Subgroups — C₆₇×#61677 #30740928

Order 17152.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3215	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
24	C₂×#135×C₆₇	C₂²	1	2	yes	—
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	#562×C₆₇	—	2	1	no	—
27	#562×C₆₇	—	2	1	no	—
28	#554×C₆₇	—	2	1	no	—
29	#554×C₆₇	C₂²	1	2	yes	complemented
30	#550×C₆₇	—	2	1	no	—
31	#550×C₆₇	C₂²	1	2	yes	complemented
32	#548×C₆₇	C₂²	1	2	yes	—
33	#548×C₆₇	C₂²	1	2	yes	—
34	#547×C₆₇	C₂²	1	2	yes	complemented
35	#547×C₆₇	C₂²	1	2	yes	complemented
36	#546×C₆₇	—	2	2	no	—
37	#546×C₆₇	—	2	2	no	—
38	#546×C₆₇	C₂²	1	2	yes	—
39	#546×C₆₇	C₂²	1	2	yes	—
40	#540×C₆₇	—	2	2	no	—
41	#537×C₆₇	—	2	2	no	—
42	#537×C₆₇	C₂²	1	2	yes	—
43	#537×C₆₇	C₂²	1	2	yes	complemented
44	#536×C₆₇	—	2	1	no	—
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#535×C₆₇	—	2	1	no	—
47	#535×C₆₇	C₂²	1	1	yes	characteristic
48	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#532×C₆₇	—	2	1	no	—
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#124×C₆₇	—	2	1	no	—
53	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	#497×C₆₇	C₂²	1	2	yes	complemented
56	#496×C₆₇	C₂²	1	2	yes	complemented
57	#489×C₆₇	C₂²	1	2	yes	complemented
58	#489×C₆₇	C₂²	1	2	yes	complemented
59	#485×C₆₇	C₂²	1	2	yes	complemented
60	#484×C₆₇	C₂²	1	2	yes	complemented
61	#483×C₆₇	C₂²	1	2	yes	complemented
62	#482×C₆₇	C₂²	1	2	yes	complemented
63	#481×C₆₇	C₂²	1	2	yes	complemented
64	#480×C₆₇	C₂²	1	2	yes	complemented
65	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#469×C₆₇	C₂²	1	2	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#467×C₆₇	C₂²	1	2	yes	complemented
74	#466×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	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#452×C₆₇	C₂²	1	2	yes	complemented
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#451×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	complemented
92	#450×C₆₇	C₂²	1	2	yes	—
93	#450×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	—
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#448×C₆₇	C₂²	1	2	yes	complemented
101	#447×C₆₇	C₂²	1	2	yes	—
102	#447×C₆₇	C₂²	1	2	yes	—
103	#442×C₆₇	C₂²	1	2	yes	complemented
104	#441×C₆₇	C₂²	1	2	yes	complemented
105	#440×C₆₇	C₂²	1	2	yes	complemented
106	#440×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	#435×C₆₇	C₂²	1	2	yes	complemented
110	#435×C₆₇	C₂²	1	2	yes	complemented
111	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#417×C₆₇	C₂²	1	2	yes	—
114	#417×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
116	C₂×#102×C₆₇	C₂²	1	2	yes	—
117	#408×C₆₇	C₂²	1	2	yes	—
118	#408×C₆₇	C₂²	1	2	yes	complemented
119	2₋¹⁺⁴×C₆₇	—	4	2	no	—
120	2₋¹⁺⁴×C₆₇	—	4	2	no	—
121	H(5,𝔽₂)×C₆₇	—	4	2	no	—
122	H(5,𝔽₂)×C₆₇	—	4	2	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	2	1	no	—
125	C₂×#41×C₆₇	—	2	2	no	—
126	C₂×#41×C₆₇	—	2	2	no	—
127	C₂×#41×C₆₇	—	2	1	no	—
128	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×#41×C₆₇	C₂³	1	2	yes	—
130	C₂×#41×C₆₇	C₂³	1	2	yes	—
131	C₂×#41×C₆₇	C₂³	1	2	yes	—
132	C₂×#41×C₆₇	C₂³	1	2	yes	—
133	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₆₇	—	2	1	no	—
136	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	—	2	1	no	—
139	C₂²×D₄×C₆₇	—	2	2	no	—
140	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	#137×C₆₇	—	4	4	no	—
143	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
144	#135×C₆₇	—	4	4	no	—
145	#135×C₆₇	—	4	4	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	—	2	1	no	—
163	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	—	2	1	no	—
168	#127×C₆₇	—	2	2	no	—
169	#127×C₆₇	D₄	1	1	yes	characteristic
170	#127×C₆₇	C₂³	1	1	yes	characteristic
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	1	no	—
173	#124×C₆₇	—	2	1	no	—
174	#124×C₆₇	—	2	1	no	—
175	#124×C₆₇	—	2	2	no	—
176	#124×C₆₇	—	2	2	no	—
177	#124×C₆₇	—	2	1	no	—
178	#124×C₆₇	—	2	1	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	D₄	1	1	yes	characteristic
181	#124×C₆₇	D₄	1	1	yes	characteristic
182	#124×C₆₇	C₂³	1	2	yes	—
183	#124×C₆₇	C₂³	1	2	yes	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
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	1	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	D₄	1	2	yes	—
219	#121×C₆₇	D₄	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	#121×C₆₇	C₂³	1	2	yes	—
225	#120×C₆₇	—	2	2	no	—
226	#120×C₆₇	—	2	2	no	—
227	#120×C₆₇	—	2	2	no	—
228	C₄×Q₈×C₆₇	—	2	1	no	—
229	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	#117×C₆₇	—	2	1	no	—
245	#117×C₆₇	—	2	1	no	—
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
250	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
251	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
253	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
254	C₂×C₄²×C₆₇	—	2	1	no	—
255	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
256	#107×C₆₇	C₂³	1	2	yes	—
257	#107×C₆₇	C₂³	1	2	yes	—
258	#106×C₆₇	C₂³	1	2	yes	—
259	#106×C₆₇	C₂³	1	2	yes	—
260	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
264	#103×C₆₇	C₂³	1	2	yes	—
265	#103×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	#102×C₆₇	C₂³	1	2	yes	—
273	#102×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	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×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	#97×C₆₇	C₂³	1	2	yes	—
287	#97×C₆₇	C₂³	1	2	yes	—
288	C₂⁴×C₆₇	—	2	2	no	—
289	C₂⁴×C₆₇	—	2	1	no	—
290	#41×C₆₇	—	2	2	no	—
291	#41×C₆₇	—	2	2	no	—
292	#41×C₆₇	—	2	4	no	—
293	#41×C₆₇	—	2	4	no	—
294	#41×C₆₇	—	4	1	no	—
295	#41×C₆₇	—	4	1	no	—
296	#41×C₆₇	—	4	1	no	—
297	#41×C₆₇	—	4	1	no	—
298	#41×C₆₇	—	4	2	no	—
299	#41×C₆₇	—	4	2	no	—
300	#41×C₆₇	—	4	4	no	—
301	#41×C₆₇	—	4	4	no	—
302	#41×C₆₇	—	4	2	no	—
303	#41×C₆₇	—	4	2	no	—
304	#41×C₆₇	—	4	2	no	—
305	#41×C₆₇	—	4	2	no	—
306	#41×C₆₇	—	4	8	no	—
307	#41×C₆₇	—	8	2	no	—
308	#41×C₆₇	—	8	4	no	—
309	C₂×Q₈×C₆₇	—	2	1	no	—
310	C₂×Q₈×C₆₇	—	2	2	no	—
311	C₂×Q₈×C₆₇	—	2	1	no	—
312	C₂×Q₈×C₆₇	—	2	1	no	—
313	C₂×Q₈×C₆₇	—	2	4	no	—
314	C₂×Q₈×C₆₇	—	4	2	no	—
315	C₂×Q₈×C₆₇	—	4	1	no	—
316	C₂×Q₈×C₆₇	—	4	1	no	—
317	C₂×Q₈×C₆₇	—	4	4	no	—
318	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
321	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₆₇	—	2	1	no	—
324	C₂×D₄×C₆₇	—	2	4	no	—
325	C₂×D₄×C₆₇	—	2	2	no	—
326	C₂×D₄×C₆₇	—	2	2	no	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	4	2	no	—
339	C₂×D₄×C₆₇	—	4	1	no	—
340	C₂×D₄×C₆₇	—	4	1	no	—
341	C₂×D₄×C₆₇	—	4	4	no	—
342	C₂×D₄×C₆₇	—	4	8	no	—
343	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
350	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	2	2	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
369	Q₁₆×C₆₇	—	2	4	no	—
370	Q₁₆×C₆₇	—	4	2	no	—
371	Q₁₆×C₆₇	—	4	2	no	—
372	SD₁₆×C₆₇	—	2	4	no	—
373	SD₁₆×C₆₇	—	2	4	no	—
374	SD₁₆×C₆₇	—	4	2	no	—
375	SD₁₆×C₆₇	—	4	2	no	—
376	SD₁₆×C₆₇	—	4	2	no	—
377	SD₁₆×C₆₇	—	4	2	no	—
378	D₈×C₆₇	—	2	4	no	—
379	D₈×C₆₇	—	4	2	no	—
380	D₈×C₆₇	—	4	2	no	—
381	M₁₆×C₆₇	—	4	2	no	—
382	M₁₆×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	—	4	2	no	—
384	C₂×C₈×C₆₇	—	4	2	no	—
385	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₄²×C₆₇	—	2	1	no	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	—	2	1	no	—
434	C₄²×C₆₇	—	2	2	no	—
435	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂³×C₆₇	—	2	1	no	—
440	C₂³×C₆₇	—	2	2	no	—
441	C₂³×C₆₇	—	2	2	no	—
442	C₂³×C₆₇	—	4	4	no	—
443	C₂³×C₆₇	—	4	2	no	—
444	C₂³×C₆₇	—	8	1	no	—
445	C₂³×C₆₇	—	8	2	no	—
446	C₂³×C₆₇	—	8	1	no	—
447	C₂³×C₆₇	—	8	2	no	—
448	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
449	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
451	Q₈×C₆₇	—	2	1	no	—
452	Q₈×C₆₇	—	2	2	no	—
453	Q₈×C₆₇	—	2	2	no	—
454	Q₈×C₆₇	—	2	2	no	—
455	Q₈×C₆₇	—	2	2	no	—
456	Q₈×C₆₇	—	4	1	no	—
457	Q₈×C₆₇	—	4	1	no	—
458	Q₈×C₆₇	—	4	4	no	—
459	Q₈×C₆₇	—	4	2	no	—
460	Q₈×C₆₇	—	4	2	no	—
461	Q₈×C₆₇	—	8	1	no	—
462	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
463	D₄×C₆₇	—	2	4	no	—
464	D₄×C₆₇	—	2	1	no	—
465	D₄×C₆₇	—	2	2	no	—
466	D₄×C₆₇	—	2	2	no	—
467	D₄×C₆₇	—	2	2	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	4	1	no	—
470	D₄×C₆₇	—	4	2	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	1	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	4	no	—
476	D₄×C₆₇	—	4	4	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	4	no	—
480	D₄×C₆₇	—	8	1	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	2	no	—
484	D₄×C₆₇	—	8	2	no	—
485	D₄×C₆₇	—	8	2	no	—
486	D₄×C₆₇	—	8	2	no	—
487	D₄×C₆₇	—	8	2	no	—
488	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
489	C₂×C₄×C₆₇	—	2	4	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	4	1	no	—
504	C₂×C₄×C₆₇	—	4	1	no	—
505	C₂×C₄×C₆₇	—	4	4	no	—
506	C₂×C₄×C₆₇	—	4	4	no	—
507	C₂×C₄×C₆₇	—	4	4	no	—
508	C₂×C₄×C₆₇	—	4	4	no	—
509	C₂×C₄×C₆₇	—	4	2	no	—
510	C₂×C₄×C₆₇	—	8	1	no	—
511	C₂×C₄×C₆₇	—	8	1	no	—
512	C₂×C₄×C₆₇	—	8	2	no	—
513	C₂×C₄×C₆₇	—	8	2	no	—
514	C₂×C₄×C₆₇	—	8	2	no	—
515	C₂×C₄×C₆₇	—	8	2	no	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
524	C₈×C₆₇	—	2	2	no	—
525	C₈×C₆₇	—	2	2	no	—
526	C₈×C₆₇	—	2	2	no	—
527	C₈×C₆₇	—	2	2	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	2	no	—
531	C₂²×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	1	no	—
535	C₂²×C₆₇	—	2	2	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	2	no	—
538	C₂²×C₆₇	—	4	1	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	2	no	—
541	C₂²×C₆₇	—	4	2	no	—
542	C₂²×C₆₇	—	4	2	no	—
543	C₂²×C₆₇	—	4	2	no	—
544	C₂²×C₆₇	—	4	2	no	—
545	C₂²×C₆₇	—	4	2	no	—
546	C₂²×C₆₇	—	16	4	no	—
547	C₂²×C₆₇	—	16	2	no	—
548	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₆₇	—	2	1	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	1	no	—
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	1	no	—
554	C₄×C₆₇	—	2	2	no	—
555	C₄×C₆₇	—	2	2	no	—
556	C₄×C₆₇	—	2	2	no	—
557	C₄×C₆₇	—	4	2	no	—
558	C₄×C₆₇	—	4	2	no	—
559	C₄×C₆₇	—	4	1	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	2	no	—
562	C₄×C₆₇	—	4	2	no	—
563	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	#61677	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
566	C₂×C₆₇	—	4	2	no	—
567	C₂×C₆₇	—	4	1	no	—
568	C₂×C₆₇	—	4	2	no	—
569	C₂×C₆₇	—	4	2	no	—
570	C₂×C₆₇	—	8	2	no	—
571	C₂×C₆₇	—	8	2	no	—
572	C₂×C₆₇	#3484	1	1	yes	characteristic
573	C₂×C₆₇	#3585	1	1	yes	characteristic
574	C₂×C₆₇	#3586	1	1	yes	characteristic
575	#3548	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3316	C₂×C₆₇	1	2	yes	complemented
578	#3314	C₂×C₆₇	1	2	yes	complemented
579	#3308	C₂×C₆₇	1	2	yes	complemented
580	#3306	C₂×C₆₇	1	2	yes	complemented
581	#3271	C₂×C₆₇	1	2	yes	complemented
582	#3269	C₂×C₆₇	1	2	yes	complemented
583	#3268	C₂×C₆₇	1	2	yes	complemented
584	#3267	C₂×C₆₇	1	2	yes	complemented
585	#3215	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3213	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3201	C₂×C₆₇	1	2	yes	complemented
588	#3198	C₂×C₆₇	1	2	yes	complemented
589	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3013	C₂×C₆₇	1	2	yes	complemented
592	#3012	C₂×C₆₇	1	2	yes	complemented
593	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
594	C₆₇	#61677	1	1	yes	characteristic, direct product factor, Sylow
595	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
597	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
598	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
599	C₂×#135	C₂²×C₆₇	1	2	yes	—
600	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
601	#562	—	2	1	no	—
602	#562	—	2	1	no	—
603	#554	—	2	1	no	—
604	#554	C₂²×C₆₇	1	2	yes	complemented
605	#550	—	2	1	no	—
606	#550	C₂²×C₆₇	1	2	yes	complemented
607	#548	C₂²×C₆₇	1	2	yes	—
608	#548	C₂²×C₆₇	1	2	yes	—
609	#547	C₂²×C₆₇	1	2	yes	complemented
610	#547	C₂²×C₆₇	1	2	yes	complemented
611	#546	—	2	2	no	—
612	#546	—	2	2	no	—
613	#546	C₂²×C₆₇	1	2	yes	—
614	#546	C₂²×C₆₇	1	2	yes	—
615	#540	—	2	2	no	—
616	#537	—	2	2	no	—
617	#537	C₂²×C₆₇	1	2	yes	—
618	#537	C₂²×C₆₇	1	2	yes	complemented
619	#536	—	2	1	no	—
620	#536	C₂²×C₆₇	1	1	yes	characteristic
621	#535	—	2	1	no	—
622	#535	C₂²×C₆₇	1	1	yes	characteristic
623	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#532	—	2	1	no	—
625	#532	C₂²×C₆₇	1	1	yes	characteristic
626	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	C₂×#124	—	2	1	no	—
628	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
629	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
630	#497	C₂²×C₆₇	1	2	yes	complemented
631	#496	C₂²×C₆₇	1	2	yes	complemented
632	#489	C₂²×C₆₇	1	2	yes	complemented
633	#489	C₂²×C₆₇	1	2	yes	complemented
634	#485	C₂²×C₆₇	1	2	yes	complemented
635	#484	C₂²×C₆₇	1	2	yes	complemented
636	#483	C₂²×C₆₇	1	2	yes	complemented
637	#482	C₂²×C₆₇	1	2	yes	complemented
638	#481	C₂²×C₆₇	1	2	yes	complemented
639	#480	C₂²×C₆₇	1	2	yes	complemented
640	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#470	C₂²×C₆₇	1	2	yes	complemented
645	#469	C₂²×C₆₇	1	2	yes	complemented
646	#468	C₂²×C₆₇	1	2	yes	complemented
647	#468	C₂²×C₆₇	1	2	yes	complemented
648	#467	C₂²×C₆₇	1	2	yes	complemented
649	#466	C₂²×C₆₇	1	2	yes	complemented
650	#465	C₂²×C₆₇	1	2	yes	complemented
651	#465	C₂²×C₆₇	1	2	yes	complemented
652	#464	C₂²×C₆₇	1	2	yes	complemented
653	#464	C₂²×C₆₇	1	2	yes	complemented
654	#463	C₂²×C₆₇	1	2	yes	complemented
655	#463	C₂²×C₆₇	1	2	yes	complemented
656	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
660	#452	C₂²×C₆₇	1	2	yes	—
661	#452	C₂²×C₆₇	1	2	yes	—
662	#452	C₂²×C₆₇	1	2	yes	complemented
663	#452	C₂²×C₆₇	1	2	yes	complemented
664	#452	C₂²×C₆₇	1	2	yes	complemented
665	#451	C₂²×C₆₇	1	2	yes	complemented
666	#451	C₂²×C₆₇	1	2	yes	complemented
667	#450	C₂²×C₆₇	1	2	yes	—
668	#450	C₂²×C₆₇	1	2	yes	—
669	#449	C₂²×C₆₇	1	2	yes	—
670	#449	C₂²×C₆₇	1	2	yes	—
671	#449	C₂²×C₆₇	1	2	yes	complemented
672	#449	C₂²×C₆₇	1	2	yes	complemented
673	#449	C₂²×C₆₇	1	2	yes	complemented
674	#448	C₂²×C₆₇	1	2	yes	complemented
675	#448	C₂²×C₆₇	1	2	yes	complemented
676	#447	C₂²×C₆₇	1	2	yes	—
677	#447	C₂²×C₆₇	1	2	yes	—
678	#442	C₂²×C₆₇	1	2	yes	complemented
679	#441	C₂²×C₆₇	1	2	yes	complemented
680	#440	C₂²×C₆₇	1	2	yes	complemented
681	#440	C₂²×C₆₇	1	2	yes	complemented
682	#435	C₂²×C₆₇	1	2	yes	complemented
683	#435	C₂²×C₆₇	1	2	yes	complemented
684	#435	C₂²×C₆₇	1	2	yes	complemented
685	#435	C₂²×C₆₇	1	2	yes	complemented
686	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#417	C₂²×C₆₇	1	2	yes	—
689	#417	C₂²×C₆₇	1	2	yes	complemented
690	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
691	C₂×#102	C₂²×C₆₇	1	2	yes	—
692	#408	C₂²×C₆₇	1	2	yes	—
693	#408	C₂²×C₆₇	1	2	yes	complemented
694	2₋¹⁺⁴	—	4	2	no	—
695	2₋¹⁺⁴	—	4	2	no	—
696	H(5,𝔽₂)	—	4	2	no	—
697	H(5,𝔽₂)	—	4	2	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	2	no	—
701	C₂×#41	—	2	2	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×#41	C₂³×C₆₇	1	2	yes	—
705	C₂×#41	C₂³×C₆₇	1	2	yes	—
706	C₂×#41	C₂³×C₆₇	1	2	yes	—
707	C₂×#41	C₂³×C₆₇	1	2	yes	—
708	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
712	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	—	2	2	no	—
715	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
716	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
717	#137	—	4	4	no	—
718	AGL(1,ℤ/8)	—	4	4	no	—
719	#135	—	4	4	no	—
720	#135	—	4	4	no	—
721	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
730	C₂×D₈	C₂³×C₆₇	1	2	yes	—
731	C₂×D₈	C₂³×C₆₇	1	2	yes	—
732	C₂×D₈	C₂³×C₆₇	1	2	yes	—
733	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
735	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
736	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
742	#127	—	2	1	no	—
743	#127	—	2	2	no	—
744	#127	D₄×C₆₇	1	1	yes	characteristic
745	#127	C₂³×C₆₇	1	1	yes	characteristic
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#124	—	2	1	no	—
749	#124	—	2	1	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	1	no	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	D₄×C₆₇	1	1	yes	characteristic
756	#124	D₄×C₆₇	1	1	yes	characteristic
757	#124	C₂³×C₆₇	1	2	yes	—
758	#124	C₂³×C₆₇	1	2	yes	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	D₄×C₆₇	1	2	yes	—
794	#121	D₄×C₆₇	1	2	yes	—
795	#121	C₂³×C₆₇	1	2	yes	—
796	#121	C₂³×C₆₇	1	2	yes	—
797	#121	C₂³×C₆₇	1	2	yes	—
798	#121	C₂³×C₆₇	1	2	yes	—
799	#121	C₂³×C₆₇	1	2	yes	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	2	yes	—
817	C₄×D₄	C₂³×C₆₇	1	2	yes	—
818	C₄×D₄	C₂³×C₆₇	1	2	yes	—
819	#117	—	2	1	no	—
820	#117	—	2	1	no	—
821	#117	C₂³×C₆₇	1	1	yes	characteristic
822	C₂×C₄⋊C₄	—	2	2	no	—
823	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
824	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	1	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₄²	—	2	1	no	—
830	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
831	#107	C₂³×C₆₇	1	2	yes	—
832	#107	C₂³×C₆₇	1	2	yes	—
833	#106	C₂³×C₆₇	1	2	yes	—
834	#106	C₂³×C₆₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
839	#103	C₂³×C₆₇	1	2	yes	—
840	#103	C₂³×C₆₇	1	2	yes	—
841	#103	C₂³×C₆₇	1	2	yes	—
842	#103	C₂³×C₆₇	1	2	yes	—
843	#103	C₂³×C₆₇	1	2	yes	—
844	#103	C₂³×C₆₇	1	2	yes	—
845	#103	C₂³×C₆₇	1	2	yes	—
846	#103	C₂³×C₆₇	1	2	yes	—
847	#102	C₂³×C₆₇	1	2	yes	—
848	#102	C₂³×C₆₇	1	2	yes	—
849	#102	C₂³×C₆₇	1	2	yes	—
850	#102	C₂³×C₆₇	1	2	yes	—
851	#102	C₂³×C₆₇	1	2	yes	—
852	#102	C₂³×C₆₇	1	2	yes	—
853	#102	C₂³×C₆₇	1	2	yes	—
854	#102	C₂³×C₆₇	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
861	#97	C₂³×C₆₇	1	2	yes	—
862	#97	C₂³×C₆₇	1	2	yes	—
863	C₂⁴	—	2	2	no	—
864	C₂⁴	—	2	1	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	2	4	no	—
868	#41	—	2	4	no	—
869	#41	—	4	1	no	—
870	#41	—	4	1	no	—
871	#41	—	4	1	no	—
872	#41	—	4	1	no	—
873	#41	—	4	2	no	—
874	#41	—	4	2	no	—
875	#41	—	4	4	no	—
876	#41	—	4	4	no	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	4	2	no	—
881	#41	—	4	8	no	—
882	#41	—	8	2	no	—
883	#41	—	8	4	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	4	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	—	4	1	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	4	no	—
893	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
894	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	1	no	—
915	C₂×D₄	—	4	1	no	—
916	C₂×D₄	—	4	4	no	—
917	C₂×D₄	—	4	8	no	—
918	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
919	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
920	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
921	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
923	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
925	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
926	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
944	Q₁₆	—	2	4	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	D₈	—	2	4	no	—
954	D₈	—	4	2	no	—
955	D₈	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
961	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
962	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
963	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1011	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	4	4	no	—
1018	C₂³	—	4	2	no	—
1019	C₂³	—	8	1	no	—
1020	C₂³	—	8	2	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1024	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1025	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	4	1	no	—
1032	Q₈	—	4	1	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	4	2	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1038	D₄	—	2	4	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	4	1	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	8	1	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1064	C₂×C₄	—	2	4	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	4	4	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1098	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1099	C₈	—	2	2	no	—
1100	C₈	—	2	2	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	16	4	no	—
1122	C₂²	—	16	2	no	—
1123	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1139	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1140	C₂	—	4	1	no	—
1141	C₂	—	4	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	8	2	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₆₇×#3484	1	1	yes	characteristic
1147	C₂	C₆₇×#3585	1	1	yes	characteristic
1148	C₂	C₆₇×#3586	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3548	C₂	semidirect
2. C₆₇×#3500	C₂	semidirect
3. C₆₇×#3316	C₂	semidirect
4. C₆₇×#3314	C₂	semidirect
5. C₆₇×#3308	C₂	semidirect
6. C₆₇×#3306	C₂	semidirect
7. C₆₇×#3271	C₂	semidirect
8. C₆₇×#3269	C₂	semidirect
9. C₆₇×#3268	C₂	semidirect
10. C₆₇×#3267	C₂	semidirect
11. C₆₇×#3215	C₂	semidirect
12. C₆₇×#3213	C₂	semidirect
13. C₆₇×#3201	C₂	semidirect
14. C₆₇×#3198	C₂	semidirect
15. C₆₇×#3116	C₂	semidirect
16. C₆₇×#3115	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3012	C₂	semidirect
19. C₆₇×#2980	C₂	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
31. #550×C₆₇	C₂²	semidirect
34. #547×C₆₇	C₂²	semidirect
35. #547×C₆₇	C₂²	semidirect
43. #537×C₆₇	C₂²	semidirect
48. #533×C₆₇	C₂²	semidirect
51. #532×C₆₇	C₂²	semidirect
55. #497×C₆₇	C₂²	semidirect
56. #496×C₆₇	C₂²	semidirect
57. #489×C₆₇	C₂²	semidirect
58. #489×C₆₇	C₂²	semidirect
59. #485×C₆₇	C₂²	semidirect
60. #484×C₆₇	C₂²	semidirect
61. #483×C₆₇	C₂²	semidirect
62. #482×C₆₇	C₂²	semidirect
63. #481×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #477×C₆₇	C₂²	semidirect
66. #476×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #467×C₆₇	C₂²	semidirect
74. #466×C₆₇	C₂²	semidirect
75. #465×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
83. #460×C₆₇	C₂²	semidirect
84. #459×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #452×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #451×C₆₇	C₂²	semidirect
91. #451×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
103. #442×C₆₇	C₂²	semidirect
104. #441×C₆₇	C₂²	semidirect
105. #440×C₆₇	C₂²	semidirect
106. #440×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. #435×C₆₇	C₂²	semidirect
110. #435×C₆₇	C₂²	semidirect
111. #432×C₆₇	C₂²	semidirect
112. #432×C₆₇	C₂²	semidirect
114. #417×C₆₇	C₂²	semidirect
115. C₂×#103×C₆₇	C₂²	semidirect
118. #408×C₆₇	C₂²	semidirect
565. #61677	C₆₇	direct (N × H)
575. #3548	C₂×C₆₇	semidirect
576. #3500	C₂×C₆₇	semidirect
577. #3316	C₂×C₆₇	semidirect
578. #3314	C₂×C₆₇	semidirect
579. #3308	C₂×C₆₇	semidirect
580. #3306	C₂×C₆₇	semidirect
581. #3271	C₂×C₆₇	semidirect
582. #3269	C₂×C₆₇	semidirect
583. #3268	C₂×C₆₇	semidirect
584. #3267	C₂×C₆₇	semidirect
585. #3215	C₂×C₆₇	semidirect
586. #3213	C₂×C₆₇	semidirect
587. #3201	C₂×C₆₇	semidirect
588. #3198	C₂×C₆₇	semidirect
589. #3116	C₂×C₆₇	semidirect
590. #3115	C₂×C₆₇	semidirect
591. #3013	C₂×C₆₇	semidirect
592. #3012	C₂×C₆₇	semidirect
593. #2980	C₂×C₆₇	semidirect
594. C₆₇	#61677	direct (N × H)
597. C₂×#137	C₂²×C₆₇	semidirect
600. C₂×#135	C₂²×C₆₇	semidirect
604. #554	C₂²×C₆₇	semidirect
606. #550	C₂²×C₆₇	semidirect
609. #547	C₂²×C₆₇	semidirect
610. #547	C₂²×C₆₇	semidirect
618. #537	C₂²×C₆₇	semidirect
623. #533	C₂²×C₆₇	semidirect
626. #532	C₂²×C₆₇	semidirect
630. #497	C₂²×C₆₇	semidirect
631. #496	C₂²×C₆₇	semidirect
632. #489	C₂²×C₆₇	semidirect
633. #489	C₂²×C₆₇	semidirect
634. #485	C₂²×C₆₇	semidirect
635. #484	C₂²×C₆₇	semidirect
636. #483	C₂²×C₆₇	semidirect
637. #482	C₂²×C₆₇	semidirect
638. #481	C₂²×C₆₇	semidirect
639. #480	C₂²×C₆₇	semidirect
640. #477	C₂²×C₆₇	semidirect
641. #476	C₂²×C₆₇	semidirect
642. #475	C₂²×C₆₇	semidirect
643. #474	C₂²×C₆₇	semidirect
644. #470	C₂²×C₆₇	semidirect
645. #469	C₂²×C₆₇	semidirect
646. #468	C₂²×C₆₇	semidirect
647. #468	C₂²×C₆₇	semidirect
648. #467	C₂²×C₆₇	semidirect
649. #466	C₂²×C₆₇	semidirect
650. #465	C₂²×C₆₇	semidirect
651. #465	C₂²×C₆₇	semidirect
652. #464	C₂²×C₆₇	semidirect
653. #464	C₂²×C₆₇	semidirect
654. #463	C₂²×C₆₇	semidirect
655. #463	C₂²×C₆₇	semidirect
656. #462	C₂²×C₆₇	semidirect
657. #461	C₂²×C₆₇	semidirect
658. #460	C₂²×C₆₇	semidirect
659. #459	C₂²×C₆₇	semidirect
662. #452	C₂²×C₆₇	semidirect
663. #452	C₂²×C₆₇	semidirect
664. #452	C₂²×C₆₇	semidirect
665. #451	C₂²×C₆₇	semidirect
666. #451	C₂²×C₆₇	semidirect
671. #449	C₂²×C₆₇	semidirect
672. #449	C₂²×C₆₇	semidirect
673. #449	C₂²×C₆₇	semidirect
674. #448	C₂²×C₆₇	semidirect
675. #448	C₂²×C₆₇	semidirect
678. #442	C₂²×C₆₇	semidirect
679. #441	C₂²×C₆₇	semidirect
680. #440	C₂²×C₆₇	semidirect
681. #440	C₂²×C₆₇	semidirect
682. #435	C₂²×C₆₇	semidirect
683. #435	C₂²×C₆₇	semidirect
684. #435	C₂²×C₆₇	semidirect
685. #435	C₂²×C₆₇	semidirect
686. #432	C₂²×C₆₇	semidirect
687. #432	C₂²×C₆₇	semidirect
689. #417	C₂²×C₆₇	semidirect
690. C₂×#103	C₂²×C₆₇	semidirect
693. #408	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×#3548	2
C₆₇×#3500	2
C₆₇×#3316	2
C₆₇×#3314	2
C₆₇×#3308	2
C₆₇×#3306	2
C₆₇×#3271	2
C₆₇×#3269	2
C₆₇×#3268	2
C₆₇×#3267	2
C₆₇×#3215	2
C₆₇×#3213	2
C₆₇×#3201	2
C₆₇×#3198	2
C₆₇×#3116	2
C₆₇×#3115	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#2980	2
#61677	67

Subgroups — C67×#61677 #30740928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61677 #30740928