Subgroups — C₆₇×#61737 #30740988

Order 17152.

2012 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3343	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3334	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3308	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3193	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×#484×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	—	2	1	no	—
19	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	#554×C₆₇	—	2	1	no	—
21	#552×C₆₇	C₂²	1	2	yes	complemented
22	#551×C₆₇	—	2	2	no	—
23	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#548×C₆₇	C₂²	1	2	yes	complemented
25	#547×C₆₇	—	2	1	no	—
26	#547×C₆₇	—	2	2	no	—
27	#547×C₆₇	—	2	1	no	—
28	#547×C₆₇	C₂²	1	2	yes	—
29	#547×C₆₇	C₂²	1	4	yes	—
30	#547×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#546×C₆₇	—	2	1	no	—
34	#542×C₆₇	—	2	1	no	—
35	#539×C₆₇	—	2	2	no	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	#529×C₆₇	C₂²	1	1	yes	characteristic
39	#525×C₆₇	C₂²	1	2	yes	—
40	C₂×#123×C₆₇	—	2	2	no	—
41	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
43	C₂×#121×C₆₇	C₂²	1	2	yes	—
44	#520×C₆₇	—	2	1	no	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
48	#501×C₆₇	C₂²	1	2	yes	complemented
49	#500×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#487×C₆₇	C₂²	1	2	yes	complemented
52	#484×C₆₇	C₂²	1	1	yes	characteristic
53	#484×C₆₇	C₂²	1	2	yes	—
54	#484×C₆₇	C₂²	1	2	yes	—
55	#484×C₆₇	C₂²	1	2	yes	—
56	#484×C₆₇	C₂²	1	2	yes	—
57	#484×C₆₇	C₂²	1	4	yes	complemented
58	#484×C₆₇	C₂²	1	4	yes	complemented
59	#483×C₆₇	C₂²	1	4	yes	complemented
60	#482×C₆₇	C₂²	1	4	yes	complemented
61	#481×C₆₇	C₂²	1	1	yes	characteristic
62	#481×C₆₇	C₂²	1	2	yes	—
63	#480×C₆₇	C₂²	1	4	yes	complemented
64	#480×C₆₇	C₂²	1	4	yes	complemented
65	#478×C₆₇	C₂²	1	2	yes	complemented
66	#477×C₆₇	C₂²	1	4	yes	complemented
67	#475×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#474×C₆₇	C₂²	1	2	yes	complemented
70	#468×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	4	yes	complemented
72	#466×C₆₇	C₂²	1	4	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#463×C₆₇	C₂²	1	2	yes	complemented
75	#461×C₆₇	C₂²	1	2	yes	complemented
76	#450×C₆₇	C₂²	1	1	yes	characteristic
77	#450×C₆₇	C₂²	1	2	yes	—
78	#449×C₆₇	C₂²	1	4	yes	complemented
79	#448×C₆₇	C₂²	1	4	yes	complemented
80	#447×C₆₇	C₂²	1	1	yes	characteristic
81	#440×C₆₇	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
83	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
84	#436×C₆₇	C₂²	1	2	yes	complemented
85	#435×C₆₇	C₂²	1	4	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	#432×C₆₇	C₂²	1	1	yes	characteristic
88	#431×C₆₇	C₂²	1	1	yes	characteristic
89	#428×C₆₇	C₂²	1	4	yes	complemented
90	C₂×#107×C₆₇	C₂²	1	4	yes	complemented
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	—	2	4	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	4	8	no	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	—	2	1	no	—
102	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	2	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂×D₈×C₆₇	C₂³	1	2	yes	—
112	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₆₇	—	2	1	no	—
115	C₄⋊Q₈×C₆₇	—	2	1	no	—
116	C₄⋊Q₈×C₆₇	—	2	1	no	—
117	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
121	#126×C₆₇	—	2	2	no	—
122	#126×C₆₇	—	2	2	no	—
123	#126×C₆₇	—	2	1	no	—
124	#125×C₆₇	—	2	2	no	—
125	#125×C₆₇	—	2	1	no	—
126	#125×C₆₇	C₂³	1	1	yes	characteristic
127	#124×C₆₇	—	2	1	no	—
128	#124×C₆₇	—	2	2	no	—
129	#124×C₆₇	C₂³	1	1	yes	characteristic
130	#123×C₆₇	—	2	2	no	—
131	#123×C₆₇	—	2	2	no	—
132	#123×C₆₇	—	2	1	no	—
133	#123×C₆₇	—	2	4	no	—
134	#123×C₆₇	—	2	4	no	—
135	#123×C₆₇	—	2	4	no	—
136	#123×C₆₇	—	2	4	no	—
137	#123×C₆₇	—	2	2	no	—
138	#123×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	—	2	4	no	—
144	C₂²⋊Q₈×C₆₇	—	2	2	no	—
145	C₂²⋊Q₈×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	—	2	1	no	—
147	C₂²⋊Q₈×C₆₇	—	2	2	no	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	1	no	—
155	#121×C₆₇	—	2	2	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	C₂³	1	4	yes	—
158	#121×C₆₇	C₂³	1	4	yes	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	1	yes	characteristic
161	#120×C₆₇	—	2	2	no	—
162	C₄×Q₈×C₆₇	—	2	1	no	—
163	C₄×Q₈×C₆₇	—	2	1	no	—
164	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	1	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₇	C₂³	1	2	yes	—
182	#117×C₆₇	—	2	1	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	1	no	—
185	#117×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
188	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
203	#107×C₆₇	C₂³	1	4	yes	—
204	#107×C₆₇	C₂³	1	4	yes	—
205	#107×C₆₇	C₂³	1	4	yes	—
206	#107×C₆₇	C₂³	1	4	yes	—
207	#107×C₆₇	C₂³	1	2	yes	—
208	#106×C₆₇	C₂³	1	4	yes	—
209	#106×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	2	yes	—
217	#102×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
223	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
227	#97×C₆₇	C₂³	1	2	yes	—
228	C₄×C₈×C₆₇	C₂³	1	2	yes	—
229	C₂⁴×C₆₇	—	2	1	no	—
230	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
231	#41×C₆₇	—	4	4	no	—
232	#41×C₆₇	—	4	16	no	—
233	#41×C₆₇	—	4	8	no	—
234	#41×C₆₇	—	4	4	no	—
235	#41×C₆₇	—	4	8	no	—
236	C₂×Q₈×C₆₇	—	2	1	no	—
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	2	no	—
240	C₂×Q₈×C₆₇	—	4	4	no	—
241	C₂×Q₈×C₆₇	—	4	4	no	—
242	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	1	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂×D₄×C₆₇	—	4	8	no	—
253	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	—	2	1	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	4	4	no	—
269	C₂²×C₄×C₆₇	—	4	4	no	—
270	C₂²×C₄×C₆₇	—	4	8	no	—
271	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	SD₁₆×C₆₇	—	4	4	no	—
280	SD₁₆×C₆₇	—	4	2	no	—
281	D₈×C₆₇	—	4	2	no	—
282	M₁₆×C₆₇	—	4	4	no	—
283	C₂×C₈×C₆₇	—	4	4	no	—
284	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
285	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
286	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	—	2	1	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	1	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	1	no	—
300	C₄⋊C₄×C₆₇	—	2	1	no	—
301	C₄⋊C₄×C₆₇	—	2	1	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	1	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
314	C₂²⋊C₄×C₆₇	—	2	1	no	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	1	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₂²⋊C₄×C₆₇	—	2	1	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	1	no	—
329	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	—	2	1	no	—
336	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂³×C₆₇	—	2	4	no	—
341	C₂³×C₆₇	—	2	4	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	4	2	no	—
345	C₂³×C₆₇	—	4	2	no	—
346	C₂³×C₆₇	—	4	2	no	—
347	C₂³×C₆₇	—	4	2	no	—
348	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
349	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
350	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₆₇	—	2	2	no	—
352	Q₈×C₆₇	—	2	4	no	—
353	Q₈×C₆₇	—	4	4	no	—
354	Q₈×C₆₇	—	4	4	no	—
355	Q₈×C₆₇	—	4	2	no	—
356	Q₈×C₆₇	—	8	2	no	—
357	D₄×C₆₇	—	2	4	no	—
358	D₄×C₆₇	—	2	2	no	—
359	D₄×C₆₇	—	2	2	no	—
360	D₄×C₆₇	—	2	2	no	—
361	D₄×C₆₇	—	2	2	no	—
362	D₄×C₆₇	—	4	2	no	—
363	D₄×C₆₇	—	4	8	no	—
364	D₄×C₆₇	—	4	8	no	—
365	D₄×C₆₇	—	4	4	no	—
366	D₄×C₆₇	—	4	2	no	—
367	D₄×C₆₇	—	8	2	no	—
368	D₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	4	no	—
381	C₂×C₄×C₆₇	—	4	2	no	—
382	C₂×C₄×C₆₇	—	4	2	no	—
383	C₂×C₄×C₆₇	—	4	2	no	—
384	C₂×C₄×C₆₇	—	4	4	no	—
385	C₂×C₄×C₆₇	—	4	2	no	—
386	C₂×C₄×C₆₇	—	4	4	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	4	4	no	—
391	C₂×C₄×C₆₇	—	4	2	no	—
392	C₂×C₄×C₆₇	—	8	2	no	—
393	C₂×C₄×C₆₇	—	8	2	no	—
394	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
402	C₈×C₆₇	—	2	2	no	—
403	C₈×C₆₇	—	2	4	no	—
404	C₈×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	2	no	—
407	C₂²×C₆₇	—	2	1	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	4	8	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	8	4	no	—
420	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
421	C₂²×C₆₇	#578	1	2	yes	—
422	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₆₇	—	2	1	no	—
424	C₄×C₆₇	—	2	2	no	—
425	C₄×C₆₇	—	2	2	no	—
426	C₄×C₆₇	—	2	1	no	—
427	C₄×C₆₇	—	2	1	no	—
428	C₄×C₆₇	—	2	1	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	—	4	1	no	—
431	C₄×C₆₇	—	4	1	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	4	no	—
434	C₄×C₆₇	—	4	2	no	—
435	C₄×C₆₇	—	4	1	no	—
436	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
437	C₄×C₆₇	#585	1	2	yes	—
438	#61737	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂×C₆₇	—	2	2	no	—
440	C₂×C₆₇	—	2	4	no	—
441	C₂×C₆₇	—	4	2	no	—
442	C₂×C₆₇	—	8	1	no	—
443	C₂×C₆₇	—	8	2	no	—
444	C₂×C₆₇	#3485	1	1	yes	characteristic
445	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
447	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#3353	C₂×C₆₇	1	2	yes	complemented
450	#3343	C₂×C₆₇	1	4	yes	complemented
451	#3334	C₂×C₆₇	1	2	yes	complemented
452	#3330	C₂×C₆₇	1	2	yes	complemented
453	#3308	C₂×C₆₇	1	4	yes	complemented
454	#3298	C₂×C₆₇	1	2	yes	complemented
455	#3239	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3230	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#3193	C₂×C₆₇	1	2	yes	complemented
458	#3188	C₂×C₆₇	1	2	yes	complemented
459	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#3092	C₂×C₆₇	1	2	yes	complemented
462	C₂×#484	C₂×C₆₇	1	2	yes	complemented
463	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₆₇	#61737	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²×#41	—	2	1	no	—
466	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
467	#554	—	2	1	no	—
468	#552	C₂²×C₆₇	1	2	yes	complemented
469	#551	—	2	2	no	—
470	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	#548	C₂²×C₆₇	1	2	yes	complemented
472	#547	—	2	1	no	—
473	#547	—	2	2	no	—
474	#547	—	2	1	no	—
475	#547	C₂²×C₆₇	1	2	yes	—
476	#547	C₂²×C₆₇	1	2	yes	—
477	#547	C₂²×C₆₇	1	4	yes	—
478	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	#546	—	2	1	no	—
481	#542	—	2	1	no	—
482	#539	—	2	2	no	—
483	#533	C₂²×C₆₇	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
485	#529	C₂²×C₆₇	1	1	yes	characteristic
486	#525	C₂²×C₆₇	1	2	yes	—
487	C₂×#123	—	2	2	no	—
488	C₂×C₂²⋊Q₈	—	2	1	no	—
489	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
490	C₂×#121	C₂²×C₆₇	1	2	yes	—
491	#520	—	2	1	no	—
492	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
494	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
495	#501	C₂²×C₆₇	1	2	yes	complemented
496	#500	C₂²×C₆₇	1	2	yes	complemented
497	#489	C₂²×C₆₇	1	2	yes	complemented
498	#487	C₂²×C₆₇	1	2	yes	complemented
499	#484	C₂²×C₆₇	1	1	yes	characteristic
500	#484	C₂²×C₆₇	1	2	yes	—
501	#484	C₂²×C₆₇	1	2	yes	—
502	#484	C₂²×C₆₇	1	2	yes	—
503	#484	C₂²×C₆₇	1	2	yes	—
504	#484	C₂²×C₆₇	1	4	yes	complemented
505	#484	C₂²×C₆₇	1	4	yes	complemented
506	#483	C₂²×C₆₇	1	4	yes	complemented
507	#482	C₂²×C₆₇	1	4	yes	complemented
508	#481	C₂²×C₆₇	1	1	yes	characteristic
509	#481	C₂²×C₆₇	1	2	yes	—
510	#480	C₂²×C₆₇	1	4	yes	complemented
511	#480	C₂²×C₆₇	1	4	yes	complemented
512	#478	C₂²×C₆₇	1	2	yes	complemented
513	#477	C₂²×C₆₇	1	4	yes	complemented
514	#475	C₂²×C₆₇	1	2	yes	complemented
515	#474	C₂²×C₆₇	1	2	yes	complemented
516	#474	C₂²×C₆₇	1	2	yes	complemented
517	#468	C₂²×C₆₇	1	4	yes	complemented
518	#468	C₂²×C₆₇	1	4	yes	complemented
519	#466	C₂²×C₆₇	1	4	yes	complemented
520	#465	C₂²×C₆₇	1	4	yes	complemented
521	#463	C₂²×C₆₇	1	2	yes	complemented
522	#461	C₂²×C₆₇	1	2	yes	complemented
523	#450	C₂²×C₆₇	1	1	yes	characteristic
524	#450	C₂²×C₆₇	1	2	yes	—
525	#449	C₂²×C₆₇	1	4	yes	complemented
526	#448	C₂²×C₆₇	1	4	yes	complemented
527	#447	C₂²×C₆₇	1	1	yes	characteristic
528	#440	C₂²×C₆₇	1	4	yes	complemented
529	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
530	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
531	#436	C₂²×C₆₇	1	2	yes	complemented
532	#435	C₂²×C₆₇	1	4	yes	complemented
533	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
534	#432	C₂²×C₆₇	1	1	yes	characteristic
535	#431	C₂²×C₆₇	1	1	yes	characteristic
536	#428	C₂²×C₆₇	1	4	yes	complemented
537	C₂×#107	C₂²×C₆₇	1	4	yes	complemented
538	#417	C₂²×C₆₇	1	4	yes	complemented
539	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
540	#407	C₂²×C₆₇	1	2	yes	—
541	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	4	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	4	8	no	—
547	C₂×#41	C₂³×C₆₇	1	2	yes	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
550	C₂²×D₄	—	2	2	no	—
551	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂³×C₄	—	2	2	no	—
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
558	C₂×D₈	C₂³×C₆₇	1	2	yes	—
559	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
560	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#126	—	2	1	no	—
571	#125	—	2	2	no	—
572	#125	—	2	1	no	—
573	#125	C₂³×C₆₇	1	1	yes	characteristic
574	#124	—	2	1	no	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₆₇	1	1	yes	characteristic
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	1	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	4	no	—
583	#123	—	2	4	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
596	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	C₂³×C₆₇	1	4	yes	—
605	#121	C₂³×C₆₇	1	4	yes	—
606	#121	C₂³×C₆₇	1	1	yes	characteristic
607	#121	C₂³×C₆₇	1	2	yes	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
621	C₄×D₄	D₄×C₆₇	1	2	yes	—
622	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₆₇	1	2	yes	—
624	C₄×D₄	C₂³×C₆₇	1	2	yes	—
625	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₆₇	1	2	yes	—
629	#117	—	2	1	no	—
630	#117	—	2	2	no	—
631	#117	—	2	1	no	—
632	#117	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	2	no	—
648	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
650	#107	C₂³×C₆₇	1	2	yes	—
651	#107	C₂³×C₆₇	1	4	yes	—
652	#107	C₂³×C₆₇	1	4	yes	—
653	#107	C₂³×C₆₇	1	4	yes	—
654	#107	C₂³×C₆₇	1	4	yes	—
655	#106	C₂³×C₆₇	1	2	yes	—
656	#106	C₂³×C₆₇	1	4	yes	—
657	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
659	#103	C₂³×C₆₇	1	2	yes	—
660	#103	C₂³×C₆₇	1	4	yes	—
661	#103	C₂³×C₆₇	1	4	yes	—
662	#103	C₂³×C₆₇	1	4	yes	—
663	#103	C₂³×C₆₇	1	4	yes	—
664	#102	C₂³×C₆₇	1	2	yes	—
665	#102	C₂³×C₆₇	1	4	yes	—
666	#102	C₂³×C₆₇	1	2	yes	—
667	#102	C₂³×C₆₇	1	2	yes	—
668	#102	C₂³×C₆₇	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
674	#97	C₂³×C₆₇	1	2	yes	—
675	C₄×C₈	C₂³×C₆₇	1	2	yes	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
678	#41	—	4	4	no	—
679	#41	—	4	16	no	—
680	#41	—	4	8	no	—
681	#41	—	4	8	no	—
682	#41	—	4	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
701	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
702	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	4	4	no	—
717	C₂²×C₄	—	4	8	no	—
718	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	2	no	—
728	D₈	—	4	2	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
732	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
733	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
777	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
778	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
779	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	1	no	—
783	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
785	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
796	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
797	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
798	Q₈	—	2	2	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	4	4	no	—
801	Q₈	—	4	4	no	—
802	Q₈	—	4	2	no	—
803	Q₈	—	8	2	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	2	no	—
815	D₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
848	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
849	C₈	—	2	2	no	—
850	C₈	—	2	4	no	—
851	C₈	—	2	2	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	8	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	8	4	no	—
867	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
868	C₂²	#578×C₆₇	1	2	yes	—
869	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	4	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
884	C₄	#585×C₆₇	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	2	no	—
888	C₂	—	8	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₆₇×#3485	1	1	yes	characteristic
891	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
892	C₂	C₂×#578×C₆₇	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×#3520	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₆₇×#3353	C₂	semidirect
4. C₆₇×#3343	C₂	semidirect
5. C₆₇×#3334	C₂	semidirect
6. C₆₇×#3330	C₂	semidirect
7. C₆₇×#3308	C₂	semidirect
8. C₆₇×#3298	C₂	semidirect
9. C₆₇×#3239	C₂	semidirect
10. C₆₇×#3230	C₂	semidirect
11. C₆₇×#3193	C₂	semidirect
12. C₆₇×#3188	C₂	semidirect
13. C₆₇×#3110	C₂	semidirect
14. C₆₇×#3105	C₂	semidirect
15. C₆₇×#3092	C₂	semidirect
16. C₂×#484×C₆₇	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
19. #556×C₆₇	C₂²	semidirect
21. #552×C₆₇	C₂²	semidirect
23. D₄×Q₈×C₆₇	C₂²	semidirect
24. #548×C₆₇	C₂²	semidirect
31. #547×C₆₇	C₂²	semidirect
32. #547×C₆₇	C₂²	semidirect
48. #501×C₆₇	C₂²	semidirect
49. #500×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #487×C₆₇	C₂²	semidirect
57. #484×C₆₇	C₂²	semidirect
58. #484×C₆₇	C₂²	semidirect
59. #483×C₆₇	C₂²	semidirect
60. #482×C₆₇	C₂²	semidirect
63. #480×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #478×C₆₇	C₂²	semidirect
66. #477×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #474×C₆₇	C₂²	semidirect
70. #468×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #466×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #463×C₆₇	C₂²	semidirect
75. #461×C₆₇	C₂²	semidirect
78. #449×C₆₇	C₂²	semidirect
79. #448×C₆₇	C₂²	semidirect
81. #440×C₆₇	C₂²	semidirect
82. C₄×SD₁₆×C₆₇	C₂²	semidirect
83. C₄×D₈×C₆₇	C₂²	semidirect
84. #436×C₆₇	C₂²	semidirect
85. #435×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
89. #428×C₆₇	C₂²	semidirect
90. C₂×#107×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. C₂×#103×C₆₇	C₂²	semidirect
438. #61737	C₆₇	direct (N × H)
447. #3520	C₂×C₆₇	semidirect
448. C₂×#547	C₂×C₆₇	semidirect
449. #3353	C₂×C₆₇	semidirect
450. #3343	C₂×C₆₇	semidirect
451. #3334	C₂×C₆₇	semidirect
452. #3330	C₂×C₆₇	semidirect
453. #3308	C₂×C₆₇	semidirect
454. #3298	C₂×C₆₇	semidirect
455. #3239	C₂×C₆₇	semidirect
456. #3230	C₂×C₆₇	semidirect
457. #3193	C₂×C₆₇	semidirect
458. #3188	C₂×C₆₇	semidirect
459. #3110	C₂×C₆₇	semidirect
460. #3105	C₂×C₆₇	semidirect
461. #3092	C₂×C₆₇	semidirect
462. C₂×#484	C₂×C₆₇	semidirect
463. #2974	C₂×C₆₇	semidirect
464. C₆₇	#61737	direct (N × H)
466. #556	C₂²×C₆₇	semidirect
468. #552	C₂²×C₆₇	semidirect
470. D₄×Q₈	C₂²×C₆₇	semidirect
471. #548	C₂²×C₆₇	semidirect
478. #547	C₂²×C₆₇	semidirect
479. #547	C₂²×C₆₇	semidirect
495. #501	C₂²×C₆₇	semidirect
496. #500	C₂²×C₆₇	semidirect
497. #489	C₂²×C₆₇	semidirect
498. #487	C₂²×C₆₇	semidirect
504. #484	C₂²×C₆₇	semidirect
505. #484	C₂²×C₆₇	semidirect
506. #483	C₂²×C₆₇	semidirect
507. #482	C₂²×C₆₇	semidirect
510. #480	C₂²×C₆₇	semidirect
511. #480	C₂²×C₆₇	semidirect
512. #478	C₂²×C₆₇	semidirect
513. #477	C₂²×C₆₇	semidirect
514. #475	C₂²×C₆₇	semidirect
515. #474	C₂²×C₆₇	semidirect
516. #474	C₂²×C₆₇	semidirect
517. #468	C₂²×C₆₇	semidirect
518. #468	C₂²×C₆₇	semidirect
519. #466	C₂²×C₆₇	semidirect
520. #465	C₂²×C₆₇	semidirect
521. #463	C₂²×C₆₇	semidirect
522. #461	C₂²×C₆₇	semidirect
525. #449	C₂²×C₆₇	semidirect
526. #448	C₂²×C₆₇	semidirect
528. #440	C₂²×C₆₇	semidirect
529. C₄×SD₁₆	C₂²×C₆₇	semidirect
530. C₄×D₈	C₂²×C₆₇	semidirect
531. #436	C₂²×C₆₇	semidirect
532. #435	C₂²×C₆₇	semidirect
533. C₈×D₄	C₂²×C₆₇	semidirect
536. #428	C₂²×C₆₇	semidirect
537. C₂×#107	C₂²×C₆₇	semidirect
538. #417	C₂²×C₆₇	semidirect
539. C₂×#103	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×#3520	2
C₂×#547×C₆₇	2
C₆₇×#3353	2
C₆₇×#3343	2
C₆₇×#3334	2
C₆₇×#3330	2
C₆₇×#3308	2
C₆₇×#3298	2
C₆₇×#3239	2
C₆₇×#3230	2
C₆₇×#3193	2
C₆₇×#3188	2
C₆₇×#3110	2
C₆₇×#3105	2
C₆₇×#3092	2
C₂×#484×C₆₇	2
C₆₇×#2974	2
#61737	67

Subgroups — C67×#61737 #30740988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61737 #30740988