Subgroups — C₆₇×#61600 #30740851

Order 17152.

2568 conjugacy classes of subgroups.

The subgroup lattice has 970 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	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3310	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3193	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3003	C₂	1	2	yes	maximal, complemented
16	C₂×#450×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₆₇	—	2	1	no	—
19	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
21	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
22	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	#554×C₆₇	—	2	1	no	—
24	#552×C₆₇	C₂²	1	2	yes	complemented
25	#551×C₆₇	—	2	2	no	—
26	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#548×C₆₇	C₂²	1	2	yes	complemented
28	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#546×C₆₇	—	2	1	no	—
31	D₄²×C₆₇	—	2	1	no	—
32	D₄²×C₆₇	—	2	2	no	—
33	D₄²×C₆₇	—	2	1	no	—
34	D₄²×C₆₇	C₂²	1	4	yes	—
35	D₄²×C₆₇	C₂²	1	2	yes	—
36	D₄²×C₆₇	C₂²	1	2	yes	—
37	#542×C₆₇	—	2	1	no	—
38	#539×C₆₇	—	2	2	no	—
39	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
41	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#525×C₆₇	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
44	C₂×#121×C₆₇	—	2	1	no	—
45	C₂×#121×C₆₇	C₂²	1	2	yes	—
46	C₂×#120×C₆₇	—	2	2	no	—
47	#520×C₆₇	—	2	1	no	—
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	#496×C₆₇	C₂²	1	2	yes	complemented
51	#492×C₆₇	C₂²	1	2	yes	complemented
52	#490×C₆₇	C₂²	1	2	yes	complemented
53	#486×C₆₇	C₂²	1	2	yes	complemented
54	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#484×C₆₇	C₂²	1	2	yes	complemented
56	#482×C₆₇	C₂²	1	4	yes	complemented
57	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#480×C₆₇	C₂²	1	4	yes	complemented
59	#478×C₆₇	C₂²	1	2	yes	complemented
60	#474×C₆₇	C₂²	1	2	yes	complemented
61	#468×C₆₇	C₂²	1	4	yes	complemented
62	#468×C₆₇	C₂²	1	4	yes	complemented
63	#466×C₆₇	C₂²	1	4	yes	complemented
64	#465×C₆₇	C₂²	1	4	yes	complemented
65	#463×C₆₇	C₂²	1	2	yes	complemented
66	#461×C₆₇	C₂²	1	2	yes	complemented
67	#460×C₆₇	C₂²	1	4	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#450×C₆₇	C₂²	1	1	yes	characteristic
71	#450×C₆₇	C₂²	1	2	yes	—
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	complemented
74	#450×C₆₇	C₂²	1	4	yes	complemented
75	#450×C₆₇	C₂²	1	2	yes	complemented
76	#450×C₆₇	C₂²	1	2	yes	complemented
77	#450×C₆₇	C₂²	1	2	yes	complemented
78	#449×C₆₇	C₂²	1	4	yes	complemented
79	#448×C₆₇	C₂²	1	4	yes	complemented
80	#447×C₆₇	C₂²	1	1	yes	characteristic
81	#447×C₆₇	C₂²	1	4	yes	complemented
82	#447×C₆₇	C₂²	1	2	yes	complemented
83	#440×C₆₇	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
85	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
86	#436×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	4	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#418×C₆₇	C₂²	1	4	yes	complemented
92	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
95	C₂⁵×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	1	no	—
97	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
98	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	4	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	—	2	2	no	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	—	2	1	no	—
105	C₂²×D₄×C₆₇	—	2	2	no	—
106	C₂²×D₄×C₆₇	—	2	2	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	—	4	8	no	—
109	C₂²×D₄×C₆₇	—	4	8	no	—
110	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	—	2	1	no	—
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
118	C₂×SD₁₆×C₆₇	—	4	8	no	—
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
122	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
123	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
124	C₂×D₈×C₆₇	C₂³	1	2	yes	—
125	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
126	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
127	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
128	C₄⋊Q₈×C₆₇	—	2	1	no	—
129	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
130	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
131	#127×C₆₇	—	2	1	no	—
132	#127×C₆₇	—	2	1	no	—
133	#127×C₆₇	C₂³	1	2	yes	—
134	#127×C₆₇	C₂³	1	2	yes	—
135	#126×C₆₇	—	2	2	no	—
136	#126×C₆₇	—	2	2	no	—
137	#126×C₆₇	—	2	1	no	—
138	#125×C₆₇	—	2	2	no	—
139	#125×C₆₇	—	2	1	no	—
140	#125×C₆₇	C₂³	1	1	yes	characteristic, complemented
141	#124×C₆₇	—	2	1	no	—
142	#124×C₆₇	—	2	2	no	—
143	#124×C₆₇	C₂³	1	1	yes	characteristic, complemented
144	#123×C₆₇	—	2	2	no	—
145	#123×C₆₇	—	2	2	no	—
146	#123×C₆₇	—	2	1	no	—
147	#123×C₆₇	—	2	2	no	—
148	#123×C₆₇	—	2	2	no	—
149	C₂²⋊Q₈×C₆₇	—	2	2	no	—
150	C₂²⋊Q₈×C₆₇	—	2	2	no	—
151	C₂²⋊Q₈×C₆₇	—	2	1	no	—
152	C₂²⋊Q₈×C₆₇	—	2	2	no	—
153	C₂²⋊Q₈×C₆₇	—	2	1	no	—
154	C₂²⋊Q₈×C₆₇	—	2	2	no	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
157	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
158	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
159	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	1	no	—
162	#121×C₆₇	—	2	2	no	—
163	#121×C₆₇	—	2	2	no	—
164	#121×C₆₇	—	2	2	no	—
165	#121×C₆₇	—	2	4	no	—
166	#121×C₆₇	—	2	2	no	—
167	#121×C₆₇	C₂³	1	4	yes	—
168	#121×C₆₇	C₂³	1	4	yes	—
169	#121×C₆₇	C₂³	1	1	yes	characteristic
170	#121×C₆₇	C₂³	1	2	yes	complemented
171	#120×C₆₇	—	2	2	no	—
172	#120×C₆₇	—	2	4	no	—
173	#120×C₆₇	—	2	4	no	—
174	#120×C₆₇	—	2	4	no	—
175	#120×C₆₇	—	2	4	no	—
176	C₄×Q₈×C₆₇	—	2	1	no	—
177	C₄×Q₈×C₆₇	—	2	1	no	—
178	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
179	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
180	C₄×D₄×C₆₇	—	2	1	no	—
181	C₄×D₄×C₆₇	—	2	2	no	—
182	C₄×D₄×C₆₇	—	2	2	no	—
183	C₄×D₄×C₆₇	—	2	1	no	—
184	C₄×D₄×C₆₇	—	2	2	no	—
185	C₄×D₄×C₆₇	—	2	1	no	—
186	C₄×D₄×C₆₇	—	2	1	no	—
187	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
188	C₄×D₄×C₆₇	D₄	1	2	yes	—
189	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
190	C₄×D₄×C₆₇	C₂³	1	2	yes	—
191	C₄×D₄×C₆₇	C₂³	1	2	yes	—
192	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₆₇	C₂³	1	2	yes	—
195	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
196	#117×C₆₇	—	2	1	no	—
197	#117×C₆₇	—	2	2	no	—
198	#117×C₆₇	—	2	1	no	—
199	#117×C₆₇	C₂³	1	2	yes	complemented
200	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
201	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
202	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
205	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	#107×C₆₇	C₂³	1	4	yes	complemented
211	#107×C₆₇	C₂³	1	2	yes	complemented
212	#106×C₆₇	C₂³	1	2	yes	complemented
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
214	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
215	#103×C₆₇	C₂³	1	2	yes	complemented
216	#103×C₆₇	C₂³	1	4	yes	complemented
217	#102×C₆₇	C₂³	1	2	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	complemented
221	#102×C₆₇	C₂³	1	4	yes	complemented
222	#102×C₆₇	C₂³	1	4	yes	complemented
223	#102×C₆₇	C₂³	1	4	yes	complemented
224	#102×C₆₇	C₂³	1	4	yes	complemented
225	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
230	#97×C₆₇	C₂³	1	2	yes	complemented
231	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
232	C₂⁴×C₆₇	—	2	1	no	—
233	C₂⁴×C₆₇	—	2	2	no	—
234	C₂⁴×C₆₇	—	2	4	no	—
235	C₂⁴×C₆₇	—	2	4	no	—
236	C₂⁴×C₆₇	—	4	8	no	—
237	C₂⁴×C₆₇	—	4	8	no	—
238	C₂⁴×C₆₇	—	8	4	no	—
239	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
240	#41×C₆₇	—	4	4	no	—
241	#41×C₆₇	—	4	4	no	—
242	C₂×Q₈×C₆₇	—	2	1	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	—	4	4	no	—
245	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	8	no	—
250	C₂×D₄×C₆₇	—	2	8	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	1	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	4	4	no	—
265	C₂×D₄×C₆₇	—	4	4	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	4	no	—
268	C₂×D₄×C₆₇	—	4	8	no	—
269	C₂×D₄×C₆₇	—	4	8	no	—
270	C₂×D₄×C₆₇	—	4	16	no	—
271	C₂×D₄×C₆₇	—	4	8	no	—
272	C₂×D₄×C₆₇	—	4	8	no	—
273	C₂×D₄×C₆₇	—	4	8	no	—
274	C₂×D₄×C₆₇	—	4	8	no	—
275	C₂×D₄×C₆₇	—	8	2	no	—
276	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	—	2	1	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	1	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	4	4	no	—
290	C₂²×C₄×C₆₇	—	4	4	no	—
291	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	SD₁₆×C₆₇	—	2	4	no	—
300	SD₁₆×C₆₇	—	2	8	no	—
301	SD₁₆×C₆₇	—	4	4	no	—
302	SD₁₆×C₆₇	—	4	4	no	—
303	SD₁₆×C₆₇	—	4	4	no	—
304	D₈×C₆₇	—	2	4	no	—
305	D₈×C₆₇	—	4	4	no	—
306	M₁₆×C₆₇	—	4	4	no	—
307	C₂×C₈×C₆₇	—	4	4	no	—
308	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
309	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
310	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₆₇	—	2	1	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	1	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	1	no	—
319	C₄⋊C₄×C₆₇	—	2	1	no	—
320	C₄⋊C₄×C₆₇	—	2	1	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	1	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	1	no	—
325	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
332	C₂²⋊C₄×C₆₇	—	2	1	no	—
333	C₂²⋊C₄×C₆₇	—	2	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	2	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	1	no	—
343	C₂²⋊C₄×C₆₇	—	2	1	no	—
344	C₂²⋊C₄×C₆₇	—	2	1	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	1	no	—
347	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
348	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₄²×C₆₇	—	2	2	no	—
352	C₄²×C₆₇	—	2	2	no	—
353	C₄²×C₆₇	—	2	1	no	—
354	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂³×C₆₇	—	2	4	no	—
359	C₂³×C₆₇	—	2	4	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	1	no	—
363	C₂³×C₆₇	—	2	4	no	—
364	C₂³×C₆₇	—	4	2	no	—
365	C₂³×C₆₇	—	4	8	no	—
366	C₂³×C₆₇	—	4	8	no	—
367	C₂³×C₆₇	—	4	2	no	—
368	C₂³×C₆₇	—	4	4	no	—
369	C₂³×C₆₇	—	4	4	no	—
370	C₂³×C₆₇	—	4	8	no	—
371	C₂³×C₆₇	—	4	2	no	—
372	C₂³×C₆₇	—	4	8	no	—
373	C₂³×C₆₇	—	4	4	no	—
374	C₂³×C₆₇	—	8	4	no	—
375	C₂³×C₆₇	—	8	4	no	—
376	C₂³×C₆₇	—	8	32	no	—
377	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
378	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
379	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
380	Q₈×C₆₇	—	2	2	no	—
381	Q₈×C₆₇	—	2	4	no	—
382	Q₈×C₆₇	—	4	2	no	—
383	Q₈×C₆₇	—	8	2	no	—
384	D₄×C₆₇	—	2	4	no	—
385	D₄×C₆₇	—	2	4	no	—
386	D₄×C₆₇	—	2	2	no	—
387	D₄×C₆₇	—	2	2	no	—
388	D₄×C₆₇	—	2	2	no	—
389	D₄×C₆₇	—	2	4	no	—
390	D₄×C₆₇	—	2	4	no	—
391	D₄×C₆₇	—	4	8	no	—
392	D₄×C₆₇	—	4	8	no	—
393	D₄×C₆₇	—	4	4	no	—
394	D₄×C₆₇	—	4	4	no	—
395	D₄×C₆₇	—	4	8	no	—
396	D₄×C₆₇	—	4	8	no	—
397	D₄×C₆₇	—	4	4	no	—
398	D₄×C₆₇	—	4	2	no	—
399	D₄×C₆₇	—	4	4	no	—
400	D₄×C₆₇	—	8	2	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	—	8	2	no	—
403	D₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
404	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	4	no	—
408	C₂×C₄×C₆₇	—	2	4	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	4	2	no	—
417	C₂×C₄×C₆₇	—	4	2	no	—
418	C₂×C₄×C₆₇	—	4	2	no	—
419	C₂×C₄×C₆₇	—	4	4	no	—
420	C₂×C₄×C₆₇	—	4	2	no	—
421	C₂×C₄×C₆₇	—	4	4	no	—
422	C₂×C₄×C₆₇	—	4	4	no	—
423	C₂×C₄×C₆₇	—	4	2	no	—
424	C₂×C₄×C₆₇	—	8	2	no	—
425	C₂×C₄×C₆₇	—	8	2	no	—
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
434	C₈×C₆₇	—	2	2	no	—
435	C₈×C₆₇	—	2	4	no	—
436	C₈×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	1	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	1	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	2	4	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	4	8	no	—
446	C₂²×C₆₇	—	4	8	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	1	no	—
450	C₂²×C₆₇	—	4	4	no	—
451	C₂²×C₆₇	—	4	1	no	—
452	C₂²×C₆₇	—	4	4	no	—
453	C₂²×C₆₇	—	4	1	no	—
454	C₂²×C₆₇	—	4	4	no	—
455	C₂²×C₆₇	—	8	16	no	—
456	C₂²×C₆₇	—	8	8	no	—
457	C₂²×C₆₇	—	8	16	no	—
458	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
459	C₂²×C₆₇	#577	1	2	yes	—
460	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₆₇	—	2	1	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	—	2	2	no	—
464	C₄×C₆₇	—	2	1	no	—
465	C₄×C₆₇	—	2	1	no	—
466	C₄×C₆₇	—	2	1	no	—
467	C₄×C₆₇	—	4	2	no	—
468	C₄×C₆₇	—	4	1	no	—
469	C₄×C₆₇	—	4	1	no	—
470	C₄×C₆₇	—	4	2	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	1	no	—
473	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
474	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
475	#61600	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂×C₆₇	—	2	2	no	—
477	C₂×C₆₇	—	2	4	no	—
478	C₂×C₆₇	—	4	2	no	—
479	C₂×C₆₇	—	4	4	no	—
480	C₂×C₆₇	—	8	1	no	—
481	C₂×C₆₇	—	8	4	no	—
482	C₂×C₆₇	#3484	1	1	yes	characteristic
483	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
484	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
485	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
486	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3324	C₂×C₆₇	1	2	yes	complemented
488	#3310	C₂×C₆₇	1	4	yes	complemented
489	#3294	C₂×C₆₇	1	2	yes	complemented
490	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
491	#3272	C₂×C₆₇	1	2	yes	complemented
492	#3265	C₂×C₆₇	1	4	yes	complemented
493	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#3208	C₂×C₆₇	1	1	yes	characteristic, complemented
495	#3193	C₂×C₆₇	1	2	yes	complemented
496	#3188	C₂×C₆₇	1	2	yes	complemented
497	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
498	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
499	#3003	C₂×C₆₇	1	2	yes	complemented
500	C₂×#450	C₂×C₆₇	1	2	yes	complemented
501	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
502	C₆₇	#61600	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³×D₄	—	2	1	no	—
504	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
505	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
506	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
507	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	#554	—	2	1	no	—
509	#552	C₂²×C₆₇	1	2	yes	complemented
510	#551	—	2	2	no	—
511	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
512	#548	C₂²×C₆₇	1	2	yes	complemented
513	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	#546	—	2	1	no	—
516	D₄²	—	2	1	no	—
517	D₄²	—	2	2	no	—
518	D₄²	—	2	1	no	—
519	D₄²	C₂²×C₆₇	1	4	yes	—
520	D₄²	C₂²×C₆₇	1	2	yes	—
521	D₄²	C₂²×C₆₇	1	2	yes	—
522	#542	—	2	1	no	—
523	#539	—	2	2	no	—
524	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
526	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	#525	C₂²×C₆₇	1	2	yes	complemented
528	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
529	C₂×#121	—	2	1	no	—
530	C₂×#121	C₂²×C₆₇	1	2	yes	—
531	C₂×#120	—	2	2	no	—
532	#520	—	2	1	no	—
533	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
534	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
535	#496	C₂²×C₆₇	1	2	yes	complemented
536	#492	C₂²×C₆₇	1	2	yes	complemented
537	#490	C₂²×C₆₇	1	2	yes	complemented
538	#486	C₂²×C₆₇	1	2	yes	complemented
539	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	#484	C₂²×C₆₇	1	2	yes	complemented
541	#482	C₂²×C₆₇	1	4	yes	complemented
542	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	#480	C₂²×C₆₇	1	4	yes	complemented
544	#478	C₂²×C₆₇	1	2	yes	complemented
545	#474	C₂²×C₆₇	1	2	yes	complemented
546	#468	C₂²×C₆₇	1	4	yes	complemented
547	#468	C₂²×C₆₇	1	4	yes	complemented
548	#466	C₂²×C₆₇	1	4	yes	complemented
549	#465	C₂²×C₆₇	1	4	yes	complemented
550	#463	C₂²×C₆₇	1	2	yes	complemented
551	#461	C₂²×C₆₇	1	2	yes	complemented
552	#460	C₂²×C₆₇	1	4	yes	complemented
553	#460	C₂²×C₆₇	1	2	yes	complemented
554	#459	C₂²×C₆₇	1	2	yes	complemented
555	#450	C₂²×C₆₇	1	1	yes	characteristic
556	#450	C₂²×C₆₇	1	2	yes	—
557	#450	C₂²×C₆₇	1	2	yes	complemented
558	#450	C₂²×C₆₇	1	2	yes	complemented
559	#450	C₂²×C₆₇	1	2	yes	complemented
560	#450	C₂²×C₆₇	1	4	yes	complemented
561	#450	C₂²×C₆₇	1	4	yes	complemented
562	#450	C₂²×C₆₇	1	4	yes	complemented
563	#449	C₂²×C₆₇	1	4	yes	complemented
564	#448	C₂²×C₆₇	1	4	yes	complemented
565	#447	C₂²×C₆₇	1	1	yes	characteristic
566	#447	C₂²×C₆₇	1	2	yes	complemented
567	#447	C₂²×C₆₇	1	4	yes	complemented
568	#440	C₂²×C₆₇	1	4	yes	complemented
569	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
570	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
571	#436	C₂²×C₆₇	1	2	yes	complemented
572	#435	C₂²×C₆₇	1	4	yes	complemented
573	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
574	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	#418	C₂²×C₆₇	1	4	yes	complemented
577	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
578	#407	C₂²×C₆₇	1	2	yes	complemented
579	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
580	C₂⁵	—	2	2	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
583	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	4	no	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	—	2	2	no	—
588	C₂²×D₄	—	2	2	no	—
589	C₂²×D₄	—	2	1	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	2	2	no	—
592	C₂²×D₄	—	2	1	no	—
593	C₂²×D₄	—	4	8	no	—
594	C₂²×D₄	—	4	8	no	—
595	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
598	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
599	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
600	C₂³×C₄	—	2	1	no	—
601	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
602	AGL(1,ℤ/8)	—	4	8	no	—
603	C₂×SD₁₆	—	4	8	no	—
604	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
606	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
607	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
608	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
609	C₂×D₈	C₂³×C₆₇	1	2	yes	—
610	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
611	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
612	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
613	C₄⋊Q₈	—	2	1	no	—
614	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
615	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
616	#127	—	2	1	no	—
617	#127	—	2	1	no	—
618	#127	C₂³×C₆₇	1	2	yes	—
619	#127	C₂³×C₆₇	1	2	yes	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	1	no	—
623	#125	—	2	2	no	—
624	#125	—	2	1	no	—
625	#125	C₂³×C₆₇	1	1	yes	characteristic, complemented
626	#124	—	2	1	no	—
627	#124	—	2	2	no	—
628	#124	C₂³×C₆₇	1	1	yes	characteristic, complemented
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	1	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
641	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
643	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
644	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
645	#121	—	2	2	no	—
646	#121	—	2	1	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	4	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₆₇	1	4	yes	—
653	#121	C₂³×C₆₇	1	4	yes	—
654	#121	C₂³×C₆₇	1	1	yes	characteristic
655	#121	C₂³×C₆₇	1	2	yes	complemented
656	#120	—	2	2	no	—
657	#120	—	2	4	no	—
658	#120	—	2	4	no	—
659	#120	—	2	4	no	—
660	#120	—	2	4	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
664	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
673	C₄×D₄	D₄×C₆₇	1	2	yes	—
674	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₆₇	1	2	yes	—
676	C₄×D₄	C₂³×C₆₇	1	2	yes	—
677	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₄×D₄	C₂³×C₆₇	1	2	yes	—
680	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
681	#117	—	2	1	no	—
682	#117	—	2	2	no	—
683	#117	—	2	1	no	—
684	#117	C₂³×C₆₇	1	2	yes	complemented
685	C₂×C₄⋊C₄	—	2	2	no	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	#107	C₂³×C₆₇	1	2	yes	complemented
696	#107	C₂³×C₆₇	1	4	yes	complemented
697	#106	C₂³×C₆₇	1	2	yes	complemented
698	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
699	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
700	#103	C₂³×C₆₇	1	2	yes	complemented
701	#103	C₂³×C₆₇	1	4	yes	complemented
702	#102	C₂³×C₆₇	1	2	yes	—
703	#102	C₂³×C₆₇	1	4	yes	—
704	#102	C₂³×C₆₇	1	2	yes	—
705	#102	C₂³×C₆₇	1	4	yes	complemented
706	#102	C₂³×C₆₇	1	4	yes	complemented
707	#102	C₂³×C₆₇	1	4	yes	complemented
708	#102	C₂³×C₆₇	1	4	yes	complemented
709	#102	C₂³×C₆₇	1	2	yes	complemented
710	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
713	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
714	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
715	#97	C₂³×C₆₇	1	2	yes	complemented
716	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	2	2	no	—
719	C₂⁴	—	2	4	no	—
720	C₂⁴	—	2	4	no	—
721	C₂⁴	—	4	8	no	—
722	C₂⁴	—	4	8	no	—
723	C₂⁴	—	8	4	no	—
724	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
725	#41	—	4	4	no	—
726	#41	—	4	4	no	—
727	C₂×Q₈	—	2	1	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	4	4	no	—
730	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	8	no	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	4	4	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	—	4	4	no	—
752	C₂×D₄	—	4	4	no	—
753	C₂×D₄	—	4	8	no	—
754	C₂×D₄	—	4	8	no	—
755	C₂×D₄	—	4	16	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	8	no	—
758	C₂×D₄	—	4	8	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	8	2	no	—
761	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
762	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
763	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
764	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
765	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	4	4	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
777	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
778	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	SD₁₆	—	2	4	no	—
785	SD₁₆	—	2	8	no	—
786	SD₁₆	—	4	4	no	—
787	SD₁₆	—	4	4	no	—
788	SD₁₆	—	4	4	no	—
789	D₈	—	2	4	no	—
790	D₈	—	4	4	no	—
791	M₁₆	—	4	4	no	—
792	C₂×C₈	—	4	4	no	—
793	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
811	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
812	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
813	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
817	C₂²⋊C₄	—	2	1	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	1	no	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	1	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
833	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
834	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
835	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	1	no	—
839	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
840	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
841	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
842	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
843	C₂³	—	2	4	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	4	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	4	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	4	8	no	—
851	C₂³	—	4	8	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	8	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	8	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	8	4	no	—
860	C₂³	—	8	4	no	—
861	C₂³	—	8	32	no	—
862	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
863	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
864	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
865	Q₈	—	2	2	no	—
866	Q₈	—	2	4	no	—
867	Q₈	—	4	2	no	—
868	Q₈	—	8	2	no	—
869	D₄	—	2	4	no	—
870	D₄	—	2	4	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	4	no	—
875	D₄	—	2	4	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	8	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	4	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	D₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
889	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	4	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	4	2	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	2	no	—
909	C₂×C₄	—	8	2	no	—
910	C₂×C₄	—	8	2	no	—
911	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
916	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
918	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
919	C₈	—	2	2	no	—
920	C₈	—	2	4	no	—
921	C₈	—	2	2	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	4	8	no	—
931	C₂²	—	4	8	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	4	no	—
940	C₂²	—	8	16	no	—
941	C₂²	—	8	8	no	—
942	C₂²	—	8	16	no	—
943	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
944	C₂²	#577×C₆₇	1	2	yes	—
945	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	1	no	—
958	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
959	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
960	C₂	—	2	2	no	—
961	C₂	—	2	4	no	—
962	C₂	—	4	2	no	—
963	C₂	—	4	4	no	—
964	C₂	—	8	4	no	—
965	C₂	—	8	1	no	—
966	C₂	C₆₇×#3484	1	1	yes	characteristic
967	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
968	C₂	C₂×#577×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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₂×D₄²×C₆₇	C₂	semidirect
3. C₆₇×#3324	C₂	semidirect
4. C₆₇×#3310	C₂	semidirect
5. C₆₇×#3294	C₂	semidirect
6. D₄×SD₁₆×C₆₇	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3265	C₂	semidirect
9. C₆₇×#3217	C₂	semidirect
10. C₆₇×#3208	C₂	semidirect
11. C₆₇×#3193	C₂	semidirect
12. C₆₇×#3188	C₂	semidirect
13. C₆₇×#3110	C₂	semidirect
14. C₆₇×#3105	C₂	semidirect
15. C₆₇×#3003	C₂	semidirect
16. C₂×#450×C₆₇	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
21. C₂²×SD₁₆×C₆₇	C₂²	semidirect
22. #556×C₆₇	C₂²	semidirect
24. #552×C₆₇	C₂²	semidirect
26. D₄×Q₈×C₆₇	C₂²	semidirect
27. #548×C₆₇	C₂²	semidirect
28. #547×C₆₇	C₂²	semidirect
29. #547×C₆₇	C₂²	semidirect
39. #533×C₆₇	C₂²	semidirect
41. #529×C₆₇	C₂²	semidirect
42. #525×C₆₇	C₂²	semidirect
43. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
50. #496×C₆₇	C₂²	semidirect
51. #492×C₆₇	C₂²	semidirect
52. #490×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
55. #484×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
57. #481×C₆₇	C₂²	semidirect
58. #480×C₆₇	C₂²	semidirect
59. #478×C₆₇	C₂²	semidirect
60. #474×C₆₇	C₂²	semidirect
61. #468×C₆₇	C₂²	semidirect
62. #468×C₆₇	C₂²	semidirect
63. #466×C₆₇	C₂²	semidirect
64. #465×C₆₇	C₂²	semidirect
65. #463×C₆₇	C₂²	semidirect
66. #461×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #450×C₆₇	C₂²	semidirect
74. #450×C₆₇	C₂²	semidirect
75. #450×C₆₇	C₂²	semidirect
76. #450×C₆₇	C₂²	semidirect
77. #450×C₆₇	C₂²	semidirect
78. #449×C₆₇	C₂²	semidirect
79. #448×C₆₇	C₂²	semidirect
81. #447×C₆₇	C₂²	semidirect
82. #447×C₆₇	C₂²	semidirect
83. #440×C₆₇	C₂²	semidirect
84. C₄×SD₁₆×C₆₇	C₂²	semidirect
85. C₄×D₈×C₆₇	C₂²	semidirect
86. #436×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
89. #432×C₆₇	C₂²	semidirect
90. #431×C₆₇	C₂²	semidirect
91. #418×C₆₇	C₂²	semidirect
92. C₂×#102×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
97. C₂×#41×C₆₇	C₂³	semidirect
98. C₂²×Q₈×C₆₇	C₂³	semidirect
121. C₂×SD₁₆×C₆₇	C₂³	semidirect
122. C₂×SD₁₆×C₆₇	C₂³	semidirect
123. C₂×SD₁₆×C₆₇	C₂³	semidirect
125. C₂×D₈×C₆₇	C₂³	semidirect
126. C₂×M₁₆×C₆₇	C₂³	semidirect
127. C₂²×C₈×C₆₇	C₂³	semidirect
129. C₄⋊Q₈×C₆₇	C₂³	semidirect
130. C₄⋊Q₈×C₆₇	C₂³	semidirect
140. #125×C₆₇	C₂³	semidirect
143. #124×C₆₇	C₂³	semidirect
157. C₂²⋊Q₈×C₆₇	C₂³	semidirect
158. C₂²⋊Q₈×C₆₇	C₂³	semidirect
159. C₂²⋊Q₈×C₆₇	C₂³	semidirect
170. #121×C₆₇	C₂³	semidirect
178. C₄×Q₈×C₆₇	C₂³	semidirect
179. C₄×Q₈×C₆₇	C₂³	semidirect
195. C₄×D₄×C₆₇	C₂³	semidirect
199. #117×C₆₇	C₂³	semidirect
204. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
210. #107×C₆₇	C₂³	semidirect
211. #107×C₆₇	C₂³	semidirect
212. #106×C₆₇	C₂³	semidirect
213. C₄⋊C₈×C₆₇	C₂³	semidirect
214. C₄⋊C₈×C₆₇	C₂³	semidirect
215. #103×C₆₇	C₂³	semidirect
216. #103×C₆₇	C₂³	semidirect
220. #102×C₆₇	C₂³	semidirect
221. #102×C₆₇	C₂³	semidirect
222. #102×C₆₇	C₂³	semidirect
223. #102×C₆₇	C₂³	semidirect
224. #102×C₆₇	C₂³	semidirect
228. C₂²⋊C₈×C₆₇	C₂³	semidirect
229. C₂²⋊C₈×C₆₇	C₂³	semidirect
230. #97×C₆₇	C₂³	semidirect
231. C₄×C₈×C₆₇	C₂³	semidirect
403. D₄×C₆₇	AGL(1,ℤ/8)	semidirect
475. #61600	C₆₇	direct (N × H)
485. #3520	C₂×C₆₇	semidirect
486. C₂×D₄²	C₂×C₆₇	semidirect
487. #3324	C₂×C₆₇	semidirect
488. #3310	C₂×C₆₇	semidirect
489. #3294	C₂×C₆₇	semidirect
490. D₄×SD₁₆	C₂×C₆₇	semidirect
491. #3272	C₂×C₆₇	semidirect
492. #3265	C₂×C₆₇	semidirect
493. #3217	C₂×C₆₇	semidirect
494. #3208	C₂×C₆₇	semidirect
495. #3193	C₂×C₆₇	semidirect
496. #3188	C₂×C₆₇	semidirect
497. #3110	C₂×C₆₇	semidirect
498. #3105	C₂×C₆₇	semidirect
499. #3003	C₂×C₆₇	semidirect
500. C₂×#450	C₂×C₆₇	semidirect
501. #2974	C₂×C₆₇	semidirect
502. C₆₇	#61600	direct (N × H)
505. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
506. C₂²×SD₁₆	C₂²×C₆₇	semidirect
507. #556	C₂²×C₆₇	semidirect
509. #552	C₂²×C₆₇	semidirect
511. D₄×Q₈	C₂²×C₆₇	semidirect
512. #548	C₂²×C₆₇	semidirect
513. #547	C₂²×C₆₇	semidirect
514. #547	C₂²×C₆₇	semidirect
524. #533	C₂²×C₆₇	semidirect
526. #529	C₂²×C₆₇	semidirect
527. #525	C₂²×C₆₇	semidirect
528. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
535. #496	C₂²×C₆₇	semidirect
536. #492	C₂²×C₆₇	semidirect
537. #490	C₂²×C₆₇	semidirect
538. #486	C₂²×C₆₇	semidirect
539. #484	C₂²×C₆₇	semidirect
540. #484	C₂²×C₆₇	semidirect
541. #482	C₂²×C₆₇	semidirect
542. #481	C₂²×C₆₇	semidirect
543. #480	C₂²×C₆₇	semidirect
544. #478	C₂²×C₆₇	semidirect
545. #474	C₂²×C₆₇	semidirect
546. #468	C₂²×C₆₇	semidirect
547. #468	C₂²×C₆₇	semidirect
548. #466	C₂²×C₆₇	semidirect
549. #465	C₂²×C₆₇	semidirect
550. #463	C₂²×C₆₇	semidirect
551. #461	C₂²×C₆₇	semidirect
552. #460	C₂²×C₆₇	semidirect
553. #460	C₂²×C₆₇	semidirect
554. #459	C₂²×C₆₇	semidirect
557. #450	C₂²×C₆₇	semidirect
558. #450	C₂²×C₆₇	semidirect
559. #450	C₂²×C₆₇	semidirect
560. #450	C₂²×C₆₇	semidirect
561. #450	C₂²×C₆₇	semidirect
562. #450	C₂²×C₆₇	semidirect
563. #449	C₂²×C₆₇	semidirect
564. #448	C₂²×C₆₇	semidirect
566. #447	C₂²×C₆₇	semidirect
567. #447	C₂²×C₆₇	semidirect
568. #440	C₂²×C₆₇	semidirect
569. C₄×SD₁₆	C₂²×C₆₇	semidirect
570. C₄×D₈	C₂²×C₆₇	semidirect
571. #436	C₂²×C₆₇	semidirect
572. #435	C₂²×C₆₇	semidirect
573. C₈×D₄	C₂²×C₆₇	semidirect
574. #432	C₂²×C₆₇	semidirect
575. #431	C₂²×C₆₇	semidirect
576. #418	C₂²×C₆₇	semidirect
577. C₂×#102	C₂²×C₆₇	semidirect
578. #407	C₂²×C₆₇	semidirect
579. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
582. C₂×#41	C₂³×C₆₇	semidirect
583. C₂²×Q₈	C₂³×C₆₇	semidirect
606. C₂×SD₁₆	C₂³×C₆₇	semidirect
607. C₂×SD₁₆	C₂³×C₆₇	semidirect
608. C₂×SD₁₆	C₂³×C₆₇	semidirect
610. C₂×D₈	C₂³×C₆₇	semidirect
611. C₂×M₁₆	C₂³×C₆₇	semidirect
612. C₂²×C₈	C₂³×C₆₇	semidirect
614. C₄⋊Q₈	C₂³×C₆₇	semidirect
615. C₄⋊Q₈	C₂³×C₆₇	semidirect
625. #125	C₂³×C₆₇	semidirect
628. #124	C₂³×C₆₇	semidirect
642. C₂²⋊Q₈	C₂³×C₆₇	semidirect
643. C₂²⋊Q₈	C₂³×C₆₇	semidirect
644. C₂²⋊Q₈	C₂³×C₆₇	semidirect
655. #121	C₂³×C₆₇	semidirect
663. C₄×Q₈	C₂³×C₆₇	semidirect
664. C₄×Q₈	C₂³×C₆₇	semidirect
680. C₄×D₄	C₂³×C₆₇	semidirect
684. #117	C₂³×C₆₇	semidirect
689. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
695. #107	C₂³×C₆₇	semidirect
696. #107	C₂³×C₆₇	semidirect
697. #106	C₂³×C₆₇	semidirect
698. C₄⋊C₈	C₂³×C₆₇	semidirect
699. C₄⋊C₈	C₂³×C₆₇	semidirect
700. #103	C₂³×C₆₇	semidirect
701. #103	C₂³×C₆₇	semidirect
705. #102	C₂³×C₆₇	semidirect
706. #102	C₂³×C₆₇	semidirect
707. #102	C₂³×C₆₇	semidirect
708. #102	C₂³×C₆₇	semidirect
709. #102	C₂³×C₆₇	semidirect
713. C₂²⋊C₈	C₂³×C₆₇	semidirect
714. C₂²⋊C₈	C₂³×C₆₇	semidirect
715. #97	C₂³×C₆₇	semidirect
716. C₄×C₈	C₂³×C₆₇	semidirect
888. D₄	AGL(1,ℤ/8)×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
C₂×D₄²×C₆₇	2
C₆₇×#3324	2
C₆₇×#3310	2
C₆₇×#3294	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3272	2
C₆₇×#3265	2
C₆₇×#3217	2
C₆₇×#3208	2
C₆₇×#3193	2
C₆₇×#3188	2
C₆₇×#3110	2
C₆₇×#3105	2
C₆₇×#3003	2
C₂×#450×C₆₇	2
C₆₇×#2974	2
#61600	67

Subgroups — C67×#61600 #30740851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61600 #30740851