Subgroups — C₆₇×#61377 #30740628

Order 17152.

1742 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3388	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3388	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3386	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3385	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3164	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3082	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3081	C₂	1	2	yes	maximal
11	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2949	C₂	1	2	yes	maximal
15	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
17	Q₈²×C₆₇	—	2	1	no	—
18	Q₈²×C₆₇	C₂²	1	2	yes	complemented
19	#557×C₆₇	—	2	1	no	—
20	#557×C₆₇	—	2	2	no	—
21	#557×C₆₇	C₂²	1	4	yes	complemented
22	#557×C₆₇	C₂²	1	2	yes	complemented
23	#554×C₆₇	—	2	1	no	—
24	#554×C₆₇	—	2	2	no	—
25	#554×C₆₇	C₂²	1	4	yes	—
26	#554×C₆₇	C₂²	1	2	yes	—
27	D₄×Q₈×C₆₇	—	2	1	no	—
28	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
29	#544×C₆₇	—	2	2	no	—
30	#544×C₆₇	C₂²	1	2	yes	—
31	#544×C₆₇	C₂²	1	2	yes	—
32	#543×C₆₇	—	2	2	no	—
33	#533×C₆₇	—	2	2	no	—
34	#533×C₆₇	C₂²	1	1	yes	characteristic
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
38	#519×C₆₇	C₂²	1	2	yes	—
39	#518×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	#501×C₆₇	C₂²	1	2	yes	complemented
43	#501×C₆₇	C₂²	1	4	yes	complemented
44	#501×C₆₇	C₂²	1	2	yes	complemented
45	#501×C₆₇	C₂²	1	4	yes	complemented
46	#501×C₆₇	C₂²	1	2	yes	complemented
47	#501×C₆₇	C₂²	1	2	yes	complemented
48	#500×C₆₇	C₂²	1	4	yes	complemented
49	#499×C₆₇	C₂²	1	4	yes	complemented
50	#479×C₆₇	C₂²	1	4	yes	complemented
51	#479×C₆₇	C₂²	1	4	yes	complemented
52	#479×C₆₇	C₂²	1	4	yes	complemented
53	#478×C₆₇	C₂²	1	4	yes	—
54	#478×C₆₇	C₂²	1	4	yes	—
55	#478×C₆₇	C₂²	1	4	yes	—
56	#477×C₆₇	C₂²	1	2	yes	complemented
57	#477×C₆₇	C₂²	1	4	yes	complemented
58	#476×C₆₇	C₂²	1	2	yes	—
59	#476×C₆₇	C₂²	1	4	yes	—
60	#475×C₆₇	C₂²	1	2	yes	complemented
61	#475×C₆₇	C₂²	1	4	yes	complemented
62	#474×C₆₇	C₂²	1	2	yes	—
63	#474×C₆₇	C₂²	1	4	yes	—
64	#446×C₆₇	C₂²	1	4	yes	complemented
65	#446×C₆₇	C₂²	1	4	yes	complemented
66	#440×C₆₇	C₂²	1	4	yes	—
67	#440×C₆₇	C₂²	1	4	yes	—
68	#440×C₆₇	C₂²	1	4	yes	—
69	#440×C₆₇	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
71	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
72	#428×C₆₇	C₂²	1	2	yes	—
73	#428×C₆₇	C₂²	1	2	yes	—
74	#427×C₆₇	C₂²	1	2	yes	—
75	#427×C₆₇	C₂²	1	2	yes	—
76	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
77	#424×C₆₇	C₂²	1	2	yes	—
78	#423×C₆₇	C₂²	1	1	yes	characteristic
79	#419×C₆₇	C₂²	1	2	yes	—
80	#418×C₆₇	C₂²	1	2	yes	—
81	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
83	#405×C₆₇	C₂²	1	2	yes	—
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₆₇	—	2	2	no	—
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	—	2	1	no	—
89	C₂×SD₁₆×C₆₇	Q₈	1	8	yes	complemented
90	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄⋊Q₈×C₆₇	—	2	2	no	—
95	C₄⋊Q₈×C₆₇	—	2	4	no	—
96	C₄⋊Q₈×C₆₇	—	2	2	no	—
97	C₄⋊Q₈×C₆₇	—	2	4	no	—
98	C₄⋊Q₈×C₆₇	—	2	2	no	—
99	C₄⋊Q₈×C₆₇	—	2	2	no	—
100	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
106	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	#125×C₆₇	—	2	4	no	—
109	#125×C₆₇	—	2	4	no	—
110	#125×C₆₇	—	2	4	no	—
111	#125×C₆₇	—	2	2	no	—
112	#125×C₆₇	—	2	2	no	—
113	#125×C₆₇	D₄	1	2	yes	—
114	#125×C₆₇	C₂³	1	4	yes	—
115	#125×C₆₇	C₂³	1	2	yes	—
116	#125×C₆₇	C₂³	1	4	yes	—
117	#125×C₆₇	C₂³	1	2	yes	—
118	C₂²⋊Q₈×C₆₇	—	2	2	no	—
119	C₂²⋊Q₈×C₆₇	—	2	4	no	—
120	C₂²⋊Q₈×C₆₇	—	2	1	no	—
121	C₂²⋊Q₈×C₆₇	—	2	1	no	—
122	C₂²⋊Q₈×C₆₇	—	2	1	no	—
123	C₂²⋊Q₈×C₆₇	—	2	1	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	4	no	—
126	C₂²⋊Q₈×C₆₇	—	2	4	no	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
133	C₄×Q₈×C₆₇	—	2	2	no	—
134	C₄×Q₈×C₆₇	—	2	2	no	—
135	C₄×Q₈×C₆₇	—	2	2	no	—
136	C₄×Q₈×C₆₇	—	2	4	no	—
137	C₄×Q₈×C₆₇	—	2	2	no	—
138	C₄×Q₈×C₆₇	—	2	1	no	—
139	C₄×Q₈×C₆₇	—	2	1	no	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	—	2	1	no	—
143	C₄×Q₈×C₆₇	—	2	1	no	—
144	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
145	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	1	no	—
153	C₄×D₄×C₆₇	—	2	1	no	—
154	C₄×D₄×C₆₇	C₂³	1	2	yes	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	C₄×D₄×C₆₇	C₂³	1	4	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	#117×C₆₇	—	2	4	no	—
159	#117×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	C₂³	1	2	yes	—
161	#117×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
163	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
164	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
169	C₂×C₄²×C₆₇	—	2	1	no	—
170	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
171	#107×C₆₇	C₂³	1	2	yes	—
172	#107×C₆₇	C₂³	1	4	yes	—
173	#107×C₆₇	C₂³	1	4	yes	—
174	#107×C₆₇	C₂³	1	2	yes	—
175	#107×C₆₇	C₂³	1	2	yes	—
176	#107×C₆₇	C₂³	1	4	yes	—
177	#107×C₆₇	C₂³	1	2	yes	—
178	#106×C₆₇	C₂³	1	2	yes	—
179	#106×C₆₇	C₂³	1	4	yes	—
180	#106×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	2	yes	—
182	#106×C₆₇	C₂³	1	2	yes	—
183	#106×C₆₇	C₂³	1	2	yes	—
184	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
185	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
186	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
188	#103×C₆₇	C₂³	1	4	yes	—
189	#103×C₆₇	C₂³	1	4	yes	—
190	#103×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	4	yes	—
194	#97×C₆₇	C₂³	1	2	yes	—
195	#97×C₆₇	C₂³	1	2	yes	—
196	#97×C₆₇	C₂³	1	4	yes	—
197	C₄×C₈×C₆₇	C₂³	1	4	yes	—
198	C₂⁴×C₆₇	—	2	1	no	—
199	C₂×Q₈×C₆₇	—	2	1	no	—
200	C₂×Q₈×C₆₇	—	2	1	no	—
201	C₂×Q₈×C₆₇	—	2	1	no	—
202	C₂×Q₈×C₆₇	—	2	1	no	—
203	C₂×Q₈×C₆₇	—	2	1	no	—
204	C₂×Q₈×C₆₇	—	2	4	no	—
205	C₂×Q₈×C₆₇	—	2	4	no	—
206	C₂×Q₈×C₆₇	—	2	2	no	—
207	C₂×Q₈×C₆₇	—	8	4	no	—
208	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₆₇	C₂×Q₈	1	4	yes	complemented
211	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
212	C₂×D₄×C₆₇	—	2	1	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
215	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	—	2	1	no	—
217	C₂²×C₄×C₆₇	—	2	1	no	—
218	C₂²×C₄×C₆₇	—	2	1	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	8	2	no	—
224	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	SD₁₆×C₆₇	C₂×Q₈	1	16	yes	complemented
228	M₁₆×C₆₇	—	2	4	no	—
229	C₂×C₈×C₆₇	—	2	2	no	—
230	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	complemented
231	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
232	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
233	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₆₇	—	2	2	no	—
235	C₄⋊C₄×C₆₇	—	2	1	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	2	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	1	no	—
242	C₄⋊C₄×C₆₇	—	2	1	no	—
243	C₄⋊C₄×C₆₇	—	2	4	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	1	no	—
247	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	2	no	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
273	C₄²×C₆₇	—	2	2	no	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	2	4	no	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	2	2	no	—
278	C₄²×C₆₇	—	2	2	no	—
279	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₄²×C₆₇	C₂⁴	1	4	yes	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	4	no	—
286	C₂³×C₆₇	—	8	1	no	—
287	C₂³×C₆₇	—	8	1	no	—
288	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₆₇	—	2	4	no	—
290	Q₈×C₆₇	—	2	2	no	—
291	Q₈×C₆₇	—	4	2	no	—
292	Q₈×C₆₇	—	4	2	no	—
293	Q₈×C₆₇	—	4	2	no	—
294	Q₈×C₆₇	—	4	2	no	—
295	Q₈×C₆₇	—	8	1	no	—
296	Q₈×C₆₇	—	8	4	no	—
297	Q₈×C₆₇	—	8	1	no	—
298	Q₈×C₆₇	—	8	4	no	—
299	Q₈×C₆₇	C₂²×Q₈	1	4	yes	—
300	D₄×C₆₇	—	2	4	no	—
301	D₄×C₆₇	—	2	2	no	—
302	D₄×C₆₇	C₂²×Q₈	1	4	yes	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	4	no	—
314	C₂×C₄×C₆₇	—	8	4	no	—
315	C₂×C₄×C₆₇	—	8	2	no	—
316	C₂×C₄×C₆₇	—	8	4	no	—
317	C₂×C₄×C₆₇	—	8	1	no	—
318	C₂×C₄×C₆₇	—	8	1	no	—
319	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
327	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
328	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
329	C₈×C₆₇	—	2	2	no	—
330	C₈×C₆₇	—	2	4	no	—
331	C₈×C₆₇	C₂²×Q₈	1	4	yes	—
332	C₂²×C₆₇	—	2	1	no	—
333	C₂²×C₆₇	—	2	1	no	—
334	C₂²×C₆₇	—	2	4	no	—
335	C₂²×C₆₇	—	4	2	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	8	4	no	—
338	C₂²×C₆₇	D₄×Q₈	1	2	yes	—
339	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
340	C₄×C₆₇	—	2	1	no	—
341	C₄×C₆₇	—	2	1	no	—
342	C₄×C₆₇	—	2	4	no	—
343	C₄×C₆₇	—	2	1	no	—
344	C₄×C₆₇	—	2	1	no	—
345	C₄×C₆₇	—	2	4	no	—
346	C₄×C₆₇	—	2	4	no	—
347	C₄×C₆₇	—	4	2	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	—	4	2	no	—
351	C₄×C₆₇	—	4	2	no	—
352	C₄×C₆₇	—	4	2	no	—
353	C₄×C₆₇	D₄×Q₈	1	2	yes	—
354	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
355	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	#61377	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂×C₆₇	—	2	2	no	—
358	C₂×C₆₇	—	4	4	no	—
359	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
360	C₂×C₆₇	#3585	1	1	yes	characteristic
361	C₂×C₆₇	#3586	1	1	yes	characteristic
362	#3502	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#3501	C₂×C₆₇	1	1	yes	characteristic
364	#3388	C₂×C₆₇	1	4	yes	complemented
365	#3388	C₂×C₆₇	1	4	yes	complemented
366	#3386	C₂×C₆₇	1	4	yes	complemented
367	#3385	C₂×C₆₇	1	4	yes	complemented
368	#3164	C₂×C₆₇	1	2	yes	complemented
369	#3162	C₂×C₆₇	1	1	yes	characteristic, complemented
370	#3082	C₂×C₆₇	1	2	yes	complemented
371	#3081	C₂×C₆₇	1	2	yes	—
372	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
373	#3077	C₂×C₆₇	1	1	yes	characteristic
374	#2961	C₂×C₆₇	1	1	yes	characteristic, complemented
375	#2949	C₂×C₆₇	1	2	yes	—
376	C₂×#440	C₂×C₆₇	1	1	yes	characteristic
377	C₆₇	#61377	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
379	Q₈²	—	2	1	no	—
380	Q₈²	C₂²×C₆₇	1	2	yes	complemented
381	#557	—	2	1	no	—
382	#557	—	2	2	no	—
383	#557	C₂²×C₆₇	1	4	yes	complemented
384	#557	C₂²×C₆₇	1	2	yes	complemented
385	#554	—	2	1	no	—
386	#554	—	2	2	no	—
387	#554	C₂²×C₆₇	1	4	yes	—
388	#554	C₂²×C₆₇	1	2	yes	—
389	D₄×Q₈	—	2	1	no	—
390	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
391	#544	—	2	2	no	—
392	#544	C₂²×C₆₇	1	2	yes	—
393	#544	C₂²×C₆₇	1	2	yes	—
394	#543	—	2	2	no	—
395	#533	—	2	2	no	—
396	#533	C₂²×C₆₇	1	1	yes	characteristic
397	#533	C₂²×C₆₇	1	1	yes	characteristic
398	#533	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×C₂²⋊Q₈	—	2	2	no	—
400	#519	C₂²×C₆₇	1	2	yes	—
401	#518	C₂²×C₆₇	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
404	#501	C₂²×C₆₇	1	2	yes	complemented
405	#501	C₂²×C₆₇	1	4	yes	complemented
406	#501	C₂²×C₆₇	1	2	yes	complemented
407	#501	C₂²×C₆₇	1	4	yes	complemented
408	#501	C₂²×C₆₇	1	2	yes	complemented
409	#501	C₂²×C₆₇	1	2	yes	complemented
410	#500	C₂²×C₆₇	1	4	yes	complemented
411	#499	C₂²×C₆₇	1	4	yes	complemented
412	#479	C₂²×C₆₇	1	4	yes	complemented
413	#479	C₂²×C₆₇	1	4	yes	complemented
414	#479	C₂²×C₆₇	1	4	yes	complemented
415	#478	C₂²×C₆₇	1	4	yes	—
416	#478	C₂²×C₆₇	1	4	yes	—
417	#478	C₂²×C₆₇	1	4	yes	—
418	#477	C₂²×C₆₇	1	2	yes	complemented
419	#477	C₂²×C₆₇	1	4	yes	complemented
420	#476	C₂²×C₆₇	1	2	yes	—
421	#476	C₂²×C₆₇	1	4	yes	—
422	#475	C₂²×C₆₇	1	2	yes	complemented
423	#475	C₂²×C₆₇	1	4	yes	complemented
424	#474	C₂²×C₆₇	1	2	yes	—
425	#474	C₂²×C₆₇	1	4	yes	—
426	#446	C₂²×C₆₇	1	4	yes	complemented
427	#446	C₂²×C₆₇	1	4	yes	complemented
428	#440	C₂²×C₆₇	1	4	yes	—
429	#440	C₂²×C₆₇	1	4	yes	—
430	#440	C₂²×C₆₇	1	4	yes	—
431	#440	C₂²×C₆₇	1	4	yes	—
432	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
433	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
434	#428	C₂²×C₆₇	1	2	yes	—
435	#428	C₂²×C₆₇	1	2	yes	—
436	#427	C₂²×C₆₇	1	2	yes	—
437	#427	C₂²×C₆₇	1	2	yes	—
438	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
439	#424	C₂²×C₆₇	1	2	yes	—
440	#423	C₂²×C₆₇	1	1	yes	characteristic
441	#419	C₂²×C₆₇	1	2	yes	—
442	#418	C₂²×C₆₇	1	2	yes	—
443	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
445	#405	C₂²×C₆₇	1	2	yes	—
446	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
450	C₂³×C₄	—	2	1	no	—
451	C₂×SD₁₆	Q₈×C₆₇	1	8	yes	complemented
452	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
453	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
454	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	4	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	—	2	4	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
463	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
469	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
470	#125	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	—	2	4	no	—
473	#125	—	2	2	no	—
474	#125	—	2	2	no	—
475	#125	D₄×C₆₇	1	2	yes	—
476	#125	C₂³×C₆₇	1	2	yes	—
477	#125	C₂³×C₆₇	1	2	yes	—
478	#125	C₂³×C₆₇	1	4	yes	—
479	#125	C₂³×C₆₇	1	4	yes	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
494	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
507	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
508	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
509	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
510	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
511	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	C₂³×C₆₇	1	2	yes	—
517	C₄×D₄	C₂³×C₆₇	1	2	yes	—
518	C₄×D₄	C₂³×C₆₇	1	4	yes	—
519	C₄×D₄	C₂³×C₆₇	1	4	yes	—
520	#117	—	2	4	no	—
521	#117	C₂³×C₆₇	1	2	yes	—
522	#117	C₂³×C₆₇	1	2	yes	—
523	#117	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
533	#107	C₂³×C₆₇	1	4	yes	—
534	#107	C₂³×C₆₇	1	2	yes	—
535	#107	C₂³×C₆₇	1	2	yes	—
536	#107	C₂³×C₆₇	1	2	yes	—
537	#107	C₂³×C₆₇	1	2	yes	—
538	#107	C₂³×C₆₇	1	4	yes	—
539	#107	C₂³×C₆₇	1	4	yes	—
540	#106	C₂³×C₆₇	1	2	yes	—
541	#106	C₂³×C₆₇	1	2	yes	—
542	#106	C₂³×C₆₇	1	2	yes	—
543	#106	C₂³×C₆₇	1	2	yes	—
544	#106	C₂³×C₆₇	1	4	yes	—
545	#106	C₂³×C₆₇	1	4	yes	—
546	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
547	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
548	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
549	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
550	#103	C₂³×C₆₇	1	4	yes	—
551	#103	C₂³×C₆₇	1	4	yes	—
552	#103	C₂³×C₆₇	1	4	yes	—
553	#102	C₂³×C₆₇	1	4	yes	—
554	#102	C₂³×C₆₇	1	4	yes	—
555	#102	C₂³×C₆₇	1	4	yes	—
556	#97	C₂³×C₆₇	1	2	yes	—
557	#97	C₂³×C₆₇	1	2	yes	—
558	#97	C₂³×C₆₇	1	4	yes	—
559	C₄×C₈	C₂³×C₆₇	1	4	yes	—
560	C₂⁴	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
571	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
572	C₂×Q₈	C₂×Q₈×C₆₇	1	4	yes	complemented
573	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
577	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
589	SD₁₆	C₂×Q₈×C₆₇	1	16	yes	complemented
590	M₁₆	—	2	4	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	complemented
593	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
594	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
595	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
618	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
621	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
643	C₄²	C₂⁴×C₆₇	1	4	yes	—
644	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
645	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	8	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
651	Q₈	—	2	4	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	4	no	—
658	Q₈	—	8	1	no	—
659	Q₈	—	8	4	no	—
660	Q₈	—	8	1	no	—
661	Q₈	C₂²×Q₈×C₆₇	1	4	yes	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	C₂²×Q₈×C₆₇	1	4	yes	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	1	no	—
680	C₂×C₄	—	8	1	no	—
681	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
685	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
688	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
689	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
690	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	4	no	—
693	C₈	C₂²×Q₈×C₆₇	1	4	yes	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	8	4	no	—
700	C₂²	D₄×Q₈×C₆₇	1	2	yes	—
701	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	D₄×Q₈×C₆₇	1	2	yes	—
716	C₄	C₂³×Q₈×C₆₇	1	1	yes	characteristic
717	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	4	no	—
720	C₂	C₂×D₄×Q₈×C₆₇	1	1	yes	characteristic
721	C₂	C₆₇×#3585	1	1	yes	characteristic
722	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3502	C₂	semidirect
3. C₆₇×#3388	C₂	semidirect
4. C₆₇×#3388	C₂	semidirect
5. C₆₇×#3386	C₂	semidirect
6. C₆₇×#3385	C₂	semidirect
7. C₆₇×#3164	C₂	semidirect
8. C₆₇×#3162	C₂	semidirect
9. C₆₇×#3082	C₂	semidirect
11. C₆₇×#3078	C₂	semidirect
13. C₆₇×#2961	C₂	semidirect
18. Q₈²×C₆₇	C₂²	semidirect
21. #557×C₆₇	C₂²	semidirect
22. #557×C₆₇	C₂²	semidirect
42. #501×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #501×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #501×C₆₇	C₂²	semidirect
48. #500×C₆₇	C₂²	semidirect
49. #499×C₆₇	C₂²	semidirect
50. #479×C₆₇	C₂²	semidirect
51. #479×C₆₇	C₂²	semidirect
52. #479×C₆₇	C₂²	semidirect
56. #477×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #475×C₆₇	C₂²	semidirect
64. #446×C₆₇	C₂²	semidirect
65. #446×C₆₇	C₂²	semidirect
89. C₂×SD₁₆×C₆₇	Q₈	semidirect
210. C₂×Q₈×C₆₇	C₂×Q₈	semidirect
227. SD₁₆×C₆₇	C₂×Q₈	semidirect
230. C₂×C₈×C₆₇	C₂×Q₈	semidirect
356. #61377	C₆₇	direct (N × H)
362. #3502	C₂×C₆₇	semidirect
364. #3388	C₂×C₆₇	semidirect
365. #3388	C₂×C₆₇	semidirect
366. #3386	C₂×C₆₇	semidirect
367. #3385	C₂×C₆₇	semidirect
368. #3164	C₂×C₆₇	semidirect
369. #3162	C₂×C₆₇	semidirect
370. #3082	C₂×C₆₇	semidirect
372. #3078	C₂×C₆₇	semidirect
374. #2961	C₂×C₆₇	semidirect
377. C₆₇	#61377	direct (N × H)
380. Q₈²	C₂²×C₆₇	semidirect
383. #557	C₂²×C₆₇	semidirect
384. #557	C₂²×C₆₇	semidirect
404. #501	C₂²×C₆₇	semidirect
405. #501	C₂²×C₆₇	semidirect
406. #501	C₂²×C₆₇	semidirect
407. #501	C₂²×C₆₇	semidirect
408. #501	C₂²×C₆₇	semidirect
409. #501	C₂²×C₆₇	semidirect
410. #500	C₂²×C₆₇	semidirect
411. #499	C₂²×C₆₇	semidirect
412. #479	C₂²×C₆₇	semidirect
413. #479	C₂²×C₆₇	semidirect
414. #479	C₂²×C₆₇	semidirect
418. #477	C₂²×C₆₇	semidirect
419. #477	C₂²×C₆₇	semidirect
422. #475	C₂²×C₆₇	semidirect
423. #475	C₂²×C₆₇	semidirect
426. #446	C₂²×C₆₇	semidirect
427. #446	C₂²×C₆₇	semidirect
451. C₂×SD₁₆	Q₈×C₆₇	semidirect
572. C₂×Q₈	C₂×Q₈×C₆₇	semidirect
589. SD₁₆	C₂×Q₈×C₆₇	semidirect
592. C₂×C₈	C₂×Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3502	2
C₆₇×#3501	2
C₆₇×#3388	2
C₆₇×#3386	2
C₆₇×#3385	2
C₆₇×#3164	2
C₆₇×#3162	2
C₆₇×#3082	2
C₆₇×#3081	2
C₆₇×#3078	2
C₆₇×#3077	2
C₆₇×#2961	2
C₆₇×#2949	2
C₂×#440×C₆₇	2
#61377	67

Subgroups — C67×#61377 #30740628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61377 #30740628