Subgroups — C₆₇×#61604 #30740855

Order 17152.

2180 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3307	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3303	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3187	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
21	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	#553×C₆₇	—	2	1	no	—
24	#553×C₆₇	C₂²	1	2	yes	complemented
25	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#547×C₆₇	—	2	1	no	—
27	#547×C₆₇	—	2	1	no	—
28	#547×C₆₇	—	2	2	no	—
29	#547×C₆₇	C₂²	1	2	yes	—
30	#547×C₆₇	C₂²	1	4	yes	complemented
31	#547×C₆₇	C₂²	1	2	yes	complemented
32	#546×C₆₇	—	2	2	no	—
33	#546×C₆₇	C₂²	1	2	yes	complemented
34	D₄²×C₆₇	—	2	1	no	—
35	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#540×C₆₇	—	2	1	no	—
37	#538×C₆₇	—	2	2	no	—
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#529×C₆₇	C₂²	1	1	yes	characteristic
41	#525×C₆₇	C₂²	1	2	yes	—
42	C₂×#123×C₆₇	—	2	2	no	—
43	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
44	C₂×#121×C₆₇	—	2	1	no	—
45	C₂×#121×C₆₇	C₂²	1	2	yes	—
46	#518×C₆₇	—	2	1	no	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
50	#497×C₆₇	C₂²	1	2	yes	complemented
51	#492×C₆₇	C₂²	1	2	yes	complemented
52	#491×C₆₇	C₂²	1	2	yes	complemented
53	#487×C₆₇	C₂²	1	2	yes	complemented
54	#485×C₆₇	C₂²	1	4	yes	complemented
55	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#483×C₆₇	C₂²	1	4	yes	complemented
57	#481×C₆₇	C₂²	1	1	yes	characteristic
58	#481×C₆₇	C₂²	1	2	yes	complemented
59	#478×C₆₇	C₂²	1	2	yes	complemented
60	#476×C₆₇	C₂²	1	2	yes	complemented
61	#470×C₆₇	C₂²	1	4	yes	complemented
62	#468×C₆₇	C₂²	1	4	yes	complemented
63	#465×C₆₇	C₂²	1	4	yes	complemented
64	#465×C₆₇	C₂²	1	4	yes	complemented
65	#463×C₆₇	C₂²	1	2	yes	complemented
66	#462×C₆₇	C₂²	1	2	yes	complemented
67	#461×C₆₇	C₂²	1	4	yes	complemented
68	#461×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#451×C₆₇	C₂²	1	2	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	complemented
74	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#449×C₆₇	C₂²	1	4	yes	complemented
77	#449×C₆₇	C₂²	1	4	yes	complemented
78	#448×C₆₇	C₂²	1	2	yes	—
79	#448×C₆₇	C₂²	1	2	yes	complemented
80	#448×C₆₇	C₂²	1	2	yes	complemented
81	#447×C₆₇	C₂²	1	1	yes	characteristic
82	#447×C₆₇	C₂²	1	2	yes	complemented
83	#442×C₆₇	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
85	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
86	#436×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	4	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	#416×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	4	8	no	—
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	—	2	1	no	—
106	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
107	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₆₇	—	2	1	no	—
110	C₂³×C₄×C₆₇	—	2	2	no	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
113	#135×C₆₇	—	4	8	no	—
114	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×D₈×C₆₇	C₂³	1	4	yes	—
120	C₂×D₈×C₆₇	C₂³	1	2	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
122	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₆₇	—	2	1	no	—
124	C₄⋊Q₈×C₆₇	—	2	1	no	—
125	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	#127×C₆₇	—	2	1	no	—
129	#127×C₆₇	C₂³	1	1	yes	characteristic
130	#126×C₆₇	—	2	2	no	—
131	#126×C₆₇	—	2	1	no	—
132	#125×C₆₇	—	2	1	no	—
133	#125×C₆₇	C₂³	1	1	yes	characteristic
134	#124×C₆₇	—	2	2	no	—
135	#124×C₆₇	—	2	1	no	—
136	#124×C₆₇	C₂³	1	1	yes	characteristic
137	#123×C₆₇	—	2	2	no	—
138	#123×C₆₇	—	2	1	no	—
139	#123×C₆₇	—	2	2	no	—
140	#123×C₆₇	—	2	4	no	—
141	#123×C₆₇	—	2	4	no	—
142	#123×C₆₇	—	2	4	no	—
143	#123×C₆₇	—	2	4	no	—
144	#123×C₆₇	—	2	2	no	—
145	C₂²⋊Q₈×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	—	2	2	no	—
147	C₂²⋊Q₈×C₆₇	—	2	2	no	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
152	#121×C₆₇	—	2	2	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	—	2	2	no	—
156	#121×C₆₇	—	2	1	no	—
157	#121×C₆₇	—	2	2	no	—
158	#121×C₆₇	—	2	2	no	—
159	#121×C₆₇	—	2	1	no	—
160	#121×C₆₇	—	2	1	no	—
161	#121×C₆₇	—	2	2	no	—
162	#121×C₆₇	—	2	2	no	—
163	#121×C₆₇	C₂³	1	1	yes	characteristic
164	#121×C₆₇	C₂³	1	2	yes	—
165	#121×C₆₇	C₂³	1	2	yes	—
166	#121×C₆₇	C₂³	1	2	yes	—
167	#121×C₆₇	C₂³	1	2	yes	—
168	#120×C₆₇	—	2	2	no	—
169	#120×C₆₇	—	2	2	no	—
170	#120×C₆₇	—	2	2	no	—
171	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	—	2	2	no	—
175	C₄×D₄×C₆₇	—	2	1	no	—
176	C₄×D₄×C₆₇	—	2	1	no	—
177	C₄×D₄×C₆₇	—	2	2	no	—
178	C₄×D₄×C₆₇	—	2	1	no	—
179	C₄×D₄×C₆₇	—	2	1	no	—
180	C₄×D₄×C₆₇	—	2	1	no	—
181	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
182	C₄×D₄×C₆₇	D₄	1	2	yes	—
183	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
184	C₄×D₄×C₆₇	C₂³	1	2	yes	—
185	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₆₇	C₂³	1	2	yes	—
187	C₄×D₄×C₆₇	C₂³	1	2	yes	—
188	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₆₇	C₂³	1	2	yes	—
190	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
191	#117×C₆₇	—	2	1	no	—
192	#117×C₆₇	—	2	1	no	—
193	#117×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
200	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	#107×C₆₇	C₂³	1	2	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×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	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	#97×C₆₇	C₂³	1	2	yes	—
230	C₄×C₈×C₆₇	C₂³	1	2	yes	—
231	C₂⁴×C₆₇	—	2	1	no	—
232	C₂⁴×C₆₇	—	2	2	no	—
233	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	8	no	—
236	#41×C₆₇	—	4	4	no	—
237	#41×C₆₇	—	4	4	no	—
238	#41×C₆₇	—	4	4	no	—
239	#41×C₆₇	—	4	8	no	—
240	#41×C₆₇	—	4	8	no	—
241	#41×C₆₇	—	8	2	no	—
242	C₂×Q₈×C₆₇	—	2	2	no	—
243	C₂×Q₈×C₆₇	—	2	1	no	—
244	C₂×Q₈×C₆₇	—	4	4	no	—
245	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	1	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	1	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	2	1	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	4	4	no	—
262	C₂×D₄×C₆₇	—	4	4	no	—
263	C₂×D₄×C₆₇	—	4	8	no	—
264	C₂×D₄×C₆₇	—	8	4	no	—
265	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
268	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	—	2	1	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	4	4	no	—
282	C₂²×C₄×C₆₇	—	4	4	no	—
283	C₂²×C₄×C₆₇	—	4	8	no	—
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	2	yes	—
287	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	Q₁₆×C₆₇	—	4	4	no	—
293	SD₁₆×C₆₇	—	2	4	no	—
294	SD₁₆×C₆₇	—	4	4	no	—
295	SD₁₆×C₆₇	—	4	4	no	—
296	SD₁₆×C₆₇	—	4	4	no	—
297	D₈×C₆₇	—	2	8	no	—
298	D₈×C₆₇	—	2	4	no	—
299	M₁₆×C₆₇	—	4	4	no	—
300	C₂×C₈×C₆₇	—	4	4	no	—
301	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
302	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
303	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	4	no	—
307	C₄⋊C₄×C₆₇	—	2	4	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	1	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
321	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²⋊C₄×C₆₇	—	2	2	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	1	no	—
330	C₂²⋊C₄×C₆₇	—	2	1	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	—	2	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	2	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	1	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	1	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	1	no	—
347	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	4	2	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	4	2	no	—
359	C₂³×C₆₇	—	4	4	no	—
360	C₂³×C₆₇	—	4	2	no	—
361	C₂³×C₆₇	—	8	2	no	—
362	C₂³×C₆₇	—	8	2	no	—
363	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
364	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
365	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	2	4	no	—
368	Q₈×C₆₇	—	2	4	no	—
369	Q₈×C₆₇	—	4	4	no	—
370	Q₈×C₆₇	—	8	1	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	2	no	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	2	2	no	—
376	D₄×C₆₇	—	2	4	no	—
377	D₄×C₆₇	—	4	2	no	—
378	D₄×C₆₇	—	4	8	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	4	no	—
381	D₄×C₆₇	—	4	2	no	—
382	D₄×C₆₇	—	4	4	no	—
383	D₄×C₆₇	—	4	2	no	—
384	D₄×C₆₇	—	8	2	no	—
385	D₄×C₆₇	—	8	1	no	—
386	D₄×C₆₇	—	8	2	no	—
387	D₄×C₆₇	—	8	2	no	—
388	D₄×C₆₇	—	8	2	no	—
389	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	4	no	—
393	C₂×C₄×C₆₇	—	2	4	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	4	no	—
401	C₂×C₄×C₆₇	—	4	2	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	4	2	no	—
404	C₂×C₄×C₆₇	—	4	8	no	—
405	C₂×C₄×C₆₇	—	4	8	no	—
406	C₂×C₄×C₆₇	—	4	4	no	—
407	C₂×C₄×C₆₇	—	4	2	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	—	8	2	no	—
412	C₂×C₄×C₆₇	—	8	2	no	—
413	C₂×C₄×C₆₇	—	8	2	no	—
414	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
422	C₈×C₆₇	—	2	2	no	—
423	C₈×C₆₇	—	2	4	no	—
424	C₈×C₆₇	—	2	2	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	2	2	no	—
431	C₂²×C₆₇	—	2	2	no	—
432	C₂²×C₆₇	—	2	2	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	4	8	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	1	no	—
439	C₂²×C₆₇	—	4	1	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	8	4	no	—
444	C₂²×C₆₇	—	16	4	no	—
445	C₂²×C₆₇	#577	1	2	yes	—
446	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	1	no	—
450	C₄×C₆₇	—	2	1	no	—
451	C₄×C₆₇	—	2	1	no	—
452	C₄×C₆₇	—	2	1	no	—
453	C₄×C₆₇	—	4	4	no	—
454	C₄×C₆₇	—	4	1	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	1	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	#575	1	2	yes	—
460	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
461	#61604	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂×C₆₇	—	2	2	no	—
463	C₂×C₆₇	—	4	2	no	—
464	C₂×C₆₇	—	4	2	no	—
465	C₂×C₆₇	—	4	4	no	—
466	C₂×C₆₇	—	8	2	no	—
467	C₂×C₆₇	—	8	1	no	—
468	C₂×C₆₇	#3484	1	1	yes	characteristic
469	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
470	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
471	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
472	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3331	C₂×C₆₇	1	2	yes	complemented
474	#3307	C₂×C₆₇	1	4	yes	complemented
475	#3303	C₂×C₆₇	1	2	yes	complemented
476	#3284	C₂×C₆₇	1	2	yes	complemented
477	#3272	C₂×C₆₇	1	2	yes	complemented
478	#3267	C₂×C₆₇	1	4	yes	complemented
479	#3218	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#3206	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3196	C₂×C₆₇	1	2	yes	complemented
482	#3187	C₂×C₆₇	1	2	yes	complemented
483	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
485	#3006	C₂×C₆₇	1	2	yes	complemented
486	#3002	C₂×C₆₇	1	2	yes	complemented
487	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
488	C₆₇	#61604	1	1	yes	characteristic, direct product factor, Sylow
489	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
490	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
491	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
492	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
493	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	#553	—	2	1	no	—
495	#553	C₂²×C₆₇	1	2	yes	complemented
496	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	#547	—	2	1	no	—
498	#547	—	2	1	no	—
499	#547	—	2	2	no	—
500	#547	C₂²×C₆₇	1	2	yes	—
501	#547	C₂²×C₆₇	1	4	yes	complemented
502	#547	C₂²×C₆₇	1	2	yes	complemented
503	#546	—	2	2	no	—
504	#546	C₂²×C₆₇	1	2	yes	complemented
505	D₄²	—	2	1	no	—
506	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
507	#540	—	2	1	no	—
508	#538	—	2	2	no	—
509	#532	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	#529	C₂²×C₆₇	1	1	yes	characteristic
512	#525	C₂²×C₆₇	1	2	yes	—
513	C₂×#123	—	2	2	no	—
514	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
515	C₂×#121	—	2	1	no	—
516	C₂×#121	C₂²×C₆₇	1	2	yes	—
517	#518	—	2	1	no	—
518	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	C₂²×C₄⋊C₄	—	2	1	no	—
521	#497	C₂²×C₆₇	1	2	yes	complemented
522	#492	C₂²×C₆₇	1	2	yes	complemented
523	#491	C₂²×C₆₇	1	2	yes	complemented
524	#487	C₂²×C₆₇	1	2	yes	complemented
525	#485	C₂²×C₆₇	1	4	yes	complemented
526	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	#483	C₂²×C₆₇	1	4	yes	complemented
528	#481	C₂²×C₆₇	1	1	yes	characteristic
529	#481	C₂²×C₆₇	1	2	yes	complemented
530	#478	C₂²×C₆₇	1	2	yes	complemented
531	#476	C₂²×C₆₇	1	2	yes	complemented
532	#470	C₂²×C₆₇	1	4	yes	complemented
533	#468	C₂²×C₆₇	1	4	yes	complemented
534	#465	C₂²×C₆₇	1	4	yes	complemented
535	#465	C₂²×C₆₇	1	4	yes	complemented
536	#463	C₂²×C₆₇	1	2	yes	complemented
537	#462	C₂²×C₆₇	1	2	yes	complemented
538	#461	C₂²×C₆₇	1	4	yes	complemented
539	#461	C₂²×C₆₇	1	2	yes	complemented
540	#459	C₂²×C₆₇	1	2	yes	complemented
541	#452	C₂²×C₆₇	1	4	yes	complemented
542	#452	C₂²×C₆₇	1	4	yes	complemented
543	#451	C₂²×C₆₇	1	2	yes	complemented
544	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
545	#450	C₂²×C₆₇	1	4	yes	complemented
546	#449	C₂²×C₆₇	1	4	yes	complemented
547	#449	C₂²×C₆₇	1	4	yes	complemented
548	#449	C₂²×C₆₇	1	4	yes	complemented
549	#448	C₂²×C₆₇	1	2	yes	—
550	#448	C₂²×C₆₇	1	2	yes	complemented
551	#448	C₂²×C₆₇	1	2	yes	complemented
552	#447	C₂²×C₆₇	1	1	yes	characteristic
553	#447	C₂²×C₆₇	1	2	yes	complemented
554	#442	C₂²×C₆₇	1	4	yes	complemented
555	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
556	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
557	#436	C₂²×C₆₇	1	2	yes	complemented
558	#435	C₂²×C₆₇	1	4	yes	complemented
559	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
560	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
561	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#417	C₂²×C₆₇	1	4	yes	complemented
563	#416	C₂²×C₆₇	1	4	yes	complemented
564	#407	C₂²×C₆₇	1	2	yes	complemented
565	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	2	1	no	—
569	C₂×#41	—	4	8	no	—
570	C₂×#41	C₂³×C₆₇	1	4	yes	—
571	C₂×#41	C₂³×C₆₇	1	4	yes	—
572	C₂×#41	C₂³×C₆₇	1	2	yes	—
573	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
580	C₂³×C₄	—	2	1	no	—
581	C₂³×C₄	—	2	2	no	—
582	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
583	AGL(1,ℤ/8)	—	4	8	no	—
584	#135	—	4	8	no	—
585	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
589	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
590	C₂×D₈	C₂³×C₆₇	1	4	yes	—
591	C₂×D₈	C₂³×C₆₇	1	2	yes	—
592	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
593	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
594	C₄⋊Q₈	—	2	1	no	—
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
597	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
599	#127	—	2	1	no	—
600	#127	C₂³×C₆₇	1	1	yes	characteristic
601	#126	—	2	2	no	—
602	#126	—	2	1	no	—
603	#125	—	2	1	no	—
604	#125	C₂³×C₆₇	1	1	yes	characteristic
605	#124	—	2	2	no	—
606	#124	—	2	1	no	—
607	#124	C₂³×C₆₇	1	1	yes	characteristic
608	#123	—	2	2	no	—
609	#123	—	2	1	no	—
610	#123	—	2	2	no	—
611	#123	—	2	4	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	4	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
620	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
621	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
622	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	4	no	—
626	#121	—	2	2	no	—
627	#121	—	2	1	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
639	#120	—	2	2	no	—
640	#120	—	2	2	no	—
641	#120	—	2	2	no	—
642	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
653	C₄×D₄	D₄×C₆₇	1	2	yes	—
654	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₆₇	1	2	yes	—
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₄×D₄	C₂³×C₆₇	1	2	yes	—
659	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₆₇	1	2	yes	—
661	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
662	#117	—	2	1	no	—
663	#117	—	2	1	no	—
664	#117	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	—	2	1	no	—
666	C₂×C₄⋊C₄	—	2	2	no	—
667	C₂×C₄⋊C₄	—	2	1	no	—
668	C₂×C₄⋊C₄	—	2	2	no	—
669	C₂×C₄⋊C₄	—	2	2	no	—
670	C₂×C₄⋊C₄	—	2	4	no	—
671	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	—	2	2	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	2	no	—
677	C₂×C₂²⋊C₄	—	2	2	no	—
678	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
680	#107	C₂³×C₆₇	1	2	yes	—
681	#106	C₂³×C₆₇	1	2	yes	—
682	#106	C₂³×C₆₇	1	4	yes	—
683	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
685	#103	C₂³×C₆₇	1	4	yes	—
686	#103	C₂³×C₆₇	1	4	yes	—
687	#103	C₂³×C₆₇	1	4	yes	—
688	#103	C₂³×C₆₇	1	4	yes	—
689	#103	C₂³×C₆₇	1	2	yes	—
690	#102	C₂³×C₆₇	1	2	yes	—
691	#102	C₂³×C₆₇	1	4	yes	—
692	#102	C₂³×C₆₇	1	2	yes	—
693	#102	C₂³×C₆₇	1	2	yes	—
694	#102	C₂³×C₆₇	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
696	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
698	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
699	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
700	#97	C₂³×C₆₇	1	2	yes	—
701	C₄×C₈	C₂³×C₆₇	1	2	yes	—
702	C₂⁴	—	2	1	no	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
705	#41	—	2	8	no	—
706	#41	—	2	8	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	#41	—	4	8	no	—
711	#41	—	4	8	no	—
712	#41	—	8	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	4	4	no	—
716	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
717	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	8	4	no	—
736	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
737	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
739	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
741	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	4	4	no	—
753	C₂²×C₄	—	4	4	no	—
754	C₂²×C₄	—	4	8	no	—
755	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
759	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
763	Q₁₆	—	4	4	no	—
764	SD₁₆	—	2	4	no	—
765	SD₁₆	—	4	4	no	—
766	SD₁₆	—	4	4	no	—
767	SD₁₆	—	4	4	no	—
768	D₈	—	2	8	no	—
769	D₈	—	2	4	no	—
770	M₁₆	—	4	4	no	—
771	C₂×C₈	—	4	4	no	—
772	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
773	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
774	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	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	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	—	2	1	no	—
802	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	1	no	—
818	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
819	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
820	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
821	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	8	2	no	—
833	C₂³	—	8	2	no	—
834	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
835	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
836	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
837	Q₈	—	2	2	no	—
838	Q₈	—	2	4	no	—
839	Q₈	—	2	4	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	2	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	8	2	no	—
856	D₄	—	8	1	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	2	no	—
859	D₄	—	8	2	no	—
860	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	2	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
892	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
893	C₈	—	2	2	no	—
894	C₈	—	2	4	no	—
895	C₈	—	2	2	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	4	8	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	8	4	no	—
915	C₂²	—	16	4	no	—
916	C₂²	#577×C₆₇	1	2	yes	—
917	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	4	no	—
929	C₄	—	4	1	no	—
930	C₄	#575×C₆₇	1	2	yes	—
931	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
932	C₂	—	2	2	no	—
933	C₂	—	4	2	no	—
934	C₂	—	4	2	no	—
935	C₂	—	4	4	no	—
936	C₂	—	8	1	no	—
937	C₂	—	8	2	no	—
938	C₂	C₆₇×#3484	1	1	yes	characteristic
939	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
940	C₂	C₂×#577×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×#3519	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3307	C₂	semidirect
5. C₆₇×#3303	C₂	semidirect
6. C₆₇×#3284	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3267	C₂	semidirect
9. C₆₇×#3218	C₂	semidirect
10. C₆₇×#3206	C₂	semidirect
11. C₆₇×#3196	C₂	semidirect
12. C₆₇×#3187	C₂	semidirect
13. C₆₇×#3109	C₂	semidirect
14. C₆₇×#3105	C₂	semidirect
15. C₆₇×#3006	C₂	semidirect
16. C₆₇×#3002	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
21. #555×C₆₇	C₂²	semidirect
22. #554×C₆₇	C₂²	semidirect
24. #553×C₆₇	C₂²	semidirect
25. #550×C₆₇	C₂²	semidirect
30. #547×C₆₇	C₂²	semidirect
31. #547×C₆₇	C₂²	semidirect
33. #546×C₆₇	C₂²	semidirect
35. D₄²×C₆₇	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
43. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
48. C₂×C₄×D₄×C₆₇	C₂²	semidirect
50. #497×C₆₇	C₂²	semidirect
51. #492×C₆₇	C₂²	semidirect
52. #491×C₆₇	C₂²	semidirect
53. #487×C₆₇	C₂²	semidirect
54. #485×C₆₇	C₂²	semidirect
55. #484×C₆₇	C₂²	semidirect
56. #483×C₆₇	C₂²	semidirect
58. #481×C₆₇	C₂²	semidirect
59. #478×C₆₇	C₂²	semidirect
60. #476×C₆₇	C₂²	semidirect
61. #470×C₆₇	C₂²	semidirect
62. #468×C₆₇	C₂²	semidirect
63. #465×C₆₇	C₂²	semidirect
64. #465×C₆₇	C₂²	semidirect
65. #463×C₆₇	C₂²	semidirect
66. #462×C₆₇	C₂²	semidirect
67. #461×C₆₇	C₂²	semidirect
68. #461×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #451×C₆₇	C₂²	semidirect
73. #450×C₆₇	C₂²	semidirect
74. #450×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #449×C₆₇	C₂²	semidirect
77. #449×C₆₇	C₂²	semidirect
79. #448×C₆₇	C₂²	semidirect
80. #448×C₆₇	C₂²	semidirect
82. #447×C₆₇	C₂²	semidirect
83. #442×C₆₇	C₂²	semidirect
84. C₄×SD₁₆×C₆₇	C₂²	semidirect
85. C₄×D₈×C₆₇	C₂²	semidirect
86. #436×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
89. #432×C₆₇	C₂²	semidirect
90. #431×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. #416×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
461. #61604	C₆₇	direct (N × H)
471. #3519	C₂×C₆₇	semidirect
472. C₂×#547	C₂×C₆₇	semidirect
473. #3331	C₂×C₆₇	semidirect
474. #3307	C₂×C₆₇	semidirect
475. #3303	C₂×C₆₇	semidirect
476. #3284	C₂×C₆₇	semidirect
477. #3272	C₂×C₆₇	semidirect
478. #3267	C₂×C₆₇	semidirect
479. #3218	C₂×C₆₇	semidirect
480. #3206	C₂×C₆₇	semidirect
481. #3196	C₂×C₆₇	semidirect
482. #3187	C₂×C₆₇	semidirect
483. #3109	C₂×C₆₇	semidirect
484. #3105	C₂×C₆₇	semidirect
485. #3006	C₂×C₆₇	semidirect
486. #3002	C₂×C₆₇	semidirect
487. #2974	C₂×C₆₇	semidirect
488. C₆₇	#61604	direct (N × H)
489. C₂²×#41	C₂²×C₆₇	semidirect
490. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
491. C₂×#135	C₂²×C₆₇	semidirect
492. #555	C₂²×C₆₇	semidirect
493. #554	C₂²×C₆₇	semidirect
495. #553	C₂²×C₆₇	semidirect
496. #550	C₂²×C₆₇	semidirect
501. #547	C₂²×C₆₇	semidirect
502. #547	C₂²×C₆₇	semidirect
504. #546	C₂²×C₆₇	semidirect
506. D₄²	C₂²×C₆₇	semidirect
510. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
514. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
519. C₂×C₄×D₄	C₂²×C₆₇	semidirect
521. #497	C₂²×C₆₇	semidirect
522. #492	C₂²×C₆₇	semidirect
523. #491	C₂²×C₆₇	semidirect
524. #487	C₂²×C₆₇	semidirect
525. #485	C₂²×C₆₇	semidirect
526. #484	C₂²×C₆₇	semidirect
527. #483	C₂²×C₆₇	semidirect
529. #481	C₂²×C₆₇	semidirect
530. #478	C₂²×C₆₇	semidirect
531. #476	C₂²×C₆₇	semidirect
532. #470	C₂²×C₆₇	semidirect
533. #468	C₂²×C₆₇	semidirect
534. #465	C₂²×C₆₇	semidirect
535. #465	C₂²×C₆₇	semidirect
536. #463	C₂²×C₆₇	semidirect
537. #462	C₂²×C₆₇	semidirect
538. #461	C₂²×C₆₇	semidirect
539. #461	C₂²×C₆₇	semidirect
540. #459	C₂²×C₆₇	semidirect
541. #452	C₂²×C₆₇	semidirect
542. #452	C₂²×C₆₇	semidirect
543. #451	C₂²×C₆₇	semidirect
544. #450	C₂²×C₆₇	semidirect
545. #450	C₂²×C₆₇	semidirect
546. #449	C₂²×C₆₇	semidirect
547. #449	C₂²×C₆₇	semidirect
548. #449	C₂²×C₆₇	semidirect
550. #448	C₂²×C₆₇	semidirect
551. #448	C₂²×C₆₇	semidirect
553. #447	C₂²×C₆₇	semidirect
554. #442	C₂²×C₆₇	semidirect
555. C₄×SD₁₆	C₂²×C₆₇	semidirect
556. C₄×D₈	C₂²×C₆₇	semidirect
557. #436	C₂²×C₆₇	semidirect
558. #435	C₂²×C₆₇	semidirect
559. C₈×D₄	C₂²×C₆₇	semidirect
560. #432	C₂²×C₆₇	semidirect
561. #431	C₂²×C₆₇	semidirect
562. #417	C₂²×C₆₇	semidirect
563. #416	C₂²×C₆₇	semidirect
564. #407	C₂²×C₆₇	semidirect
565. 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×#3519	2
C₂×#547×C₆₇	2
C₆₇×#3331	2
C₆₇×#3307	2
C₆₇×#3303	2
C₆₇×#3284	2
C₆₇×#3272	2
C₆₇×#3267	2
C₆₇×#3218	2
C₆₇×#3206	2
C₆₇×#3196	2
C₆₇×#3187	2
C₆₇×#3109	2
C₆₇×#3105	2
C₆₇×#3006	2
C₆₇×#3002	2
C₆₇×#2974	2
#61604	67

Subgroups — C67×#61604 #30740855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61604 #30740855