Subgroups — C₆₇×#60377 #30739628

Order 17152.

4756 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3013	C₂	1	3	yes	maximal, complemented
6	C₆₇×#3012	C₂	1	3	yes	maximal, complemented
7	C₆₇×#3011	C₂	1	3	yes	maximal, complemented
8	C₆₇×#3009	C₂	1	3	yes	maximal, complemented
9	C₆₇×#3007	C₂	1	3	yes	maximal, complemented
10	C₆₇×#3005	C₂	1	3	yes	maximal, complemented
11	C₆₇×#3002	C₂	1	3	yes	maximal, complemented
12	C₂×#452×C₆₇	C₂	1	3	yes	maximal, complemented
13	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
16	#585×C₆₇	—	2	8	no	—
17	#585×C₆₇	—	2	8	no	—
18	C₂×2₋¹⁺⁴×C₆₇	—	2	1	no	—
19	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	3	yes	—
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×H(5,𝔽₂)×C₆₇	—	2	3	no	—
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	3	yes	—
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	—	2	3	no	—
26	C₂²×#41×C₆₇	—	2	1	no	—
27	C₂²×#41×C₆₇	C₂²	1	3	yes	—
28	C₂²×#41×C₆₇	C₂²	1	3	yes	—
29	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
30	#578×C₆₇	—	2	8	no	—
31	#577×C₆₇	—	2	8	no	—
32	C₂×#137×C₆₇	C₂²	1	3	yes	complemented
33	C₂×#137×C₆₇	C₂²	1	3	yes	complemented
34	C₂×#137×C₆₇	C₂²	1	3	yes	complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	3	yes	complemented
36	C₂×#135×C₆₇	C₂²	1	3	yes	complemented
37	C₂×#135×C₆₇	C₂²	1	3	yes	complemented
38	C₂²×Q₁₆×C₆₇	C₂²	1	3	yes	complemented
39	C₂²×SD₁₆×C₆₇	C₂²	1	3	yes	complemented
40	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	D₄×Q₈×C₆₇	—	2	1	no	—
43	#548×C₆₇	—	2	1	no	—
44	#547×C₆₇	—	2	3	no	—
45	#546×C₆₇	—	2	3	no	—
46	#537×C₆₇	C₂²	1	3	yes	complemented
47	#536×C₆₇	C₂²	1	3	yes	complemented
48	#525×C₆₇	C₂²	1	3	yes	complemented
49	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	3	yes	complemented
50	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#452×C₆₇	C₂²	1	6	yes	complemented
52	#452×C₆₇	C₂²	1	6	yes	complemented
53	#452×C₆₇	C₂²	1	6	yes	complemented
54	#452×C₆₇	C₂²	1	3	yes	complemented
55	#452×C₆₇	C₂²	1	6	yes	complemented
56	#452×C₆₇	C₂²	1	3	yes	complemented
57	#451×C₆₇	C₂²	1	3	yes	complemented
58	#451×C₆₇	C₂²	1	6	yes	complemented
59	#450×C₆₇	C₂²	1	3	yes	complemented
60	#450×C₆₇	C₂²	1	6	yes	complemented
61	#449×C₆₇	C₂²	1	6	yes	complemented
62	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#449×C₆₇	C₂²	1	3	yes	complemented
64	#448×C₆₇	C₂²	1	3	yes	complemented
65	#447×C₆₇	C₂²	1	3	yes	complemented
66	#419×C₆₇	C₂²	1	3	yes	complemented
67	#418×C₆₇	C₂²	1	3	yes	complemented
68	#417×C₆₇	C₂²	1	3	yes	complemented
69	#417×C₆₇	C₂²	1	3	yes	complemented
70	#416×C₆₇	C₂²	1	3	yes	complemented
71	#416×C₆₇	C₂²	1	3	yes	complemented
72	C₂×#103×C₆₇	C₂²	1	3	yes	complemented
73	C₂×#102×C₆₇	C₂²	1	3	yes	complemented
74	#408×C₆₇	C₂²	1	3	yes	complemented
75	#408×C₆₇	C₂²	1	3	yes	complemented
76	#407×C₆₇	C₂²	1	3	yes	complemented
77	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
78	2₋¹⁺⁴×C₆₇	—	2	16	no	—
79	2₋¹⁺⁴×C₆₇	—	2	12	no	—
80	2₋¹⁺⁴×C₆₇	—	2	4	no	—
81	2₋¹⁺⁴×C₆₇	—	2	12	no	—
82	2₋¹⁺⁴×C₆₇	—	2	4	no	—
83	2₋¹⁺⁴×C₆₇	—	2	4	no	—
84	2₋¹⁺⁴×C₆₇	D₄	1	8	yes	complemented
85	H(5,𝔽₂)×C₆₇	—	2	48	no	—
86	H(5,𝔽₂)×C₆₇	—	2	12	no	—
87	H(5,𝔽₂)×C₆₇	—	2	4	no	—
88	H(5,𝔽₂)×C₆₇	—	2	12	no	—
89	H(5,𝔽₂)×C₆₇	D₄	1	8	yes	complemented
90	C₂×#41×C₆₇	—	2	16	no	—
91	C₂×#41×C₆₇	—	2	48	no	—
92	C₂×#41×C₆₇	—	2	12	no	—
93	C₂×#41×C₆₇	—	2	12	no	—
94	C₂×#41×C₆₇	—	2	4	no	—
95	C₂×#41×C₆₇	—	2	4	no	—
96	C₂×#41×C₆₇	—	2	3	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	2	12	no	—
99	C₂×#41×C₆₇	—	2	6	no	—
100	C₂×#41×C₆₇	—	2	3	no	—
101	C₂×#41×C₆₇	—	2	3	no	—
102	C₂×#41×C₆₇	—	2	12	no	—
103	C₂×#41×C₆₇	—	2	3	no	—
104	C₂×#41×C₆₇	—	2	3	no	—
105	C₂×#41×C₆₇	—	2	3	no	—
106	C₂×#41×C₆₇	—	2	3	no	—
107	C₂×#41×C₆₇	—	2	3	no	—
108	C₂×#41×C₆₇	D₄	1	3	yes	—
109	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
110	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×#41×C₆₇	C₂³	1	3	yes	—
112	C₂×#41×C₆₇	C₂³	1	6	yes	—
113	C₂×#41×C₆₇	C₂³	1	3	yes	—
114	C₂×#41×C₆₇	C₂³	1	3	yes	—
115	C₂×#41×C₆₇	C₂³	1	3	yes	—
116	C₂×#41×C₆₇	C₂³	1	3	yes	—
117	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₆₇	—	2	3	no	—
119	C₂²×Q₈×C₆₇	—	2	1	no	—
120	C₂²×Q₈×C₆₇	—	2	1	no	—
121	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
122	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
123	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
125	C₂²×D₄×C₆₇	—	2	3	no	—
126	C₂²×D₄×C₆₇	—	2	3	no	—
127	C₂²×D₄×C₆₇	—	2	6	no	—
128	C₂²×D₄×C₆₇	—	2	3	no	—
129	C₂²×D₄×C₆₇	—	2	3	no	—
130	C₂²×D₄×C₆₇	D₄	1	3	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
133	C₂³×C₄×C₆₇	—	2	3	no	—
134	C₂³×C₄×C₆₇	—	2	3	no	—
135	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
136	#137×C₆₇	—	2	12	no	—
137	#137×C₆₇	—	2	12	no	—
138	#137×C₆₇	—	2	12	no	—
139	AGL(1,ℤ/8)×C₆₇	—	2	12	no	—
140	#135×C₆₇	—	2	12	no	—
141	#135×C₆₇	—	2	12	no	—
142	C₂×Q₁₆×C₆₇	—	2	12	no	—
143	C₂×Q₁₆×C₆₇	C₂³	1	3	yes	—
144	C₂×Q₁₆×C₆₇	C₂³	1	3	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	6	yes	—
146	C₂×SD₁₆×C₆₇	—	2	12	no	—
147	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	—
152	C₂×D₈×C₆₇	C₂³	1	3	yes	—
153	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
154	#131×C₆₇	—	2	4	no	—
155	#131×C₆₇	—	2	4	no	—
156	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
158	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
160	C₄⋊Q₈×C₆₇	—	2	3	no	—
161	#124×C₆₇	—	2	3	no	—
162	#123×C₆₇	—	2	6	no	—
163	#123×C₆₇	—	2	3	no	—
164	C₂²⋊Q₈×C₆₇	—	2	3	no	—
165	C₂²⋊Q₈×C₆₇	—	2	3	no	—
166	C₂²⋊Q₈×C₆₇	—	2	3	no	—
167	C₂²⋊Q₈×C₆₇	C₂³	1	6	yes	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	—
169	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	—
170	#121×C₆₇	—	2	6	no	—
171	#121×C₆₇	—	2	3	no	—
172	#121×C₆₇	C₂³	1	3	yes	—
173	#121×C₆₇	C₂³	1	1	yes	characteristic
174	#120×C₆₇	—	2	3	no	—
175	C₄×Q₈×C₆₇	—	2	1	no	—
176	C₄×D₄×C₆₇	—	2	3	no	—
177	C₄×D₄×C₆₇	—	2	3	no	—
178	C₄×D₄×C₆₇	—	2	3	no	—
179	#117×C₆₇	C₂³	1	3	yes	—
180	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
182	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
183	#103×C₆₇	C₂³	1	3	yes	—
184	#103×C₆₇	C₂³	1	3	yes	—
185	#103×C₆₇	C₂³	1	1	yes	characteristic
186	#103×C₆₇	C₂³	1	6	yes	—
187	#103×C₆₇	C₂³	1	3	yes	—
188	#102×C₆₇	C₂³	1	1	yes	characteristic
189	#102×C₆₇	C₂³	1	6	yes	—
190	#102×C₆₇	C₂³	1	3	yes	—
191	#102×C₆₇	C₂³	1	3	yes	—
192	#102×C₆₇	C₂³	1	3	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
197	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
198	C₂⁴×C₆₇	—	2	3	no	—
199	C₂⁴×C₆₇	—	2	3	no	—
200	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
201	#41×C₆₇	—	2	24	no	—
202	#41×C₆₇	—	2	24	no	—
203	#41×C₆₇	—	2	48	no	—
204	#41×C₆₇	—	2	24	no	—
205	#41×C₆₇	—	2	24	no	—
206	#41×C₆₇	—	2	24	no	—
207	#41×C₆₇	—	2	24	no	—
208	#41×C₆₇	—	2	4	no	—
209	#41×C₆₇	—	2	8	no	—
210	#41×C₆₇	—	2	2	no	—
211	#41×C₆₇	—	2	6	no	—
212	#41×C₆₇	—	2	12	no	—
213	#41×C₆₇	—	2	12	no	—
214	#41×C₆₇	—	2	24	no	—
215	#41×C₆₇	—	2	2	no	—
216	#41×C₆₇	—	2	6	no	—
217	#41×C₆₇	—	2	12	no	—
218	#41×C₆₇	—	2	6	no	—
219	#41×C₆₇	—	2	6	no	—
220	#41×C₆₇	—	2	6	no	—
221	#41×C₆₇	—	2	6	no	—
222	#41×C₆₇	—	2	6	no	—
223	#41×C₆₇	—	2	6	no	—
224	#41×C₆₇	—	4	12	no	—
225	#41×C₆₇	C₂×D₄	1	12	yes	—
226	#41×C₆₇	C₂×D₄	1	12	yes	—
227	#41×C₆₇	C₂×D₄	1	4	yes	—
228	#41×C₆₇	C₂×D₄	1	4	yes	—
229	C₂×Q₈×C₆₇	—	2	24	no	—
230	C₂×Q₈×C₆₇	—	2	8	no	—
231	C₂×Q₈×C₆₇	—	2	4	no	—
232	C₂×Q₈×C₆₇	—	2	6	no	—
233	C₂×Q₈×C₆₇	—	2	6	no	—
234	C₂×Q₈×C₆₇	—	2	3	no	—
235	C₂×Q₈×C₆₇	—	2	3	no	—
236	C₂×Q₈×C₆₇	—	2	6	no	—
237	C₂×Q₈×C₆₇	—	2	3	no	—
238	C₂×Q₈×C₆₇	—	2	6	no	—
239	C₂×Q₈×C₆₇	—	2	6	no	—
240	C₂×Q₈×C₆₇	—	4	4	no	—
241	C₂×Q₈×C₆₇	C₂×D₄	1	12	yes	—
242	C₂×Q₈×C₆₇	C₂×D₄	1	3	yes	—
243	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
245	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
247	C₂×D₄×C₆₇	—	2	24	no	—
248	C₂×D₄×C₆₇	—	2	48	no	—
249	C₂×D₄×C₆₇	—	2	24	no	—
250	C₂×D₄×C₆₇	—	2	24	no	—
251	C₂×D₄×C₆₇	—	2	6	no	—
252	C₂×D₄×C₆₇	—	2	3	no	—
253	C₂×D₄×C₆₇	—	2	1	no	—
254	C₂×D₄×C₆₇	—	2	3	no	—
255	C₂×D₄×C₆₇	—	2	3	no	—
256	C₂×D₄×C₆₇	—	2	24	no	—
257	C₂×D₄×C₆₇	—	2	12	no	—
258	C₂×D₄×C₆₇	—	2	6	no	—
259	C₂×D₄×C₆₇	—	2	6	no	—
260	C₂×D₄×C₆₇	—	2	1	no	—
261	C₂×D₄×C₆₇	—	2	3	no	—
262	C₂×D₄×C₆₇	—	2	3	no	—
263	C₂×D₄×C₆₇	—	2	3	no	—
264	C₂×D₄×C₆₇	—	2	3	no	—
265	C₂×D₄×C₆₇	—	2	6	no	—
266	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
267	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
268	C₂×D₄×C₆₇	C₂×D₄	1	12	yes	—
269	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
273	C₂²×C₄×C₆₇	—	2	24	no	—
274	C₂²×C₄×C₆₇	—	2	24	no	—
275	C₂²×C₄×C₆₇	—	2	3	no	—
276	C₂²×C₄×C₆₇	—	2	3	no	—
277	C₂²×C₄×C₆₇	—	2	3	no	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	6	no	—
280	C₂²×C₄×C₆₇	—	2	3	no	—
281	C₂²×C₄×C₆₇	—	2	3	no	—
282	C₂²×C₄×C₆₇	—	2	6	no	—
283	C₂²×C₄×C₆₇	—	2	6	no	—
284	C₂²×C₄×C₆₇	—	2	3	no	—
285	C₂²×C₄×C₆₇	—	2	3	no	—
286	C₂²×C₄×C₆₇	—	2	3	no	—
287	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
288	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
289	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
293	Q₁₆×C₆₇	—	2	6	no	—
294	Q₁₆×C₆₇	—	2	12	no	—
295	Q₁₆×C₆₇	—	2	6	no	—
296	SD₁₆×C₆₇	—	2	2	no	—
297	SD₁₆×C₆₇	—	2	6	no	—
298	SD₁₆×C₆₇	—	2	6	no	—
299	SD₁₆×C₆₇	—	2	12	no	—
300	SD₁₆×C₆₇	—	2	6	no	—
301	D₈×C₆₇	—	2	2	no	—
302	D₈×C₆₇	—	2	6	no	—
303	M₁₆×C₆₇	—	2	6	no	—
304	M₁₆×C₆₇	—	2	6	no	—
305	C₂×C₈×C₆₇	—	2	6	no	—
306	C₂×C₈×C₆₇	—	2	6	no	—
307	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
311	C₄⋊C₄×C₆₇	—	2	3	no	—
312	C₄⋊C₄×C₆₇	—	2	6	no	—
313	C₄⋊C₄×C₆₇	—	2	3	no	—
314	C₄⋊C₄×C₆₇	—	2	3	no	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²⋊C₄×C₆₇	—	2	3	no	—
318	C₂²⋊C₄×C₆₇	—	2	6	no	—
319	C₂²⋊C₄×C₆₇	—	2	3	no	—
320	C₂²⋊C₄×C₆₇	—	2	3	no	—
321	C₂²⋊C₄×C₆₇	—	2	1	no	—
322	C₂²⋊C₄×C₆₇	—	2	3	no	—
323	C₄²×C₆₇	—	2	3	no	—
324	C₂³×C₆₇	—	2	12	no	—
325	C₂³×C₆₇	—	2	3	no	—
326	C₂³×C₆₇	—	2	1	no	—
327	C₂³×C₆₇	—	2	6	no	—
328	C₂³×C₆₇	—	2	12	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	4	3	no	—
331	C₂³×C₆₇	—	4	3	no	—
332	C₂³×C₆₇	—	8	3	no	—
333	C₂³×C₆₇	—	8	3	no	—
334	C₂³×C₆₇	—	8	3	no	—
335	C₂³×C₆₇	—	8	3	no	—
336	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
337	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
339	Q₈×C₆₇	—	2	12	no	—
340	Q₈×C₆₇	—	2	12	no	—
341	Q₈×C₆₇	—	2	6	no	—
342	Q₈×C₆₇	—	2	1	no	—
343	Q₈×C₆₇	—	2	3	no	—
344	Q₈×C₆₇	—	2	3	no	—
345	Q₈×C₆₇	—	2	3	no	—
346	Q₈×C₆₇	—	4	6	no	—
347	Q₈×C₆₇	#120	1	4	yes	—
348	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
349	Q₈×C₆₇	C₂²×D₄	1	6	yes	—
350	D₄×C₆₇	—	2	24	no	—
351	D₄×C₆₇	—	2	12	no	—
352	D₄×C₆₇	—	2	4	no	—
353	D₄×C₆₇	—	2	12	no	—
354	D₄×C₆₇	—	2	12	no	—
355	D₄×C₆₇	—	2	12	no	—
356	D₄×C₆₇	—	2	12	no	—
357	D₄×C₆₇	—	2	6	no	—
358	D₄×C₆₇	—	2	12	no	—
359	D₄×C₆₇	—	2	3	no	—
360	D₄×C₆₇	—	2	1	no	—
361	D₄×C₆₇	—	2	1	no	—
362	D₄×C₆₇	—	2	1	no	—
363	D₄×C₆₇	—	4	2	no	—
364	D₄×C₆₇	—	4	6	no	—
365	D₄×C₆₇	—	8	3	no	—
366	D₄×C₆₇	#120	1	12	yes	—
367	D₄×C₆₇	C₂²×D₄	1	2	yes	—
368	D₄×C₆₇	C₂²×D₄	1	6	yes	—
369	C₂×C₄×C₆₇	—	2	12	no	—
370	C₂×C₄×C₆₇	—	2	4	no	—
371	C₂×C₄×C₆₇	—	2	12	no	—
372	C₂×C₄×C₆₇	—	2	24	no	—
373	C₂×C₄×C₆₇	—	2	6	no	—
374	C₂×C₄×C₆₇	—	2	12	no	—
375	C₂×C₄×C₆₇	—	2	3	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	6	no	—
378	C₂×C₄×C₆₇	—	2	12	no	—
379	C₂×C₄×C₆₇	—	2	12	no	—
380	C₂×C₄×C₆₇	—	2	6	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	3	no	—
384	C₂×C₄×C₆₇	—	2	3	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	3	no	—
387	C₂×C₄×C₆₇	—	2	3	no	—
388	C₂×C₄×C₆₇	—	4	6	no	—
389	C₂×C₄×C₆₇	—	4	6	no	—
390	C₂×C₄×C₆₇	—	8	3	no	—
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
393	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
394	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
395	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
396	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
397	C₈×C₆₇	—	2	1	no	—
398	C₈×C₆₇	—	2	1	no	—
399	C₈×C₆₇	—	2	3	no	—
400	C₈×C₆₇	—	2	3	no	—
401	C₂²×C₆₇	—	2	3	no	—
402	C₂²×C₆₇	—	2	3	no	—
403	C₂²×C₆₇	—	2	3	no	—
404	C₂²×C₆₇	—	2	1	no	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	3	no	—
407	C₂²×C₆₇	—	2	3	no	—
408	C₂²×C₆₇	—	2	1	no	—
409	C₂²×C₆₇	—	2	6	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	4	3	no	—
412	C₂²×C₆₇	—	4	1	no	—
413	C₂²×C₆₇	—	4	3	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	1	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	8	6	no	—
419	C₂²×C₆₇	—	8	12	no	—
420	C₂²×C₆₇	—	8	12	no	—
421	C₂²×C₆₇	C₂×#120	1	6	yes	—
422	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₆₇	—	2	1	no	—
424	C₄×C₆₇	—	2	6	no	—
425	C₄×C₆₇	—	2	2	no	—
426	C₄×C₆₇	—	2	3	no	—
427	C₄×C₆₇	—	4	3	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	3	no	—
430	C₄×C₆₇	C₂×#120	1	6	yes	—
431	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
432	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
433	#60377	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₆₇	—	2	6	no	—
435	C₂×C₆₇	—	4	3	no	—
436	C₂×C₆₇	—	4	1	no	—
437	C₂×C₆₇	—	4	6	no	—
438	C₂×C₆₇	—	4	2	no	—
439	C₂×C₆₇	—	8	1	no	—
440	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
441	C₂×C₆₇	#3584	1	1	yes	characteristic
442	C₂×C₆₇	#3586	1	1	yes	characteristic
443	C₂×#585	C₂×C₆₇	1	1	yes	characteristic, complemented
444	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
445	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#3013	C₂×C₆₇	1	3	yes	complemented
448	#3012	C₂×C₆₇	1	3	yes	complemented
449	#3011	C₂×C₆₇	1	3	yes	complemented
450	#3009	C₂×C₆₇	1	3	yes	complemented
451	#3007	C₂×C₆₇	1	3	yes	complemented
452	#3005	C₂×C₆₇	1	3	yes	complemented
453	#3002	C₂×C₆₇	1	3	yes	complemented
454	C₂×#452	C₂×C₆₇	1	3	yes	complemented
455	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2897	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
458	C₆₇	#60377	1	1	yes	characteristic, direct product factor, Sylow
459	#585	—	2	8	no	—
460	#585	—	2	8	no	—
461	C₂×2₋¹⁺⁴	—	2	1	no	—
462	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	3	yes	—
463	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
465	C₂×H(5,𝔽₂)	—	2	3	no	—
466	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	3	yes	—
467	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
468	C₂²×#41	—	2	3	no	—
469	C₂²×#41	—	2	1	no	—
470	C₂²×#41	C₂²×C₆₇	1	3	yes	—
471	C₂²×#41	C₂²×C₆₇	1	3	yes	—
472	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
473	#578	—	2	8	no	—
474	#577	—	2	8	no	—
475	C₂×#137	C₂²×C₆₇	1	3	yes	complemented
476	C₂×#137	C₂²×C₆₇	1	3	yes	complemented
477	C₂×#137	C₂²×C₆₇	1	3	yes	complemented
478	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	3	yes	complemented
479	C₂×#135	C₂²×C₆₇	1	3	yes	complemented
480	C₂×#135	C₂²×C₆₇	1	3	yes	complemented
481	C₂²×Q₁₆	C₂²×C₆₇	1	3	yes	complemented
482	C₂²×SD₁₆	C₂²×C₆₇	1	3	yes	complemented
483	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	D₄×Q₈	—	2	1	no	—
486	#548	—	2	1	no	—
487	#547	—	2	3	no	—
488	#546	—	2	3	no	—
489	#537	C₂²×C₆₇	1	3	yes	complemented
490	#536	C₂²×C₆₇	1	3	yes	complemented
491	#525	C₂²×C₆₇	1	3	yes	complemented
492	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	3	yes	complemented
493	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	#452	C₂²×C₆₇	1	3	yes	complemented
495	#452	C₂²×C₆₇	1	6	yes	complemented
496	#452	C₂²×C₆₇	1	6	yes	complemented
497	#452	C₂²×C₆₇	1	6	yes	complemented
498	#452	C₂²×C₆₇	1	3	yes	complemented
499	#452	C₂²×C₆₇	1	6	yes	complemented
500	#451	C₂²×C₆₇	1	3	yes	complemented
501	#451	C₂²×C₆₇	1	6	yes	complemented
502	#450	C₂²×C₆₇	1	3	yes	complemented
503	#450	C₂²×C₆₇	1	6	yes	complemented
504	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	#449	C₂²×C₆₇	1	3	yes	complemented
506	#449	C₂²×C₆₇	1	6	yes	complemented
507	#448	C₂²×C₆₇	1	3	yes	complemented
508	#447	C₂²×C₆₇	1	3	yes	complemented
509	#419	C₂²×C₆₇	1	3	yes	complemented
510	#418	C₂²×C₆₇	1	3	yes	complemented
511	#417	C₂²×C₆₇	1	3	yes	complemented
512	#417	C₂²×C₆₇	1	3	yes	complemented
513	#416	C₂²×C₆₇	1	3	yes	complemented
514	#416	C₂²×C₆₇	1	3	yes	complemented
515	C₂×#103	C₂²×C₆₇	1	3	yes	complemented
516	C₂×#102	C₂²×C₆₇	1	3	yes	complemented
517	#408	C₂²×C₆₇	1	3	yes	complemented
518	#408	C₂²×C₆₇	1	3	yes	complemented
519	#407	C₂²×C₆₇	1	3	yes	complemented
520	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
521	2₋¹⁺⁴	—	2	16	no	—
522	2₋¹⁺⁴	—	2	12	no	—
523	2₋¹⁺⁴	—	2	4	no	—
524	2₋¹⁺⁴	—	2	12	no	—
525	2₋¹⁺⁴	—	2	4	no	—
526	2₋¹⁺⁴	—	2	4	no	—
527	2₋¹⁺⁴	D₄×C₆₇	1	8	yes	complemented
528	H(5,𝔽₂)	—	2	48	no	—
529	H(5,𝔽₂)	—	2	12	no	—
530	H(5,𝔽₂)	—	2	4	no	—
531	H(5,𝔽₂)	—	2	12	no	—
532	H(5,𝔽₂)	D₄×C₆₇	1	8	yes	complemented
533	C₂×#41	—	2	16	no	—
534	C₂×#41	—	2	48	no	—
535	C₂×#41	—	2	12	no	—
536	C₂×#41	—	2	12	no	—
537	C₂×#41	—	2	4	no	—
538	C₂×#41	—	2	4	no	—
539	C₂×#41	—	2	3	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	12	no	—
542	C₂×#41	—	2	6	no	—
543	C₂×#41	—	2	3	no	—
544	C₂×#41	—	2	3	no	—
545	C₂×#41	—	2	12	no	—
546	C₂×#41	—	2	3	no	—
547	C₂×#41	—	2	3	no	—
548	C₂×#41	—	2	3	no	—
549	C₂×#41	—	2	3	no	—
550	C₂×#41	—	2	3	no	—
551	C₂×#41	D₄×C₆₇	1	3	yes	—
552	C₂×#41	D₄×C₆₇	1	1	yes	characteristic
553	C₂×#41	C₂³×C₆₇	1	3	yes	—
554	C₂×#41	C₂³×C₆₇	1	3	yes	—
555	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×#41	C₂³×C₆₇	1	6	yes	—
557	C₂×#41	C₂³×C₆₇	1	3	yes	—
558	C₂×#41	C₂³×C₆₇	1	3	yes	—
559	C₂×#41	C₂³×C₆₇	1	3	yes	—
560	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
561	C₂²×Q₈	—	2	3	no	—
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	—	2	1	no	—
564	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
566	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
567	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
568	C₂²×D₄	—	2	3	no	—
569	C₂²×D₄	—	2	3	no	—
570	C₂²×D₄	—	2	6	no	—
571	C₂²×D₄	—	2	3	no	—
572	C₂²×D₄	—	2	3	no	—
573	C₂²×D₄	D₄×C₆₇	1	3	yes	—
574	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
575	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
576	C₂³×C₄	—	2	3	no	—
577	C₂³×C₄	—	2	3	no	—
578	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
579	#137	—	2	12	no	—
580	#137	—	2	12	no	—
581	#137	—	2	12	no	—
582	AGL(1,ℤ/8)	—	2	12	no	—
583	#135	—	2	12	no	—
584	#135	—	2	12	no	—
585	C₂×Q₁₆	—	2	12	no	—
586	C₂×Q₁₆	C₂³×C₆₇	1	3	yes	—
587	C₂×Q₁₆	C₂³×C₆₇	1	6	yes	—
588	C₂×Q₁₆	C₂³×C₆₇	1	3	yes	—
589	C₂×SD₁₆	—	2	12	no	—
590	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
591	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	—
592	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
595	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×D₈	C₂³×C₆₇	1	3	yes	—
597	#131	—	2	4	no	—
598	#131	—	2	4	no	—
599	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
600	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
601	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
602	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
603	C₄⋊Q₈	—	2	3	no	—
604	#124	—	2	3	no	—
605	#123	—	2	6	no	—
606	#123	—	2	3	no	—
607	C₂²⋊Q₈	—	2	3	no	—
608	C₂²⋊Q₈	—	2	3	no	—
609	C₂²⋊Q₈	—	2	3	no	—
610	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	—
611	C₂²⋊Q₈	C₂³×C₆₇	1	6	yes	—
612	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	—
613	#121	—	2	6	no	—
614	#121	—	2	3	no	—
615	#121	C₂³×C₆₇	1	1	yes	characteristic
616	#121	C₂³×C₆₇	1	3	yes	—
617	#120	—	2	3	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×D₄	—	2	3	no	—
620	C₄×D₄	—	2	3	no	—
621	C₄×D₄	—	2	3	no	—
622	#117	C₂³×C₆₇	1	3	yes	—
623	C₂×C₄⋊C₄	—	2	3	no	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
625	C₂×C₂²⋊C₄	—	2	3	no	—
626	#103	C₂³×C₆₇	1	3	yes	—
627	#103	C₂³×C₆₇	1	6	yes	—
628	#103	C₂³×C₆₇	1	1	yes	characteristic
629	#103	C₂³×C₆₇	1	3	yes	—
630	#103	C₂³×C₆₇	1	3	yes	—
631	#102	C₂³×C₆₇	1	3	yes	—
632	#102	C₂³×C₆₇	1	6	yes	—
633	#102	C₂³×C₆₇	1	1	yes	characteristic
634	#102	C₂³×C₆₇	1	3	yes	—
635	#102	C₂³×C₆₇	1	3	yes	—
636	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
637	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
638	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
639	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
640	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	—
641	C₂⁴	—	2	3	no	—
642	C₂⁴	—	2	3	no	—
643	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
644	#41	—	2	24	no	—
645	#41	—	2	24	no	—
646	#41	—	2	48	no	—
647	#41	—	2	24	no	—
648	#41	—	2	24	no	—
649	#41	—	2	24	no	—
650	#41	—	2	24	no	—
651	#41	—	2	4	no	—
652	#41	—	2	8	no	—
653	#41	—	2	2	no	—
654	#41	—	2	6	no	—
655	#41	—	2	12	no	—
656	#41	—	2	12	no	—
657	#41	—	2	24	no	—
658	#41	—	2	2	no	—
659	#41	—	2	6	no	—
660	#41	—	2	12	no	—
661	#41	—	2	6	no	—
662	#41	—	2	6	no	—
663	#41	—	2	6	no	—
664	#41	—	2	6	no	—
665	#41	—	2	6	no	—
666	#41	—	2	6	no	—
667	#41	—	4	12	no	—
668	#41	C₂×D₄×C₆₇	1	12	yes	—
669	#41	C₂×D₄×C₆₇	1	12	yes	—
670	#41	C₂×D₄×C₆₇	1	4	yes	—
671	#41	C₂×D₄×C₆₇	1	4	yes	—
672	C₂×Q₈	—	2	24	no	—
673	C₂×Q₈	—	2	8	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	2	6	no	—
676	C₂×Q₈	—	2	6	no	—
677	C₂×Q₈	—	2	3	no	—
678	C₂×Q₈	—	2	3	no	—
679	C₂×Q₈	—	2	6	no	—
680	C₂×Q₈	—	2	3	no	—
681	C₂×Q₈	—	2	6	no	—
682	C₂×Q₈	—	2	6	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	C₂×D₄×C₆₇	1	12	yes	—
685	C₂×Q₈	C₂×D₄×C₆₇	1	3	yes	—
686	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₆₇	1	3	yes	—
688	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₆₇	1	3	yes	—
690	C₂×D₄	—	2	24	no	—
691	C₂×D₄	—	2	48	no	—
692	C₂×D₄	—	2	24	no	—
693	C₂×D₄	—	2	24	no	—
694	C₂×D₄	—	2	6	no	—
695	C₂×D₄	—	2	3	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	3	no	—
698	C₂×D₄	—	2	3	no	—
699	C₂×D₄	—	2	24	no	—
700	C₂×D₄	—	2	12	no	—
701	C₂×D₄	—	2	6	no	—
702	C₂×D₄	—	2	6	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	3	no	—
705	C₂×D₄	—	2	3	no	—
706	C₂×D₄	—	2	3	no	—
707	C₂×D₄	—	2	3	no	—
708	C₂×D₄	—	2	6	no	—
709	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
710	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
711	C₂×D₄	C₂×D₄×C₆₇	1	12	yes	—
712	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
713	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂×D₄	C₂⁴×C₆₇	1	3	yes	—
716	C₂²×C₄	—	2	24	no	—
717	C₂²×C₄	—	2	24	no	—
718	C₂²×C₄	—	2	3	no	—
719	C₂²×C₄	—	2	3	no	—
720	C₂²×C₄	—	2	3	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	6	no	—
723	C₂²×C₄	—	2	3	no	—
724	C₂²×C₄	—	2	3	no	—
725	C₂²×C₄	—	2	6	no	—
726	C₂²×C₄	—	2	6	no	—
727	C₂²×C₄	—	2	3	no	—
728	C₂²×C₄	—	2	3	no	—
729	C₂²×C₄	—	2	3	no	—
730	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
731	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
732	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
736	Q₁₆	—	2	6	no	—
737	Q₁₆	—	2	12	no	—
738	Q₁₆	—	2	6	no	—
739	SD₁₆	—	2	2	no	—
740	SD₁₆	—	2	6	no	—
741	SD₁₆	—	2	6	no	—
742	SD₁₆	—	2	12	no	—
743	SD₁₆	—	2	6	no	—
744	D₈	—	2	2	no	—
745	D₈	—	2	6	no	—
746	M₁₆	—	2	6	no	—
747	M₁₆	—	2	6	no	—
748	C₂×C₈	—	2	6	no	—
749	C₂×C₈	—	2	6	no	—
750	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
752	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
754	C₄⋊C₄	—	2	3	no	—
755	C₄⋊C₄	—	2	6	no	—
756	C₄⋊C₄	—	2	3	no	—
757	C₄⋊C₄	—	2	3	no	—
758	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
759	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	C₂²⋊C₄	—	2	3	no	—
761	C₂²⋊C₄	—	2	6	no	—
762	C₂²⋊C₄	—	2	3	no	—
763	C₂²⋊C₄	—	2	3	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	3	no	—
766	C₄²	—	2	3	no	—
767	C₂³	—	2	12	no	—
768	C₂³	—	2	3	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	6	no	—
771	C₂³	—	2	12	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	4	3	no	—
774	C₂³	—	4	3	no	—
775	C₂³	—	8	3	no	—
776	C₂³	—	8	3	no	—
777	C₂³	—	8	3	no	—
778	C₂³	—	8	3	no	—
779	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
780	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
782	Q₈	—	2	12	no	—
783	Q₈	—	2	12	no	—
784	Q₈	—	2	6	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	3	no	—
787	Q₈	—	2	3	no	—
788	Q₈	—	2	3	no	—
789	Q₈	—	4	6	no	—
790	Q₈	#120×C₆₇	1	4	yes	—
791	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
792	Q₈	C₂²×D₄×C₆₇	1	6	yes	—
793	D₄	—	2	24	no	—
794	D₄	—	2	12	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	12	no	—
797	D₄	—	2	12	no	—
798	D₄	—	2	12	no	—
799	D₄	—	2	12	no	—
800	D₄	—	2	6	no	—
801	D₄	—	2	12	no	—
802	D₄	—	2	3	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	1	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	6	no	—
808	D₄	—	8	3	no	—
809	D₄	#120×C₆₇	1	12	yes	—
810	D₄	C₂²×D₄×C₆₇	1	2	yes	—
811	D₄	C₂²×D₄×C₆₇	1	6	yes	—
812	C₂×C₄	—	2	12	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	12	no	—
815	C₂×C₄	—	2	24	no	—
816	C₂×C₄	—	2	6	no	—
817	C₂×C₄	—	2	12	no	—
818	C₂×C₄	—	2	3	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	6	no	—
821	C₂×C₄	—	2	12	no	—
822	C₂×C₄	—	2	12	no	—
823	C₂×C₄	—	2	6	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	3	no	—
827	C₂×C₄	—	2	3	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	3	no	—
830	C₂×C₄	—	2	3	no	—
831	C₂×C₄	—	4	6	no	—
832	C₂×C₄	—	4	6	no	—
833	C₂×C₄	—	8	3	no	—
834	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
836	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
837	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
838	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
839	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
840	C₈	—	2	1	no	—
841	C₈	—	2	1	no	—
842	C₈	—	2	3	no	—
843	C₈	—	2	3	no	—
844	C₂²	—	2	3	no	—
845	C₂²	—	2	3	no	—
846	C₂²	—	2	3	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	3	no	—
850	C₂²	—	2	3	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	6	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	3	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	3	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	8	6	no	—
862	C₂²	—	8	12	no	—
863	C₂²	—	8	12	no	—
864	C₂²	C₂×#120×C₆₇	1	6	yes	—
865	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	6	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	3	no	—
870	C₄	—	4	3	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	3	no	—
873	C₄	C₂×#120×C₆₇	1	6	yes	—
874	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
875	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
876	C₂	—	2	6	no	—
877	C₂	—	4	3	no	—
878	C₂	—	4	1	no	—
879	C₂	—	4	6	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	1	no	—
882	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
883	C₂	C₆₇×#3584	1	1	yes	characteristic
884	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 ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₆₇	C₂	semidirect
2. C₂×#578×C₆₇	C₂	semidirect
3. C₂×#577×C₆₇	C₂	semidirect
4. C₆₇×#3489	C₂	semidirect
5. C₆₇×#3013	C₂	semidirect
6. C₆₇×#3012	C₂	semidirect
7. C₆₇×#3011	C₂	semidirect
8. C₆₇×#3009	C₂	semidirect
9. C₆₇×#3007	C₂	semidirect
10. C₆₇×#3005	C₂	semidirect
11. C₆₇×#3002	C₂	semidirect
12. C₂×#452×C₆₇	C₂	semidirect
13. C₆₇×#2898	C₂	semidirect
14. C₆₇×#2897	C₂	semidirect
15. C₆₇×#2880	C₂	semidirect
21. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×#137×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. C₂×#135×C₆₇	C₂²	semidirect
38. C₂²×Q₁₆×C₆₇	C₂²	semidirect
39. C₂²×SD₁₆×C₆₇	C₂²	semidirect
40. C₂×#131×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
47. #536×C₆₇	C₂²	semidirect
48. #525×C₆₇	C₂²	semidirect
49. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
50. #520×C₆₇	C₂²	semidirect
51. #452×C₆₇	C₂²	semidirect
52. #452×C₆₇	C₂²	semidirect
53. #452×C₆₇	C₂²	semidirect
54. #452×C₆₇	C₂²	semidirect
55. #452×C₆₇	C₂²	semidirect
56. #452×C₆₇	C₂²	semidirect
57. #451×C₆₇	C₂²	semidirect
58. #451×C₆₇	C₂²	semidirect
59. #450×C₆₇	C₂²	semidirect
60. #450×C₆₇	C₂²	semidirect
61. #449×C₆₇	C₂²	semidirect
62. #449×C₆₇	C₂²	semidirect
63. #449×C₆₇	C₂²	semidirect
64. #448×C₆₇	C₂²	semidirect
65. #447×C₆₇	C₂²	semidirect
66. #419×C₆₇	C₂²	semidirect
67. #418×C₆₇	C₂²	semidirect
68. #417×C₆₇	C₂²	semidirect
69. #417×C₆₇	C₂²	semidirect
70. #416×C₆₇	C₂²	semidirect
71. #416×C₆₇	C₂²	semidirect
72. C₂×#103×C₆₇	C₂²	semidirect
73. C₂×#102×C₆₇	C₂²	semidirect
74. #408×C₆₇	C₂²	semidirect
75. #408×C₆₇	C₂²	semidirect
76. #407×C₆₇	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
84. 2₋¹⁺⁴×C₆₇	D₄	semidirect
89. H(5,𝔽₂)×C₆₇	D₄	semidirect
433. #60377	C₆₇	direct (N × H)
443. C₂×#585	C₂×C₆₇	semidirect
444. C₂×#578	C₂×C₆₇	semidirect
445. C₂×#577	C₂×C₆₇	semidirect
446. #3489	C₂×C₆₇	semidirect
447. #3013	C₂×C₆₇	semidirect
448. #3012	C₂×C₆₇	semidirect
449. #3011	C₂×C₆₇	semidirect
450. #3009	C₂×C₆₇	semidirect
451. #3007	C₂×C₆₇	semidirect
452. #3005	C₂×C₆₇	semidirect
453. #3002	C₂×C₆₇	semidirect
454. C₂×#452	C₂×C₆₇	semidirect
455. #2898	C₂×C₆₇	semidirect
456. #2897	C₂×C₆₇	semidirect
457. #2880	C₂×C₆₇	semidirect
458. C₆₇	#60377	direct (N × H)
464. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
475. C₂×#137	C₂²×C₆₇	semidirect
476. C₂×#137	C₂²×C₆₇	semidirect
477. C₂×#137	C₂²×C₆₇	semidirect
478. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
479. C₂×#135	C₂²×C₆₇	semidirect
480. C₂×#135	C₂²×C₆₇	semidirect
481. C₂²×Q₁₆	C₂²×C₆₇	semidirect
482. C₂²×SD₁₆	C₂²×C₆₇	semidirect
483. C₂×#131	C₂²×C₆₇	semidirect
484. C₂×#131	C₂²×C₆₇	semidirect
489. #537	C₂²×C₆₇	semidirect
490. #536	C₂²×C₆₇	semidirect
491. #525	C₂²×C₆₇	semidirect
492. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
493. #520	C₂²×C₆₇	semidirect
494. #452	C₂²×C₆₇	semidirect
495. #452	C₂²×C₆₇	semidirect
496. #452	C₂²×C₆₇	semidirect
497. #452	C₂²×C₆₇	semidirect
498. #452	C₂²×C₆₇	semidirect
499. #452	C₂²×C₆₇	semidirect
500. #451	C₂²×C₆₇	semidirect
501. #451	C₂²×C₆₇	semidirect
502. #450	C₂²×C₆₇	semidirect
503. #450	C₂²×C₆₇	semidirect
504. #449	C₂²×C₆₇	semidirect
505. #449	C₂²×C₆₇	semidirect
506. #449	C₂²×C₆₇	semidirect
507. #448	C₂²×C₆₇	semidirect
508. #447	C₂²×C₆₇	semidirect
509. #419	C₂²×C₆₇	semidirect
510. #418	C₂²×C₆₇	semidirect
511. #417	C₂²×C₆₇	semidirect
512. #417	C₂²×C₆₇	semidirect
513. #416	C₂²×C₆₇	semidirect
514. #416	C₂²×C₆₇	semidirect
515. C₂×#103	C₂²×C₆₇	semidirect
516. C₂×#102	C₂²×C₆₇	semidirect
517. #408	C₂²×C₆₇	semidirect
518. #408	C₂²×C₆₇	semidirect
519. #407	C₂²×C₆₇	semidirect
520. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
527. 2₋¹⁺⁴	D₄×C₆₇	semidirect
532. H(5,𝔽₂)	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₆₇	2
C₂×#578×C₆₇	2
C₂×#577×C₆₇	2
C₆₇×#3489	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3011	2
C₆₇×#3009	2
C₆₇×#3007	2
C₆₇×#3005	2
C₆₇×#3002	2
C₂×#452×C₆₇	2
C₆₇×#2898	2
C₆₇×#2897	2
C₆₇×#2880	2
#60377	67

Subgroups — C67×#60377 #30739628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60377 #30739628