Subgroups — C₆₇×#61000 #30740251

Order 17152.

1802 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3247	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3191	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3180	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#555×C₆₇	—	2	2	no	—
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	—	2	2	no	—
23	#551×C₆₇	—	2	2	no	—
24	#551×C₆₇	—	2	2	no	—
25	#547×C₆₇	—	2	2	no	—
26	#546×C₆₇	—	2	2	no	—
27	#546×C₆₇	—	2	2	no	—
28	#544×C₆₇	C₂²	1	2	yes	complemented
29	#542×C₆₇	C₂²	1	2	yes	—
30	#542×C₆₇	C₂²	1	2	yes	—
31	#540×C₆₇	C₂²	1	2	yes	—
32	#540×C₆₇	C₂²	1	2	yes	—
33	#535×C₆₇	C₂²	1	2	yes	complemented
34	#532×C₆₇	C₂²	1	2	yes	complemented
35	#532×C₆₇	C₂²	1	2	yes	complemented
36	#529×C₆₇	C₂²	1	2	yes	complemented
37	#529×C₆₇	C₂²	1	2	yes	complemented
38	#525×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	2	yes	complemented
41	#518×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#496×C₆₇	C₂²	1	2	yes	complemented
47	#495×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#490×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#488×C₆₇	C₂²	1	2	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	complemented
54	#484×C₆₇	C₂²	1	2	yes	complemented
55	#482×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	2	yes	—
57	#482×C₆₇	C₂²	1	2	yes	complemented
58	#481×C₆₇	C₂²	1	2	yes	complemented
59	#480×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	2	yes	complemented
62	#478×C₆₇	C₂²	1	2	yes	complemented
63	#478×C₆₇	C₂²	1	2	yes	complemented
64	#478×C₆₇	C₂²	1	2	yes	complemented
65	#477×C₆₇	C₂²	1	2	yes	complemented
66	#476×C₆₇	C₂²	1	2	yes	complemented
67	#474×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#467×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#466×C₆₇	C₂²	1	1	yes	characteristic
71	#466×C₆₇	C₂²	1	1	yes	characteristic
72	#466×C₆₇	C₂²	1	2	yes	—
73	#466×C₆₇	C₂²	1	2	yes	complemented
74	#466×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#466×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#465×C₆₇	C₂²	1	2	yes	complemented
78	#465×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#463×C₆₇	C₂²	1	2	yes	complemented
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#460×C₆₇	C₂²	1	2	yes	complemented
84	#459×C₆₇	C₂²	1	2	yes	complemented
85	#459×C₆₇	C₂²	1	2	yes	complemented
86	#459×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#450×C₆₇	C₂²	1	2	yes	complemented
89	#449×C₆₇	C₂²	1	2	yes	—
90	#449×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	complemented
92	#447×C₆₇	C₂²	1	2	yes	—
93	#447×C₆₇	C₂²	1	2	yes	—
94	#447×C₆₇	C₂²	1	2	yes	complemented
95	#442×C₆₇	C₂²	1	2	yes	complemented
96	#442×C₆₇	C₂²	1	2	yes	complemented
97	#440×C₆₇	C₂²	1	2	yes	complemented
98	#440×C₆₇	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
101	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	complemented
106	#433×C₆₇	C₂²	1	2	yes	complemented
107	#433×C₆₇	C₂²	1	2	yes	complemented
108	#433×C₆₇	C₂²	1	2	yes	complemented
109	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
112	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	—	2	2	no	—
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×D₈×C₆₇	C₂³	1	2	yes	—
126	C₂×D₈×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₆₇	C₂³	1	2	yes	—
130	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₇	—	2	2	no	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	#127×C₆₇	C₂³	1	2	yes	—
139	#127×C₆₇	C₂³	1	2	yes	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#125×C₆₇	—	2	2	no	—
145	#125×C₆₇	C₂³	1	2	yes	—
146	#125×C₆₇	C₂³	1	2	yes	—
147	#124×C₆₇	—	2	2	no	—
148	#124×C₆₇	—	2	2	no	—
149	#124×C₆₇	—	2	2	no	—
150	#124×C₆₇	—	2	2	no	—
151	#124×C₆₇	C₂³	1	2	yes	—
152	#124×C₆₇	C₂³	1	2	yes	—
153	#123×C₆₇	—	2	2	no	—
154	#123×C₆₇	—	2	2	no	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	2	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	#121×C₆₇	—	2	2	no	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	2	no	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	C₂³	1	2	yes	—
179	#121×C₆₇	C₂³	1	2	yes	—
180	#121×C₆₇	C₂³	1	2	yes	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#120×C₆₇	—	2	2	no	—
185	#120×C₆₇	—	2	2	no	—
186	#120×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×D₄×C₆₇	—	2	2	no	—
190	C₄×D₄×C₆₇	—	2	2	no	—
191	C₄×D₄×C₆₇	—	2	2	no	—
192	C₄×D₄×C₆₇	—	2	2	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	C₂³	1	2	yes	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	C₄×D₄×C₆₇	C₂³	1	2	yes	—
203	C₄×D₄×C₆₇	C₂³	1	2	yes	—
204	C₄×D₄×C₆₇	C₂³	1	2	yes	—
205	#117×C₆₇	—	2	2	no	—
206	#117×C₆₇	—	2	2	no	—
207	#117×C₆₇	—	2	2	no	—
208	#117×C₆₇	D₄	1	2	yes	—
209	#117×C₆₇	D₄	1	2	yes	—
210	#117×C₆₇	C₂³	1	2	yes	—
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
218	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	#107×C₆₇	C₂³	1	1	yes	characteristic
225	#107×C₆₇	C₂³	1	2	yes	—
226	#107×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	2	yes	—
228	#107×C₆₇	C₂³	1	1	yes	characteristic
229	#107×C₆₇	C₂³	1	2	yes	—
230	#107×C₆₇	C₂³	1	1	yes	characteristic
231	#106×C₆₇	C₂³	1	2	yes	—
232	#106×C₆₇	C₂³	1	2	yes	—
233	#106×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#102×C₆₇	C₂³	1	2	yes	—
243	#102×C₆₇	C₂³	1	2	yes	—
244	#102×C₆₇	C₂³	1	2	yes	—
245	#102×C₆₇	C₂³	1	2	yes	—
246	#102×C₆₇	C₂³	1	2	yes	—
247	#102×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	#97×C₆₇	C₂³	1	2	yes	—
259	#97×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	C₂⁴×C₆₇	—	2	2	no	—
265	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
266	#41×C₆₇	—	4	2	no	—
267	#41×C₆₇	—	4	2	no	—
268	#41×C₆₇	—	8	4	no	—
269	#41×C₆₇	—	8	4	no	—
270	C₂×Q₈×C₆₇	—	2	2	no	—
271	C₂×Q₈×C₆₇	—	2	2	no	—
272	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	—	8	4	no	—
288	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	—	2	2	no	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	2	no	—
298	C₂²×C₄×C₆₇	—	2	2	no	—
299	C₂²×C₄×C₆₇	—	4	1	no	—
300	C₂²×C₄×C₆₇	—	4	1	no	—
301	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
309	Q₁₆×C₆₇	—	4	1	no	—
310	SD₁₆×C₆₇	—	4	2	no	—
311	SD₁₆×C₆₇	—	4	2	no	—
312	SD₁₆×C₆₇	—	4	2	no	—
313	D₈×C₆₇	—	4	2	no	—
314	D₈×C₆₇	—	4	1	no	—
315	D₈×C₆₇	—	4	1	no	—
316	D₈×C₆₇	—	4	2	no	—
317	D₈×C₆₇	—	4	2	no	—
318	D₈×C₆₇	—	4	1	no	—
319	C₂×C₈×C₆₇	—	4	1	no	—
320	C₂×C₈×C₆₇	—	4	1	no	—
321	C₂×C₈×C₆₇	—	4	1	no	—
322	C₂×C₈×C₆₇	—	4	1	no	—
323	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
326	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
327	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	2	no	—
339	C₄⋊C₄×C₆₇	—	2	2	no	—
340	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	—	2	2	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	2	no	—
366	C₂²⋊C₄×C₆₇	—	2	2	no	—
367	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₄²×C₆₇	—	2	2	no	—
372	C₄²×C₆₇	—	2	2	no	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₆₇	C₂×D₄	1	2	yes	—
376	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₆₇	C₂⁴	1	2	yes	—
378	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	4	1	no	—
385	C₂³×C₆₇	—	4	1	no	—
386	C₂³×C₆₇	—	4	4	no	—
387	C₂³×C₆₇	—	8	2	no	—
388	C₂³×C₆₇	—	8	2	no	—
389	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
390	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	Q₈×C₆₇	—	2	2	no	—
392	Q₈×C₆₇	—	2	2	no	—
393	Q₈×C₆₇	—	8	2	no	—
394	Q₈×C₆₇	—	8	2	no	—
395	D₄×C₆₇	—	2	2	no	—
396	D₄×C₆₇	—	2	2	no	—
397	D₄×C₆₇	—	2	2	no	—
398	D₄×C₆₇	—	2	2	no	—
399	D₄×C₆₇	—	2	2	no	—
400	D₄×C₆₇	—	2	2	no	—
401	D₄×C₆₇	—	4	4	no	—
402	D₄×C₆₇	—	4	4	no	—
403	D₄×C₆₇	—	4	4	no	—
404	D₄×C₆₇	—	4	4	no	—
405	D₄×C₆₇	—	4	4	no	—
406	D₄×C₆₇	—	8	2	no	—
407	D₄×C₆₇	—	8	2	no	—
408	D₄×C₆₇	—	8	2	no	—
409	D₄×C₆₇	—	8	2	no	—
410	D₄×C₆₇	—	8	2	no	—
411	D₄×C₆₇	—	8	2	no	—
412	D₄×C₆₇	—	8	2	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	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	4	1	no	—
425	C₂×C₄×C₆₇	—	4	2	no	—
426	C₂×C₄×C₆₇	—	4	1	no	—
427	C₂×C₄×C₆₇	—	4	1	no	—
428	C₂×C₄×C₆₇	—	4	4	no	—
429	C₂×C₄×C₆₇	—	8	2	no	—
430	C₂×C₄×C₆₇	—	8	2	no	—
431	C₂×C₄×C₆₇	—	8	2	no	—
432	C₂×C₄×C₆₇	—	8	2	no	—
433	C₂×C₄×C₆₇	—	8	2	no	—
434	C₂×C₄×C₆₇	—	8	2	no	—
435	C₂×C₄×C₆₇	—	8	2	no	—
436	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
445	C₈×C₆₇	—	2	1	no	—
446	C₈×C₆₇	—	2	1	no	—
447	C₈×C₆₇	—	2	2	no	—
448	C₈×C₆₇	—	2	2	no	—
449	C₈×C₆₇	—	2	1	no	—
450	C₈×C₆₇	—	2	1	no	—
451	C₂²×C₆₇	—	2	1	no	—
452	C₂²×C₆₇	—	2	1	no	—
453	C₂²×C₆₇	—	2	2	no	—
454	C₂²×C₆₇	—	2	2	no	—
455	C₂²×C₆₇	—	2	2	no	—
456	C₂²×C₆₇	—	4	2	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	—	8	2	no	—
466	C₂²×C₆₇	—	16	4	no	—
467	C₂²×C₆₇	#576	1	2	yes	—
468	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
469	C₄×C₆₇	—	2	1	no	—
470	C₄×C₆₇	—	2	2	no	—
471	C₄×C₆₇	—	2	1	no	—
472	C₄×C₆₇	—	2	2	no	—
473	C₄×C₆₇	—	2	1	no	—
474	C₄×C₆₇	—	2	1	no	—
475	C₄×C₆₇	—	2	2	no	—
476	C₄×C₆₇	—	2	1	no	—
477	C₄×C₆₇	—	4	2	no	—
478	C₄×C₆₇	—	4	2	no	—
479	C₄×C₆₇	—	4	2	no	—
480	C₄×C₆₇	—	4	2	no	—
481	C₄×C₆₇	—	4	2	no	—
482	C₄×C₆₇	#585	1	1	yes	characteristic
483	C₄×C₆₇	#585	1	1	yes	characteristic
484	#61000	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
485	C₂×C₆₇	—	2	2	no	—
486	C₂×C₆₇	—	4	2	no	—
487	C₂×C₆₇	—	8	2	no	—
488	C₂×C₆₇	—	8	2	no	—
489	C₂×C₆₇	—	8	2	no	—
490	C₂×C₆₇	#3449	1	1	yes	characteristic
491	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
492	C₂×C₆₇	#3584	1	1	yes	characteristic
493	#3494	C₂×C₆₇	1	2	yes	complemented
494	#3250	C₂×C₆₇	1	1	yes	characteristic, complemented
495	#3247	C₂×C₆₇	1	2	yes	complemented
496	#3245	C₂×C₆₇	1	1	yes	characteristic, complemented
497	#3243	C₂×C₆₇	1	2	yes	complemented
498	#3241	C₂×C₆₇	1	2	yes	complemented
499	#3224	C₂×C₆₇	1	2	yes	complemented
500	#3220	C₂×C₆₇	1	2	yes	complemented
501	#3191	C₂×C₆₇	1	1	yes	characteristic, complemented
502	#3188	C₂×C₆₇	1	2	yes	complemented
503	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
504	#3180	C₂×C₆₇	1	2	yes	complemented
505	#3169	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#3168	C₂×C₆₇	1	1	yes	characteristic, complemented
507	#3124	C₂×C₆₇	1	2	yes	complemented
508	#3122	C₂×C₆₇	1	2	yes	complemented
509	#3119	C₂×C₆₇	1	2	yes	complemented
510	#3118	C₂×C₆₇	1	2	yes	complemented
511	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
512	C₆₇	#61000	1	1	yes	characteristic, direct product factor, Sylow
513	#555	—	2	2	no	—
514	#553	—	2	2	no	—
515	#553	—	2	2	no	—
516	#551	—	2	2	no	—
517	#551	—	2	2	no	—
518	#547	—	2	2	no	—
519	#546	—	2	2	no	—
520	#546	—	2	2	no	—
521	#544	C₂²×C₆₇	1	2	yes	complemented
522	#542	C₂²×C₆₇	1	2	yes	—
523	#542	C₂²×C₆₇	1	2	yes	—
524	#540	C₂²×C₆₇	1	2	yes	—
525	#540	C₂²×C₆₇	1	2	yes	—
526	#535	C₂²×C₆₇	1	2	yes	complemented
527	#532	C₂²×C₆₇	1	2	yes	complemented
528	#532	C₂²×C₆₇	1	2	yes	complemented
529	#529	C₂²×C₆₇	1	2	yes	complemented
530	#529	C₂²×C₆₇	1	2	yes	complemented
531	#525	C₂²×C₆₇	1	2	yes	—
532	C₂×#121	C₂²×C₆₇	1	2	yes	—
533	#520	C₂²×C₆₇	1	2	yes	complemented
534	#518	C₂²×C₆₇	1	2	yes	complemented
535	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
536	#501	C₂²×C₆₇	1	2	yes	complemented
537	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	#496	C₂²×C₆₇	1	2	yes	complemented
540	#495	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#490	C₂²×C₆₇	1	2	yes	complemented
543	#489	C₂²×C₆₇	1	2	yes	complemented
544	#488	C₂²×C₆₇	1	2	yes	complemented
545	#486	C₂²×C₆₇	1	2	yes	complemented
546	#485	C₂²×C₆₇	1	2	yes	complemented
547	#484	C₂²×C₆₇	1	2	yes	complemented
548	#482	C₂²×C₆₇	1	2	yes	—
549	#482	C₂²×C₆₇	1	2	yes	—
550	#482	C₂²×C₆₇	1	2	yes	complemented
551	#481	C₂²×C₆₇	1	2	yes	complemented
552	#480	C₂²×C₆₇	1	2	yes	—
553	#480	C₂²×C₆₇	1	2	yes	—
554	#479	C₂²×C₆₇	1	2	yes	complemented
555	#478	C₂²×C₆₇	1	2	yes	complemented
556	#478	C₂²×C₆₇	1	2	yes	complemented
557	#478	C₂²×C₆₇	1	2	yes	complemented
558	#477	C₂²×C₆₇	1	2	yes	complemented
559	#476	C₂²×C₆₇	1	2	yes	complemented
560	#474	C₂²×C₆₇	1	2	yes	complemented
561	#474	C₂²×C₆₇	1	2	yes	complemented
562	#467	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	#466	C₂²×C₆₇	1	1	yes	characteristic
564	#466	C₂²×C₆₇	1	1	yes	characteristic
565	#466	C₂²×C₆₇	1	2	yes	—
566	#466	C₂²×C₆₇	1	2	yes	complemented
567	#466	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#466	C₂²×C₆₇	1	2	yes	complemented
569	#465	C₂²×C₆₇	1	2	yes	complemented
570	#465	C₂²×C₆₇	1	2	yes	complemented
571	#465	C₂²×C₆₇	1	2	yes	complemented
572	#464	C₂²×C₆₇	1	2	yes	complemented
573	#463	C₂²×C₆₇	1	2	yes	complemented
574	#463	C₂²×C₆₇	1	2	yes	complemented
575	#463	C₂²×C₆₇	1	2	yes	complemented
576	#460	C₂²×C₆₇	1	2	yes	complemented
577	#459	C₂²×C₆₇	1	2	yes	complemented
578	#459	C₂²×C₆₇	1	2	yes	complemented
579	#459	C₂²×C₆₇	1	2	yes	complemented
580	#452	C₂²×C₆₇	1	2	yes	complemented
581	#450	C₂²×C₆₇	1	2	yes	complemented
582	#449	C₂²×C₆₇	1	2	yes	—
583	#449	C₂²×C₆₇	1	2	yes	—
584	#449	C₂²×C₆₇	1	2	yes	complemented
585	#447	C₂²×C₆₇	1	2	yes	—
586	#447	C₂²×C₆₇	1	2	yes	—
587	#447	C₂²×C₆₇	1	2	yes	complemented
588	#442	C₂²×C₆₇	1	2	yes	complemented
589	#442	C₂²×C₆₇	1	2	yes	complemented
590	#440	C₂²×C₆₇	1	2	yes	complemented
591	#440	C₂²×C₆₇	1	2	yes	complemented
592	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
594	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
597	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
598	#433	C₂²×C₆₇	1	2	yes	complemented
599	#433	C₂²×C₆₇	1	2	yes	complemented
600	#433	C₂²×C₆₇	1	2	yes	complemented
601	#433	C₂²×C₆₇	1	2	yes	complemented
602	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
603	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
604	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
607	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	C₂×#41	—	2	2	no	—
609	C₂×#41	—	2	2	no	—
610	C₂×#41	C₂³×C₆₇	1	2	yes	—
611	C₂²×D₄	—	2	2	no	—
612	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
613	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
616	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
618	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×D₈	C₂³×C₆₇	1	2	yes	—
621	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×D₈	C₂³×C₆₇	1	2	yes	—
623	C₂×D₈	C₂³×C₆₇	1	2	yes	—
624	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
627	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
630	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
631	#127	C₂³×C₆₇	1	2	yes	—
632	#127	C₂³×C₆₇	1	2	yes	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	C₂³×C₆₇	1	2	yes	—
639	#125	C₂³×C₆₇	1	2	yes	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	—	2	2	no	—
644	#124	C₂³×C₆₇	1	2	yes	—
645	#124	C₂³×C₆₇	1	2	yes	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
660	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	2	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	C₂³×C₆₇	1	2	yes	—
672	#121	C₂³×C₆₇	1	2	yes	—
673	#121	C₂³×C₆₇	1	2	yes	—
674	#121	C₂³×C₆₇	1	2	yes	—
675	#121	C₂³×C₆₇	1	2	yes	—
676	#121	C₂³×C₆₇	1	2	yes	—
677	#120	—	2	2	no	—
678	#120	—	2	2	no	—
679	#120	—	2	2	no	—
680	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
681	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	C₂³×C₆₇	1	2	yes	—
693	C₄×D₄	C₂³×C₆₇	1	2	yes	—
694	C₄×D₄	C₂³×C₆₇	1	2	yes	—
695	C₄×D₄	C₂³×C₆₇	1	2	yes	—
696	C₄×D₄	C₂³×C₆₇	1	2	yes	—
697	C₄×D₄	C₂³×C₆₇	1	2	yes	—
698	#117	—	2	2	no	—
699	#117	—	2	2	no	—
700	#117	—	2	2	no	—
701	#117	D₄×C₆₇	1	2	yes	—
702	#117	D₄×C₆₇	1	2	yes	—
703	#117	C₂³×C₆₇	1	2	yes	—
704	#117	C₂³×C₆₇	1	2	yes	—
705	#117	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	—	2	2	no	—
707	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	—	2	2	no	—
711	C₂×C₂²⋊C₄	—	2	2	no	—
712	C₂×C₂²⋊C₄	—	2	2	no	—
713	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
717	#107	C₂³×C₆₇	1	1	yes	characteristic
718	#107	C₂³×C₆₇	1	1	yes	characteristic
719	#107	C₂³×C₆₇	1	2	yes	—
720	#107	C₂³×C₆₇	1	1	yes	characteristic
721	#107	C₂³×C₆₇	1	1	yes	characteristic
722	#107	C₂³×C₆₇	1	2	yes	—
723	#107	C₂³×C₆₇	1	2	yes	—
724	#106	C₂³×C₆₇	1	2	yes	—
725	#106	C₂³×C₆₇	1	2	yes	—
726	#106	C₂³×C₆₇	1	2	yes	—
727	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
728	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
729	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
730	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
731	#103	C₂³×C₆₇	1	2	yes	—
732	#103	C₂³×C₆₇	1	2	yes	—
733	#103	C₂³×C₆₇	1	2	yes	—
734	#103	C₂³×C₆₇	1	2	yes	—
735	#102	C₂³×C₆₇	1	2	yes	—
736	#102	C₂³×C₆₇	1	2	yes	—
737	#102	C₂³×C₆₇	1	2	yes	—
738	#102	C₂³×C₆₇	1	2	yes	—
739	#102	C₂³×C₆₇	1	2	yes	—
740	#102	C₂³×C₆₇	1	2	yes	—
741	#102	C₂³×C₆₇	1	2	yes	—
742	#102	C₂³×C₆₇	1	2	yes	—
743	#102	C₂³×C₆₇	1	2	yes	—
744	#102	C₂³×C₆₇	1	2	yes	—
745	#102	C₂³×C₆₇	1	2	yes	—
746	#102	C₂³×C₆₇	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
751	#97	C₂³×C₆₇	1	2	yes	—
752	#97	C₂³×C₆₇	1	2	yes	—
753	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₂⁴	—	2	2	no	—
758	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
759	#41	—	4	2	no	—
760	#41	—	4	2	no	—
761	#41	—	8	4	no	—
762	#41	—	8	4	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	8	4	no	—
781	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
782	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
783	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	4	1	no	—
793	C₂²×C₄	—	4	1	no	—
794	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
799	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
802	Q₁₆	—	4	1	no	—
803	SD₁₆	—	4	2	no	—
804	SD₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	D₈	—	4	2	no	—
807	D₈	—	4	1	no	—
808	D₈	—	4	1	no	—
809	D₈	—	4	2	no	—
810	D₈	—	4	2	no	—
811	D₈	—	4	1	no	—
812	C₂×C₈	—	4	1	no	—
813	C₂×C₈	—	4	1	no	—
814	C₂×C₈	—	4	1	no	—
815	C₂×C₈	—	4	1	no	—
816	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
821	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
840	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
868	C₄²	C₂×D₄×C₆₇	1	2	yes	—
869	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
870	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
872	C₄²	C₂⁴×C₆₇	1	2	yes	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	1	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	8	2	no	—
881	C₂³	—	8	2	no	—
882	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
883	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	8	2	no	—
887	Q₈	—	8	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	2	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
931	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
937	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
938	C₈	—	2	1	no	—
939	C₈	—	2	1	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	8	2	no	—
959	C₂²	—	16	4	no	—
960	C₂²	#576×C₆₇	1	2	yes	—
961	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	#585×C₆₇	1	1	yes	characteristic
976	C₄	#585×C₆₇	1	1	yes	characteristic
977	C₂	—	2	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	8	2	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₆₇×#3449	1	1	yes	characteristic
983	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
984	C₂	C₆₇×#3584	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×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₆₇×#3250	C₂	semidirect
3. C₆₇×#3247	C₂	semidirect
4. C₆₇×#3245	C₂	semidirect
5. C₆₇×#3243	C₂	semidirect
6. C₆₇×#3241	C₂	semidirect
7. C₆₇×#3224	C₂	semidirect
8. C₆₇×#3220	C₂	semidirect
9. C₆₇×#3191	C₂	semidirect
10. C₆₇×#3188	C₂	semidirect
11. C₆₇×#3186	C₂	semidirect
12. C₆₇×#3180	C₂	semidirect
13. C₆₇×#3169	C₂	semidirect
14. C₆₇×#3168	C₂	semidirect
15. C₆₇×#3124	C₂	semidirect
16. C₆₇×#3122	C₂	semidirect
17. C₆₇×#3119	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₂×#433×C₆₇	C₂	semidirect
28. #544×C₆₇	C₂²	semidirect
33. #535×C₆₇	C₂²	semidirect
34. #532×C₆₇	C₂²	semidirect
35. #532×C₆₇	C₂²	semidirect
36. #529×C₆₇	C₂²	semidirect
37. #529×C₆₇	C₂²	semidirect
40. #520×C₆₇	C₂²	semidirect
41. #518×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #500×C₆₇	C₂²	semidirect
45. #499×C₆₇	C₂²	semidirect
46. #496×C₆₇	C₂²	semidirect
47. #495×C₆₇	C₂²	semidirect
48. #493×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
57. #482×C₆₇	C₂²	semidirect
58. #481×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #478×C₆₇	C₂²	semidirect
64. #478×C₆₇	C₂²	semidirect
65. #477×C₆₇	C₂²	semidirect
66. #476×C₆₇	C₂²	semidirect
67. #474×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #467×C₆₇	C₂²	semidirect
73. #466×C₆₇	C₂²	semidirect
74. #466×C₆₇	C₂²	semidirect
75. #466×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #465×C₆₇	C₂²	semidirect
78. #465×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #463×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
83. #460×C₆₇	C₂²	semidirect
84. #459×C₆₇	C₂²	semidirect
85. #459×C₆₇	C₂²	semidirect
86. #459×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #450×C₆₇	C₂²	semidirect
91. #449×C₆₇	C₂²	semidirect
94. #447×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #442×C₆₇	C₂²	semidirect
97. #440×C₆₇	C₂²	semidirect
98. #440×C₆₇	C₂²	semidirect
99. C₄×Q₁₆×C₆₇	C₂²	semidirect
100. C₄×SD₁₆×C₆₇	C₂²	semidirect
101. C₄×D₈×C₆₇	C₂²	semidirect
102. C₄×D₈×C₆₇	C₂²	semidirect
103. C₄×D₈×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
105. #433×C₆₇	C₂²	semidirect
106. #433×C₆₇	C₂²	semidirect
107. #433×C₆₇	C₂²	semidirect
108. #433×C₆₇	C₂²	semidirect
109. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
110. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
113. C₂×#97×C₆₇	C₂²	semidirect
114. C₂×C₄×C₈×C₆₇	C₂²	semidirect
484. #61000	C₆₇	direct (N × H)
493. #3494	C₂×C₆₇	semidirect
494. #3250	C₂×C₆₇	semidirect
495. #3247	C₂×C₆₇	semidirect
496. #3245	C₂×C₆₇	semidirect
497. #3243	C₂×C₆₇	semidirect
498. #3241	C₂×C₆₇	semidirect
499. #3224	C₂×C₆₇	semidirect
500. #3220	C₂×C₆₇	semidirect
501. #3191	C₂×C₆₇	semidirect
502. #3188	C₂×C₆₇	semidirect
503. #3186	C₂×C₆₇	semidirect
504. #3180	C₂×C₆₇	semidirect
505. #3169	C₂×C₆₇	semidirect
506. #3168	C₂×C₆₇	semidirect
507. #3124	C₂×C₆₇	semidirect
508. #3122	C₂×C₆₇	semidirect
509. #3119	C₂×C₆₇	semidirect
510. #3118	C₂×C₆₇	semidirect
511. C₂×#433	C₂×C₆₇	semidirect
512. C₆₇	#61000	direct (N × H)
521. #544	C₂²×C₆₇	semidirect
526. #535	C₂²×C₆₇	semidirect
527. #532	C₂²×C₆₇	semidirect
528. #532	C₂²×C₆₇	semidirect
529. #529	C₂²×C₆₇	semidirect
530. #529	C₂²×C₆₇	semidirect
533. #520	C₂²×C₆₇	semidirect
534. #518	C₂²×C₆₇	semidirect
536. #501	C₂²×C₆₇	semidirect
537. #500	C₂²×C₆₇	semidirect
538. #499	C₂²×C₆₇	semidirect
539. #496	C₂²×C₆₇	semidirect
540. #495	C₂²×C₆₇	semidirect
541. #493	C₂²×C₆₇	semidirect
542. #490	C₂²×C₆₇	semidirect
543. #489	C₂²×C₆₇	semidirect
544. #488	C₂²×C₆₇	semidirect
545. #486	C₂²×C₆₇	semidirect
546. #485	C₂²×C₆₇	semidirect
547. #484	C₂²×C₆₇	semidirect
550. #482	C₂²×C₆₇	semidirect
551. #481	C₂²×C₆₇	semidirect
554. #479	C₂²×C₆₇	semidirect
555. #478	C₂²×C₆₇	semidirect
556. #478	C₂²×C₆₇	semidirect
557. #478	C₂²×C₆₇	semidirect
558. #477	C₂²×C₆₇	semidirect
559. #476	C₂²×C₆₇	semidirect
560. #474	C₂²×C₆₇	semidirect
561. #474	C₂²×C₆₇	semidirect
562. #467	C₂²×C₆₇	semidirect
566. #466	C₂²×C₆₇	semidirect
567. #466	C₂²×C₆₇	semidirect
568. #466	C₂²×C₆₇	semidirect
569. #465	C₂²×C₆₇	semidirect
570. #465	C₂²×C₆₇	semidirect
571. #465	C₂²×C₆₇	semidirect
572. #464	C₂²×C₆₇	semidirect
573. #463	C₂²×C₆₇	semidirect
574. #463	C₂²×C₆₇	semidirect
575. #463	C₂²×C₆₇	semidirect
576. #460	C₂²×C₆₇	semidirect
577. #459	C₂²×C₆₇	semidirect
578. #459	C₂²×C₆₇	semidirect
579. #459	C₂²×C₆₇	semidirect
580. #452	C₂²×C₆₇	semidirect
581. #450	C₂²×C₆₇	semidirect
584. #449	C₂²×C₆₇	semidirect
587. #447	C₂²×C₆₇	semidirect
588. #442	C₂²×C₆₇	semidirect
589. #442	C₂²×C₆₇	semidirect
590. #440	C₂²×C₆₇	semidirect
591. #440	C₂²×C₆₇	semidirect
592. C₄×Q₁₆	C₂²×C₆₇	semidirect
593. C₄×SD₁₆	C₂²×C₆₇	semidirect
594. C₄×D₈	C₂²×C₆₇	semidirect
595. C₄×D₈	C₂²×C₆₇	semidirect
596. C₄×D₈	C₂²×C₆₇	semidirect
597. C₄×D₈	C₂²×C₆₇	semidirect
598. #433	C₂²×C₆₇	semidirect
599. #433	C₂²×C₆₇	semidirect
600. #433	C₂²×C₆₇	semidirect
601. #433	C₂²×C₆₇	semidirect
602. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
603. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
606. C₂×#97	C₂²×C₆₇	semidirect
607. C₂×C₄×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×#3494	2
C₆₇×#3250	2
C₆₇×#3247	2
C₆₇×#3245	2
C₆₇×#3243	2
C₆₇×#3241	2
C₆₇×#3224	2
C₆₇×#3220	2
C₆₇×#3191	2
C₆₇×#3188	2
C₆₇×#3186	2
C₆₇×#3180	2
C₆₇×#3169	2
C₆₇×#3168	2
C₆₇×#3124	2
C₆₇×#3122	2
C₆₇×#3119	2
C₆₇×#3118	2
C₂×#433×C₆₇	2
#61000	67

Subgroups — C67×#61000 #30740251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61000 #30740251