Subgroups — C₆₇×#60212 #30739463

Order 17152.

1874 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2969	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2968	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2967	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2966	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2962	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#131×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#131×C₆₇	C₂²	1	2	yes	—
17	C₂×#131×C₆₇	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
19	#542×C₆₇	C₄	1	2	yes	—
20	#542×C₆₇	C₄	1	2	yes	—
21	#541×C₆₇	C₄	1	2	yes	—
22	#540×C₆₇	C₄	1	2	yes	—
23	#539×C₆₇	C₄	1	4	yes	—
24	#538×C₆₇	C₄	1	4	yes	—
25	#533×C₆₇	C₂²	1	1	yes	characteristic
26	#532×C₆₇	C₂²	1	1	yes	characteristic
27	#529×C₆₇	C₂²	1	4	yes	—
28	#529×C₆₇	C₂²	1	4	yes	—
29	#525×C₆₇	C₂²	1	1	yes	characteristic
30	#525×C₆₇	C₂²	1	1	yes	characteristic
31	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
32	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	#446×C₆₇	C₂²	1	4	yes	complemented
35	#446×C₆₇	C₂²	1	4	yes	complemented
36	#446×C₆₇	C₂²	1	4	yes	complemented
37	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
38	#436×C₆₇	C₂²	1	4	yes	—
39	#436×C₆₇	C₂²	1	4	yes	—
40	#436×C₆₇	C₂²	1	4	yes	complemented
41	#435×C₆₇	C₂²	1	4	yes	—
42	#435×C₆₇	C₂²	1	4	yes	—
43	#435×C₆₇	C₂²	1	4	yes	—
44	#435×C₆₇	C₂²	1	4	yes	—
45	#435×C₆₇	C₂²	1	4	yes	complemented
46	#435×C₆₇	C₂²	1	4	yes	complemented
47	C₈×D₄×C₆₇	C₂²	1	4	yes	—
48	C₈×D₄×C₆₇	C₂²	1	4	yes	—
49	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
50	#433×C₆₇	C₂²	1	2	yes	—
51	#433×C₆₇	C₂²	1	2	yes	—
52	#433×C₆₇	C₂²	1	2	yes	—
53	#433×C₆₇	C₂²	1	2	yes	—
54	#433×C₆₇	C₂²	1	2	yes	complemented
55	#433×C₆₇	C₂²	1	2	yes	complemented
56	#433×C₆₇	C₂²	1	2	yes	complemented
57	#433×C₆₇	C₂²	1	2	yes	complemented
58	#432×C₆₇	C₂²	1	4	yes	complemented
59	#431×C₆₇	C₂²	1	4	yes	complemented
60	#424×C₆₇	C₂²	1	2	yes	—
61	#424×C₆₇	C₂²	1	2	yes	—
62	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
63	#408×C₆₇	C₂²	1	2	yes	—
64	#408×C₆₇	C₂²	1	2	yes	—
65	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
66	#405×C₆₇	C₂²	1	4	yes	—
67	#405×C₆₇	C₂²	1	4	yes	—
68	#405×C₆₇	C₂²	1	2	yes	—
69	#405×C₆₇	C₂²	1	2	yes	—
70	#405×C₆₇	C₂²	1	4	yes	complemented
71	#405×C₆₇	C₂²	1	4	yes	complemented
72	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
73	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
75	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
76	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
77	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
79	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
81	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
84	#131×C₆₇	—	2	8	no	—
85	#131×C₆₇	—	2	8	no	—
86	C₂×M₁₆×C₆₇	—	2	8	no	—
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
89	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
90	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
99	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
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	#126×C₆₇	C₂×C₄	1	4	yes	—
104	#125×C₆₇	C₂×C₄	1	4	yes	—
105	#125×C₆₇	C₂×C₄	1	4	yes	—
106	#125×C₆₇	C₂×C₄	1	2	yes	—
107	#124×C₆₇	C₂×C₄	1	4	yes	—
108	#124×C₆₇	C₂×C₄	1	4	yes	—
109	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
110	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
111	#123×C₆₇	C₂×C₄	1	2	yes	—
112	#123×C₆₇	C₂×C₄	1	2	yes	—
113	#123×C₆₇	C₂×C₄	1	4	yes	—
114	#123×C₆₇	C₂×C₄	1	4	yes	—
115	#123×C₆₇	C₂×C₄	1	4	yes	—
116	#123×C₆₇	C₂×C₄	1	4	yes	—
117	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
118	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
119	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
120	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
121	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
122	#121×C₆₇	C₂×C₄	1	2	yes	—
123	#121×C₆₇	C₂×C₄	1	2	yes	—
124	#121×C₆₇	C₂×C₄	1	4	yes	—
125	#121×C₆₇	C₂×C₄	1	4	yes	—
126	#121×C₆₇	C₂×C₄	1	4	yes	—
127	#120×C₆₇	C₂×C₄	1	2	yes	—
128	#120×C₆₇	C₂×C₄	1	2	yes	—
129	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
130	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
131	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
132	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
133	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
134	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
135	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
136	C₄×D₄×C₆₇	C₂³	1	4	yes	—
137	C₄×D₄×C₆₇	C₂³	1	4	yes	—
138	C₄×D₄×C₆₇	C₂³	1	4	yes	—
139	#117×C₆₇	C₂×C₄	1	2	yes	—
140	#117×C₆₇	C₂×C₄	1	2	yes	—
141	#117×C₆₇	C₂³	1	2	yes	—
142	#117×C₆₇	C₂³	1	2	yes	—
143	#117×C₆₇	C₂³	1	1	yes	characteristic
144	#117×C₆₇	C₂³	1	1	yes	characteristic
145	#117×C₆₇	C₂³	1	2	yes	—
146	#117×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
153	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
156	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
158	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
160	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
162	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
163	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
164	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
165	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
166	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
167	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
168	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
169	#97×C₆₇	C₂³	1	1	yes	characteristic
170	#97×C₆₇	C₂³	1	1	yes	characteristic
171	#97×C₆₇	C₂³	1	2	yes	—
172	#97×C₆₇	C₂³	1	2	yes	—
173	#97×C₆₇	C₂³	1	4	yes	—
174	#97×C₆₇	C₂³	1	2	yes	—
175	#97×C₆₇	C₂³	1	4	yes	—
176	#97×C₆₇	C₂³	1	4	yes	—
177	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₆₇	C₂³	1	2	yes	—
180	C₄×C₈×C₆₇	C₂³	1	2	yes	—
181	C₄×C₈×C₆₇	C₂³	1	4	yes	—
182	C₄×C₈×C₆₇	C₂³	1	2	yes	—
183	C₄×C₈×C₆₇	C₂³	1	4	yes	—
184	C₄×C₈×C₆₇	C₂³	1	4	yes	—
185	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	#41×C₆₇	—	2	4	no	—
187	#41×C₆₇	—	2	4	no	—
188	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
191	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
192	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
197	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₆₇	—	2	4	no	—
199	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	M₁₆×C₆₇	—	2	4	no	—
210	M₁₆×C₆₇	—	2	8	no	—
211	M₁₆×C₆₇	—	2	8	no	—
212	M₁₆×C₆₇	—	2	8	no	—
213	M₁₆×C₆₇	#41	1	8	yes	—
214	C₂×C₈×C₆₇	—	2	4	no	—
215	C₂×C₈×C₆₇	—	2	4	no	—
216	C₂×C₈×C₆₇	—	2	8	no	—
217	C₂×C₈×C₆₇	—	2	8	no	—
218	C₂×C₈×C₆₇	—	2	8	no	—
219	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
220	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
221	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
222	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
224	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
228	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
229	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
233	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	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	4	yes	—
238	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
239	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
240	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
241	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
242	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
243	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
244	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	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	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
253	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
254	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
257	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
258	C₄²×C₆₇	C₂⁴	1	2	yes	—
259	C₄²×C₆₇	C₂⁴	1	2	yes	—
260	C₄²×C₆₇	C₂⁴	1	2	yes	—
261	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂³×C₆₇	—	2	2	no	—
264	C₂³×C₆₇	—	4	2	no	—
265	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
266	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
267	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
268	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
269	Q₈×C₆₇	—	2	2	no	—
270	Q₈×C₆₇	—	2	2	no	—
271	Q₈×C₆₇	—	4	4	no	—
272	D₄×C₆₇	—	2	4	no	—
273	D₄×C₆₇	—	2	4	no	—
274	D₄×C₆₇	—	2	2	no	—
275	D₄×C₆₇	—	2	2	no	—
276	D₄×C₆₇	—	4	4	no	—
277	D₄×C₆₇	—	4	4	no	—
278	D₄×C₆₇	—	4	4	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	4	2	no	—
286	C₂×C₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	—	4	4	no	—
288	C₂×C₄×C₆₇	—	4	2	no	—
289	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
301	C₈×C₆₇	—	2	2	no	—
302	C₈×C₆₇	—	2	2	no	—
303	C₈×C₆₇	—	2	2	no	—
304	C₈×C₆₇	—	2	2	no	—
305	C₈×C₆₇	—	2	4	no	—
306	C₈×C₆₇	C₂×#41	1	8	yes	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	2	no	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	4	no	—
312	C₂²×C₆₇	—	2	4	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	8	2	no	—
316	C₂²×C₆₇	C₄×#41	1	2	yes	—
317	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	2	no	—
320	C₄×C₆₇	—	2	2	no	—
321	C₄×C₆₇	—	2	2	no	—
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	—	2	2	no	—
324	C₄×C₆₇	—	2	4	no	—
325	C₄×C₆₇	—	2	4	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	C₄×#41	1	2	yes	—
328	C₄×C₆₇	C₂²×#41	1	2	yes	—
329	#60212	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₆₇	—	2	2	no	—
331	C₂×C₆₇	—	4	2	no	—
332	C₂×C₆₇	—	4	2	no	—
333	C₂×C₆₇	—	4	2	no	—
334	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
335	C₂×C₆₇	#3573	1	2	yes	—
336	#3455	C₂×C₆₇	1	1	yes	characteristic
337	#2969	C₂×C₆₇	1	4	yes	complemented
338	#2968	C₂×C₆₇	1	4	yes	complemented
339	#2967	C₂×C₆₇	1	4	yes	complemented
340	#2966	C₂×C₆₇	1	4	yes	complemented
341	#2962	C₂×C₆₇	1	2	yes	complemented
342	#2935	C₂×C₆₇	1	2	yes	complemented
343	#2933	C₂×C₆₇	1	2	yes	complemented
344	#2933	C₂×C₆₇	1	2	yes	complemented
345	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
346	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
347	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
348	#2875	C₂×C₆₇	1	1	yes	characteristic, complemented
349	C₄×#131	C₂×C₆₇	1	1	yes	characteristic, complemented
350	#2873	C₂×C₆₇	1	1	yes	characteristic, complemented
351	C₆₇	#60212	1	1	yes	characteristic, direct product factor, Sylow
352	C₂×#131	C₂²×C₆₇	1	2	yes	—
353	C₂×#131	C₂²×C₆₇	1	2	yes	—
354	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
355	#542	C₄×C₆₇	1	2	yes	—
356	#542	C₄×C₆₇	1	2	yes	—
357	#541	C₄×C₆₇	1	2	yes	—
358	#540	C₄×C₆₇	1	2	yes	—
359	#539	C₄×C₆₇	1	4	yes	—
360	#538	C₄×C₆₇	1	4	yes	—
361	#533	C₂²×C₆₇	1	1	yes	characteristic
362	#532	C₂²×C₆₇	1	1	yes	characteristic
363	#529	C₂²×C₆₇	1	4	yes	—
364	#529	C₂²×C₆₇	1	4	yes	—
365	#525	C₂²×C₆₇	1	1	yes	characteristic
366	#525	C₂²×C₆₇	1	1	yes	characteristic
367	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
368	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
369	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
370	#446	C₂²×C₆₇	1	4	yes	complemented
371	#446	C₂²×C₆₇	1	4	yes	complemented
372	#446	C₂²×C₆₇	1	4	yes	complemented
373	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
374	#436	C₂²×C₆₇	1	4	yes	—
375	#436	C₂²×C₆₇	1	4	yes	—
376	#436	C₂²×C₆₇	1	4	yes	complemented
377	#435	C₂²×C₆₇	1	4	yes	—
378	#435	C₂²×C₆₇	1	4	yes	—
379	#435	C₂²×C₆₇	1	4	yes	—
380	#435	C₂²×C₆₇	1	4	yes	—
381	#435	C₂²×C₆₇	1	4	yes	complemented
382	#435	C₂²×C₆₇	1	4	yes	complemented
383	C₈×D₄	C₂²×C₆₇	1	4	yes	—
384	C₈×D₄	C₂²×C₆₇	1	4	yes	—
385	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
386	#433	C₂²×C₆₇	1	2	yes	—
387	#433	C₂²×C₆₇	1	2	yes	—
388	#433	C₂²×C₆₇	1	2	yes	—
389	#433	C₂²×C₆₇	1	2	yes	—
390	#433	C₂²×C₆₇	1	2	yes	complemented
391	#433	C₂²×C₆₇	1	2	yes	complemented
392	#433	C₂²×C₆₇	1	2	yes	complemented
393	#433	C₂²×C₆₇	1	2	yes	complemented
394	#432	C₂²×C₆₇	1	4	yes	complemented
395	#431	C₂²×C₆₇	1	4	yes	complemented
396	#424	C₂²×C₆₇	1	2	yes	—
397	#424	C₂²×C₆₇	1	2	yes	—
398	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
399	#408	C₂²×C₆₇	1	2	yes	—
400	#408	C₂²×C₆₇	1	2	yes	—
401	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
402	#405	C₂²×C₆₇	1	4	yes	—
403	#405	C₂²×C₆₇	1	4	yes	—
404	#405	C₂²×C₆₇	1	2	yes	—
405	#405	C₂²×C₆₇	1	2	yes	—
406	#405	C₂²×C₆₇	1	4	yes	complemented
407	#405	C₂²×C₆₇	1	4	yes	complemented
408	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
409	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
410	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
411	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
412	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
413	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
415	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
417	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
418	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
420	#131	—	2	8	no	—
421	#131	—	2	8	no	—
422	C₂×M₁₆	—	2	8	no	—
423	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
424	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
425	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
426	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
427	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
428	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
429	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
430	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
431	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
432	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
433	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
434	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
435	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
436	#126	C₂×C₄×C₆₇	1	4	yes	—
437	#126	C₂×C₄×C₆₇	1	4	yes	—
438	#126	C₂×C₄×C₆₇	1	4	yes	—
439	#126	C₂×C₄×C₆₇	1	4	yes	—
440	#125	C₂×C₄×C₆₇	1	4	yes	—
441	#125	C₂×C₄×C₆₇	1	4	yes	—
442	#125	C₂×C₄×C₆₇	1	2	yes	—
443	#124	C₂×C₄×C₆₇	1	4	yes	—
444	#124	C₂×C₄×C₆₇	1	4	yes	—
445	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
446	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
447	#123	C₂×C₄×C₆₇	1	2	yes	—
448	#123	C₂×C₄×C₆₇	1	2	yes	—
449	#123	C₂×C₄×C₆₇	1	4	yes	—
450	#123	C₂×C₄×C₆₇	1	4	yes	—
451	#123	C₂×C₄×C₆₇	1	4	yes	—
452	#123	C₂×C₄×C₆₇	1	4	yes	—
453	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
454	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
456	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
457	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
458	#121	C₂×C₄×C₆₇	1	2	yes	—
459	#121	C₂×C₄×C₆₇	1	2	yes	—
460	#121	C₂×C₄×C₆₇	1	4	yes	—
461	#121	C₂×C₄×C₆₇	1	4	yes	—
462	#121	C₂×C₄×C₆₇	1	4	yes	—
463	#120	C₂×C₄×C₆₇	1	2	yes	—
464	#120	C₂×C₄×C₆₇	1	2	yes	—
465	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
466	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
467	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
468	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
469	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
470	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
471	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
472	C₄×D₄	C₂³×C₆₇	1	4	yes	—
473	C₄×D₄	C₂³×C₆₇	1	4	yes	—
474	C₄×D₄	C₂³×C₆₇	1	4	yes	—
475	#117	C₂×C₄×C₆₇	1	2	yes	—
476	#117	C₂×C₄×C₆₇	1	2	yes	—
477	#117	C₂³×C₆₇	1	2	yes	—
478	#117	C₂³×C₆₇	1	2	yes	—
479	#117	C₂³×C₆₇	1	1	yes	characteristic
480	#117	C₂³×C₆₇	1	1	yes	characteristic
481	#117	C₂³×C₆₇	1	2	yes	—
482	#117	C₂³×C₆₇	1	2	yes	—
483	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
485	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
489	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
490	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
491	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
492	C₄⋊C₈	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	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
498	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
499	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
500	C₂²⋊C₈	C₂³×C₆₇	1	2	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	#97	C₂³×C₆₇	1	1	yes	characteristic
506	#97	C₂³×C₆₇	1	1	yes	characteristic
507	#97	C₂³×C₆₇	1	2	yes	—
508	#97	C₂³×C₆₇	1	2	yes	—
509	#97	C₂³×C₆₇	1	4	yes	—
510	#97	C₂³×C₆₇	1	2	yes	—
511	#97	C₂³×C₆₇	1	4	yes	—
512	#97	C₂³×C₆₇	1	4	yes	—
513	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
514	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₄×C₈	C₂³×C₆₇	1	2	yes	—
516	C₄×C₈	C₂³×C₆₇	1	2	yes	—
517	C₄×C₈	C₂³×C₆₇	1	4	yes	—
518	C₄×C₈	C₂³×C₆₇	1	2	yes	—
519	C₄×C₈	C₂³×C₆₇	1	4	yes	—
520	C₄×C₈	C₂³×C₆₇	1	4	yes	—
521	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
522	#41	—	2	4	no	—
523	#41	—	2	4	no	—
524	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
525	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
526	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
527	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
529	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
530	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
531	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
532	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
533	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
537	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
538	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
539	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
540	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
545	M₁₆	—	2	4	no	—
546	M₁₆	—	2	8	no	—
547	M₁₆	—	2	8	no	—
548	M₁₆	—	2	8	no	—
549	M₁₆	#41×C₆₇	1	8	yes	—
550	C₂×C₈	—	2	4	no	—
551	C₂×C₈	—	2	4	no	—
552	C₂×C₈	—	2	8	no	—
553	C₂×C₈	—	2	8	no	—
554	C₂×C₈	—	2	8	no	—
555	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
556	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
557	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
558	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
559	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
560	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
562	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
563	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
564	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
565	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
566	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
570	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
585	C₂²⋊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	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
590	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
593	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
594	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
595	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
596	C₄²	C₂⁴×C₆₇	1	2	yes	—
597	C₄²	C₂⁴×C₆₇	1	2	yes	—
598	C₄²	C₂⁴×C₆₇	1	2	yes	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
602	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
603	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
604	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	4	4	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	4	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	D₄	—	4	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
627	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
628	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
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	2	yes	—
633	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
636	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₈	—	2	4	no	—
642	C₈	C₂×#41×C₆₇	1	8	yes	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	C₄×#41×C₆₇	1	2	yes	—
653	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	C₄×#41×C₆₇	1	2	yes	—
664	C₄	C₂²×#41×C₆₇	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	2	no	—
669	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
670	C₂	C₆₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3455	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×#2969	C₂	semidirect
3. C₆₇×#2968	C₂	semidirect
4. C₆₇×#2967	C₂	semidirect
5. C₆₇×#2966	C₂	semidirect
6. C₆₇×#2962	C₂	semidirect
7. C₆₇×#2935	C₂	semidirect
8. C₆₇×#2933	C₂	semidirect
9. C₆₇×#2933	C₂	semidirect
10. C₆₇×#2923	C₂	semidirect
11. C₆₇×#2922	C₂	semidirect
12. C₂×#433×C₆₇	C₂	semidirect
13. C₆₇×#2875	C₂	semidirect
14. C₄×#131×C₆₇	C₂	semidirect
15. C₆₇×#2873	C₂	semidirect
34. #446×C₆₇	C₂²	semidirect
35. #446×C₆₇	C₂²	semidirect
36. #446×C₆₇	C₂²	semidirect
37. C₈×Q₈×C₆₇	C₂²	semidirect
40. #436×C₆₇	C₂²	semidirect
45. #435×C₆₇	C₂²	semidirect
46. #435×C₆₇	C₂²	semidirect
49. C₈×D₄×C₆₇	C₂²	semidirect
54. #433×C₆₇	C₂²	semidirect
55. #433×C₆₇	C₂²	semidirect
56. #433×C₆₇	C₂²	semidirect
57. #433×C₆₇	C₂²	semidirect
58. #432×C₆₇	C₂²	semidirect
59. #431×C₆₇	C₂²	semidirect
70. #405×C₆₇	C₂²	semidirect
71. #405×C₆₇	C₂²	semidirect
75. C₄×M₁₆×C₆₇	C₂²	semidirect
76. C₄×M₁₆×C₆₇	C₂²	semidirect
78. C₂×#97×C₆₇	C₂²	semidirect
80. C₂×C₄×C₈×C₆₇	C₂²	semidirect
329. #60212	C₆₇	direct (N × H)
337. #2969	C₂×C₆₇	semidirect
338. #2968	C₂×C₆₇	semidirect
339. #2967	C₂×C₆₇	semidirect
340. #2966	C₂×C₆₇	semidirect
341. #2962	C₂×C₆₇	semidirect
342. #2935	C₂×C₆₇	semidirect
343. #2933	C₂×C₆₇	semidirect
344. #2933	C₂×C₆₇	semidirect
345. #2923	C₂×C₆₇	semidirect
346. #2922	C₂×C₆₇	semidirect
347. C₂×#433	C₂×C₆₇	semidirect
348. #2875	C₂×C₆₇	semidirect
349. C₄×#131	C₂×C₆₇	semidirect
350. #2873	C₂×C₆₇	semidirect
351. C₆₇	#60212	direct (N × H)
370. #446	C₂²×C₆₇	semidirect
371. #446	C₂²×C₆₇	semidirect
372. #446	C₂²×C₆₇	semidirect
373. C₈×Q₈	C₂²×C₆₇	semidirect
376. #436	C₂²×C₆₇	semidirect
381. #435	C₂²×C₆₇	semidirect
382. #435	C₂²×C₆₇	semidirect
385. C₈×D₄	C₂²×C₆₇	semidirect
390. #433	C₂²×C₆₇	semidirect
391. #433	C₂²×C₆₇	semidirect
392. #433	C₂²×C₆₇	semidirect
393. #433	C₂²×C₆₇	semidirect
394. #432	C₂²×C₆₇	semidirect
395. #431	C₂²×C₆₇	semidirect
406. #405	C₂²×C₆₇	semidirect
407. #405	C₂²×C₆₇	semidirect
411. C₄×M₁₆	C₂²×C₆₇	semidirect
412. C₄×M₁₆	C₂²×C₆₇	semidirect
414. C₂×#97	C₂²×C₆₇	semidirect
416. C₂×C₄×C₈	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×#3455	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2962	2
C₆₇×#2935	2
C₆₇×#2933	2
C₆₇×#2923	2
C₆₇×#2922	2
C₂×#433×C₆₇	2
C₆₇×#2875	2
C₄×#131×C₆₇	2
C₆₇×#2873	2
#60212	67

Subgroups — C67×#60212 #30739463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60212 #30739463