2	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	2	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	4	2	no	—
189	C₂×D₄×C₆₇	—	4	4	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂²×C₄×C₆₇	—	2	4	no	—
192	C₂²×C₄×C₆₇	—	2	2	no	—
193	C₂²×C₄×C₆₇	—	2	2	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	4	no	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	4	2	no	—
198	C₂²×C₄×C₆₇	—	4	2	no	—
199	C₂²×C₄×C₆₇	—	4	4	no	—
200	C₂²×C₄×C₆₇	—	4	2	no	—
201	C₂²×C₄×C₆₇	—	4	2	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	4	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
219	C₄⋊C₄×C₆₇	—	2	4	no	—
220	C₄⋊C₄×C₆₇	—	2	4	no	—
221	C₄⋊C₄×C₆₇	—	2	4	no	—
222	C₄⋊C₄×C₆₇	—	2	4	no	—
223	C₄⋊C₄×C₆₇	—	2	4	no	—
224	C₄⋊C₄×C₆₇	—	2	4	no	—
225	C₄⋊C₄×C₆₇	—	2	4	no	—
226	C₄⋊C₄×C₆₇	—	2	4	no	—
227	C₄⋊C₄×C₆₇	—	2	2	no	—
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	2	2	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	8	no	—
232	C₄⋊C₄×C₆₇	—	2	8	no	—
233	C₄⋊C₄×C₆₇	—	4	4	no	—
234	C₄⋊C₄×C₆₇	—	4	4	no	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	—	2	4	no	—
238	C₂²⋊C₄×C₆₇	—	2	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	4	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	—	2	4	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	4	no	—
247	C₂²⋊C₄×C₆₇	—	2	8	no	—
248	C₂²⋊C₄×C₆₇	—	2	8	no	—
249	C₂²⋊C₄×C₆₇	—	4	4	no	—
250	C₂²⋊C₄×C₆₇	—	4	4	no	—
251	C₂²⋊C₄×C₆₇	—	4	4	no	—
252	C₂²⋊C₄×C₆₇	—	4	4	no	—
253	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
254	C₄²×C₆₇	—	2	4	no	—
255	C₄²×C₆₇	—	2	8	no	—
256	C₄²×C₆₇	—	4	2	no	—
257	C₄²×C₆₇	—	4	4	no	—
258	C₄²×C₆₇	—	4	2	no	—
259	C₄²×C₆₇	C₂×D₄	1	4	yes	—
260	C₄²×C₆₇	C₂×D₄	1	4	yes	—
261	C₄²×C₆₇	C₂×D₄	1	4	yes	—
262	C₄²×C₆₇	C₂×D₄	1	4	yes	—
263	C₂³×C₆₇	—	2	2	no	—
264	C₂³×C₆₇	—	2	2	no	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	—	2	2	no	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	4	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	4	no	—
272	C₂³×C₆₇	—	2	4	no	—
273	C₂³×C₆₇	—	2	4	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	4	4	no	—
276	C₂³×C₆₇	—	4	4	no	—
277	C₂³×C₆₇	—	4	4	no	—
278	C₂³×C₆₇	—	8	8	no	—
279	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
280	C₂³×C₆₇	C₂×#41	1	4	yes	—
281	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
282	Q₈×C₆₇	—	4	4	no	—
283	D₄×C₆₇	—	4	4	no	—
284	D₄×C₆₇	—	4	8	no	—
285	D₄×C₆₇	—	8	8	no	—
286	C₂×C₄×C₆₇	—	2	8	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	4	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	4	no	—
306	C₂×C₄×C₆₇	—	2	4	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	4	no	—
309	C₂×C₄×C₆₇	—	2	4	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	4	4	no	—
313	C₂×C₄×C₆₇	—	4	4	no	—
314	C₂×C₄×C₆₇	—	4	8	no	—
315	C₂×C₄×C₆₇	—	4	4	no	—
316	C₂×C₄×C₆₇	—	4	4	no	—
317	C₂×C₄×C₆₇	—	4	4	no	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
325	C₂²×C₆₇	—	2	2	no	—
326	C₂²×C₆₇	—	2	2	no	—
327	C₂²×C₆₇	—	2	8	no	—
328	C₂²×C₆₇	—	4	2	no	—
329	C₂²×C₆₇	—	4	2	no	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	4	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	—	4	4	no	—
337	C₂²×C₆₇	—	4	4	no	—
338	C₂²×C₆₇	—	8	8	no	—
339	C₂²×C₆₇	#532	1	4	yes	—
340	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
341	C₂²×C₆₇	C₂²×#41	1	2	yes	—
342	C₂²×C₆₇	#585	1	2	yes	—
343	C₂²×C₆₇	#585	1	2	yes	—
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	2	2	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	2	no	—
350	C₄×C₆₇	—	2	8	no	—
351	C₄×C₆₇	—	4	2	no	—
352	C₄×C₆₇	—	4	2	no	—
353	C₄×C₆₇	—	4	2	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	2	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	—	4	4	no	—
358	#35145	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
359	C₂×C₆₇	—	2	4	no	—
360	C₂×C₆₇	—	8	2	no	—
361	C₂×C₆₇	—	8	2	no	—
362	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
363	C₂×C₆₇	#3449	1	1	yes	characteristic
364	C₂×C₆₇	#3449	1	1	yes	characteristic
365	C₂×C₆₇	#3521	1	4	yes	—
366	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₂²×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
368	#2860	C₂×C₆₇	1	4	yes	complemented
369	#2664	C₂×C₆₇	1	2	yes	complemented
370	#2662	C₂×C₆₇	1	2	yes	complemented
371	#2604	C₂×C₆₇	1	2	yes	complemented
372	#2603	C₂×C₆₇	1	2	yes	complemented
373	#2601	C₂×C₆₇	1	4	yes	complemented
374	#2591	C₂×C₆₇	1	1	yes	characteristic, complemented
375	#2583	C₂×C₆₇	1	1	yes	characteristic, complemented
376	#2561	C₂×C₆₇	1	1	yes	characteristic, complemented
377	#2539	C₂×C₆₇	1	1	yes	characteristic
378	#2413	C₂×C₆₇	1	2	yes	complemented
379	#2411	C₂×C₆₇	1	2	yes	complemented
380	#2322	C₂×C₆₇	1	2	yes	complemented
381	#2321	C₂×C₆₇	1	2	yes	complemented
382	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
383	C₆₇	#35145	1	1	yes	characteristic, direct product factor, Sylow
384	#529	—	2	8	no	—
385	C₂×#126	—	2	8	no	—
386	C₂×#126	C₂²×C₆₇	1	2	yes	—
387	C₂×#126	C₂²×C₆₇	1	2	yes	—
388	C₂×#126	C₂²×C₆₇	1	2	yes	—
389	C₂×#126	C₂²×C₆₇	1	2	yes	—
390	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
391	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
392	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#123	C₂²×C₆₇	1	2	yes	—
394	C₂×#123	C₂²×C₆₇	1	2	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
397	C₂×#120	C₂²×C₆₇	1	2	yes	—
398	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
399	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
401	C₂×#117	C₂²×C₆₇	1	2	yes	—
402	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
403	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
410	#400	C₂²×C₆₇	1	2	yes	complemented
411	#399	C₂²×C₆₇	1	2	yes	—
412	#398	C₂²×C₆₇	1	2	yes	complemented
413	#398	C₂²×C₆₇	1	4	yes	complemented
414	#397	C₂²×C₆₇	1	2	yes	—
415	#396	C₂²×C₆₇	1	4	yes	—
416	#396	C₂²×C₆₇	1	4	yes	complemented
417	#395	C₂²×C₆₇	1	2	yes	complemented
418	#394	C₂²×C₆₇	1	4	yes	—
419	#394	C₂²×C₆₇	1	2	yes	complemented
420	#393	C₂²×C₆₇	1	2	yes	—
421	#392	C₂²×C₆₇	1	2	yes	—
422	#390	C₂²×C₆₇	1	4	yes	—
423	#390	C₂²×C₆₇	1	4	yes	—
424	#390	C₂²×C₆₇	1	4	yes	—
425	#389	C₂²×C₆₇	1	4	yes	complemented
426	#389	C₂²×C₆₇	1	4	yes	complemented
427	#389	C₂²×C₆₇	1	4	yes	complemented
428	#388	C₂²×C₆₇	1	4	yes	—
429	#388	C₂²×C₆₇	1	4	yes	—
430	#388	C₂²×C₆₇	1	4	yes	—
431	#388	C₂²×C₆₇	1	4	yes	—
432	#388	C₂²×C₆₇	1	4	yes	complemented
433	#388	C₂²×C₆₇	1	4	yes	complemented
434	#388	C₂²×C₆₇	1	4	yes	complemented
435	#387	C₂²×C₆₇	1	4	yes	complemented
436	#386	C₂²×C₆₇	1	2	yes	—
437	#386	C₂²×C₆₇	1	4	yes	—
438	#386	C₂²×C₆₇	1	2	yes	—
439	#385	C₂²×C₆₇	1	2	yes	—
440	#385	C₂²×C₆₇	1	2	yes	—
441	#385	C₂²×C₆₇	1	4	yes	complemented
442	#381	C₂²×C₆₇	1	2	yes	—
443	#379	C₂²×C₆₇	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
445	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
446	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
449	#376	C₂²×C₆₇	1	2	yes	complemented
450	C₄³	C₂²×C₆₇	1	2	yes	complemented
451	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
454	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
456	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
461	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
463	#126	—	2	8	no	—
464	#126	—	2	8	no	—
465	#126	—	2	8	no	—
466	#126	—	2	8	no	—
467	#126	—	2	8	no	—
468	#125	—	2	4	no	—
469	#124	—	2	4	no	—
470	#123	—	2	8	no	—
471	#123	—	2	8	no	—
472	C₂²⋊Q₈	—	2	4	no	—
473	#121	—	2	4	no	—
474	#120	—	2	8	no	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	2	4	no	—
478	#117	—	2	8	no	—
479	#117	—	2	8	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	4	no	—
482	C₂×C₄⋊C₄	—	2	4	no	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
522	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
523	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
526	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
527	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
531	#95	C₂³×C₆₇	1	4	yes	—
532	#95	C₂³×C₆₇	1	2	yes	—
533	#95	C₂³×C₆₇	1	2	yes	—
534	#95	C₂³×C₆₇	1	4	yes	—
535	#95	C₂³×C₆₇	1	4	yes	—
536	#95	C₂³×C₆₇	1	4	yes	—
537	#95	C₂³×C₆₇	1	4	yes	—
538	#95	C₂³×C₆₇	1	4	yes	—
539	#95	C₂³×C₆₇	1	4	yes	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	4	no	—
542	C₂⁴	—	4	2	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
545	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
546	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
570	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	8	no	—
622	C₄²	—	4	2	no	—
623	C₄²	—	4	4	no	—
624	C₄²	—	4	2	no	—
625	C₄²	C₂×D₄×C₆₇	1	4	yes	—
626	C₄²	C₂×D₄×C₆₇	1	4	yes	—
627	C₄²	C₂×D₄×C₆₇	1	4	yes	—
628	C₄²	C₂×D₄×C₆₇	1	4	yes	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	4	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	8	8	no	—
645	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
646	C₂³	C₂×#41×C₆₇	1	4	yes	—
647	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
648	Q₈	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	8	no	—
651	D₄	—	8	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
690	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
691	C₂²	—	2	8	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	8	8	no	—
705	C₂²	#532×C₆₇	1	4	yes	—
706	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₆₇	1	2	yes	—
708	C₂²	#585×C₆₇	1	2	yes	—
709	C₂²	#585×C₆₇	1	2	yes	—
710	C₄	—	2	8	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₂	—	2	4	no	—
725	C₂	—	8	2	no	—
726	C₂	—	8	2	no	—
727	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
728	C₂	C₆₇×#3449	1	1	yes	characteristic
729	C₂	C₆₇×#3449	1	1	yes	characteristic
730	C₂	C₆₇×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2539	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₆₇	C₂	semidirect
2. C₂²×#126×C₆₇	C₂	semidirect
3. C₆₇×#2860	C₂	semidirect
4. C₆₇×#2664	C₂	semidirect
5. C₆₇×#2662	C₂	semidirect
6. C₆₇×#2604	C₂	semidirect
7. C₆₇×#2603	C₂	semidirect
8. C₆₇×#2601	C₂	semidirect
9. C₆₇×#2591	C₂	semidirect
10. C₆₇×#2583	C₂	semidirect
11. C₆₇×#2561	C₂	semidirect
13. C₆₇×#2413	C₂	semidirect
14. C₆₇×#2411	C₂	semidirect
15. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2321	C₂	semidirect
17. C₄×#117×C₆₇	C₂	semidirect
24. C₂×#126×C₆₇	C₂²	semidirect
25. C₂×#125×C₆₇	C₂²	semidirect
26. C₂×#124×C₆₇	C₂²	semidirect
32. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×#117×C₆₇	C₂²	semidirect
44. #400×C₆₇	C₂²	semidirect
46. #398×C₆₇	C₂²	semidirect
47. #398×C₆₇	C₂²	semidirect
50. #396×C₆₇	C₂²	semidirect
51. #395×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
59. #389×C₆₇	C₂²	semidirect
60. #389×C₆₇	C₂²	semidirect
61. #389×C₆₇	C₂²	semidirect
66. #388×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
75. #385×C₆₇	C₂²	semidirect
78. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
79. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
83. #376×C₆₇	C₂²	semidirect
84. C₄³×C₆₇	C₂²	semidirect
155. C₂×C₄²×C₆₇	D₄	semidirect
358. #35145	C₆₇	direct (N × H)
366. C₂×#529	C₂×C₆₇	semidirect
367. C₂²×#126	C₂×C₆₇	semidirect
368. #2860	C₂×C₆₇	semidirect
369. #2664	C₂×C₆₇	semidirect
370. #2662	C₂×C₆₇	semidirect
371. #2604	C₂×C₆₇	semidirect
372. #2603	C₂×C₆₇	semidirect
373. #2601	C₂×C₆₇	semidirect
374. #2591	C₂×C₆₇	semidirect
375. #2583	C₂×C₆₇	semidirect
376. #2561	C₂×C₆₇	semidirect
378. #2413	C₂×C₆₇	semidirect
379. #2411	C₂×C₆₇	semidirect
380. #2322	C₂×C₆₇	semidirect
381. #2321	C₂×C₆₇	semidirect
382. C₄×#117	C₂×C₆₇	semidirect
383. C₆₇	#35145	direct (N × H)
390. C₂×#126	C₂²×C₆₇	semidirect
391. C₂×#125	C₂²×C₆₇	semidirect
392. C₂×#124	C₂²×C₆₇	semidirect
398. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
400. C₂×C₄×D₄	C₂²×C₆₇	semidirect
402. C₂×#117	C₂²×C₆₇	semidirect
410. #400	C₂²×C₆₇	semidirect
412. #398	C₂²×C₆₇	semidirect
413. #398	C₂²×C₆₇	semidirect
416. #396	C₂²×C₆₇	semidirect
417. #395	C₂²×C₆₇	semidirect
419. #394	C₂²×C₆₇	semidirect
425. #389	C₂²×C₆₇	semidirect
426. #389	C₂²×C₆₇	semidirect
427. #389	C₂²×C₆₇	semidirect
432. #388	C₂²×C₆₇	semidirect
433. #388	C₂²×C₆₇	semidirect
434. #388	C₂²×C₆₇	semidirect
435. #387	C₂²×C₆₇	semidirect
441. #385	C₂²×C₆₇	semidirect
444. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
445. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
449. #376	C₂²×C₆₇	semidirect
450. C₄³	C₂²×C₆₇	semidirect
521. C₂×C₄²	D₄×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
C₂²×#126×C₆₇	2
C₆₇×#2860	2
C₆₇×#2664	2
C₆₇×#2662	2
C₆₇×#2604	2
C₆₇×#2603	2
C₆₇×#2601	2
C₆₇×#2591	2
C₆₇×#2583	2
C₆₇×#2561	2
C₆₇×#2539	2
C₆₇×#2413	2
C₆₇×#2411	2
C₆₇×#2322	2
C₆₇×#2321	2
C₄×#117×C₆₇	2
#35145	67

Subgroups — C67×#35145 #30714396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35145 #30714396