Subgroups — C₆₇×#61638 #30740889

Order 17152.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3321	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3305	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3304	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3200	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3199	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3191	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#135×C₆₇	C₂²	1	2	yes	—
25	C₂×#135×C₆₇	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	H(3,𝔽₄)×C₆₇	—	2	1	no	—
29	#560×C₆₇	—	2	1	no	—
30	#559×C₆₇	—	2	1	no	—
31	#556×C₆₇	C₂²	1	2	yes	complemented
32	#555×C₆₇	C₂²	1	2	yes	complemented
33	#551×C₆₇	—	2	1	no	—
34	#550×C₆₇	—	2	2	no	—
35	#550×C₆₇	C₂²	1	2	yes	—
36	#550×C₆₇	C₂²	1	2	yes	complemented
37	#548×C₆₇	—	2	2	no	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#548×C₆₇	C₂²	1	2	yes	complemented
40	#548×C₆₇	C₂²	1	2	yes	complemented
41	#546×C₆₇	C₂²	1	2	yes	complemented
42	#542×C₆₇	—	2	2	no	—
43	#542×C₆₇	C₂²	1	2	yes	—
44	#538×C₆₇	—	2	2	no	—
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#535×C₆₇	—	2	1	no	—
47	#535×C₆₇	—	2	1	no	—
48	#535×C₆₇	C₂²	1	1	yes	characteristic
49	#535×C₆₇	C₂²	1	1	yes	characteristic
50	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#525×C₆₇	—	2	1	no	—
52	#525×C₆₇	—	2	1	no	—
53	#525×C₆₇	C₂²	1	2	yes	—
54	#525×C₆₇	C₂²	1	1	yes	characteristic
55	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#496×C₆₇	C₂²	1	2	yes	complemented
58	#495×C₆₇	C₂²	1	2	yes	complemented
59	#489×C₆₇	C₂²	1	2	yes	complemented
60	#486×C₆₇	C₂²	1	2	yes	complemented
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#485×C₆₇	C₂²	1	2	yes	complemented
63	#482×C₆₇	C₂²	1	2	yes	—
64	#482×C₆₇	C₂²	1	2	yes	complemented
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#482×C₆₇	C₂²	1	2	yes	complemented
67	#477×C₆₇	C₂²	1	2	yes	complemented
68	#475×C₆₇	C₂²	1	2	yes	complemented
69	#469×C₆₇	C₂²	1	2	yes	complemented
70	#468×C₆₇	C₂²	1	2	yes	complemented
71	#467×C₆₇	C₂²	1	2	yes	complemented
72	#466×C₆₇	C₂²	1	2	yes	complemented
73	#466×C₆₇	C₂²	1	2	yes	complemented
74	#465×C₆₇	C₂²	1	2	yes	complemented
75	#465×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#460×C₆₇	C₂²	1	2	yes	complemented
82	#459×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	complemented
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#452×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#451×C₆₇	C₂²	1	2	yes	complemented
89	#451×C₆₇	C₂²	1	2	yes	complemented
90	#450×C₆₇	C₂²	1	2	yes	complemented
91	#449×C₆₇	C₂²	1	2	yes	—
92	#449×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	complemented
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#448×C₆₇	C₂²	1	2	yes	—
97	#448×C₆₇	C₂²	1	2	yes	complemented
98	#448×C₆₇	C₂²	1	2	yes	complemented
99	#447×C₆₇	C₂²	1	2	yes	—
100	#447×C₆₇	C₂²	1	2	yes	complemented
101	#441×C₆₇	C₂²	1	2	yes	complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	#435×C₆₇	C₂²	1	2	yes	complemented
106	#435×C₆₇	C₂²	1	2	yes	complemented
107	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
109	#433×C₆₇	C₂²	1	2	yes	complemented
110	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#416×C₆₇	C₂²	1	2	yes	complemented
115	#416×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	1	yes	characteristic
117	#408×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
119	2₋¹⁺⁴×C₆₇	—	4	2	no	—
120	2₋¹⁺⁴×C₆₇	—	4	2	no	—
121	C₂×#41×C₆₇	—	2	1	no	—
122	C₂×#41×C₆₇	—	2	1	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	2	2	no	—
125	C₂×#41×C₆₇	—	4	2	no	—
126	C₂×#41×C₆₇	—	4	2	no	—
127	C₂×#41×C₆₇	C₂³	1	2	yes	—
128	C₂×#41×C₆₇	C₂³	1	2	yes	—
129	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×#41×C₆₇	C₂³	1	2	yes	—
133	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₆₇	—	2	1	no	—
135	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	—	2	1	no	—
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	#137×C₆₇	—	4	2	no	—
145	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
146	#135×C₆₇	—	4	4	no	—
147	#135×C₆₇	—	4	4	no	—
148	C₂×Q₁₆×C₆₇	—	4	2	no	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	—	4	2	no	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×D₈×C₆₇	C₂³	1	2	yes	—
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
166	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₇	—	2	1	no	—
169	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
170	#127×C₆₇	—	2	2	no	—
171	#127×C₆₇	—	2	2	no	—
172	#127×C₆₇	—	2	1	no	—
173	#127×C₆₇	—	2	1	no	—
174	#127×C₆₇	C₂³	1	2	yes	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#126×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	1	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	2	no	—
185	#124×C₆₇	—	2	2	no	—
186	#124×C₆₇	—	2	2	no	—
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	C₂³	1	2	yes	—
189	#124×C₆₇	C₂³	1	2	yes	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	1	no	—
192	#123×C₆₇	—	2	1	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	D₄	1	1	yes	characteristic
197	#123×C₆₇	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	D₄	1	2	yes	—
218	#121×C₆₇	C₂³	1	2	yes	—
219	#121×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	C₂³	1	2	yes	—
221	#121×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	C₂³	1	2	yes	—
223	#121×C₆₇	C₂³	1	2	yes	—
224	#120×C₆₇	—	2	2	no	—
225	#120×C₆₇	—	2	1	no	—
226	#120×C₆₇	—	2	1	no	—
227	#120×C₆₇	—	2	1	no	—
228	#120×C₆₇	—	2	1	no	—
229	#120×C₆₇	—	2	1	no	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	1	no	—
232	#120×C₆₇	—	2	1	no	—
233	#120×C₆₇	D₄	1	1	yes	characteristic
234	#120×C₆₇	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₆₇	—	2	2	no	—
236	C₄×Q₈×C₆₇	—	2	2	no	—
237	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	2	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	2	yes	—
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	—	2	2	no	—
252	#117×C₆₇	—	2	1	no	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	2	yes	—
258	#117×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
260	#107×C₆₇	C₂³	1	2	yes	—
261	#107×C₆₇	C₂³	1	2	yes	—
262	#106×C₆₇	C₂³	1	2	yes	—
263	#106×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#103×C₆₇	C₂³	1	2	yes	—
272	#103×C₆₇	C₂³	1	2	yes	—
273	#103×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	#102×C₆₇	C₂³	1	2	yes	—
277	#102×C₆₇	C₂³	1	2	yes	—
278	#102×C₆₇	C₂³	1	2	yes	—
279	#102×C₆₇	C₂³	1	2	yes	—
280	#102×C₆₇	C₂³	1	2	yes	—
281	#102×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#97×C₆₇	C₂³	1	2	yes	—
289	C₄×C₈×C₆₇	C₂³	1	2	yes	—
290	C₂⁴×C₆₇	—	2	1	no	—
291	C₂⁴×C₆₇	—	2	1	no	—
292	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
293	#41×C₆₇	—	2	4	no	—
294	#41×C₆₇	—	2	4	no	—
295	#41×C₆₇	—	2	2	no	—
296	#41×C₆₇	—	2	2	no	—
297	#41×C₆₇	—	4	1	no	—
298	#41×C₆₇	—	4	1	no	—
299	#41×C₆₇	—	4	2	no	—
300	#41×C₆₇	—	4	2	no	—
301	#41×C₆₇	—	4	1	no	—
302	#41×C₆₇	—	4	1	no	—
303	#41×C₆₇	—	4	1	no	—
304	#41×C₆₇	—	4	1	no	—
305	#41×C₆₇	—	4	4	no	—
306	#41×C₆₇	—	4	4	no	—
307	#41×C₆₇	—	4	2	no	—
308	#41×C₆₇	—	4	2	no	—
309	#41×C₆₇	—	4	8	no	—
310	#41×C₆₇	—	4	4	no	—
311	C₂×Q₈×C₆₇	—	2	2	no	—
312	C₂×Q₈×C₆₇	—	2	2	no	—
313	C₂×Q₈×C₆₇	—	2	1	no	—
314	C₂×Q₈×C₆₇	—	2	1	no	—
315	C₂×Q₈×C₆₇	—	2	1	no	—
316	C₂×Q₈×C₆₇	—	2	2	no	—
317	C₂×Q₈×C₆₇	—	2	1	no	—
318	C₂×Q₈×C₆₇	—	2	2	no	—
319	C₂×Q₈×C₆₇	—	2	2	no	—
320	C₂×Q₈×C₆₇	—	4	1	no	—
321	C₂×Q₈×C₆₇	—	4	1	no	—
322	C₂×Q₈×C₆₇	—	4	1	no	—
323	C₂×Q₈×C₆₇	—	4	1	no	—
324	C₂×Q₈×C₆₇	—	4	4	no	—
325	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₆₇	—	2	1	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	2	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	2	no	—
344	C₂×D₄×C₆₇	—	2	2	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	4	1	no	—
347	C₂×D₄×C₆₇	—	4	1	no	—
348	C₂×D₄×C₆₇	—	4	1	no	—
349	C₂×D₄×C₆₇	—	4	1	no	—
350	C₂×D₄×C₆₇	—	4	4	no	—
351	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
357	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	4	1	no	—
371	C₂²×C₄×C₆₇	—	4	1	no	—
372	C₂²×C₄×C₆₇	—	4	4	no	—
373	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	Q₁₆×C₆₇	—	2	4	no	—
380	Q₁₆×C₆₇	—	2	4	no	—
381	Q₁₆×C₆₇	—	4	2	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	4	no	—
384	SD₁₆×C₆₇	—	4	2	no	—
385	SD₁₆×C₆₇	—	4	2	no	—
386	SD₁₆×C₆₇	—	4	2	no	—
387	SD₁₆×C₆₇	—	4	2	no	—
388	D₈×C₆₇	—	4	2	no	—
389	D₈×C₆₇	—	4	2	no	—
390	D₈×C₆₇	—	4	2	no	—
391	M₁₆×C₆₇	—	4	1	no	—
392	M₁₆×C₆₇	—	4	1	no	—
393	C₂×C₈×C₆₇	—	4	1	no	—
394	C₂×C₈×C₆₇	—	4	1	no	—
395	C₂×C₈×C₆₇	—	4	2	no	—
396	C₂×C₈×C₆₇	—	4	2	no	—
397	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
398	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
399	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
400	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	1	no	—
417	C₂²⋊C₄×C₆₇	—	2	1	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	2	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	—	2	1	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	2	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	4	1	no	—
452	C₂³×C₆₇	—	4	2	no	—
453	C₂³×C₆₇	—	4	2	no	—
454	C₂³×C₆₇	—	8	2	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	—	8	2	no	—
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₆₇	—	2	4	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	2	2	no	—
465	Q₈×C₆₇	—	2	1	no	—
466	Q₈×C₆₇	—	2	2	no	—
467	Q₈×C₆₇	—	2	1	no	—
468	Q₈×C₆₇	—	4	1	no	—
469	Q₈×C₆₇	—	4	2	no	—
470	Q₈×C₆₇	—	4	2	no	—
471	Q₈×C₆₇	—	8	2	no	—
472	Q₈×C₆₇	—	8	1	no	—
473	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
474	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	1	no	—
477	D₄×C₆₇	—	2	2	no	—
478	D₄×C₆₇	—	2	2	no	—
479	D₄×C₆₇	—	2	2	no	—
480	D₄×C₆₇	—	2	1	no	—
481	D₄×C₆₇	—	4	2	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	1	no	—
484	D₄×C₆₇	—	4	1	no	—
485	D₄×C₆₇	—	4	1	no	—
486	D₄×C₆₇	—	4	4	no	—
487	D₄×C₆₇	—	4	4	no	—
488	D₄×C₆₇	—	4	2	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	8	2	no	—
493	D₄×C₆₇	—	8	2	no	—
494	D₄×C₆₇	—	8	1	no	—
495	D₄×C₆₇	—	8	2	no	—
496	D₄×C₆₇	—	8	2	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	2	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	—	8	2	no	—
502	C₂×C₄×C₆₇	—	2	4	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	2	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	4	1	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	4	no	—
521	C₂×C₄×C₆₇	—	4	4	no	—
522	C₂×C₄×C₆₇	—	4	2	no	—
523	C₂×C₄×C₆₇	—	4	2	no	—
524	C₂×C₄×C₆₇	—	4	2	no	—
525	C₂×C₄×C₆₇	—	4	2	no	—
526	C₂×C₄×C₆₇	—	4	2	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	8	1	no	—
530	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
537	C₈×C₆₇	—	2	2	no	—
538	C₈×C₆₇	—	2	2	no	—
539	C₈×C₆₇	—	2	2	no	—
540	C₈×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	2	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	4	2	no	—
551	C₂²×C₆₇	—	4	2	no	—
552	C₂²×C₆₇	—	4	2	no	—
553	C₂²×C₆₇	—	4	2	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	2	no	—
557	C₂²×C₆₇	—	4	2	no	—
558	C₂²×C₆₇	—	8	2	no	—
559	C₂²×C₆₇	—	8	4	no	—
560	C₂²×C₆₇	—	16	2	no	—
561	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₆₇	—	2	2	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	1	no	—
570	C₄×C₆₇	—	4	2	no	—
571	C₄×C₆₇	—	4	2	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	—	4	1	no	—
574	C₄×C₆₇	—	4	2	no	—
575	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	#61638	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
578	C₂×C₆₇	—	4	1	no	—
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	1	no	—
581	C₂×C₆₇	—	4	1	no	—
582	C₂×C₆₇	—	8	1	no	—
583	C₂×C₆₇	—	8	2	no	—
584	C₂×C₆₇	—	8	2	no	—
585	C₂×C₆₇	#3484	1	1	yes	characteristic
586	C₂×C₆₇	#3584	1	2	yes	—
587	#3540	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3321	C₂×C₆₇	1	2	yes	complemented
590	#3313	C₂×C₆₇	1	2	yes	complemented
591	#3305	C₂×C₆₇	1	2	yes	complemented
592	#3304	C₂×C₆₇	1	2	yes	complemented
593	#3285	C₂×C₆₇	1	2	yes	complemented
594	#3282	C₂×C₆₇	1	2	yes	complemented
595	#3271	C₂×C₆₇	1	2	yes	complemented
596	#3268	C₂×C₆₇	1	2	yes	complemented
597	#3224	C₂×C₆₇	1	2	yes	complemented
598	#3200	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3199	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3191	C₂×C₆₇	1	2	yes	complemented
601	#3121	C₂×C₆₇	1	2	yes	complemented
602	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3002	C₂×C₆₇	1	2	yes	complemented
605	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
606	C₆₇	#61638	1	1	yes	characteristic, direct product factor, Sylow
607	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
608	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
609	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	C₂×#135	C₂²×C₆₇	1	2	yes	—
612	C₂×#135	C₂²×C₆₇	1	2	yes	—
613	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
614	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
615	H(3,𝔽₄)	—	2	1	no	—
616	#560	—	2	1	no	—
617	#559	—	2	1	no	—
618	#556	C₂²×C₆₇	1	2	yes	complemented
619	#555	C₂²×C₆₇	1	2	yes	complemented
620	#551	—	2	1	no	—
621	#550	—	2	2	no	—
622	#550	C₂²×C₆₇	1	2	yes	—
623	#550	C₂²×C₆₇	1	2	yes	complemented
624	#548	—	2	2	no	—
625	#548	C₂²×C₆₇	1	2	yes	—
626	#548	C₂²×C₆₇	1	2	yes	complemented
627	#548	C₂²×C₆₇	1	2	yes	complemented
628	#546	C₂²×C₆₇	1	2	yes	complemented
629	#542	—	2	2	no	—
630	#542	C₂²×C₆₇	1	2	yes	—
631	#538	—	2	2	no	—
632	#536	C₂²×C₆₇	1	1	yes	characteristic
633	#535	—	2	1	no	—
634	#535	—	2	1	no	—
635	#535	C₂²×C₆₇	1	1	yes	characteristic
636	#535	C₂²×C₆₇	1	1	yes	characteristic
637	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#525	—	2	1	no	—
639	#525	—	2	1	no	—
640	#525	C₂²×C₆₇	1	2	yes	—
641	#525	C₂²×C₆₇	1	1	yes	characteristic
642	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#496	C₂²×C₆₇	1	2	yes	complemented
645	#495	C₂²×C₆₇	1	2	yes	complemented
646	#489	C₂²×C₆₇	1	2	yes	complemented
647	#486	C₂²×C₆₇	1	2	yes	complemented
648	#485	C₂²×C₆₇	1	2	yes	complemented
649	#485	C₂²×C₆₇	1	2	yes	complemented
650	#482	C₂²×C₆₇	1	2	yes	—
651	#482	C₂²×C₆₇	1	2	yes	complemented
652	#482	C₂²×C₆₇	1	2	yes	complemented
653	#482	C₂²×C₆₇	1	2	yes	complemented
654	#477	C₂²×C₆₇	1	2	yes	complemented
655	#475	C₂²×C₆₇	1	2	yes	complemented
656	#469	C₂²×C₆₇	1	2	yes	complemented
657	#468	C₂²×C₆₇	1	2	yes	complemented
658	#467	C₂²×C₆₇	1	2	yes	complemented
659	#466	C₂²×C₆₇	1	2	yes	complemented
660	#466	C₂²×C₆₇	1	2	yes	complemented
661	#465	C₂²×C₆₇	1	2	yes	complemented
662	#465	C₂²×C₆₇	1	2	yes	complemented
663	#465	C₂²×C₆₇	1	2	yes	complemented
664	#464	C₂²×C₆₇	1	2	yes	complemented
665	#464	C₂²×C₆₇	1	2	yes	complemented
666	#464	C₂²×C₆₇	1	2	yes	complemented
667	#463	C₂²×C₆₇	1	2	yes	complemented
668	#460	C₂²×C₆₇	1	2	yes	complemented
669	#459	C₂²×C₆₇	1	2	yes	complemented
670	#452	C₂²×C₆₇	1	2	yes	complemented
671	#452	C₂²×C₆₇	1	2	yes	complemented
672	#452	C₂²×C₆₇	1	2	yes	complemented
673	#452	C₂²×C₆₇	1	2	yes	complemented
674	#452	C₂²×C₆₇	1	2	yes	complemented
675	#451	C₂²×C₆₇	1	2	yes	complemented
676	#451	C₂²×C₆₇	1	2	yes	complemented
677	#450	C₂²×C₆₇	1	2	yes	complemented
678	#449	C₂²×C₆₇	1	2	yes	—
679	#449	C₂²×C₆₇	1	2	yes	—
680	#449	C₂²×C₆₇	1	2	yes	—
681	#449	C₂²×C₆₇	1	2	yes	complemented
682	#449	C₂²×C₆₇	1	2	yes	complemented
683	#448	C₂²×C₆₇	1	2	yes	—
684	#448	C₂²×C₆₇	1	2	yes	complemented
685	#448	C₂²×C₆₇	1	2	yes	complemented
686	#447	C₂²×C₆₇	1	2	yes	—
687	#447	C₂²×C₆₇	1	2	yes	complemented
688	#441	C₂²×C₆₇	1	2	yes	complemented
689	#440	C₂²×C₆₇	1	2	yes	complemented
690	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
692	#435	C₂²×C₆₇	1	2	yes	complemented
693	#435	C₂²×C₆₇	1	2	yes	complemented
694	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
695	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
696	#433	C₂²×C₆₇	1	2	yes	complemented
697	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#416	C₂²×C₆₇	1	2	yes	complemented
700	#416	C₂²×C₆₇	1	2	yes	complemented
701	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#408	C₂²×C₆₇	1	1	yes	characteristic
704	#408	C₂²×C₆₇	1	1	yes	characteristic
705	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
706	2₋¹⁺⁴	—	4	2	no	—
707	2₋¹⁺⁴	—	4	2	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	2	no	—
712	C₂×#41	—	4	2	no	—
713	C₂×#41	—	4	2	no	—
714	C₂×#41	C₂³×C₆₇	1	2	yes	—
715	C₂×#41	C₂³×C₆₇	1	2	yes	—
716	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
717	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×#41	C₂³×C₆₇	1	2	yes	—
719	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
721	C₂²×Q₈	—	2	1	no	—
722	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
724	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂³×C₄	—	2	1	no	—
730	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
731	#137	—	4	2	no	—
732	AGL(1,ℤ/8)	—	4	2	no	—
733	#135	—	4	4	no	—
734	#135	—	4	4	no	—
735	C₂×Q₁₆	—	4	2	no	—
736	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×SD₁₆	—	4	2	no	—
740	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
746	C₂×D₈	C₂³×C₆₇	1	2	yes	—
747	C₂×D₈	C₂³×C₆₇	1	2	yes	—
748	C₂×D₈	C₂³×C₆₇	1	2	yes	—
749	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
754	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
755	C₄⋊Q₈	—	2	1	no	—
756	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
757	#127	—	2	2	no	—
758	#127	—	2	2	no	—
759	#127	—	2	1	no	—
760	#127	—	2	1	no	—
761	#127	C₂³×C₆₇	1	2	yes	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	C₂³×C₆₇	1	2	yes	—
776	#124	C₂³×C₆₇	1	2	yes	—
777	#123	—	2	1	no	—
778	#123	—	2	1	no	—
779	#123	—	2	1	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	D₄×C₆₇	1	1	yes	characteristic
784	#123	D₄×C₆₇	1	1	yes	characteristic
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	D₄×C₆₇	1	2	yes	—
805	#121	C₂³×C₆₇	1	2	yes	—
806	#121	C₂³×C₆₇	1	2	yes	—
807	#121	C₂³×C₆₇	1	2	yes	—
808	#121	C₂³×C₆₇	1	2	yes	—
809	#121	C₂³×C₆₇	1	2	yes	—
810	#121	C₂³×C₆₇	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	1	no	—
813	#120	—	2	1	no	—
814	#120	—	2	1	no	—
815	#120	—	2	1	no	—
816	#120	—	2	1	no	—
817	#120	—	2	2	no	—
818	#120	—	2	1	no	—
819	#120	—	2	1	no	—
820	#120	D₄×C₆₇	1	1	yes	characteristic
821	#120	D₄×C₆₇	1	1	yes	characteristic
822	C₄×Q₈	—	2	2	no	—
823	C₄×Q₈	—	2	2	no	—
824	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
825	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
826	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	C₄×D₄	C₂³×C₆₇	1	2	yes	—
837	C₄×D₄	C₂³×C₆₇	1	2	yes	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	C₂³×C₆₇	1	1	yes	characteristic
842	#117	C₂³×C₆₇	1	2	yes	—
843	#117	C₂³×C₆₇	1	1	yes	characteristic
844	#117	C₂³×C₆₇	1	1	yes	characteristic
845	#117	C₂³×C₆₇	1	1	yes	characteristic
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	#107	C₂³×C₆₇	1	2	yes	—
848	#107	C₂³×C₆₇	1	2	yes	—
849	#106	C₂³×C₆₇	1	2	yes	—
850	#106	C₂³×C₆₇	1	2	yes	—
851	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
853	#103	C₂³×C₆₇	1	2	yes	—
854	#103	C₂³×C₆₇	1	2	yes	—
855	#103	C₂³×C₆₇	1	2	yes	—
856	#103	C₂³×C₆₇	1	2	yes	—
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#102	C₂³×C₆₇	1	2	yes	—
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	2	yes	—
866	#102	C₂³×C₆₇	1	2	yes	—
867	#102	C₂³×C₆₇	1	2	yes	—
868	#102	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
875	#97	C₂³×C₆₇	1	2	yes	—
876	C₄×C₈	C₂³×C₆₇	1	2	yes	—
877	C₂⁴	—	2	1	no	—
878	C₂⁴	—	2	1	no	—
879	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
880	#41	—	2	4	no	—
881	#41	—	2	4	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	—	4	1	no	—
885	#41	—	4	1	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	1	no	—
889	#41	—	4	1	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	4	4	no	—
893	#41	—	4	4	no	—
894	#41	—	4	2	no	—
895	#41	—	4	2	no	—
896	#41	—	4	8	no	—
897	#41	—	4	4	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	1	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	1	no	—
911	C₂×Q₈	—	4	4	no	—
912	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	4	1	no	—
934	C₂×D₄	—	4	1	no	—
935	C₂×D₄	—	4	1	no	—
936	C₂×D₄	—	4	1	no	—
937	C₂×D₄	—	4	4	no	—
938	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
941	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
942	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
944	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	4	1	no	—
958	C₂²×C₄	—	4	1	no	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
966	Q₁₆	—	2	4	no	—
967	Q₁₆	—	2	4	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	4	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	D₈	—	4	2	no	—
976	D₈	—	4	2	no	—
977	D₈	—	4	2	no	—
978	M₁₆	—	4	1	no	—
979	M₁₆	—	4	1	no	—
980	C₂×C₈	—	4	1	no	—
981	C₂×C₈	—	4	1	no	—
982	C₂×C₈	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
985	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
986	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
987	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂⁴×C₆₇	1	2	yes	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1045	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1046	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1047	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1048	Q₈	—	2	4	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1061	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	8	2	no	—
1146	C₂²	—	8	4	no	—
1147	C₂²	—	16	2	no	—
1148	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1149	C₄	—	2	2	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1163	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	4	1	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	8	2	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	C₆₇×#3484	1	1	yes	characteristic
1172	C₂	C₆₇×#3584	1	2	yes	—

	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3540	C₂	semidirect
2. C₆₇×#3487	C₂	semidirect
3. C₆₇×#3321	C₂	semidirect
4. C₆₇×#3313	C₂	semidirect
5. C₆₇×#3305	C₂	semidirect
6. C₆₇×#3304	C₂	semidirect
7. C₆₇×#3285	C₂	semidirect
8. C₆₇×#3282	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3268	C₂	semidirect
11. C₆₇×#3224	C₂	semidirect
12. C₆₇×#3200	C₂	semidirect
13. C₆₇×#3199	C₂	semidirect
14. C₆₇×#3191	C₂	semidirect
15. C₆₇×#3121	C₂	semidirect
16. C₆₇×#3011	C₂	semidirect
17. C₆₇×#3010	C₂	semidirect
18. C₆₇×#3002	C₂	semidirect
19. C₆₇×#2977	C₂	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂²×Q₁₆×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
32. #555×C₆₇	C₂²	semidirect
36. #550×C₆₇	C₂²	semidirect
39. #548×C₆₇	C₂²	semidirect
40. #548×C₆₇	C₂²	semidirect
41. #546×C₆₇	C₂²	semidirect
50. #535×C₆₇	C₂²	semidirect
55. #525×C₆₇	C₂²	semidirect
56. #519×C₆₇	C₂²	semidirect
57. #496×C₆₇	C₂²	semidirect
58. #495×C₆₇	C₂²	semidirect
59. #489×C₆₇	C₂²	semidirect
60. #486×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #485×C₆₇	C₂²	semidirect
64. #482×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
67. #477×C₆₇	C₂²	semidirect
68. #475×C₆₇	C₂²	semidirect
69. #469×C₆₇	C₂²	semidirect
70. #468×C₆₇	C₂²	semidirect
71. #467×C₆₇	C₂²	semidirect
72. #466×C₆₇	C₂²	semidirect
73. #466×C₆₇	C₂²	semidirect
74. #465×C₆₇	C₂²	semidirect
75. #465×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #460×C₆₇	C₂²	semidirect
82. #459×C₆₇	C₂²	semidirect
83. #452×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #452×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #451×C₆₇	C₂²	semidirect
89. #451×C₆₇	C₂²	semidirect
90. #450×C₆₇	C₂²	semidirect
94. #449×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
97. #448×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
100. #447×C₆₇	C₂²	semidirect
101. #441×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. C₄×Q₁₆×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. #435×C₆₇	C₂²	semidirect
106. #435×C₆₇	C₂²	semidirect
107. C₈×D₄×C₆₇	C₂²	semidirect
108. C₈×D₄×C₆₇	C₂²	semidirect
109. #433×C₆₇	C₂²	semidirect
110. #419×C₆₇	C₂²	semidirect
111. #419×C₆₇	C₂²	semidirect
112. #416×C₆₇	C₂²	semidirect
113. #416×C₆₇	C₂²	semidirect
114. #416×C₆₇	C₂²	semidirect
115. #416×C₆₇	C₂²	semidirect
118. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
577. #61638	C₆₇	direct (N × H)
587. #3540	C₂×C₆₇	semidirect
588. #3487	C₂×C₆₇	semidirect
589. #3321	C₂×C₆₇	semidirect
590. #3313	C₂×C₆₇	semidirect
591. #3305	C₂×C₆₇	semidirect
592. #3304	C₂×C₆₇	semidirect
593. #3285	C₂×C₆₇	semidirect
594. #3282	C₂×C₆₇	semidirect
595. #3271	C₂×C₆₇	semidirect
596. #3268	C₂×C₆₇	semidirect
597. #3224	C₂×C₆₇	semidirect
598. #3200	C₂×C₆₇	semidirect
599. #3199	C₂×C₆₇	semidirect
600. #3191	C₂×C₆₇	semidirect
601. #3121	C₂×C₆₇	semidirect
602. #3011	C₂×C₆₇	semidirect
603. #3010	C₂×C₆₇	semidirect
604. #3002	C₂×C₆₇	semidirect
605. #2977	C₂×C₆₇	semidirect
606. C₆₇	#61638	direct (N × H)
608. C₂²×#41	C₂²×C₆₇	semidirect
609. C₂×#137	C₂²×C₆₇	semidirect
610. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
613. C₂²×Q₁₆	C₂²×C₆₇	semidirect
614. C₂²×SD₁₆	C₂²×C₆₇	semidirect
618. #556	C₂²×C₆₇	semidirect
619. #555	C₂²×C₆₇	semidirect
623. #550	C₂²×C₆₇	semidirect
626. #548	C₂²×C₆₇	semidirect
627. #548	C₂²×C₆₇	semidirect
628. #546	C₂²×C₆₇	semidirect
637. #535	C₂²×C₆₇	semidirect
642. #525	C₂²×C₆₇	semidirect
643. #519	C₂²×C₆₇	semidirect
644. #496	C₂²×C₆₇	semidirect
645. #495	C₂²×C₆₇	semidirect
646. #489	C₂²×C₆₇	semidirect
647. #486	C₂²×C₆₇	semidirect
648. #485	C₂²×C₆₇	semidirect
649. #485	C₂²×C₆₇	semidirect
651. #482	C₂²×C₆₇	semidirect
652. #482	C₂²×C₆₇	semidirect
653. #482	C₂²×C₆₇	semidirect
654. #477	C₂²×C₆₇	semidirect
655. #475	C₂²×C₆₇	semidirect
656. #469	C₂²×C₆₇	semidirect
657. #468	C₂²×C₆₇	semidirect
658. #467	C₂²×C₆₇	semidirect
659. #466	C₂²×C₆₇	semidirect
660. #466	C₂²×C₆₇	semidirect
661. #465	C₂²×C₆₇	semidirect
662. #465	C₂²×C₆₇	semidirect
663. #465	C₂²×C₆₇	semidirect
664. #464	C₂²×C₆₇	semidirect
665. #464	C₂²×C₆₇	semidirect
666. #464	C₂²×C₆₇	semidirect
667. #463	C₂²×C₆₇	semidirect
668. #460	C₂²×C₆₇	semidirect
669. #459	C₂²×C₆₇	semidirect
670. #452	C₂²×C₆₇	semidirect
671. #452	C₂²×C₆₇	semidirect
672. #452	C₂²×C₆₇	semidirect
673. #452	C₂²×C₆₇	semidirect
674. #452	C₂²×C₆₇	semidirect
675. #451	C₂²×C₆₇	semidirect
676. #451	C₂²×C₆₇	semidirect
677. #450	C₂²×C₆₇	semidirect
681. #449	C₂²×C₆₇	semidirect
682. #449	C₂²×C₆₇	semidirect
684. #448	C₂²×C₆₇	semidirect
685. #448	C₂²×C₆₇	semidirect
687. #447	C₂²×C₆₇	semidirect
688. #441	C₂²×C₆₇	semidirect
689. #440	C₂²×C₆₇	semidirect
690. C₄×Q₁₆	C₂²×C₆₇	semidirect
691. C₄×SD₁₆	C₂²×C₆₇	semidirect
692. #435	C₂²×C₆₇	semidirect
693. #435	C₂²×C₆₇	semidirect
694. C₈×D₄	C₂²×C₆₇	semidirect
695. C₈×D₄	C₂²×C₆₇	semidirect
696. #433	C₂²×C₆₇	semidirect
697. #419	C₂²×C₆₇	semidirect
698. #419	C₂²×C₆₇	semidirect
699. #416	C₂²×C₆₇	semidirect
700. #416	C₂²×C₆₇	semidirect
701. #416	C₂²×C₆₇	semidirect
702. #416	C₂²×C₆₇	semidirect
705. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3540	2
C₆₇×#3487	2
C₆₇×#3321	2
C₆₇×#3313	2
C₆₇×#3305	2
C₆₇×#3304	2
C₆₇×#3285	2
C₆₇×#3282	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3224	2
C₆₇×#3200	2
C₆₇×#3199	2
C₆₇×#3191	2
C₆₇×#3121	2
C₆₇×#3011	2
C₆₇×#3010	2
C₆₇×#3002	2
C₆₇×#2977	2
#61638	67

Subgroups — C67×#61638 #30740889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61638 #30740889