Subgroups — C₆₇×#61482 #30740733

Order 17152.

1882 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3367	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3338	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3124	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3110	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2951	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₆₇	C₂²	1	2	yes	—
19	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
20	#556×C₆₇	C₂²	1	2	yes	complemented
21	#554×C₆₇	C₂²	1	4	yes	—
22	#552×C₆₇	—	2	2	no	—
23	#551×C₆₇	—	2	4	no	—
24	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
25	#548×C₆₇	—	2	2	no	—
26	#547×C₆₇	C₂²	1	2	yes	complemented
27	#547×C₆₇	C₂²	1	2	yes	complemented
28	#546×C₆₇	C₂²	1	4	yes	—
29	#542×C₆₇	C₂²	1	4	yes	complemented
30	#539×C₆₇	—	2	4	no	—
31	#533×C₆₇	C₂²	1	2	yes	—
32	#529×C₆₇	C₂²	1	1	yes	characteristic
33	#525×C₆₇	—	2	2	no	—
34	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
35	#520×C₆₇	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#500×C₆₇	C₂²	1	2	yes	complemented
39	#495×C₆₇	C₂²	1	2	yes	—
40	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#489×C₆₇	C₂²	1	4	yes	complemented
42	#487×C₆₇	C₂²	1	2	yes	complemented
43	#484×C₆₇	C₂²	1	4	yes	—
44	#484×C₆₇	C₂²	1	4	yes	complemented
45	#480×C₆₇	C₂²	1	4	yes	complemented
46	#477×C₆₇	C₂²	1	4	yes	complemented
47	#474×C₆₇	C₂²	1	4	yes	complemented
48	#474×C₆₇	C₂²	1	2	yes	complemented
49	#474×C₆₇	C₂²	1	2	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#467×C₆₇	C₂²	1	2	yes	—
52	#467×C₆₇	C₂²	1	2	yes	—
53	#467×C₆₇	C₂²	1	2	yes	complemented
54	#466×C₆₇	C₂²	1	2	yes	—
55	#464×C₆₇	C₂²	1	4	yes	complemented
56	#463×C₆₇	C₂²	1	4	yes	—
57	#461×C₆₇	C₂²	1	2	yes	complemented
58	#461×C₆₇	C₂²	1	2	yes	complemented
59	#452×C₆₇	C₂²	1	4	yes	complemented
60	#450×C₆₇	C₂²	1	4	yes	—
61	#449×C₆₇	C₂²	1	4	yes	—
62	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#440×C₆₇	C₂²	1	4	yes	complemented
65	#440×C₆₇	C₂²	1	4	yes	complemented
66	#440×C₆₇	C₂²	1	4	yes	complemented
67	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
68	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
69	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
70	C₄×D₈×C₆₇	C₂²	1	2	yes	—
71	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₆₇	C₂²	1	2	yes	—
73	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₆₇	C₂²	1	2	yes	—
75	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
77	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#435×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#433×C₆₇	C₂²	1	2	yes	complemented
82	#432×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
84	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
85	#417×C₆₇	C₂²	1	4	yes	complemented
86	C₂×#102×C₆₇	C₂²	1	2	yes	—
87	#405×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×#41×C₆₇	—	2	2	no	—
90	C₂×#41×C₆₇	C₂³	1	4	yes	—
91	C₂²×Q₈×C₆₇	—	2	2	no	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂³×C₄×C₆₇	—	2	2	no	—
94	#135×C₆₇	—	2	8	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
97	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×D₈×C₆₇	—	2	4	no	—
100	C₂×D₈×C₆₇	C₂³	1	2	yes	—
101	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
110	#126×C₆₇	—	2	4	no	—
111	#126×C₆₇	—	2	4	no	—
112	#126×C₆₇	D₄	1	2	yes	—
113	#125×C₆₇	—	2	4	no	—
114	#125×C₆₇	—	2	2	no	—
115	#125×C₆₇	D₄	1	1	yes	characteristic
116	#124×C₆₇	—	2	4	no	—
117	#124×C₆₇	D₄	1	1	yes	characteristic
118	#124×C₆₇	C₂³	1	4	yes	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	—	2	4	no	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	2	no	—
126	C₂²⋊Q₈×C₆₇	—	2	4	no	—
127	C₂²⋊Q₈×C₆₇	—	2	2	no	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
133	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	D₄	1	1	yes	characteristic
138	#121×C₆₇	C₂³	1	4	yes	—
139	#120×C₆₇	—	2	4	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
142	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
143	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₆₇	—	2	4	no	—
145	C₄×D₄×C₆₇	—	2	4	no	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	2	no	—
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	C₂³	1	2	yes	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	C₄×D₄×C₆₇	C₂³	1	2	yes	—
153	C₄×D₄×C₆₇	C₂³	1	2	yes	—
154	C₄×D₄×C₆₇	C₂³	1	2	yes	—
155	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
156	#117×C₆₇	—	2	2	no	—
157	#117×C₆₇	—	2	4	no	—
158	#117×C₆₇	—	2	2	no	—
159	#117×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
161	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
165	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	#107×C₆₇	C₂³	1	2	yes	—
168	#107×C₆₇	C₂³	1	2	yes	—
169	#107×C₆₇	C₂³	1	1	yes	characteristic
170	#107×C₆₇	C₂³	1	4	yes	—
171	#107×C₆₇	C₂³	1	4	yes	—
172	#107×C₆₇	C₂³	1	2	yes	—
173	#107×C₆₇	C₂³	1	1	yes	characteristic
174	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	4	yes	—
180	#103×C₆₇	C₂³	1	4	yes	—
181	#103×C₆₇	C₂³	1	4	yes	—
182	#102×C₆₇	C₂³	1	4	yes	—
183	#102×C₆₇	C₂³	1	4	yes	—
184	#102×C₆₇	C₂³	1	2	yes	—
185	#102×C₆₇	C₂³	1	2	yes	—
186	#102×C₆₇	C₂³	1	2	yes	—
187	#102×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
191	#97×C₆₇	C₂³	1	2	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₇	C₂³	1	2	yes	—
196	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂⁴×C₆₇	—	2	2	no	—
199	#41×C₆₇	—	2	8	no	—
200	#41×C₆₇	—	4	4	no	—
201	#41×C₆₇	—	8	4	no	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	2	4	no	—
204	C₂×Q₈×C₆₇	—	8	4	no	—
205	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	8	4	no	—
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	Q₁₆×C₆₇	—	2	4	no	—
230	Q₁₆×C₆₇	—	4	2	no	—
231	SD₁₆×C₆₇	—	2	8	no	—
232	SD₁₆×C₆₇	—	4	4	no	—
233	D₈×C₆₇	—	2	4	no	—
234	D₈×C₆₇	—	2	2	no	—
235	D₈×C₆₇	#41	1	4	yes	complemented
236	M₁₆×C₆₇	—	4	2	no	—
237	C₂×C₈×C₆₇	—	2	2	no	—
238	C₂×C₈×C₆₇	—	2	4	no	—
239	C₂×C₈×C₆₇	—	4	1	no	—
240	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
244	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	2	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂×D₄	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	4	yes	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄²×C₆₇	—	2	4	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₄²×C₆₇	C₂⁴	1	2	yes	—
286	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	4	4	no	—
290	C₂³×C₆₇	—	4	4	no	—
291	C₂³×C₆₇	—	8	2	no	—
292	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₆₇	—	2	2	no	—
295	Q₈×C₆₇	—	2	4	no	—
296	Q₈×C₆₇	—	2	4	no	—
297	Q₈×C₆₇	—	4	4	no	—
298	Q₈×C₆₇	—	8	4	no	—
299	D₄×C₆₇	—	2	4	no	—
300	D₄×C₆₇	—	2	2	no	—
301	D₄×C₆₇	—	2	2	no	—
302	D₄×C₆₇	—	2	2	no	—
303	D₄×C₆₇	—	2	2	no	—
304	D₄×C₆₇	—	4	4	no	—
305	D₄×C₆₇	—	4	8	no	—
306	D₄×C₆₇	—	8	4	no	—
307	D₄×C₆₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	4	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	4	8	no	—
319	C₂×C₄×C₆₇	—	4	4	no	—
320	C₂×C₄×C₆₇	—	4	4	no	—
321	C₂×C₄×C₆₇	—	8	2	no	—
322	C₂×C₄×C₆₇	—	8	2	no	—
323	C₂×C₄×C₆₇	—	8	4	no	—
324	C₂×C₄×C₆₇	—	8	2	no	—
325	C₂×C₄×C₆₇	—	8	4	no	—
326	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
335	C₈×C₆₇	—	2	1	no	—
336	C₈×C₆₇	—	2	2	no	—
337	C₈×C₆₇	—	2	1	no	—
338	C₈×C₆₇	—	2	1	no	—
339	C₈×C₆₇	—	2	2	no	—
340	C₈×C₆₇	C₂×#41	1	2	yes	—
341	C₂²×C₆₇	—	2	1	no	—
342	C₂²×C₆₇	—	2	1	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	8	8	no	—
353	C₂²×C₆₇	#578	1	2	yes	—
354	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	2	1	no	—
357	C₄×C₆₇	—	2	1	no	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	2	1	no	—
360	C₄×C₆₇	—	2	1	no	—
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	4	4	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	4	no	—
366	C₄×C₆₇	#576	1	2	yes	—
367	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
368	C₄×C₆₇	#585	1	1	yes	characteristic
369	#61482	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂×C₆₇	—	2	2	no	—
371	C₂×C₆₇	—	4	2	no	—
372	C₂×C₆₇	—	4	4	no	—
373	C₂×C₆₇	—	8	2	no	—
374	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
375	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
376	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
377	#3520	C₂×C₆₇	1	2	yes	complemented
378	#3393	C₂×C₆₇	1	1	yes	characteristic, complemented
379	Q₈×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
380	#3367	C₂×C₆₇	1	2	yes	complemented
381	#3338	C₂×C₆₇	1	2	yes	complemented
382	#3334	C₂×C₆₇	1	1	yes	characteristic, complemented
383	#3330	C₂×C₆₇	1	2	yes	complemented
384	#3314	C₂×C₆₇	1	4	yes	complemented
385	#3283	C₂×C₆₇	1	1	yes	characteristic, complemented
386	#3280	C₂×C₆₇	1	2	yes	complemented
387	#3175	C₂×C₆₇	1	2	yes	complemented
388	#3170	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#3124	C₂×C₆₇	1	4	yes	complemented
390	#3110	C₂×C₆₇	1	2	yes	complemented
391	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2951	C₂×C₆₇	1	2	yes	complemented
393	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₆₇	#61482	1	1	yes	characteristic, direct product factor, Sylow
395	C₂×#135	C₂²×C₆₇	1	2	yes	—
396	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
397	#556	C₂²×C₆₇	1	2	yes	complemented
398	#554	C₂²×C₆₇	1	4	yes	—
399	#552	—	2	2	no	—
400	#551	—	2	4	no	—
401	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
402	#548	—	2	2	no	—
403	#547	C₂²×C₆₇	1	2	yes	complemented
404	#547	C₂²×C₆₇	1	2	yes	complemented
405	#546	C₂²×C₆₇	1	4	yes	—
406	#542	C₂²×C₆₇	1	4	yes	complemented
407	#539	—	2	4	no	—
408	#533	C₂²×C₆₇	1	2	yes	—
409	#529	C₂²×C₆₇	1	1	yes	characteristic
410	#525	—	2	2	no	—
411	C₂×C₂²⋊Q₈	—	2	2	no	—
412	#520	C₂²×C₆₇	1	4	yes	complemented
413	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
414	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
415	#500	C₂²×C₆₇	1	2	yes	complemented
416	#495	C₂²×C₆₇	1	2	yes	—
417	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
418	#489	C₂²×C₆₇	1	4	yes	complemented
419	#487	C₂²×C₆₇	1	2	yes	complemented
420	#484	C₂²×C₆₇	1	4	yes	—
421	#484	C₂²×C₆₇	1	4	yes	complemented
422	#480	C₂²×C₆₇	1	4	yes	complemented
423	#477	C₂²×C₆₇	1	4	yes	complemented
424	#474	C₂²×C₆₇	1	2	yes	complemented
425	#474	C₂²×C₆₇	1	2	yes	complemented
426	#474	C₂²×C₆₇	1	4	yes	complemented
427	#468	C₂²×C₆₇	1	4	yes	complemented
428	#467	C₂²×C₆₇	1	2	yes	—
429	#467	C₂²×C₆₇	1	2	yes	—
430	#467	C₂²×C₆₇	1	2	yes	complemented
431	#466	C₂²×C₆₇	1	2	yes	—
432	#464	C₂²×C₆₇	1	4	yes	complemented
433	#463	C₂²×C₆₇	1	4	yes	—
434	#461	C₂²×C₆₇	1	2	yes	complemented
435	#461	C₂²×C₆₇	1	2	yes	complemented
436	#452	C₂²×C₆₇	1	4	yes	complemented
437	#450	C₂²×C₆₇	1	4	yes	—
438	#449	C₂²×C₆₇	1	4	yes	—
439	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
441	#440	C₂²×C₆₇	1	4	yes	complemented
442	#440	C₂²×C₆₇	1	4	yes	complemented
443	#440	C₂²×C₆₇	1	4	yes	complemented
444	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
445	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
446	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
447	C₄×D₈	C₂²×C₆₇	1	2	yes	—
448	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
450	C₄×D₈	C₂²×C₆₇	1	2	yes	—
451	C₄×D₈	C₂²×C₆₇	1	2	yes	—
452	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
453	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
454	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
455	#435	C₂²×C₆₇	1	2	yes	—
456	C₈×D₄	C₂²×C₆₇	1	2	yes	—
457	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	#433	C₂²×C₆₇	1	2	yes	complemented
459	#432	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
462	#417	C₂²×C₆₇	1	4	yes	complemented
463	C₂×#102	C₂²×C₆₇	1	2	yes	—
464	#405	C₂²×C₆₇	1	2	yes	complemented
465	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#41	—	2	2	no	—
467	C₂×#41	C₂³×C₆₇	1	4	yes	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
470	C₂³×C₄	—	2	2	no	—
471	#135	—	2	8	no	—
472	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
473	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
476	C₂×D₈	—	2	4	no	—
477	C₂×D₈	C₂³×C₆₇	1	2	yes	—
478	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
479	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
480	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
481	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
483	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
486	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#126	D₄×C₆₇	1	2	yes	—
490	#125	—	2	4	no	—
491	#125	—	2	2	no	—
492	#125	D₄×C₆₇	1	1	yes	characteristic
493	#124	—	2	4	no	—
494	#124	D₄×C₆₇	1	1	yes	characteristic
495	#124	C₂³×C₆₇	1	4	yes	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	D₄×C₆₇	1	2	yes	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
510	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
511	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
512	#121	—	2	2	no	—
513	#121	—	2	4	no	—
514	#121	D₄×C₆₇	1	1	yes	characteristic
515	#121	C₂³×C₆₇	1	4	yes	—
516	#120	—	2	4	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
519	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
520	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	C₂³×C₆₇	1	2	yes	—
527	C₄×D₄	C₂³×C₆₇	1	2	yes	—
528	C₄×D₄	C₂³×C₆₇	1	2	yes	—
529	C₄×D₄	C₂³×C₆₇	1	2	yes	—
530	C₄×D₄	C₂³×C₆₇	1	4	yes	—
531	C₄×D₄	C₂³×C₆₇	1	2	yes	—
532	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
533	#117	—	2	2	no	—
534	#117	—	2	4	no	—
535	#117	—	2	2	no	—
536	#117	C₂³×C₆₇	1	2	yes	—
537	C₂×C₄⋊C₄	—	2	4	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
544	#107	C₂³×C₆₇	1	1	yes	characteristic
545	#107	C₂³×C₆₇	1	1	yes	characteristic
546	#107	C₂³×C₆₇	1	2	yes	—
547	#107	C₂³×C₆₇	1	2	yes	—
548	#107	C₂³×C₆₇	1	4	yes	—
549	#107	C₂³×C₆₇	1	2	yes	—
550	#107	C₂³×C₆₇	1	4	yes	—
551	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
554	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
555	#103	C₂³×C₆₇	1	4	yes	—
556	#103	C₂³×C₆₇	1	4	yes	—
557	#103	C₂³×C₆₇	1	4	yes	—
558	#103	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	2	yes	—
560	#102	C₂³×C₆₇	1	2	yes	—
561	#102	C₂³×C₆₇	1	2	yes	—
562	#102	C₂³×C₆₇	1	2	yes	—
563	#102	C₂³×C₆₇	1	4	yes	—
564	#102	C₂³×C₆₇	1	4	yes	—
565	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
567	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
568	#97	C₂³×C₆₇	1	2	yes	—
569	#97	C₂³×C₆₇	1	2	yes	—
570	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₆₇	1	2	yes	—
575	C₂⁴	—	2	2	no	—
576	#41	—	2	8	no	—
577	#41	—	4	4	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	8	4	no	—
582	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
583	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
590	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
591	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
592	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	8	4	no	—
602	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
606	Q₁₆	—	2	4	no	—
607	Q₁₆	—	4	2	no	—
608	SD₁₆	—	2	8	no	—
609	SD₁₆	—	4	4	no	—
610	D₈	—	2	4	no	—
611	D₈	—	2	2	no	—
612	D₈	#41×C₆₇	1	4	yes	complemented
613	M₁₆	—	4	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	4	no	—
616	C₂×C₈	—	4	1	no	—
617	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
621	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
622	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
655	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
656	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₄²	C₂⁴×C₆₇	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	8	2	no	—
669	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
670	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	4	4	no	—
675	Q₈	—	8	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	8	no	—
683	D₄	—	8	4	no	—
684	D₄	C₂×#41×C₆₇	1	4	yes	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
711	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	2	no	—
717	C₈	C₂×#41×C₆₇	1	2	yes	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	8	no	—
730	C₂²	#578×C₆₇	1	2	yes	—
731	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	1	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	#576×C₆₇	1	2	yes	—
744	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
745	C₄	#585×C₆₇	1	1	yes	characteristic
746	C₂	—	2	2	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
751	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
752	C₂	C₂×#578×C₆₇	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₆₇×#3393	C₂	semidirect
3. Q₈×D₈×C₆₇	C₂	semidirect
4. C₆₇×#3367	C₂	semidirect
5. C₆₇×#3338	C₂	semidirect
6. C₆₇×#3334	C₂	semidirect
7. C₆₇×#3330	C₂	semidirect
8. C₆₇×#3314	C₂	semidirect
9. C₆₇×#3283	C₂	semidirect
10. C₆₇×#3280	C₂	semidirect
11. C₆₇×#3175	C₂	semidirect
12. C₆₇×#3170	C₂	semidirect
13. C₆₇×#3124	C₂	semidirect
14. C₆₇×#3110	C₂	semidirect
15. C₆₇×#2966	C₂	semidirect
16. C₆₇×#2951	C₂	semidirect
17. C₂×C₄×D₈×C₆₇	C₂	semidirect
20. #556×C₆₇	C₂²	semidirect
24. D₄×Q₈×C₆₇	C₂²	semidirect
26. #547×C₆₇	C₂²	semidirect
27. #547×C₆₇	C₂²	semidirect
29. #542×C₆₇	C₂²	semidirect
35. #520×C₆₇	C₂²	semidirect
37. #500×C₆₇	C₂²	semidirect
38. #500×C₆₇	C₂²	semidirect
40. #494×C₆₇	C₂²	semidirect
41. #489×C₆₇	C₂²	semidirect
42. #487×C₆₇	C₂²	semidirect
44. #484×C₆₇	C₂²	semidirect
45. #480×C₆₇	C₂²	semidirect
46. #477×C₆₇	C₂²	semidirect
47. #474×C₆₇	C₂²	semidirect
48. #474×C₆₇	C₂²	semidirect
49. #474×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
53. #467×C₆₇	C₂²	semidirect
55. #464×C₆₇	C₂²	semidirect
57. #461×C₆₇	C₂²	semidirect
58. #461×C₆₇	C₂²	semidirect
59. #452×C₆₇	C₂²	semidirect
62. #446×C₆₇	C₂²	semidirect
63. C₈×Q₈×C₆₇	C₂²	semidirect
64. #440×C₆₇	C₂²	semidirect
65. #440×C₆₇	C₂²	semidirect
66. #440×C₆₇	C₂²	semidirect
67. C₄×Q₁₆×C₆₇	C₂²	semidirect
68. C₄×Q₁₆×C₆₇	C₂²	semidirect
69. C₄×Q₁₆×C₆₇	C₂²	semidirect
77. #436×C₆₇	C₂²	semidirect
80. C₈×D₄×C₆₇	C₂²	semidirect
81. #433×C₆₇	C₂²	semidirect
84. C₂×#107×C₆₇	C₂²	semidirect
85. #417×C₆₇	C₂²	semidirect
87. #405×C₆₇	C₂²	semidirect
235. D₈×C₆₇	#41	semidirect
369. #61482	C₆₇	direct (N × H)
377. #3520	C₂×C₆₇	semidirect
378. #3393	C₂×C₆₇	semidirect
379. Q₈×D₈	C₂×C₆₇	semidirect
380. #3367	C₂×C₆₇	semidirect
381. #3338	C₂×C₆₇	semidirect
382. #3334	C₂×C₆₇	semidirect
383. #3330	C₂×C₆₇	semidirect
384. #3314	C₂×C₆₇	semidirect
385. #3283	C₂×C₆₇	semidirect
386. #3280	C₂×C₆₇	semidirect
387. #3175	C₂×C₆₇	semidirect
388. #3170	C₂×C₆₇	semidirect
389. #3124	C₂×C₆₇	semidirect
390. #3110	C₂×C₆₇	semidirect
391. #2966	C₂×C₆₇	semidirect
392. #2951	C₂×C₆₇	semidirect
393. C₂×C₄×D₈	C₂×C₆₇	semidirect
394. C₆₇	#61482	direct (N × H)
397. #556	C₂²×C₆₇	semidirect
401. D₄×Q₈	C₂²×C₆₇	semidirect
403. #547	C₂²×C₆₇	semidirect
404. #547	C₂²×C₆₇	semidirect
406. #542	C₂²×C₆₇	semidirect
412. #520	C₂²×C₆₇	semidirect
414. #500	C₂²×C₆₇	semidirect
415. #500	C₂²×C₆₇	semidirect
417. #494	C₂²×C₆₇	semidirect
418. #489	C₂²×C₆₇	semidirect
419. #487	C₂²×C₆₇	semidirect
421. #484	C₂²×C₆₇	semidirect
422. #480	C₂²×C₆₇	semidirect
423. #477	C₂²×C₆₇	semidirect
424. #474	C₂²×C₆₇	semidirect
425. #474	C₂²×C₆₇	semidirect
426. #474	C₂²×C₆₇	semidirect
427. #468	C₂²×C₆₇	semidirect
430. #467	C₂²×C₆₇	semidirect
432. #464	C₂²×C₆₇	semidirect
434. #461	C₂²×C₆₇	semidirect
435. #461	C₂²×C₆₇	semidirect
436. #452	C₂²×C₆₇	semidirect
439. #446	C₂²×C₆₇	semidirect
440. C₈×Q₈	C₂²×C₆₇	semidirect
441. #440	C₂²×C₆₇	semidirect
442. #440	C₂²×C₆₇	semidirect
443. #440	C₂²×C₆₇	semidirect
444. C₄×Q₁₆	C₂²×C₆₇	semidirect
445. C₄×Q₁₆	C₂²×C₆₇	semidirect
446. C₄×Q₁₆	C₂²×C₆₇	semidirect
454. #436	C₂²×C₆₇	semidirect
457. C₈×D₄	C₂²×C₆₇	semidirect
458. #433	C₂²×C₆₇	semidirect
461. C₂×#107	C₂²×C₆₇	semidirect
462. #417	C₂²×C₆₇	semidirect
464. #405	C₂²×C₆₇	semidirect
612. D₈	#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×#3520	2
C₆₇×#3393	2
Q₈×D₈×C₆₇	2
C₆₇×#3367	2
C₆₇×#3338	2
C₆₇×#3334	2
C₆₇×#3330	2
C₆₇×#3314	2
C₆₇×#3283	2
C₆₇×#3280	2
C₆₇×#3175	2
C₆₇×#3170	2
C₆₇×#3124	2
C₆₇×#3110	2
C₆₇×#2966	2
C₆₇×#2951	2
C₂×C₄×D₈×C₆₇	2
#61482	67

Subgroups — C67×#61482 #30740733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61482 #30740733