Subgroups — C₆₇×#61332 #30740583

Order 17152.

1862 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3376	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3373	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3370	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3366	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3084	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3041	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
15	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
17	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
18	#559×C₆₇	C₂²	1	4	yes	complemented
19	#556×C₆₇	C₂²	1	2	yes	complemented
20	#555×C₆₇	—	2	1	no	—
21	#554×C₆₇	—	2	1	no	—
22	#554×C₆₇	—	2	2	no	—
23	#554×C₆₇	C₂²	1	4	yes	complemented
24	#554×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	—	2	2	no	—
26	#550×C₆₇	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₆₇	—	2	1	no	—
28	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
29	#547×C₆₇	—	2	1	no	—
30	#544×C₆₇	C₂²	1	2	yes	—
31	#543×C₆₇	—	2	2	no	—
32	#538×C₆₇	—	2	2	no	—
33	#535×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	C₂²	1	1	yes	characteristic
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	#532×C₆₇	C₂²	1	1	yes	characteristic
37	#525×C₆₇	—	2	2	no	—
38	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
39	#520×C₆₇	C₂²	1	2	yes	—
40	#518×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#491×C₆₇	C₂²	1	2	yes	complemented
44	#490×C₆₇	C₂²	1	2	yes	complemented
45	#490×C₆₇	C₂²	1	4	yes	complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#489×C₆₇	C₂²	1	2	yes	complemented
48	#489×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#486×C₆₇	C₂²	1	4	yes	complemented
51	#479×C₆₇	C₂²	1	4	yes	complemented
52	#478×C₆₇	C₂²	1	4	yes	complemented
53	#478×C₆₇	C₂²	1	4	yes	complemented
54	#476×C₆₇	C₂²	1	2	yes	complemented
55	#476×C₆₇	C₂²	1	4	yes	complemented
56	#475×C₆₇	C₂²	1	4	yes	complemented
57	#474×C₆₇	C₂²	1	2	yes	complemented
58	#463×C₆₇	C₂²	1	4	yes	—
59	#463×C₆₇	C₂²	1	4	yes	—
60	#463×C₆₇	C₂²	1	4	yes	complemented
61	#461×C₆₇	C₂²	1	2	yes	complemented
62	#459×C₆₇	C₂²	1	4	yes	—
63	#459×C₆₇	C₂²	1	4	yes	—
64	#459×C₆₇	C₂²	1	2	yes	complemented
65	#446×C₆₇	C₂²	1	4	yes	complemented
66	#446×C₆₇	C₂²	1	4	yes	complemented
67	#442×C₆₇	C₂²	1	4	yes	—
68	#442×C₆₇	C₂²	1	4	yes	—
69	#442×C₆₇	C₂²	1	4	yes	complemented
70	#440×C₆₇	C₂²	1	4	yes	complemented
71	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
72	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
73	#428×C₆₇	C₂²	1	2	yes	—
74	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
75	#424×C₆₇	C₂²	1	2	yes	—
76	#423×C₆₇	C₂²	1	1	yes	characteristic
77	#418×C₆₇	C₂²	1	2	yes	—
78	#417×C₆₇	C₂²	1	2	yes	—
79	#416×C₆₇	C₂²	1	2	yes	—
80	#416×C₆₇	C₂²	1	2	yes	—
81	C₂×#102×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	C₂×#41×C₆₇	—	2	2	no	—
86	C₂×#41×C₆₇	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	—	2	1	no	—
92	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
93	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
94	C₂×D₈×C₆₇	—	2	4	no	—
95	C₂×D₈×C₆₇	C₂³	1	4	yes	—
96	C₂×D₈×C₆₇	C₂³	1	4	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₇	—	2	2	no	—
101	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	#127×C₆₇	C₂³	1	4	yes	—
108	#127×C₆₇	C₂³	1	1	yes	characteristic
109	#126×C₆₇	—	2	4	no	—
110	#125×C₆₇	—	2	2	no	—
111	#125×C₆₇	D₄	1	2	yes	—
112	#125×C₆₇	C₂³	1	2	yes	—
113	#125×C₆₇	C₂³	1	4	yes	—
114	#124×C₆₇	—	2	4	no	—
115	#124×C₆₇	C₂³	1	4	yes	—
116	#124×C₆₇	C₂³	1	2	yes	—
117	#123×C₆₇	—	2	4	no	—
118	#123×C₆₇	—	2	4	no	—
119	C₂²⋊Q₈×C₆₇	—	2	2	no	—
120	C₂²⋊Q₈×C₆₇	—	2	2	no	—
121	C₂²⋊Q₈×C₆₇	—	2	4	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	D₄	1	2	yes	—
131	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
132	#121×C₆₇	—	2	1	no	—
133	#121×C₆₇	—	2	1	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	4	no	—
138	#120×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	—	2	1	no	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
142	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
143	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
144	C₄×D₄×C₆₇	—	2	2	no	—
145	C₄×D₄×C₆₇	—	2	2	no	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	4	no	—
148	C₄×D₄×C₆₇	—	2	1	no	—
149	C₄×D₄×C₆₇	—	2	1	no	—
150	C₄×D₄×C₆₇	—	2	1	no	—
151	C₄×D₄×C₆₇	—	2	1	no	—
152	C₄×D₄×C₆₇	—	2	1	no	—
153	C₄×D₄×C₆₇	—	2	1	no	—
154	C₄×D₄×C₆₇	C₂³	1	4	yes	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	C₄×D₄×C₆₇	C₂³	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	4	yes	—
160	C₄×D₄×C₆₇	C₂³	1	2	yes	—
161	#117×C₆₇	—	2	2	no	—
162	#117×C₆₇	—	2	2	no	—
163	#117×C₆₇	C₂³	1	2	yes	—
164	#117×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
166	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	#107×C₆₇	C₂³	1	4	yes	—
175	#106×C₆₇	C₂³	1	4	yes	—
176	#106×C₆₇	C₂³	1	4	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
178	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
181	#103×C₆₇	C₂³	1	4	yes	—
182	#103×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#102×C₆₇	C₂³	1	2	yes	—
187	#102×C₆₇	C₂³	1	2	yes	—
188	#102×C₆₇	C₂³	1	4	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	#102×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	2	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	2	yes	—
194	#102×C₆₇	C₂³	1	4	yes	—
195	#97×C₆₇	C₂³	1	2	yes	—
196	#97×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	4	yes	—
199	C₂⁴×C₆₇	—	2	1	no	—
200	C₂⁴×C₆₇	—	2	1	no	—
201	#41×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	2	4	no	—
203	#41×C₆₇	—	8	4	no	—
204	C₂×Q₈×C₆₇	—	2	1	no	—
205	C₂×Q₈×C₆₇	—	2	1	no	—
206	C₂×Q₈×C₆₇	—	2	4	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	C₂⁴	1	2	yes	—
211	C₂×D₄×C₆₇	—	2	2	no	—
212	C₂×D₄×C₆₇	—	2	1	no	—
213	C₂×D₄×C₆₇	—	2	1	no	—
214	C₂×D₄×C₆₇	—	2	1	no	—
215	C₂×D₄×C₆₇	—	2	4	no	—
216	C₂×D₄×C₆₇	—	2	1	no	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	—	2	2	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	#41	1	4	yes	complemented
222	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	—	2	1	no	—
226	C₂²×C₄×C₆₇	—	2	1	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	2	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	8	2	no	—
236	C₂²×C₄×C₆₇	—	8	2	no	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₆₇	—	2	8	no	—
241	D₈×C₆₇	—	2	8	no	—
242	D₈×C₆₇	—	2	8	no	—
243	M₁₆×C₆₇	—	2	4	no	—
244	C₂×C₈×C₆₇	—	2	2	no	—
245	C₂×C₈×C₆₇	—	2	2	no	—
246	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
248	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	1	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
267	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₆₇	—	2	2	no	—
272	C₂²⋊C₄×C₆₇	—	2	2	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	2	no	—
276	C₂²⋊C₄×C₆₇	—	2	2	no	—
277	C₂²⋊C₄×C₆₇	—	2	2	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	2	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	—	2	2	no	—
283	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	2	no	—
286	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₄²×C₆₇	C₂⁴	1	4	yes	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	4	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	4	2	no	—
296	C₂³×C₆₇	—	8	1	no	—
297	C₂³×C₆₇	—	8	1	no	—
298	C₂³×C₆₇	—	8	1	no	—
299	C₂³×C₆₇	—	8	1	no	—
300	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₆₇	—	2	2	no	—
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	4	2	no	—
304	Q₈×C₆₇	—	4	2	no	—
305	Q₈×C₆₇	—	4	2	no	—
306	Q₈×C₆₇	—	8	1	no	—
307	Q₈×C₆₇	—	8	4	no	—
308	D₄×C₆₇	—	2	4	no	—
309	D₄×C₆₇	—	2	2	no	—
310	D₄×C₆₇	—	2	2	no	—
311	D₄×C₆₇	—	2	2	no	—
312	D₄×C₆₇	—	2	2	no	—
313	D₄×C₆₇	—	2	2	no	—
314	D₄×C₆₇	—	4	2	no	—
315	D₄×C₆₇	—	4	4	no	—
316	D₄×C₆₇	—	4	2	no	—
317	D₄×C₆₇	—	8	1	no	—
318	D₄×C₆₇	—	8	4	no	—
319	D₄×C₆₇	—	8	4	no	—
320	D₄×C₆₇	C₂×#41	1	4	yes	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	4	1	no	—
327	C₂×C₄×C₆₇	—	4	1	no	—
328	C₂×C₄×C₆₇	—	4	4	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	—	8	4	no	—
332	C₂×C₄×C₆₇	—	8	2	no	—
333	C₂×C₄×C₆₇	—	8	2	no	—
334	C₂×C₄×C₆₇	—	8	4	no	—
335	C₂×C₄×C₆₇	—	8	4	no	—
336	C₂×C₄×C₆₇	—	8	1	no	—
337	C₂×C₄×C₆₇	—	8	1	no	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
347	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
348	C₈×C₆₇	—	2	2	no	—
349	C₈×C₆₇	—	2	4	no	—
350	C₈×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	1	no	—
352	C₂²×C₆₇	—	2	1	no	—
353	C₂²×C₆₇	—	2	4	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	—	4	2	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	8	4	no	—
363	C₂²×C₆₇	—	8	4	no	—
364	C₂²×C₆₇	#548	1	2	yes	—
365	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₆₇	—	2	1	no	—
367	C₄×C₆₇	—	2	1	no	—
368	C₄×C₆₇	—	2	1	no	—
369	C₄×C₆₇	—	2	1	no	—
370	C₄×C₆₇	—	2	4	no	—
371	C₄×C₆₇	—	2	4	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	#548	1	2	yes	—
378	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
379	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
380	#61332	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₆₇	—	2	2	no	—
382	C₂×C₆₇	—	4	4	no	—
383	C₂×C₆₇	—	8	2	no	—
384	C₂×C₆₇	—	8	2	no	—
385	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
386	C₂×C₆₇	#3585	1	1	yes	characteristic
387	C₂×C₆₇	#3585	1	1	yes	characteristic
388	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
390	#3376	C₂×C₆₇	1	4	yes	complemented
391	#3373	C₂×C₆₇	1	4	yes	complemented
392	#3370	C₂×C₆₇	1	4	yes	complemented
393	#3366	C₂×C₆₇	1	4	yes	complemented
394	#3136	C₂×C₆₇	1	2	yes	complemented
395	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#3084	C₂×C₆₇	1	2	yes	complemented
397	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#3041	C₂×C₆₇	1	2	yes	complemented
399	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#2961	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#2946	C₂×C₆₇	1	2	yes	complemented
402	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₆₇	#61332	1	1	yes	characteristic, direct product factor, Sylow
404	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
405	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
406	#559	C₂²×C₆₇	1	4	yes	complemented
407	#556	C₂²×C₆₇	1	2	yes	complemented
408	#555	—	2	1	no	—
409	#554	—	2	1	no	—
410	#554	—	2	2	no	—
411	#554	C₂²×C₆₇	1	4	yes	complemented
412	#554	C₂²×C₆₇	1	2	yes	complemented
413	#553	—	2	2	no	—
414	#550	C₂²×C₆₇	1	2	yes	complemented
415	D₄×Q₈	—	2	1	no	—
416	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
417	#547	—	2	1	no	—
418	#544	C₂²×C₆₇	1	2	yes	—
419	#543	—	2	2	no	—
420	#538	—	2	2	no	—
421	#535	C₂²×C₆₇	1	2	yes	—
422	#533	C₂²×C₆₇	1	1	yes	characteristic
423	#533	C₂²×C₆₇	1	1	yes	characteristic
424	#532	C₂²×C₆₇	1	1	yes	characteristic
425	#525	—	2	2	no	—
426	C₂×C₂²⋊Q₈	—	2	2	no	—
427	#520	C₂²×C₆₇	1	2	yes	—
428	#518	C₂²×C₆₇	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
431	#491	C₂²×C₆₇	1	2	yes	complemented
432	#490	C₂²×C₆₇	1	2	yes	complemented
433	#490	C₂²×C₆₇	1	4	yes	complemented
434	#489	C₂²×C₆₇	1	2	yes	complemented
435	#489	C₂²×C₆₇	1	2	yes	complemented
436	#489	C₂²×C₆₇	1	4	yes	complemented
437	#488	C₂²×C₆₇	1	4	yes	complemented
438	#486	C₂²×C₆₇	1	4	yes	complemented
439	#479	C₂²×C₆₇	1	4	yes	complemented
440	#478	C₂²×C₆₇	1	4	yes	complemented
441	#478	C₂²×C₆₇	1	4	yes	complemented
442	#476	C₂²×C₆₇	1	2	yes	complemented
443	#476	C₂²×C₆₇	1	4	yes	complemented
444	#475	C₂²×C₆₇	1	4	yes	complemented
445	#474	C₂²×C₆₇	1	2	yes	complemented
446	#463	C₂²×C₆₇	1	4	yes	—
447	#463	C₂²×C₆₇	1	4	yes	—
448	#463	C₂²×C₆₇	1	4	yes	complemented
449	#461	C₂²×C₆₇	1	2	yes	complemented
450	#459	C₂²×C₆₇	1	4	yes	—
451	#459	C₂²×C₆₇	1	4	yes	—
452	#459	C₂²×C₆₇	1	2	yes	complemented
453	#446	C₂²×C₆₇	1	4	yes	complemented
454	#446	C₂²×C₆₇	1	4	yes	complemented
455	#442	C₂²×C₆₇	1	4	yes	—
456	#442	C₂²×C₆₇	1	4	yes	—
457	#442	C₂²×C₆₇	1	4	yes	complemented
458	#440	C₂²×C₆₇	1	4	yes	complemented
459	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
460	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
461	#428	C₂²×C₆₇	1	2	yes	—
462	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
463	#424	C₂²×C₆₇	1	2	yes	—
464	#423	C₂²×C₆₇	1	1	yes	characteristic
465	#418	C₂²×C₆₇	1	2	yes	—
466	#417	C₂²×C₆₇	1	2	yes	—
467	#416	C₂²×C₆₇	1	2	yes	—
468	#416	C₂²×C₆₇	1	2	yes	—
469	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
471	#405	C₂²×C₆₇	1	2	yes	—
472	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#41	—	2	2	no	—
474	C₂×#41	C₂³×C₆₇	1	2	yes	—
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	AGL(1,ℤ/8)	—	2	8	no	—
481	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
482	C₂×D₈	—	2	4	no	—
483	C₂×D₈	C₂³×C₆₇	1	4	yes	—
484	C₂×D₈	C₂³×C₆₇	1	4	yes	—
485	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
486	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
488	C₄⋊Q₈	—	2	2	no	—
489	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
490	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
495	#127	C₂³×C₆₇	1	1	yes	characteristic
496	#127	C₂³×C₆₇	1	4	yes	—
497	#126	—	2	4	no	—
498	#125	—	2	2	no	—
499	#125	D₄×C₆₇	1	2	yes	—
500	#125	C₂³×C₆₇	1	2	yes	—
501	#125	C₂³×C₆₇	1	4	yes	—
502	#124	—	2	4	no	—
503	#124	C₂³×C₆₇	1	2	yes	—
504	#124	C₂³×C₆₇	1	4	yes	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
519	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
520	#121	—	2	1	no	—
521	#121	—	2	1	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	4	no	—
526	#120	—	2	4	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
530	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
531	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	C₂³×C₆₇	1	2	yes	—
543	C₄×D₄	C₂³×C₆₇	1	2	yes	—
544	C₄×D₄	C₂³×C₆₇	1	2	yes	—
545	C₄×D₄	C₂³×C₆₇	1	2	yes	—
546	C₄×D₄	C₂³×C₆₇	1	4	yes	—
547	C₄×D₄	C₂³×C₆₇	1	4	yes	—
548	C₄×D₄	C₂³×C₆₇	1	4	yes	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	C₂³×C₆₇	1	2	yes	—
552	#117	C₂³×C₆₇	1	2	yes	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	4	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
562	#107	C₂³×C₆₇	1	4	yes	—
563	#106	C₂³×C₆₇	1	4	yes	—
564	#106	C₂³×C₆₇	1	4	yes	—
565	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
566	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
567	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
568	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
569	#103	C₂³×C₆₇	1	2	yes	—
570	#103	C₂³×C₆₇	1	2	yes	—
571	#103	C₂³×C₆₇	1	2	yes	—
572	#103	C₂³×C₆₇	1	2	yes	—
573	#103	C₂³×C₆₇	1	4	yes	—
574	#102	C₂³×C₆₇	1	4	yes	—
575	#102	C₂³×C₆₇	1	4	yes	—
576	#102	C₂³×C₆₇	1	2	yes	—
577	#102	C₂³×C₆₇	1	2	yes	—
578	#102	C₂³×C₆₇	1	2	yes	—
579	#102	C₂³×C₆₇	1	2	yes	—
580	#102	C₂³×C₆₇	1	4	yes	—
581	#102	C₂³×C₆₇	1	4	yes	—
582	#102	C₂³×C₆₇	1	4	yes	—
583	#97	C₂³×C₆₇	1	2	yes	—
584	#97	C₂³×C₆₇	1	2	yes	—
585	#97	C₂³×C₆₇	1	4	yes	—
586	C₄×C₈	C₂³×C₆₇	1	4	yes	—
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	2	1	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	8	4	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	8	4	no	—
596	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
597	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
598	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	#41×C₆₇	1	4	yes	complemented
610	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	2	no	—
624	C₂²×C₄	—	8	2	no	—
625	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	SD₁₆	—	2	8	no	—
629	D₈	—	2	8	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	4	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
635	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
636	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
676	C₄²	C₂⁴×C₆₇	1	4	yes	—
677	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	—	8	1	no	—
687	C₂³	—	8	1	no	—
688	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	—	8	4	no	—
695	Q₈	—	8	1	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	1	no	—
707	D₄	—	8	4	no	—
708	D₄	C₂×#41×C₆₇	1	4	yes	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	1	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
734	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
735	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	4	no	—
738	C₈	—	2	2	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	8	4	no	—
751	C₂²	—	8	4	no	—
752	C₂²	#548×C₆₇	1	2	yes	—
753	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	#548×C₆₇	1	2	yes	—
766	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
767	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	4	no	—
770	C₂	—	8	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
773	C₂	C₆₇×#3585	1	1	yes	characteristic
774	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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×#3506	C₂	semidirect
2. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3376	C₂	semidirect
4. C₆₇×#3373	C₂	semidirect
5. C₆₇×#3370	C₂	semidirect
6. C₆₇×#3366	C₂	semidirect
7. C₆₇×#3136	C₂	semidirect
8. C₆₇×#3135	C₂	semidirect
9. C₆₇×#3084	C₂	semidirect
10. C₆₇×#3077	C₂	semidirect
11. C₆₇×#3041	C₂	semidirect
12. C₆₇×#3036	C₂	semidirect
13. C₆₇×#2961	C₂	semidirect
14. C₆₇×#2946	C₂	semidirect
15. C₂×#442×C₆₇	C₂	semidirect
18. #559×C₆₇	C₂²	semidirect
19. #556×C₆₇	C₂²	semidirect
23. #554×C₆₇	C₂²	semidirect
24. #554×C₆₇	C₂²	semidirect
26. #550×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
43. #491×C₆₇	C₂²	semidirect
44. #490×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #489×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #486×C₆₇	C₂²	semidirect
51. #479×C₆₇	C₂²	semidirect
52. #478×C₆₇	C₂²	semidirect
53. #478×C₆₇	C₂²	semidirect
54. #476×C₆₇	C₂²	semidirect
55. #476×C₆₇	C₂²	semidirect
56. #475×C₆₇	C₂²	semidirect
57. #474×C₆₇	C₂²	semidirect
60. #463×C₆₇	C₂²	semidirect
61. #461×C₆₇	C₂²	semidirect
64. #459×C₆₇	C₂²	semidirect
65. #446×C₆₇	C₂²	semidirect
66. #446×C₆₇	C₂²	semidirect
69. #442×C₆₇	C₂²	semidirect
70. #440×C₆₇	C₂²	semidirect
71. C₄×SD₁₆×C₆₇	C₂²	semidirect
72. C₄×D₈×C₆₇	C₂²	semidirect
221. C₂×D₄×C₆₇	#41	semidirect
380. #61332	C₆₇	direct (N × H)
388. #3506	C₂×C₆₇	semidirect
389. #3501	C₂×C₆₇	semidirect
390. #3376	C₂×C₆₇	semidirect
391. #3373	C₂×C₆₇	semidirect
392. #3370	C₂×C₆₇	semidirect
393. #3366	C₂×C₆₇	semidirect
394. #3136	C₂×C₆₇	semidirect
395. #3135	C₂×C₆₇	semidirect
396. #3084	C₂×C₆₇	semidirect
397. #3077	C₂×C₆₇	semidirect
398. #3041	C₂×C₆₇	semidirect
399. #3036	C₂×C₆₇	semidirect
400. #2961	C₂×C₆₇	semidirect
401. #2946	C₂×C₆₇	semidirect
402. C₂×#442	C₂×C₆₇	semidirect
403. C₆₇	#61332	direct (N × H)
406. #559	C₂²×C₆₇	semidirect
407. #556	C₂²×C₆₇	semidirect
411. #554	C₂²×C₆₇	semidirect
412. #554	C₂²×C₆₇	semidirect
414. #550	C₂²×C₆₇	semidirect
416. D₄×Q₈	C₂²×C₆₇	semidirect
431. #491	C₂²×C₆₇	semidirect
432. #490	C₂²×C₆₇	semidirect
433. #490	C₂²×C₆₇	semidirect
434. #489	C₂²×C₆₇	semidirect
435. #489	C₂²×C₆₇	semidirect
436. #489	C₂²×C₆₇	semidirect
437. #488	C₂²×C₆₇	semidirect
438. #486	C₂²×C₆₇	semidirect
439. #479	C₂²×C₆₇	semidirect
440. #478	C₂²×C₆₇	semidirect
441. #478	C₂²×C₆₇	semidirect
442. #476	C₂²×C₆₇	semidirect
443. #476	C₂²×C₆₇	semidirect
444. #475	C₂²×C₆₇	semidirect
445. #474	C₂²×C₆₇	semidirect
448. #463	C₂²×C₆₇	semidirect
449. #461	C₂²×C₆₇	semidirect
452. #459	C₂²×C₆₇	semidirect
453. #446	C₂²×C₆₇	semidirect
454. #446	C₂²×C₆₇	semidirect
457. #442	C₂²×C₆₇	semidirect
458. #440	C₂²×C₆₇	semidirect
459. C₄×SD₁₆	C₂²×C₆₇	semidirect
460. C₄×D₈	C₂²×C₆₇	semidirect
609. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₆₇×#3501	2
C₆₇×#3376	2
C₆₇×#3373	2
C₆₇×#3370	2
C₆₇×#3366	2
C₆₇×#3136	2
C₆₇×#3135	2
C₆₇×#3084	2
C₆₇×#3077	2
C₆₇×#3041	2
C₆₇×#3036	2
C₆₇×#2961	2
C₆₇×#2946	2
C₂×#442×C₆₇	2
#61332	67

Subgroups — C67×#61332 #30740583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61332 #30740583