Subgroups — C₆₇×#61713 #30740964

Order 17152.

1826 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3350	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3347	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3309	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3307	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3091	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	#559×C₆₇	—	2	2	no	—
17	#556×C₆₇	C₂²	1	2	yes	complemented
18	#555×C₆₇	C₂²	1	2	yes	complemented
19	#553×C₆₇	—	2	2	no	—
20	#553×C₆₇	—	2	2	no	—
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	C₂²	1	4	yes	—
23	#553×C₆₇	C₂²	1	4	yes	—
24	#550×C₆₇	C₂²	1	2	yes	complemented
25	#547×C₆₇	C₂²	1	2	yes	complemented
26	#538×C₆₇	—	2	1	no	—
27	#538×C₆₇	—	2	1	no	—
28	#535×C₆₇	—	2	1	no	—
29	#533×C₆₇	C₂²	1	1	yes	characteristic
30	#532×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#126×C₆₇	—	2	1	no	—
32	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
33	#525×C₆₇	C₂²	1	2	yes	—
34	#525×C₆₇	C₂²	1	2	yes	—
35	C₂×#123×C₆₇	—	2	1	no	—
36	C₂×#121×C₆₇	—	2	1	no	—
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	#520×C₆₇	—	2	1	no	—
40	C₂×C₄×D₄×C₆₇	—	2	1	no	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	#501×C₆₇	C₂²	1	2	yes	complemented
46	#501×C₆₇	C₂²	1	2	yes	complemented
47	#491×C₆₇	C₂²	1	2	yes	complemented
48	#490×C₆₇	C₂²	1	2	yes	complemented
49	#485×C₆₇	C₂²	1	4	yes	complemented
50	#484×C₆₇	C₂²	1	2	yes	—
51	#484×C₆₇	C₂²	1	2	yes	—
52	#483×C₆₇	C₂²	1	2	yes	—
53	#483×C₆₇	C₂²	1	4	yes	complemented
54	#482×C₆₇	C₂²	1	4	yes	complemented
55	#482×C₆₇	C₂²	1	4	yes	complemented
56	#482×C₆₇	C₂²	1	4	yes	complemented
57	#481×C₆₇	C₂²	1	2	yes	—
58	#481×C₆₇	C₂²	1	2	yes	—
59	#480×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	4	yes	complemented
61	#479×C₆₇	C₂²	1	4	yes	complemented
62	#478×C₆₇	C₂²	1	4	yes	complemented
63	#476×C₆₇	C₂²	1	2	yes	complemented
64	#474×C₆₇	C₂²	1	2	yes	complemented
65	#469×C₆₇	C₂²	1	4	yes	complemented
66	#468×C₆₇	C₂²	1	4	yes	complemented
67	#466×C₆₇	C₂²	1	4	yes	complemented
68	#465×C₆₇	C₂²	1	4	yes	complemented
69	#461×C₆₇	C₂²	1	2	yes	complemented
70	#459×C₆₇	C₂²	1	2	yes	complemented
71	#450×C₆₇	C₂²	1	2	yes	—
72	#449×C₆₇	C₂²	1	4	yes	complemented
73	#449×C₆₇	C₂²	1	4	yes	complemented
74	#447×C₆₇	C₂²	1	2	yes	—
75	#442×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	#435×C₆₇	C₂²	1	4	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	#432×C₆₇	C₂²	1	1	yes	characteristic
80	#432×C₆₇	C₂²	1	1	yes	characteristic
81	#428×C₆₇	C₂²	1	4	yes	complemented
82	#427×C₆₇	C₂²	1	4	yes	complemented
83	#417×C₆₇	C₂²	1	4	yes	complemented
84	#416×C₆₇	C₂²	1	4	yes	complemented
85	#407×C₆₇	C₂²	1	2	yes	—
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	C₂³	1	2	yes	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₇	—	2	1	no	—
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	—	2	1	no	—
95	C₂³×C₄×C₆₇	—	2	1	no	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×D₈×C₆₇	C₂³	1	4	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
105	#127×C₆₇	—	2	2	no	—
106	#127×C₆₇	C₂³	1	1	yes	characteristic
107	#126×C₆₇	—	2	4	no	—
108	#126×C₆₇	—	2	4	no	—
109	#126×C₆₇	—	2	2	no	—
110	#126×C₆₇	—	2	2	no	—
111	#125×C₆₇	—	2	1	no	—
112	#125×C₆₇	—	2	1	no	—
113	#125×C₆₇	—	2	1	no	—
114	#125×C₆₇	C₂³	1	2	yes	—
115	#125×C₆₇	C₂³	1	2	yes	—
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	—	2	2	no	—
118	#124×C₆₇	—	2	2	no	—
119	#124×C₆₇	—	2	1	no	—
120	#123×C₆₇	—	2	2	no	—
121	#123×C₆₇	—	2	2	no	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	—	2	2	no	—
125	#123×C₆₇	—	2	2	no	—
126	C₂²⋊Q₈×C₆₇	—	2	1	no	—
127	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
130	#121×C₆₇	—	2	4	no	—
131	#121×C₆₇	—	2	4	no	—
132	#121×C₆₇	—	2	2	no	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	2	no	—
136	#121×C₆₇	—	2	1	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	2	no	—
139	#121×C₆₇	C₂³	1	4	yes	—
140	#121×C₆₇	C₂³	1	4	yes	—
141	#121×C₆₇	C₂³	1	2	yes	—
142	#121×C₆₇	C₂³	1	2	yes	—
143	#121×C₆₇	C₂³	1	2	yes	—
144	#120×C₆₇	—	2	2	no	—
145	#120×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	1	no	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	4	no	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	D₄	1	2	yes	—
160	C₄×D₄×C₆₇	D₄	1	2	yes	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	C₄×D₄×C₆₇	C₂³	1	2	yes	—
163	C₄×D₄×C₆₇	C₂³	1	2	yes	—
164	C₄×D₄×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	#117×C₆₇	—	2	2	no	—
167	#117×C₆₇	—	2	1	no	—
168	#117×C₆₇	—	2	2	no	—
169	#117×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	C₂³	1	2	yes	—
171	#117×C₆₇	C₂³	1	4	yes	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
177	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	—	2	1	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	#107×C₆₇	C₂³	1	4	yes	—
191	#107×C₆₇	C₂³	1	4	yes	—
192	#107×C₆₇	C₂³	1	4	yes	—
193	#106×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	4	yes	—
195	#106×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#102×C₆₇	C₂³	1	4	yes	—
202	#102×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
210	#97×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	2	yes	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
215	#41×C₆₇	—	4	4	no	—
216	#41×C₆₇	—	4	4	no	—
217	#41×C₆₇	—	4	4	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	2	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	4	no	—
234	C₂×D₄×C₆₇	—	8	2	no	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	1	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	8	2	no	—
251	C₂²×C₄×C₆₇	—	8	2	no	—
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	SD₁₆×C₆₇	—	4	4	no	—
262	D₈×C₆₇	—	4	4	no	—
263	M₁₆×C₆₇	—	4	4	no	—
264	C₂×C₈×C₆₇	—	4	4	no	—
265	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
266	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	2	no	—
301	C₂²⋊C₄×C₆₇	—	2	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	2	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
306	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	2	2	no	—
312	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	4	1	no	—
321	C₂³×C₆₇	—	4	1	no	—
322	C₂³×C₆₇	—	4	1	no	—
323	C₂³×C₆₇	—	4	1	no	—
324	C₂³×C₆₇	—	4	2	no	—
325	C₂³×C₆₇	—	4	2	no	—
326	C₂³×C₆₇	—	4	2	no	—
327	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₆₇	—	2	4	no	—
331	Q₈×C₆₇	—	4	2	no	—
332	Q₈×C₆₇	—	8	1	no	—
333	D₄×C₆₇	—	2	2	no	—
334	D₄×C₆₇	—	2	4	no	—
335	D₄×C₆₇	—	2	2	no	—
336	D₄×C₆₇	—	4	2	no	—
337	D₄×C₆₇	—	4	2	no	—
338	D₄×C₆₇	—	4	2	no	—
339	D₄×C₆₇	—	4	2	no	—
340	D₄×C₆₇	—	4	8	no	—
341	D₄×C₆₇	—	4	4	no	—
342	D₄×C₆₇	—	8	1	no	—
343	D₄×C₆₇	—	8	2	no	—
344	D₄×C₆₇	—	8	2	no	—
345	D₄×C₆₇	—	8	4	no	—
346	D₄×C₆₇	—	8	2	no	—
347	D₄×C₆₇	—	8	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	4	2	no	—
359	C₂×C₄×C₆₇	—	4	2	no	—
360	C₂×C₄×C₆₇	—	4	1	no	—
361	C₂×C₄×C₆₇	—	4	1	no	—
362	C₂×C₄×C₆₇	—	4	1	no	—
363	C₂×C₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	4	2	no	—
366	C₂×C₄×C₆₇	—	4	2	no	—
367	C₂×C₄×C₆₇	—	8	2	no	—
368	C₂×C₄×C₆₇	—	8	2	no	—
369	C₂×C₄×C₆₇	—	8	2	no	—
370	C₂×C₄×C₆₇	—	8	2	no	—
371	C₂×C₄×C₆₇	—	8	4	no	—
372	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
380	C₈×C₆₇	—	2	4	no	—
381	C₈×C₆₇	—	2	4	no	—
382	C₂²×C₆₇	—	2	1	no	—
383	C₂²×C₆₇	—	2	1	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	2	no	—
386	C₂²×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	2	no	—
388	C₂²×C₆₇	—	2	2	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	4	4	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	8	2	no	—
398	C₂²×C₆₇	—	8	4	no	—
399	C₂²×C₆₇	#575	1	2	yes	—
400	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₆₇	—	2	1	no	—
402	C₄×C₆₇	—	2	1	no	—
403	C₄×C₆₇	—	2	1	no	—
404	C₄×C₆₇	—	2	2	no	—
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	2	1	no	—
407	C₄×C₆₇	—	2	1	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	2	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	#585	1	2	yes	—
415	#61713	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₂×C₆₇	—	2	2	no	—
417	C₂×C₆₇	—	4	2	no	—
418	C₂×C₆₇	—	4	2	no	—
419	C₂×C₆₇	—	8	2	no	—
420	C₂×C₆₇	—	8	2	no	—
421	C₂×C₆₇	#3485	1	1	yes	characteristic
422	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
423	C₂×C₆₇	#3585	1	1	yes	characteristic
424	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#3350	C₂×C₆₇	1	4	yes	complemented
427	#3347	C₂×C₆₇	1	4	yes	complemented
428	#3309	C₂×C₆₇	1	4	yes	complemented
429	#3307	C₂×C₆₇	1	4	yes	complemented
430	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#3194	C₂×C₆₇	1	2	yes	complemented
433	#3188	C₂×C₆₇	1	2	yes	complemented
434	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#3092	C₂×C₆₇	1	2	yes	complemented
437	#3091	C₂×C₆₇	1	2	yes	complemented
438	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
439	C₆₇	#61713	1	1	yes	characteristic, direct product factor, Sylow
440	#559	—	2	2	no	—
441	#556	C₂²×C₆₇	1	2	yes	complemented
442	#555	C₂²×C₆₇	1	2	yes	complemented
443	#553	—	2	2	no	—
444	#553	—	2	2	no	—
445	#553	—	2	2	no	—
446	#553	C₂²×C₆₇	1	4	yes	—
447	#553	C₂²×C₆₇	1	4	yes	—
448	#550	C₂²×C₆₇	1	2	yes	complemented
449	#547	C₂²×C₆₇	1	2	yes	complemented
450	#538	—	2	1	no	—
451	#538	—	2	1	no	—
452	#535	—	2	1	no	—
453	#533	C₂²×C₆₇	1	1	yes	characteristic
454	#532	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#126	—	2	1	no	—
456	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
457	#525	C₂²×C₆₇	1	2	yes	—
458	#525	C₂²×C₆₇	1	2	yes	—
459	C₂×#123	—	2	1	no	—
460	C₂×#121	—	2	1	no	—
461	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
463	#520	—	2	1	no	—
464	C₂×C₄×D₄	—	2	1	no	—
465	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
469	#501	C₂²×C₆₇	1	2	yes	complemented
470	#501	C₂²×C₆₇	1	2	yes	complemented
471	#491	C₂²×C₆₇	1	2	yes	complemented
472	#490	C₂²×C₆₇	1	2	yes	complemented
473	#485	C₂²×C₆₇	1	4	yes	complemented
474	#484	C₂²×C₆₇	1	2	yes	—
475	#484	C₂²×C₆₇	1	2	yes	—
476	#483	C₂²×C₆₇	1	2	yes	—
477	#483	C₂²×C₆₇	1	4	yes	complemented
478	#482	C₂²×C₆₇	1	4	yes	complemented
479	#482	C₂²×C₆₇	1	4	yes	complemented
480	#482	C₂²×C₆₇	1	4	yes	complemented
481	#481	C₂²×C₆₇	1	2	yes	—
482	#481	C₂²×C₆₇	1	2	yes	—
483	#480	C₂²×C₆₇	1	2	yes	—
484	#480	C₂²×C₆₇	1	4	yes	complemented
485	#479	C₂²×C₆₇	1	4	yes	complemented
486	#478	C₂²×C₆₇	1	4	yes	complemented
487	#476	C₂²×C₆₇	1	2	yes	complemented
488	#474	C₂²×C₆₇	1	2	yes	complemented
489	#469	C₂²×C₆₇	1	4	yes	complemented
490	#468	C₂²×C₆₇	1	4	yes	complemented
491	#466	C₂²×C₆₇	1	4	yes	complemented
492	#465	C₂²×C₆₇	1	4	yes	complemented
493	#461	C₂²×C₆₇	1	2	yes	complemented
494	#459	C₂²×C₆₇	1	2	yes	complemented
495	#450	C₂²×C₆₇	1	2	yes	—
496	#449	C₂²×C₆₇	1	4	yes	complemented
497	#449	C₂²×C₆₇	1	4	yes	complemented
498	#447	C₂²×C₆₇	1	2	yes	—
499	#442	C₂²×C₆₇	1	4	yes	complemented
500	#440	C₂²×C₆₇	1	4	yes	complemented
501	#435	C₂²×C₆₇	1	4	yes	complemented
502	#435	C₂²×C₆₇	1	4	yes	complemented
503	#432	C₂²×C₆₇	1	1	yes	characteristic
504	#432	C₂²×C₆₇	1	1	yes	characteristic
505	#428	C₂²×C₆₇	1	4	yes	complemented
506	#427	C₂²×C₆₇	1	4	yes	complemented
507	#417	C₂²×C₆₇	1	4	yes	complemented
508	#416	C₂²×C₆₇	1	4	yes	complemented
509	#407	C₂²×C₆₇	1	2	yes	—
510	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	C₂³×C₆₇	1	2	yes	—
513	C₂×#41	C₂³×C₆₇	1	2	yes	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
523	C₂×D₈	C₂³×C₆₇	1	4	yes	—
524	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
525	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
526	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
529	#127	—	2	2	no	—
530	#127	C₂³×C₆₇	1	1	yes	characteristic
531	#126	—	2	4	no	—
532	#126	—	2	4	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#125	—	2	1	no	—
536	#125	—	2	1	no	—
537	#125	—	2	1	no	—
538	#125	C₂³×C₆₇	1	2	yes	—
539	#125	C₂³×C₆₇	1	2	yes	—
540	#124	—	2	2	no	—
541	#124	—	2	2	no	—
542	#124	—	2	2	no	—
543	#124	—	2	1	no	—
544	#123	—	2	2	no	—
545	#123	—	2	2	no	—
546	#123	—	2	4	no	—
547	#123	—	2	4	no	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
552	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
553	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
554	#121	—	2	4	no	—
555	#121	—	2	4	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	1	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	C₂³×C₆₇	1	4	yes	—
564	#121	C₂³×C₆₇	1	4	yes	—
565	#121	C₂³×C₆₇	1	2	yes	—
566	#121	C₂³×C₆₇	1	2	yes	—
567	#121	C₂³×C₆₇	1	2	yes	—
568	#120	—	2	2	no	—
569	#120	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	4	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	D₄×C₆₇	1	2	yes	—
584	C₄×D₄	D₄×C₆₇	1	2	yes	—
585	C₄×D₄	C₂³×C₆₇	1	2	yes	—
586	C₄×D₄	C₂³×C₆₇	1	2	yes	—
587	C₄×D₄	C₂³×C₆₇	1	2	yes	—
588	C₄×D₄	C₂³×C₆₇	1	2	yes	—
589	C₄×D₄	C₂³×C₆₇	1	2	yes	—
590	#117	—	2	2	no	—
591	#117	—	2	1	no	—
592	#117	—	2	2	no	—
593	#117	C₂³×C₆₇	1	4	yes	—
594	#117	C₂³×C₆₇	1	2	yes	—
595	#117	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	2	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
614	#107	C₂³×C₆₇	1	4	yes	—
615	#107	C₂³×C₆₇	1	4	yes	—
616	#107	C₂³×C₆₇	1	4	yes	—
617	#106	C₂³×C₆₇	1	4	yes	—
618	#106	C₂³×C₆₇	1	4	yes	—
619	#106	C₂³×C₆₇	1	4	yes	—
620	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
621	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
622	#103	C₂³×C₆₇	1	4	yes	—
623	#103	C₂³×C₆₇	1	4	yes	—
624	#103	C₂³×C₆₇	1	4	yes	—
625	#102	C₂³×C₆₇	1	4	yes	—
626	#102	C₂³×C₆₇	1	4	yes	—
627	#102	C₂³×C₆₇	1	4	yes	—
628	#102	C₂³×C₆₇	1	4	yes	—
629	#102	C₂³×C₆₇	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
632	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
633	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
634	#97	C₂³×C₆₇	1	2	yes	—
635	#97	C₂³×C₆₇	1	2	yes	—
636	C₂⁴	—	2	1	no	—
637	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
638	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
639	#41	—	4	4	no	—
640	#41	—	4	4	no	—
641	#41	—	4	4	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
661	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
662	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	8	2	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
685	SD₁₆	—	4	4	no	—
686	D₈	—	4	4	no	—
687	M₁₆	—	4	4	no	—
688	C₂×C₈	—	4	4	no	—
689	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
690	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
708	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
730	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
731	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
732	C₄²	—	2	4	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
752	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
753	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	Q₈	—	2	4	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	1	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	2	no	—
769	D₄	—	8	2	no	—
770	D₄	—	8	2	no	—
771	D₄	—	8	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
803	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
804	C₈	—	2	4	no	—
805	C₈	—	2	4	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	8	2	no	—
822	C₂²	—	8	4	no	—
823	C₂²	#575×C₆₇	1	2	yes	—
824	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	#585×C₆₇	1	2	yes	—
839	C₂	—	2	2	no	—
840	C₂	—	4	2	no	—
841	C₂	—	4	2	no	—
842	C₂	—	8	2	no	—
843	C₂	—	8	2	no	—
844	C₂	C₆₇×#3485	1	1	yes	characteristic
845	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
846	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×#3506	C₂	semidirect
2. C₂×#553×C₆₇	C₂	semidirect
3. C₆₇×#3350	C₂	semidirect
4. C₆₇×#3347	C₂	semidirect
5. C₆₇×#3309	C₂	semidirect
6. C₆₇×#3307	C₂	semidirect
7. C₆₇×#3236	C₂	semidirect
8. C₆₇×#3234	C₂	semidirect
9. C₆₇×#3194	C₂	semidirect
10. C₆₇×#3188	C₂	semidirect
11. C₆₇×#3110	C₂	semidirect
12. C₆₇×#3109	C₂	semidirect
13. C₆₇×#3092	C₂	semidirect
14. C₆₇×#3091	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
17. #556×C₆₇	C₂²	semidirect
18. #555×C₆₇	C₂²	semidirect
24. #550×C₆₇	C₂²	semidirect
25. #547×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #491×C₆₇	C₂²	semidirect
48. #490×C₆₇	C₂²	semidirect
49. #485×C₆₇	C₂²	semidirect
53. #483×C₆₇	C₂²	semidirect
54. #482×C₆₇	C₂²	semidirect
55. #482×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
60. #480×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #476×C₆₇	C₂²	semidirect
64. #474×C₆₇	C₂²	semidirect
65. #469×C₆₇	C₂²	semidirect
66. #468×C₆₇	C₂²	semidirect
67. #466×C₆₇	C₂²	semidirect
68. #465×C₆₇	C₂²	semidirect
69. #461×C₆₇	C₂²	semidirect
70. #459×C₆₇	C₂²	semidirect
72. #449×C₆₇	C₂²	semidirect
73. #449×C₆₇	C₂²	semidirect
75. #442×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. #435×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
81. #428×C₆₇	C₂²	semidirect
82. #427×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
84. #416×C₆₇	C₂²	semidirect
415. #61713	C₆₇	direct (N × H)
424. #3506	C₂×C₆₇	semidirect
425. C₂×#553	C₂×C₆₇	semidirect
426. #3350	C₂×C₆₇	semidirect
427. #3347	C₂×C₆₇	semidirect
428. #3309	C₂×C₆₇	semidirect
429. #3307	C₂×C₆₇	semidirect
430. #3236	C₂×C₆₇	semidirect
431. #3234	C₂×C₆₇	semidirect
432. #3194	C₂×C₆₇	semidirect
433. #3188	C₂×C₆₇	semidirect
434. #3110	C₂×C₆₇	semidirect
435. #3109	C₂×C₆₇	semidirect
436. #3092	C₂×C₆₇	semidirect
437. #3091	C₂×C₆₇	semidirect
438. #2973	C₂×C₆₇	semidirect
439. C₆₇	#61713	direct (N × H)
441. #556	C₂²×C₆₇	semidirect
442. #555	C₂²×C₆₇	semidirect
448. #550	C₂²×C₆₇	semidirect
449. #547	C₂²×C₆₇	semidirect
469. #501	C₂²×C₆₇	semidirect
470. #501	C₂²×C₆₇	semidirect
471. #491	C₂²×C₆₇	semidirect
472. #490	C₂²×C₆₇	semidirect
473. #485	C₂²×C₆₇	semidirect
477. #483	C₂²×C₆₇	semidirect
478. #482	C₂²×C₆₇	semidirect
479. #482	C₂²×C₆₇	semidirect
480. #482	C₂²×C₆₇	semidirect
484. #480	C₂²×C₆₇	semidirect
485. #479	C₂²×C₆₇	semidirect
486. #478	C₂²×C₆₇	semidirect
487. #476	C₂²×C₆₇	semidirect
488. #474	C₂²×C₆₇	semidirect
489. #469	C₂²×C₆₇	semidirect
490. #468	C₂²×C₆₇	semidirect
491. #466	C₂²×C₆₇	semidirect
492. #465	C₂²×C₆₇	semidirect
493. #461	C₂²×C₆₇	semidirect
494. #459	C₂²×C₆₇	semidirect
496. #449	C₂²×C₆₇	semidirect
497. #449	C₂²×C₆₇	semidirect
499. #442	C₂²×C₆₇	semidirect
500. #440	C₂²×C₆₇	semidirect
501. #435	C₂²×C₆₇	semidirect
502. #435	C₂²×C₆₇	semidirect
505. #428	C₂²×C₆₇	semidirect
506. #427	C₂²×C₆₇	semidirect
507. #417	C₂²×C₆₇	semidirect
508. #416	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×#3506	2
C₂×#553×C₆₇	2
C₆₇×#3350	2
C₆₇×#3347	2
C₆₇×#3309	2
C₆₇×#3307	2
C₆₇×#3236	2
C₆₇×#3234	2
C₆₇×#3194	2
C₆₇×#3188	2
C₆₇×#3110	2
C₆₇×#3109	2
C₆₇×#3092	2
C₆₇×#3091	2
C₆₇×#2973	2
#61713	67

Subgroups — C67×#61713 #30740964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61713 #30740964