Subgroups — C₆₇×#60310 #30739561

Order 17152.

1914 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	C₆₇×#3459	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2977	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2972	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2966	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2933	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2929	C₂	1	2	yes	maximal, complemented
12	C₂×#435×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
15	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
16	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	#543×C₆₇	C₄	1	1	yes	characteristic
19	#539×C₆₇	C₄	1	2	yes	—
20	#539×C₆₇	C₄	1	4	yes	—
21	#538×C₆₇	C₄	1	2	yes	—
22	#538×C₆₇	C₄	1	4	yes	—
23	#534×C₆₇	C₄	1	1	yes	characteristic
24	#534×C₆₇	C₄	1	2	yes	—
25	#529×C₆₇	C₂²	1	2	yes	—
26	#529×C₆₇	C₂²	1	4	yes	—
27	#525×C₆₇	C₂²	1	2	yes	—
28	#525×C₆₇	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	#446×C₆₇	C₂²	1	2	yes	complemented
32	#446×C₆₇	C₂²	1	4	yes	complemented
33	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
34	#436×C₆₇	C₂²	1	2	yes	complemented
35	#436×C₆₇	C₂²	1	4	yes	complemented
36	#435×C₆₇	C₂²	1	4	yes	complemented
37	#435×C₆₇	C₂²	1	4	yes	complemented
38	#435×C₆₇	C₂²	1	4	yes	complemented
39	#435×C₆₇	C₂²	1	4	yes	complemented
40	#435×C₆₇	C₂²	1	4	yes	complemented
41	#435×C₆₇	C₂²	1	4	yes	complemented
42	#435×C₆₇	C₂²	1	4	yes	complemented
43	#435×C₆₇	C₂²	1	4	yes	complemented
44	#435×C₆₇	C₂²	1	4	yes	complemented
45	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
46	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
47	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
48	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
49	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
50	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
51	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
52	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
53	#433×C₆₇	C₂²	1	4	yes	complemented
54	#433×C₆₇	C₂²	1	4	yes	complemented
55	#433×C₆₇	C₂²	1	4	yes	complemented
56	#432×C₆₇	C₂²	1	2	yes	complemented
57	#431×C₆₇	C₂²	1	4	yes	complemented
58	#424×C₆₇	C₂²	1	2	yes	complemented
59	#424×C₆₇	C₂²	1	4	yes	complemented
60	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
62	#408×C₆₇	C₂²	1	2	yes	complemented
63	#408×C₆₇	C₂²	1	4	yes	complemented
64	#407×C₆₇	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
67	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
70	#405×C₆₇	C₂²	1	2	yes	complemented
71	#405×C₆₇	C₂²	1	4	yes	complemented
72	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×#41×C₆₇	C₂³	1	2	yes	—
75	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
77	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
80	#131×C₆₇	—	4	4	no	—
81	C₂×M₁₆×C₆₇	—	4	4	no	—
82	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
83	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
84	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₆₇	—	4	2	no	—
87	C₂²×C₈×C₆₇	—	4	2	no	—
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
100	#126×C₆₇	C₂×C₄	1	4	yes	—
101	#126×C₆₇	C₂×C₄	1	4	yes	—
102	#126×C₆₇	C₂×C₄	1	4	yes	—
103	#125×C₆₇	C₂×C₄	1	2	yes	—
104	#125×C₆₇	C₂×C₄	1	4	yes	—
105	#124×C₆₇	C₂×C₄	1	2	yes	—
106	#124×C₆₇	C₂×C₄	1	4	yes	—
107	#123×C₆₇	C₂×C₄	1	4	yes	—
108	#123×C₆₇	C₂×C₄	1	4	yes	—
109	#123×C₆₇	C₂×C₄	1	4	yes	—
110	#123×C₆₇	C₂×C₄	1	4	yes	—
111	#123×C₆₇	C₂×C₄	1	4	yes	—
112	#123×C₆₇	C₂×C₄	1	4	yes	—
113	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
114	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
115	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
117	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
118	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
119	#121×C₆₇	C₂×C₄	1	2	yes	—
120	#121×C₆₇	C₂×C₄	1	4	yes	—
121	#121×C₆₇	C₂×C₄	1	2	yes	—
122	#121×C₆₇	C₂×C₄	1	4	yes	—
123	#121×C₆₇	C₂×C₄	1	2	yes	—
124	#121×C₆₇	C₂×C₄	1	4	yes	—
125	#120×C₆₇	C₂×C₄	1	4	yes	—
126	#120×C₆₇	C₂×C₄	1	4	yes	—
127	#120×C₆₇	C₂×C₄	1	4	yes	—
128	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
129	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
130	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
131	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
132	C₄×D₄×C₆₇	C₂³	1	4	yes	—
133	C₄×D₄×C₆₇	C₂³	1	4	yes	—
134	C₄×D₄×C₆₇	C₂³	1	4	yes	—
135	C₄×D₄×C₆₇	C₂³	1	4	yes	—
136	C₄×D₄×C₆₇	C₂³	1	2	yes	—
137	#117×C₆₇	C₂³	1	2	yes	—
138	#117×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
147	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
156	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
157	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
160	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
162	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
163	#97×C₆₇	C₂³	1	4	yes	—
164	#97×C₆₇	C₂³	1	4	yes	—
165	#97×C₆₇	C₂³	1	4	yes	—
166	C₄×C₈×C₆₇	C₂³	1	2	yes	—
167	C₄×C₈×C₆₇	C₂³	1	2	yes	—
168	C₄×C₈×C₆₇	C₂³	1	4	yes	—
169	C₄×C₈×C₆₇	C₂³	1	4	yes	—
170	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
171	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
172	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
173	#41×C₆₇	—	4	2	no	—
174	#41×C₆₇	—	4	2	no	—
175	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	8	no	—
179	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
181	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
183	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
184	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₆₇	—	4	1	no	—
187	C₂²×C₄×C₆₇	—	4	1	no	—
188	C₂²×C₄×C₆₇	—	4	2	no	—
189	C₂²×C₄×C₆₇	—	4	1	no	—
190	C₂²×C₄×C₆₇	—	4	2	no	—
191	C₂²×C₄×C₆₇	—	4	1	no	—
192	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
206	M₁₆×C₆₇	—	2	8	no	—
207	M₁₆×C₆₇	—	4	4	no	—
208	M₁₆×C₆₇	—	4	2	no	—
209	M₁₆×C₆₇	—	4	2	no	—
210	C₂×C₈×C₆₇	—	2	2	no	—
211	C₂×C₈×C₆₇	—	2	4	no	—
212	C₂×C₈×C₆₇	—	2	4	no	—
213	C₂×C₈×C₆₇	—	4	1	no	—
214	C₂×C₈×C₆₇	—	4	2	no	—
215	C₂×C₈×C₆₇	—	4	2	no	—
216	C₂×C₈×C₆₇	—	4	1	no	—
217	C₂×C₈×C₆₇	—	4	1	no	—
218	C₂×C₈×C₆₇	—	4	4	no	—
219	C₂×C₈×C₆₇	—	4	2	no	—
220	C₂×C₈×C₆₇	—	4	2	no	—
221	C₂×C₈×C₆₇	—	4	4	no	—
222	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
225	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
226	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
227	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
228	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
230	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
235	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
236	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
238	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
239	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
240	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
241	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
242	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
243	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
244	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
245	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
246	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
247	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
248	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
249	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
250	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
251	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
252	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
253	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
254	C₄²×C₆₇	C₂⁴	1	2	yes	—
255	C₄²×C₆₇	C₂⁴	1	4	yes	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	4	no	—
258	C₂³×C₆₇	—	4	1	no	—
259	C₂³×C₆₇	—	4	1	no	—
260	C₂³×C₆₇	—	4	1	no	—
261	C₂³×C₆₇	—	4	1	no	—
262	C₂³×C₆₇	—	4	2	no	—
263	C₂³×C₆₇	—	4	2	no	—
264	C₂³×C₆₇	#131	1	4	yes	complemented
265	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
266	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
267	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
268	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
269	Q₈×C₆₇	—	4	2	no	—
270	Q₈×C₆₇	—	4	2	no	—
271	D₄×C₆₇	—	2	8	no	—
272	D₄×C₆₇	—	2	8	no	—
273	D₄×C₆₇	—	2	8	no	—
274	D₄×C₆₇	—	4	4	no	—
275	D₄×C₆₇	—	4	2	no	—
276	D₄×C₆₇	—	4	2	no	—
277	D₄×C₆₇	—	4	4	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	4	1	no	—
289	C₂×C₄×C₆₇	—	4	2	no	—
290	C₂×C₄×C₆₇	—	4	2	no	—
291	C₂×C₄×C₆₇	—	4	4	no	—
292	C₂×C₄×C₆₇	—	4	1	no	—
293	C₂×C₄×C₆₇	—	4	2	no	—
294	C₂×C₄×C₆₇	—	4	1	no	—
295	C₂×C₄×C₆₇	—	4	2	no	—
296	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
305	C₈×C₆₇	—	2	1	no	—
306	C₈×C₆₇	—	2	2	no	—
307	C₈×C₆₇	—	2	2	no	—
308	C₈×C₆₇	—	2	4	no	—
309	C₈×C₆₇	—	2	2	no	—
310	C₈×C₆₇	—	2	4	no	—
311	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₆₇	—	2	1	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	1	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	2	2	no	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	4	4	no	—
323	C₂²×C₆₇	—	4	4	no	—
324	C₂²×C₆₇	—	8	4	no	—
325	C₂²×C₆₇	C₂×#131	1	2	yes	—
326	C₂²×C₆₇	C₂×#131	1	4	yes	—
327	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₆₇	—	2	1	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	2	4	no	—
332	C₄×C₆₇	—	2	2	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	2	4	no	—
336	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₄×C₆₇	#585	1	1	yes	characteristic
338	#60310	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂×C₆₇	—	2	2	no	—
340	C₂×C₆₇	—	2	4	no	—
341	C₂×C₆₇	—	4	2	no	—
342	C₂×C₆₇	—	4	4	no	—
343	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
345	C₂×C₆₇	#3573	1	1	yes	characteristic
346	#3459	C₂×C₆₇	1	1	yes	characteristic
347	#2994	C₂×C₆₇	1	4	yes	complemented
348	#2992	C₂×C₆₇	1	2	yes	complemented
349	#2977	C₂×C₆₇	1	4	yes	complemented
350	#2976	C₂×C₆₇	1	2	yes	complemented
351	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
352	#2972	C₂×C₆₇	1	2	yes	complemented
353	#2968	C₂×C₆₇	1	4	yes	complemented
354	#2966	C₂×C₆₇	1	2	yes	complemented
355	#2933	C₂×C₆₇	1	4	yes	complemented
356	#2929	C₂×C₆₇	1	2	yes	complemented
357	C₂×#435	C₂×C₆₇	1	2	yes	complemented
358	C₂×C₈×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
359	C₆₇	#60310	1	1	yes	characteristic, direct product factor, Sylow
360	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
361	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
362	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
363	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
364	#543	C₄×C₆₇	1	1	yes	characteristic
365	#539	C₄×C₆₇	1	2	yes	—
366	#539	C₄×C₆₇	1	4	yes	—
367	#538	C₄×C₆₇	1	2	yes	—
368	#538	C₄×C₆₇	1	4	yes	—
369	#534	C₄×C₆₇	1	1	yes	characteristic
370	#534	C₄×C₆₇	1	2	yes	—
371	#529	C₂²×C₆₇	1	2	yes	—
372	#529	C₂²×C₆₇	1	4	yes	—
373	#525	C₂²×C₆₇	1	2	yes	—
374	#525	C₂²×C₆₇	1	4	yes	—
375	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
376	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
377	#446	C₂²×C₆₇	1	2	yes	complemented
378	#446	C₂²×C₆₇	1	4	yes	complemented
379	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
380	#436	C₂²×C₆₇	1	2	yes	complemented
381	#436	C₂²×C₆₇	1	4	yes	complemented
382	#435	C₂²×C₆₇	1	4	yes	complemented
383	#435	C₂²×C₆₇	1	4	yes	complemented
384	#435	C₂²×C₆₇	1	4	yes	complemented
385	#435	C₂²×C₆₇	1	4	yes	complemented
386	#435	C₂²×C₆₇	1	4	yes	complemented
387	#435	C₂²×C₆₇	1	4	yes	complemented
388	#435	C₂²×C₆₇	1	4	yes	complemented
389	#435	C₂²×C₆₇	1	4	yes	complemented
390	#435	C₂²×C₆₇	1	4	yes	complemented
391	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
392	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
393	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
394	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
395	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
396	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
397	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
398	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
399	#433	C₂²×C₆₇	1	4	yes	complemented
400	#433	C₂²×C₆₇	1	4	yes	complemented
401	#433	C₂²×C₆₇	1	4	yes	complemented
402	#432	C₂²×C₆₇	1	2	yes	complemented
403	#431	C₂²×C₆₇	1	4	yes	complemented
404	#424	C₂²×C₆₇	1	2	yes	complemented
405	#424	C₂²×C₆₇	1	4	yes	complemented
406	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
407	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
408	#408	C₂²×C₆₇	1	2	yes	complemented
409	#408	C₂²×C₆₇	1	4	yes	complemented
410	#407	C₂²×C₆₇	1	2	yes	complemented
411	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
413	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
414	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
415	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
416	#405	C₂²×C₆₇	1	2	yes	complemented
417	#405	C₂²×C₆₇	1	4	yes	complemented
418	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
419	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
420	C₂×#41	C₂³×C₆₇	1	2	yes	—
421	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
422	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
423	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
426	#131	—	4	4	no	—
427	C₂×M₁₆	—	4	4	no	—
428	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
429	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
430	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
431	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
432	C₂²×C₈	—	4	2	no	—
433	C₂²×C₈	—	4	2	no	—
434	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
436	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
437	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
438	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
441	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
442	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
443	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
445	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
446	#126	C₂×C₄×C₆₇	1	4	yes	—
447	#126	C₂×C₄×C₆₇	1	4	yes	—
448	#126	C₂×C₄×C₆₇	1	4	yes	—
449	#125	C₂×C₄×C₆₇	1	2	yes	—
450	#125	C₂×C₄×C₆₇	1	4	yes	—
451	#124	C₂×C₄×C₆₇	1	2	yes	—
452	#124	C₂×C₄×C₆₇	1	4	yes	—
453	#123	C₂×C₄×C₆₇	1	4	yes	—
454	#123	C₂×C₄×C₆₇	1	4	yes	—
455	#123	C₂×C₄×C₆₇	1	4	yes	—
456	#123	C₂×C₄×C₆₇	1	4	yes	—
457	#123	C₂×C₄×C₆₇	1	4	yes	—
458	#123	C₂×C₄×C₆₇	1	4	yes	—
459	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
460	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
461	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
462	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
463	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
464	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
465	#121	C₂×C₄×C₆₇	1	2	yes	—
466	#121	C₂×C₄×C₆₇	1	4	yes	—
467	#121	C₂×C₄×C₆₇	1	2	yes	—
468	#121	C₂×C₄×C₆₇	1	4	yes	—
469	#121	C₂×C₄×C₆₇	1	2	yes	—
470	#121	C₂×C₄×C₆₇	1	4	yes	—
471	#120	C₂×C₄×C₆₇	1	4	yes	—
472	#120	C₂×C₄×C₆₇	1	4	yes	—
473	#120	C₂×C₄×C₆₇	1	4	yes	—
474	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
476	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
477	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
478	C₄×D₄	C₂³×C₆₇	1	4	yes	—
479	C₄×D₄	C₂³×C₆₇	1	4	yes	—
480	C₄×D₄	C₂³×C₆₇	1	4	yes	—
481	C₄×D₄	C₂³×C₆₇	1	4	yes	—
482	C₄×D₄	C₂³×C₆₇	1	2	yes	—
483	#117	C₂³×C₆₇	1	2	yes	—
484	#117	C₂³×C₆₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
493	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
494	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
495	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
496	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
497	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
498	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
499	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
500	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
501	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
502	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
503	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
504	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
505	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
506	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
507	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
508	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
509	#97	C₂³×C₆₇	1	4	yes	—
510	#97	C₂³×C₆₇	1	4	yes	—
511	#97	C₂³×C₆₇	1	4	yes	—
512	C₄×C₈	C₂³×C₆₇	1	2	yes	—
513	C₄×C₈	C₂³×C₆₇	1	2	yes	—
514	C₄×C₈	C₂³×C₆₇	1	4	yes	—
515	C₄×C₈	C₂³×C₆₇	1	4	yes	—
516	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
517	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
518	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
519	#41	—	4	2	no	—
520	#41	—	4	2	no	—
521	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
522	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
526	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
527	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
528	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
529	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
530	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
531	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	1	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	1	no	—
538	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
540	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
552	M₁₆	—	2	8	no	—
553	M₁₆	—	4	4	no	—
554	M₁₆	—	4	2	no	—
555	M₁₆	—	4	2	no	—
556	C₂×C₈	—	2	2	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	4	1	no	—
560	C₂×C₈	—	4	2	no	—
561	C₂×C₈	—	4	2	no	—
562	C₂×C₈	—	4	1	no	—
563	C₂×C₈	—	4	2	no	—
564	C₂×C₈	—	4	4	no	—
565	C₂×C₈	—	4	1	no	—
566	C₂×C₈	—	4	4	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
569	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
570	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
571	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
572	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
573	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
574	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
575	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
577	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
578	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
579	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
582	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
584	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
585	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
590	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
591	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
593	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
598	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
599	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
600	C₄²	C₂⁴×C₆₇	1	2	yes	—
601	C₄²	C₂⁴×C₆₇	1	4	yes	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	#131×C₆₇	1	4	yes	complemented
611	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
612	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
613	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
614	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
615	Q₈	—	4	2	no	—
616	Q₈	—	4	2	no	—
617	D₄	—	2	8	no	—
618	D₄	—	2	8	no	—
619	D₄	—	2	8	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	4	no	—
623	D₄	—	4	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
644	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
645	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
647	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
650	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
651	C₈	—	2	1	no	—
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	2	4	no	—
655	C₈	—	2	2	no	—
656	C₈	—	2	4	no	—
657	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	C₂×#131×C₆₇	1	2	yes	—
672	C₂²	C₂×#131×C₆₇	1	4	yes	—
673	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
683	C₄	#585×C₆₇	1	1	yes	characteristic
684	C₂	—	2	2	no	—
685	C₂	—	2	4	no	—
686	C₂	—	4	2	no	—
687	C₂	—	4	4	no	—
688	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
689	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
690	C₂	C₆₇×#3573	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×#3459	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×#2994	C₂	semidirect
3. C₆₇×#2992	C₂	semidirect
4. C₆₇×#2977	C₂	semidirect
5. C₆₇×#2976	C₂	semidirect
6. C₆₇×#2973	C₂	semidirect
7. C₆₇×#2972	C₂	semidirect
8. C₆₇×#2968	C₂	semidirect
9. C₆₇×#2966	C₂	semidirect
10. C₆₇×#2933	C₂	semidirect
11. C₆₇×#2929	C₂	semidirect
12. C₂×#435×C₆₇	C₂	semidirect
13. C₂×C₈×D₄×C₆₇	C₂	semidirect
14. C₂×#131×C₆₇	C₂²	semidirect
15. C₂²×M₁₆×C₆₇	C₂²	semidirect
17. C₂³×C₈×C₆₇	C₂²	semidirect
31. #446×C₆₇	C₂²	semidirect
32. #446×C₆₇	C₂²	semidirect
33. C₈×Q₈×C₆₇	C₂²	semidirect
34. #436×C₆₇	C₂²	semidirect
35. #436×C₆₇	C₂²	semidirect
36. #435×C₆₇	C₂²	semidirect
37. #435×C₆₇	C₂²	semidirect
38. #435×C₆₇	C₂²	semidirect
39. #435×C₆₇	C₂²	semidirect
40. #435×C₆₇	C₂²	semidirect
41. #435×C₆₇	C₂²	semidirect
42. #435×C₆₇	C₂²	semidirect
43. #435×C₆₇	C₂²	semidirect
44. #435×C₆₇	C₂²	semidirect
45. C₈×D₄×C₆₇	C₂²	semidirect
46. C₈×D₄×C₆₇	C₂²	semidirect
47. C₈×D₄×C₆₇	C₂²	semidirect
48. C₈×D₄×C₆₇	C₂²	semidirect
49. C₈×D₄×C₆₇	C₂²	semidirect
50. C₈×D₄×C₆₇	C₂²	semidirect
51. C₈×D₄×C₆₇	C₂²	semidirect
52. C₈×D₄×C₆₇	C₂²	semidirect
53. #433×C₆₇	C₂²	semidirect
54. #433×C₆₇	C₂²	semidirect
55. #433×C₆₇	C₂²	semidirect
56. #432×C₆₇	C₂²	semidirect
57. #431×C₆₇	C₂²	semidirect
58. #424×C₆₇	C₂²	semidirect
59. #424×C₆₇	C₂²	semidirect
60. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
61. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
62. #408×C₆₇	C₂²	semidirect
63. #408×C₆₇	C₂²	semidirect
64. #407×C₆₇	C₂²	semidirect
67. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
68. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
69. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
70. #405×C₆₇	C₂²	semidirect
71. #405×C₆₇	C₂²	semidirect
72. C₂×#97×C₆₇	C₂²	semidirect
73. C₂×C₄×C₈×C₆₇	C₂²	semidirect
264. C₂³×C₆₇	#131	semidirect
338. #60310	C₆₇	direct (N × H)
347. #2994	C₂×C₆₇	semidirect
348. #2992	C₂×C₆₇	semidirect
349. #2977	C₂×C₆₇	semidirect
350. #2976	C₂×C₆₇	semidirect
351. #2973	C₂×C₆₇	semidirect
352. #2972	C₂×C₆₇	semidirect
353. #2968	C₂×C₆₇	semidirect
354. #2966	C₂×C₆₇	semidirect
355. #2933	C₂×C₆₇	semidirect
356. #2929	C₂×C₆₇	semidirect
357. C₂×#435	C₂×C₆₇	semidirect
358. C₂×C₈×D₄	C₂×C₆₇	semidirect
359. C₆₇	#60310	direct (N × H)
360. C₂×#131	C₂²×C₆₇	semidirect
361. C₂²×M₁₆	C₂²×C₆₇	semidirect
363. C₂³×C₈	C₂²×C₆₇	semidirect
377. #446	C₂²×C₆₇	semidirect
378. #446	C₂²×C₆₇	semidirect
379. C₈×Q₈	C₂²×C₆₇	semidirect
380. #436	C₂²×C₆₇	semidirect
381. #436	C₂²×C₆₇	semidirect
382. #435	C₂²×C₆₇	semidirect
383. #435	C₂²×C₆₇	semidirect
384. #435	C₂²×C₆₇	semidirect
385. #435	C₂²×C₆₇	semidirect
386. #435	C₂²×C₆₇	semidirect
387. #435	C₂²×C₆₇	semidirect
388. #435	C₂²×C₆₇	semidirect
389. #435	C₂²×C₆₇	semidirect
390. #435	C₂²×C₆₇	semidirect
391. C₈×D₄	C₂²×C₆₇	semidirect
392. C₈×D₄	C₂²×C₆₇	semidirect
393. C₈×D₄	C₂²×C₆₇	semidirect
394. C₈×D₄	C₂²×C₆₇	semidirect
395. C₈×D₄	C₂²×C₆₇	semidirect
396. C₈×D₄	C₂²×C₆₇	semidirect
397. C₈×D₄	C₂²×C₆₇	semidirect
398. C₈×D₄	C₂²×C₆₇	semidirect
399. #433	C₂²×C₆₇	semidirect
400. #433	C₂²×C₆₇	semidirect
401. #433	C₂²×C₆₇	semidirect
402. #432	C₂²×C₆₇	semidirect
403. #431	C₂²×C₆₇	semidirect
404. #424	C₂²×C₆₇	semidirect
405. #424	C₂²×C₆₇	semidirect
406. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
407. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
408. #408	C₂²×C₆₇	semidirect
409. #408	C₂²×C₆₇	semidirect
410. #407	C₂²×C₆₇	semidirect
413. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
414. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
415. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
416. #405	C₂²×C₆₇	semidirect
417. #405	C₂²×C₆₇	semidirect
418. C₂×#97	C₂²×C₆₇	semidirect
419. C₂×C₄×C₈	C₂²×C₆₇	semidirect
610. C₂³	#131×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3459	2
C₆₇×#2994	2
C₆₇×#2992	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2973	2
C₆₇×#2972	2
C₆₇×#2968	2
C₆₇×#2966	2
C₆₇×#2933	2
C₆₇×#2929	2
C₂×#435×C₆₇	2
C₂×C₈×D₄×C₆₇	2
#60310	67

Subgroups — C67×#60310 #30739561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60310 #30739561