Subgroups — C₆₇×#61577 #30740828

Order 17152.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3317	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3309	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3217	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	C₂²	1	2	yes	complemented
23	#552×C₆₇	C₂²	1	2	yes	complemented
24	#551×C₆₇	—	2	2	no	—
25	#550×C₆₇	—	2	2	no	—
26	#550×C₆₇	—	2	2	no	—
27	#550×C₆₇	C₂²	1	4	yes	—
28	#550×C₆₇	C₂²	1	4	yes	complemented
29	#548×C₆₇	C₂²	1	2	yes	complemented
30	#546×C₆₇	C₂²	1	2	yes	complemented
31	#539×C₆₇	—	2	1	no	—
32	#538×C₆₇	—	2	1	no	—
33	#534×C₆₇	—	2	1	no	—
34	C₂×#127×C₆₇	—	2	1	no	—
35	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#529×C₆₇	C₂²	1	2	yes	—
37	#525×C₆₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	—	2	1	no	—
40	C₂×#121×C₆₇	—	2	1	no	—
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#518×C₆₇	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	—	2	1	no	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	#496×C₆₇	C₂²	1	4	yes	complemented
49	#490×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#482×C₆₇	C₂²	1	4	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	—
53	#481×C₆₇	C₂²	1	2	yes	complemented
54	#480×C₆₇	C₂²	1	2	yes	complemented
55	#479×C₆₇	C₂²	1	4	yes	complemented
56	#469×C₆₇	C₂²	1	4	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#466×C₆₇	C₂²	1	4	yes	complemented
59	#465×C₆₇	C₂²	1	4	yes	complemented
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#460×C₆₇	C₂²	1	4	yes	complemented
62	#459×C₆₇	C₂²	1	4	yes	complemented
63	#452×C₆₇	C₂²	1	4	yes	complemented
64	#452×C₆₇	C₂²	1	4	yes	complemented
65	#451×C₆₇	C₂²	1	2	yes	complemented
66	#450×C₆₇	C₂²	1	2	yes	complemented
67	#450×C₆₇	C₂²	1	2	yes	complemented
68	#449×C₆₇	C₂²	1	4	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#448×C₆₇	C₂²	1	2	yes	—
72	#448×C₆₇	C₂²	1	2	yes	complemented
73	#447×C₆₇	C₂²	1	2	yes	—
74	#447×C₆₇	C₂²	1	2	yes	—
75	#447×C₆₇	C₂²	1	2	yes	complemented
76	#441×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	#435×C₆₇	C₂²	1	4	yes	complemented
80	#432×C₆₇	C₂²	1	2	yes	complemented
81	#417×C₆₇	C₂²	1	2	yes	complemented
82	#417×C₆₇	C₂²	1	2	yes	complemented
83	#416×C₆₇	C₂²	1	4	yes	complemented
84	#407×C₆₇	C₂²	1	1	yes	characteristic
85	#407×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	—	2	2	no	—
90	C₂×#41×C₆₇	—	4	4	no	—
91	C₂×#41×C₆₇	—	4	4	no	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂×#41×C₆₇	C₂³	1	4	yes	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂×#41×C₆₇	C₂³	1	2	yes	—
96	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₆₇	—	2	1	no	—
99	C₂²×D₄×C₆₇	—	2	1	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	1	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	—	2	1	no	—
104	C₂²×D₄×C₆₇	—	2	1	no	—
105	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	—	2	1	no	—
110	C₂³×C₄×C₆₇	—	2	1	no	—
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	#137×C₆₇	—	4	4	no	—
114	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
115	#135×C₆₇	—	4	8	no	—
116	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×D₈×C₆₇	C₂³	1	4	yes	—
121	C₂×D₈×C₆₇	C₂³	1	4	yes	—
122	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
125	#127×C₆₇	—	2	4	no	—
126	#127×C₆₇	—	2	4	no	—
127	#127×C₆₇	—	2	2	no	—
128	#127×C₆₇	C₂³	1	4	yes	—
129	#126×C₆₇	—	2	2	no	—
130	#126×C₆₇	—	2	2	no	—
131	#126×C₆₇	—	2	2	no	—
132	#125×C₆₇	—	2	2	no	—
133	#125×C₆₇	C₂³	1	2	yes	—
134	#124×C₆₇	—	2	2	no	—
135	#124×C₆₇	C₂³	1	2	yes	—
136	#123×C₆₇	—	2	2	no	—
137	#123×C₆₇	—	2	2	no	—
138	#123×C₆₇	—	2	2	no	—
139	#123×C₆₇	—	2	2	no	—
140	#123×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	—	2	1	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	—	2	1	no	—
150	#121×C₆₇	—	2	1	no	—
151	#121×C₆₇	—	2	1	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	—	2	4	no	—
156	#121×C₆₇	—	2	4	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	2	no	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	2	yes	—
161	#121×C₆₇	C₂³	1	2	yes	—
162	#121×C₆₇	C₂³	1	2	yes	—
163	#121×C₆₇	C₂³	1	4	yes	—
164	#121×C₆₇	C₂³	1	2	yes	—
165	#120×C₆₇	—	2	2	no	—
166	#120×C₆₇	—	2	2	no	—
167	C₄×Q₈×C₆₇	—	2	2	no	—
168	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	—	2	2	no	—
173	C₄×D₄×C₆₇	—	2	4	no	—
174	C₄×D₄×C₆₇	—	2	4	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	2	no	—
177	C₄×D₄×C₆₇	D₄	1	2	yes	—
178	C₄×D₄×C₆₇	D₄	1	2	yes	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	2	yes	—
181	C₄×D₄×C₆₇	C₂³	1	2	yes	—
182	#117×C₆₇	—	2	2	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
187	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	—	2	1	no	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	#107×C₆₇	C₂³	1	4	yes	—
201	#106×C₆₇	C₂³	1	4	yes	—
202	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	4	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#103×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
216	#97×C₆₇	C₂³	1	4	yes	—
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	—	2	1	no	—
220	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
222	#41×C₆₇	—	2	8	no	—
223	#41×C₆₇	—	2	4	no	—
224	#41×C₆₇	—	2	4	no	—
225	#41×C₆₇	—	4	4	no	—
226	#41×C₆₇	—	4	2	no	—
227	#41×C₆₇	—	4	2	no	—
228	#41×C₆₇	—	4	4	no	—
229	#41×C₆₇	—	4	4	no	—
230	#41×C₆₇	—	4	4	no	—
231	#41×C₆₇	—	4	8	no	—
232	C₂×Q₈×C₆₇	—	2	4	no	—
233	C₂×Q₈×C₆₇	—	2	1	no	—
234	C₂×Q₈×C₆₇	—	2	1	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	—	4	4	no	—
258	C₂×D₄×C₆₇	—	4	4	no	—
259	C₂×D₄×C₆₇	—	4	4	no	—
260	C₂×D₄×C₆₇	—	4	4	no	—
261	C₂×D₄×C₆₇	—	8	2	no	—
262	C₂×D₄×C₆₇	—	8	2	no	—
263	C₂×D₄×C₆₇	—	8	2	no	—
264	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	1	no	—
271	C₂²×C₄×C₆₇	—	2	1	no	—
272	C₂²×C₄×C₆₇	—	2	1	no	—
273	C₂²×C₄×C₆₇	—	2	1	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	4	no	—
282	C₂²×C₄×C₆₇	—	4	4	no	—
283	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	Q₁₆×C₆₇	—	2	8	no	—
295	SD₁₆×C₆₇	—	2	8	no	—
296	SD₁₆×C₆₇	—	4	4	no	—
297	SD₁₆×C₆₇	—	4	4	no	—
298	D₈×C₆₇	—	4	4	no	—
299	D₈×C₆₇	—	4	4	no	—
300	M₁₆×C₆₇	—	4	2	no	—
301	M₁₆×C₆₇	—	4	2	no	—
302	C₂×C₈×C₆₇	—	4	4	no	—
303	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
304	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	4	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₄⋊C₄×C₆₇	—	2	1	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	2	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	2	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄²×C₆₇	—	2	4	no	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	C₂×D₄	1	2	yes	—
341	C₄²×C₆₇	C₂⁴	1	2	yes	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	4	1	no	—
348	C₂³×C₆₇	—	4	1	no	—
349	C₂³×C₆₇	—	4	1	no	—
350	C₂³×C₆₇	—	4	1	no	—
351	C₂³×C₆₇	—	4	2	no	—
352	C₂³×C₆₇	—	4	2	no	—
353	C₂³×C₆₇	—	4	2	no	—
354	C₂³×C₆₇	—	4	2	no	—
355	C₂³×C₆₇	—	4	2	no	—
356	C₂³×C₆₇	—	4	2	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	8	1	no	—
359	C₂³×C₆₇	—	8	1	no	—
360	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
361	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
362	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₆₇	—	2	4	no	—
365	Q₈×C₆₇	—	2	2	no	—
366	Q₈×C₆₇	—	2	4	no	—
367	Q₈×C₆₇	—	8	1	no	—
368	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
369	D₄×C₆₇	—	2	4	no	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	2	no	—
373	D₄×C₆₇	—	4	2	no	—
374	D₄×C₆₇	—	4	2	no	—
375	D₄×C₆₇	—	4	4	no	—
376	D₄×C₆₇	—	4	8	no	—
377	D₄×C₆₇	—	4	4	no	—
378	D₄×C₆₇	—	4	8	no	—
379	D₄×C₆₇	—	4	2	no	—
380	D₄×C₆₇	—	4	2	no	—
381	D₄×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	4	4	no	—
383	D₄×C₆₇	—	8	1	no	—
384	D₄×C₆₇	—	8	4	no	—
385	D₄×C₆₇	—	8	2	no	—
386	D₄×C₆₇	—	8	2	no	—
387	D₄×C₆₇	—	8	4	no	—
388	D₄×C₆₇	—	8	2	no	—
389	D₄×C₆₇	—	8	2	no	—
390	C₂×C₄×C₆₇	—	2	4	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	4	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	4	1	no	—
402	C₂×C₄×C₆₇	—	4	1	no	—
403	C₂×C₄×C₆₇	—	4	2	no	—
404	C₂×C₄×C₆₇	—	4	1	no	—
405	C₂×C₄×C₆₇	—	4	1	no	—
406	C₂×C₄×C₆₇	—	4	1	no	—
407	C₂×C₄×C₆₇	—	4	8	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	4	no	—
410	C₂×C₄×C₆₇	—	4	2	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	—	8	2	no	—
413	C₂×C₄×C₆₇	—	8	2	no	—
414	C₂×C₄×C₆₇	—	8	1	no	—
415	C₂×C₄×C₆₇	—	8	1	no	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
423	C₈×C₆₇	—	2	4	no	—
424	C₈×C₆₇	—	2	4	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	1	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	2	1	no	—
431	C₂²×C₆₇	—	2	2	no	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	1	no	—
434	C₂²×C₆₇	—	2	1	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	2	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	2	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	8	2	no	—
446	C₂²×C₆₇	—	8	2	no	—
447	C₂²×C₆₇	—	8	4	no	—
448	C₂²×C₆₇	—	8	4	no	—
449	C₂²×C₆₇	—	16	2	no	—
450	C₂²×C₆₇	#575	1	2	yes	—
451	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₆₇	—	2	2	no	—
453	C₄×C₆₇	—	2	4	no	—
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	1	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	4	2	no	—
460	C₄×C₆₇	—	4	2	no	—
461	C₄×C₆₇	—	4	2	no	—
462	C₄×C₆₇	—	4	2	no	—
463	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
464	#61577	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂×C₆₇	—	2	2	no	—
466	C₂×C₆₇	—	4	1	no	—
467	C₂×C₆₇	—	4	2	no	—
468	C₂×C₆₇	—	4	1	no	—
469	C₂×C₆₇	—	8	2	no	—
470	C₂×C₆₇	—	8	2	no	—
471	C₂×C₆₇	—	8	2	no	—
472	C₂×C₆₇	#3484	1	1	yes	characteristic
473	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
474	C₂×C₆₇	#3585	1	1	yes	characteristic
475	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
476	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#3317	C₂×C₆₇	1	4	yes	complemented
478	#3309	C₂×C₆₇	1	4	yes	complemented
479	#3271	C₂×C₆₇	1	4	yes	complemented
480	#3268	C₂×C₆₇	1	4	yes	complemented
481	#3217	C₂×C₆₇	1	2	yes	complemented
482	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#3188	C₂×C₆₇	1	2	yes	complemented
485	#3117	C₂×C₆₇	1	2	yes	complemented
486	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#3002	C₂×C₆₇	1	2	yes	complemented
489	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
490	C₆₇	#61577	1	1	yes	characteristic, direct product factor, Sylow
491	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
492	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
493	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
494	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
495	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
496	#553	—	2	2	no	—
497	#553	C₂²×C₆₇	1	2	yes	complemented
498	#552	C₂²×C₆₇	1	2	yes	complemented
499	#551	—	2	2	no	—
500	#550	—	2	2	no	—
501	#550	—	2	2	no	—
502	#550	C₂²×C₆₇	1	4	yes	—
503	#550	C₂²×C₆₇	1	4	yes	complemented
504	#548	C₂²×C₆₇	1	2	yes	complemented
505	#546	C₂²×C₆₇	1	2	yes	complemented
506	#539	—	2	1	no	—
507	#538	—	2	1	no	—
508	#534	—	2	1	no	—
509	C₂×#127	—	2	1	no	—
510	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	#529	C₂²×C₆₇	1	2	yes	—
512	#525	C₂²×C₆₇	1	2	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
514	C₂×#121	—	2	1	no	—
515	C₂×#121	—	2	1	no	—
516	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
517	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
519	#518	—	2	1	no	—
520	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	C₂×C₄×D₄	—	2	1	no	—
522	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
523	#496	C₂²×C₆₇	1	4	yes	complemented
524	#490	C₂²×C₆₇	1	4	yes	complemented
525	#484	C₂²×C₆₇	1	2	yes	complemented
526	#482	C₂²×C₆₇	1	4	yes	complemented
527	#481	C₂²×C₆₇	1	2	yes	—
528	#481	C₂²×C₆₇	1	2	yes	complemented
529	#480	C₂²×C₆₇	1	2	yes	complemented
530	#479	C₂²×C₆₇	1	4	yes	complemented
531	#469	C₂²×C₆₇	1	4	yes	complemented
532	#468	C₂²×C₆₇	1	4	yes	complemented
533	#466	C₂²×C₆₇	1	4	yes	complemented
534	#465	C₂²×C₆₇	1	4	yes	complemented
535	#464	C₂²×C₆₇	1	4	yes	complemented
536	#460	C₂²×C₆₇	1	4	yes	complemented
537	#459	C₂²×C₆₇	1	4	yes	complemented
538	#452	C₂²×C₆₇	1	4	yes	complemented
539	#452	C₂²×C₆₇	1	4	yes	complemented
540	#451	C₂²×C₆₇	1	2	yes	complemented
541	#450	C₂²×C₆₇	1	2	yes	complemented
542	#450	C₂²×C₆₇	1	2	yes	complemented
543	#449	C₂²×C₆₇	1	4	yes	complemented
544	#449	C₂²×C₆₇	1	4	yes	complemented
545	#449	C₂²×C₆₇	1	4	yes	complemented
546	#448	C₂²×C₆₇	1	2	yes	—
547	#448	C₂²×C₆₇	1	2	yes	complemented
548	#447	C₂²×C₆₇	1	2	yes	—
549	#447	C₂²×C₆₇	1	2	yes	—
550	#447	C₂²×C₆₇	1	2	yes	complemented
551	#441	C₂²×C₆₇	1	4	yes	complemented
552	#440	C₂²×C₆₇	1	4	yes	complemented
553	#435	C₂²×C₆₇	1	4	yes	complemented
554	#435	C₂²×C₆₇	1	4	yes	complemented
555	#432	C₂²×C₆₇	1	2	yes	complemented
556	#417	C₂²×C₆₇	1	2	yes	complemented
557	#417	C₂²×C₆₇	1	2	yes	complemented
558	#416	C₂²×C₆₇	1	4	yes	complemented
559	#407	C₂²×C₆₇	1	1	yes	characteristic
560	#407	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
562	C₂×#41	—	2	1	no	—
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	4	4	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	C₂³×C₆₇	1	2	yes	—
568	C₂×#41	C₂³×C₆₇	1	4	yes	—
569	C₂×#41	C₂³×C₆₇	1	2	yes	—
570	C₂×#41	C₂³×C₆₇	1	2	yes	—
571	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	—	2	1	no	—
580	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
584	C₂³×C₄	—	2	1	no	—
585	C₂³×C₄	—	2	1	no	—
586	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
588	#137	—	4	4	no	—
589	AGL(1,ℤ/8)	—	4	4	no	—
590	#135	—	4	8	no	—
591	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
595	C₂×D₈	C₂³×C₆₇	1	4	yes	—
596	C₂×D₈	C₂³×C₆₇	1	4	yes	—
597	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
598	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
599	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
600	#127	—	2	4	no	—
601	#127	—	2	4	no	—
602	#127	—	2	2	no	—
603	#127	C₂³×C₆₇	1	4	yes	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₆₇	1	2	yes	—
609	#124	—	2	2	no	—
610	#124	C₂³×C₆₇	1	2	yes	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
621	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	1	no	—
625	#121	—	2	1	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	2	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	4	no	—
633	#121	—	2	2	no	—
634	#121	C₂³×C₆₇	1	2	yes	—
635	#121	C₂³×C₆₇	1	2	yes	—
636	#121	C₂³×C₆₇	1	2	yes	—
637	#121	C₂³×C₆₇	1	2	yes	—
638	#121	C₂³×C₆₇	1	4	yes	—
639	#121	C₂³×C₆₇	1	2	yes	—
640	#120	—	2	2	no	—
641	#120	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
644	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	2	4	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	D₄×C₆₇	1	2	yes	—
653	C₄×D₄	D₄×C₆₇	1	2	yes	—
654	C₄×D₄	C₂³×C₆₇	1	2	yes	—
655	C₄×D₄	C₂³×C₆₇	1	2	yes	—
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	2	no	—
671	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
675	#107	C₂³×C₆₇	1	4	yes	—
676	#106	C₂³×C₆₇	1	4	yes	—
677	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
678	#103	C₂³×C₆₇	1	4	yes	—
679	#103	C₂³×C₆₇	1	4	yes	—
680	#103	C₂³×C₆₇	1	4	yes	—
681	#102	C₂³×C₆₇	1	4	yes	—
682	#102	C₂³×C₆₇	1	4	yes	—
683	#102	C₂³×C₆₇	1	4	yes	—
684	#102	C₂³×C₆₇	1	4	yes	—
685	#102	C₂³×C₆₇	1	4	yes	—
686	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
687	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
691	#97	C₂³×C₆₇	1	4	yes	—
692	C₂⁴	—	2	1	no	—
693	C₂⁴	—	2	1	no	—
694	C₂⁴	—	2	1	no	—
695	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
696	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
697	#41	—	2	8	no	—
698	#41	—	2	4	no	—
699	#41	—	2	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	2	no	—
702	#41	—	4	2	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	4	8	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
712	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	8	2	no	—
737	C₂×D₄	—	8	2	no	—
738	C₂×D₄	—	8	2	no	—
739	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	4	4	no	—
758	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
769	Q₁₆	—	2	8	no	—
770	SD₁₆	—	2	8	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	4	4	no	—
774	D₈	—	4	4	no	—
775	M₁₆	—	4	2	no	—
776	M₁₆	—	4	2	no	—
777	C₂×C₈	—	4	4	no	—
778	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
779	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
809	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
810	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
811	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	C₂×D₄×C₆₇	1	2	yes	—
816	C₄²	C₂⁴×C₆₇	1	2	yes	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	8	1	no	—
834	C₂³	—	8	1	no	—
835	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
836	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
837	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
838	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
839	Q₈	—	2	4	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	2	4	no	—
842	Q₈	—	8	1	no	—
843	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	4	no	—
858	D₄	—	8	1	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	—	8	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
897	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
898	C₈	—	2	4	no	—
899	C₈	—	2	4	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	8	2	no	—
921	C₂²	—	8	2	no	—
922	C₂²	—	8	4	no	—
923	C₂²	—	8	4	no	—
924	C₂²	—	16	2	no	—
925	C₂²	#575×C₆₇	1	2	yes	—
926	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	4	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
939	C₂	—	2	2	no	—
940	C₂	—	4	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	2	no	—
943	C₂	—	8	2	no	—
944	C₂	—	8	2	no	—
945	C₂	—	8	2	no	—
946	C₂	C₆₇×#3484	1	1	yes	characteristic
947	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
948	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×#550×C₆₇	C₂	semidirect
3. C₆₇×#3317	C₂	semidirect
4. C₆₇×#3309	C₂	semidirect
5. C₆₇×#3271	C₂	semidirect
6. C₆₇×#3268	C₂	semidirect
7. C₆₇×#3217	C₂	semidirect
8. C₆₇×#3193	C₂	semidirect
9. C₆₇×#3192	C₂	semidirect
10. C₆₇×#3188	C₂	semidirect
11. C₆₇×#3117	C₂	semidirect
12. C₆₇×#3007	C₂	semidirect
13. C₆₇×#3006	C₂	semidirect
14. C₆₇×#3002	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
17. C₂²×#41×C₆₇	C₂²	semidirect
18. C₂×#137×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
22. #553×C₆₇	C₂²	semidirect
23. #552×C₆₇	C₂²	semidirect
28. #550×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
35. C₂×#127×C₆₇	C₂²	semidirect
43. C₂×#121×C₆₇	C₂²	semidirect
45. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
48. #496×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
51. #482×C₆₇	C₂²	semidirect
53. #481×C₆₇	C₂²	semidirect
54. #480×C₆₇	C₂²	semidirect
55. #479×C₆₇	C₂²	semidirect
56. #469×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
58. #466×C₆₇	C₂²	semidirect
59. #465×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #460×C₆₇	C₂²	semidirect
62. #459×C₆₇	C₂²	semidirect
63. #452×C₆₇	C₂²	semidirect
64. #452×C₆₇	C₂²	semidirect
65. #451×C₆₇	C₂²	semidirect
66. #450×C₆₇	C₂²	semidirect
67. #450×C₆₇	C₂²	semidirect
68. #449×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
72. #448×C₆₇	C₂²	semidirect
75. #447×C₆₇	C₂²	semidirect
76. #441×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #432×C₆₇	C₂²	semidirect
81. #417×C₆₇	C₂²	semidirect
82. #417×C₆₇	C₂²	semidirect
83. #416×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
464. #61577	C₆₇	direct (N × H)
475. #3505	C₂×C₆₇	semidirect
476. C₂×#550	C₂×C₆₇	semidirect
477. #3317	C₂×C₆₇	semidirect
478. #3309	C₂×C₆₇	semidirect
479. #3271	C₂×C₆₇	semidirect
480. #3268	C₂×C₆₇	semidirect
481. #3217	C₂×C₆₇	semidirect
482. #3193	C₂×C₆₇	semidirect
483. #3192	C₂×C₆₇	semidirect
484. #3188	C₂×C₆₇	semidirect
485. #3117	C₂×C₆₇	semidirect
486. #3007	C₂×C₆₇	semidirect
487. #3006	C₂×C₆₇	semidirect
488. #3002	C₂×C₆₇	semidirect
489. #2973	C₂×C₆₇	semidirect
490. C₆₇	#61577	direct (N × H)
492. C₂²×#41	C₂²×C₆₇	semidirect
493. C₂×#137	C₂²×C₆₇	semidirect
494. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
495. C₂×#135	C₂²×C₆₇	semidirect
497. #553	C₂²×C₆₇	semidirect
498. #552	C₂²×C₆₇	semidirect
503. #550	C₂²×C₆₇	semidirect
504. #548	C₂²×C₆₇	semidirect
505. #546	C₂²×C₆₇	semidirect
510. C₂×#127	C₂²×C₆₇	semidirect
518. C₂×#121	C₂²×C₆₇	semidirect
520. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
523. #496	C₂²×C₆₇	semidirect
524. #490	C₂²×C₆₇	semidirect
525. #484	C₂²×C₆₇	semidirect
526. #482	C₂²×C₆₇	semidirect
528. #481	C₂²×C₆₇	semidirect
529. #480	C₂²×C₆₇	semidirect
530. #479	C₂²×C₆₇	semidirect
531. #469	C₂²×C₆₇	semidirect
532. #468	C₂²×C₆₇	semidirect
533. #466	C₂²×C₆₇	semidirect
534. #465	C₂²×C₆₇	semidirect
535. #464	C₂²×C₆₇	semidirect
536. #460	C₂²×C₆₇	semidirect
537. #459	C₂²×C₆₇	semidirect
538. #452	C₂²×C₆₇	semidirect
539. #452	C₂²×C₆₇	semidirect
540. #451	C₂²×C₆₇	semidirect
541. #450	C₂²×C₆₇	semidirect
542. #450	C₂²×C₆₇	semidirect
543. #449	C₂²×C₆₇	semidirect
544. #449	C₂²×C₆₇	semidirect
545. #449	C₂²×C₆₇	semidirect
547. #448	C₂²×C₆₇	semidirect
550. #447	C₂²×C₆₇	semidirect
551. #441	C₂²×C₆₇	semidirect
552. #440	C₂²×C₆₇	semidirect
553. #435	C₂²×C₆₇	semidirect
554. #435	C₂²×C₆₇	semidirect
555. #432	C₂²×C₆₇	semidirect
556. #417	C₂²×C₆₇	semidirect
557. #417	C₂²×C₆₇	semidirect
558. #416	C₂²×C₆₇	semidirect
561. 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×#3505	2
C₂×#550×C₆₇	2
C₆₇×#3317	2
C₆₇×#3309	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3217	2
C₆₇×#3193	2
C₆₇×#3192	2
C₆₇×#3188	2
C₆₇×#3117	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#3002	2
C₆₇×#2973	2
#61577	67

Subgroups — C67×#61577 #30740828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61577 #30740828