Subgroups — C₆₇×#61341 #30740592

Order 17152.

1844 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3371	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3368	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3368	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3362	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3081	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3043	C₂	1	2	yes	maximal, complemented
14	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	C₂²	1	2	yes	—
21	#559×C₆₇	C₂²	1	2	yes	—
22	Q₈²×C₆₇	—	2	1	no	—
23	Q₈²×C₆₇	C₂²	1	2	yes	complemented
24	#557×C₆₇	—	2	1	no	—
25	#557×C₆₇	—	2	2	no	—
26	#557×C₆₇	C₂²	1	2	yes	complemented
27	#557×C₆₇	C₂²	1	4	yes	complemented
28	#550×C₆₇	C₂²	1	2	yes	—
29	#550×C₆₇	C₂²	1	2	yes	—
30	#546×C₆₇	—	2	2	no	—
31	#546×C₆₇	—	2	2	no	—
32	#544×C₆₇	—	2	2	no	—
33	#544×C₆₇	C₂²	1	2	yes	—
34	#540×C₆₇	—	2	2	no	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	2	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	—	2	1	no	—
40	#532×C₆₇	—	2	1	no	—
41	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
42	#519×C₆₇	C₂²	1	2	yes	—
43	#518×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	#490×C₆₇	C₂²	1	4	yes	—
47	#490×C₆₇	C₂²	1	4	yes	complemented
48	#489×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#486×C₆₇	C₂²	1	2	yes	—
51	#486×C₆₇	C₂²	1	2	yes	—
52	#486×C₆₇	C₂²	1	4	yes	complemented
53	#479×C₆₇	C₂²	1	2	yes	complemented
54	#478×C₆₇	C₂²	1	2	yes	complemented
55	#478×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	complemented
57	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#476×C₆₇	C₂²	1	4	yes	complemented
60	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#474×C₆₇	C₂²	1	4	yes	complemented
63	#464×C₆₇	C₂²	1	4	yes	complemented
64	#464×C₆₇	C₂²	1	4	yes	complemented
65	#460×C₆₇	C₂²	1	2	yes	—
66	#460×C₆₇	C₂²	1	4	yes	—
67	#460×C₆₇	C₂²	1	2	yes	—
68	#460×C₆₇	C₂²	1	4	yes	complemented
69	#460×C₆₇	C₂²	1	4	yes	complemented
70	#446×C₆₇	C₂²	1	4	yes	complemented
71	#446×C₆₇	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
73	#441×C₆₇	C₂²	1	2	yes	complemented
74	#440×C₆₇	C₂²	1	2	yes	complemented
75	#440×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	#427×C₆₇	C₂²	1	2	yes	—
83	#424×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	#419×C₆₇	C₂²	1	1	yes	characteristic
86	#418×C₆₇	C₂²	1	2	yes	—
87	#418×C₆₇	C₂²	1	2	yes	—
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#102×C₆₇	C₂²	1	2	yes	—
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	2	no	—
95	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	1	no	—
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	#137×C₆₇	—	2	4	no	—
101	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₇	—	2	8	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	—	2	4	no	—
111	C₄⋊Q₈×C₆₇	—	2	2	no	—
112	C₄⋊Q₈×C₆₇	—	2	4	no	—
113	C₄⋊Q₈×C₆₇	—	2	2	no	—
114	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
119	#127×C₆₇	—	2	1	no	—
120	#127×C₆₇	—	2	1	no	—
121	#127×C₆₇	C₂³	1	2	yes	—
122	#127×C₆₇	C₂³	1	2	yes	—
123	#127×C₆₇	C₂³	1	4	yes	—
124	#125×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	4	no	—
126	#125×C₆₇	—	2	4	no	—
127	#125×C₆₇	—	2	2	no	—
128	#125×C₆₇	D₄	1	2	yes	—
129	#125×C₆₇	C₂³	1	4	yes	—
130	#125×C₆₇	C₂³	1	2	yes	—
131	#124×C₆₇	—	2	2	no	—
132	#124×C₆₇	—	2	2	no	—
133	#124×C₆₇	C₂³	1	4	yes	—
134	#123×C₆₇	—	2	4	no	—
135	#123×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	1	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	4	no	—
139	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
140	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	4	no	—
146	#121×C₆₇	—	2	4	no	—
147	#120×C₆₇	—	2	4	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	4	no	—
152	C₄×Q₈×C₆₇	—	2	2	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	—	2	1	no	—
155	C₄×Q₈×C₆₇	—	2	1	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	—	2	1	no	—
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	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₇	C₂³	1	4	yes	—
173	C₄×D₄×C₆₇	C₂³	1	4	yes	—
174	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
175	#117×C₆₇	—	2	4	no	—
176	#117×C₆₇	—	2	1	no	—
177	#117×C₆₇	C₂³	1	1	yes	characteristic
178	#117×C₆₇	C₂³	1	2	yes	—
179	#117×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
183	C₂×C₄²×C₆₇	—	2	1	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	2	yes	—
187	#107×C₆₇	C₂³	1	2	yes	—
188	#107×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	2	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	2	yes	—
199	#103×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#102×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	2	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	4	yes	—
212	#97×C₆₇	C₂³	1	2	yes	—
213	C₄×C₈×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	C₂⁴×C₆₇	—	2	2	no	—
216	#41×C₆₇	—	2	2	no	—
217	#41×C₆₇	—	2	2	no	—
218	#41×C₆₇	—	8	4	no	—
219	#41×C₆₇	—	8	4	no	—
220	C₂×Q₈×C₆₇	—	2	1	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	2	1	no	—
223	C₂×Q₈×C₆₇	—	2	4	no	—
224	C₂×Q₈×C₆₇	—	2	2	no	—
225	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
228	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	2	2	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	8	2	no	—
241	C₂×D₄×C₆₇	—	8	2	no	—
242	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
243	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	1	no	—
246	C₂²×C₄×C₆₇	—	2	1	no	—
247	C₂²×C₄×C₆₇	—	2	1	no	—
248	C₂²×C₄×C₆₇	—	2	1	no	—
249	C₂²×C₄×C₆₇	—	2	4	no	—
250	C₂²×C₄×C₆₇	—	2	4	no	—
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	Q₁₆×C₆₇	—	2	4	no	—
255	SD₁₆×C₆₇	—	2	8	no	—
256	SD₁₆×C₆₇	—	2	8	no	—
257	SD₁₆×C₆₇	—	2	4	no	—
258	M₁₆×C₆₇	—	2	2	no	—
259	M₁₆×C₆₇	—	2	2	no	—
260	C₂×C₈×C₆₇	—	2	4	no	—
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₆₇	C₂×D₄	1	4	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	1	yes	characteristic
289	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²⋊C₄×C₆₇	—	2	1	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
299	C₄²×C₆₇	—	2	1	no	—
300	C₄²×C₆₇	—	2	1	no	—
301	C₄²×C₆₇	—	2	1	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	2	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	4	no	—
306	C₄²×C₆₇	—	2	2	no	—
307	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄²×C₆₇	C₂⁴	1	4	yes	—
312	C₂³×C₆₇	—	2	4	no	—
313	C₂³×C₆₇	—	2	1	no	—
314	C₂³×C₆₇	—	4	4	no	—
315	C₂³×C₆₇	—	8	2	no	—
316	C₂³×C₆₇	—	8	2	no	—
317	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₆₇	—	2	4	no	—
319	Q₈×C₆₇	—	2	4	no	—
320	Q₈×C₆₇	—	2	2	no	—
321	Q₈×C₆₇	—	2	1	no	—
322	Q₈×C₆₇	—	2	1	no	—
323	Q₈×C₆₇	—	4	2	no	—
324	Q₈×C₆₇	—	4	2	no	—
325	Q₈×C₆₇	—	8	1	no	—
326	Q₈×C₆₇	—	8	4	no	—
327	Q₈×C₆₇	C₂×#41	1	4	yes	—
328	D₄×C₆₇	—	2	4	no	—
329	D₄×C₆₇	—	2	1	no	—
330	D₄×C₆₇	—	2	4	no	—
331	D₄×C₆₇	—	2	1	no	—
332	D₄×C₆₇	—	4	4	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	4	4	no	—
335	D₄×C₆₇	—	4	4	no	—
336	D₄×C₆₇	—	8	2	no	—
337	D₄×C₆₇	—	8	2	no	—
338	D₄×C₆₇	—	8	4	no	—
339	D₄×C₆₇	—	8	4	no	—
340	C₂×C₄×C₆₇	—	2	4	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	1	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	4	1	no	—
350	C₂×C₄×C₆₇	—	4	2	no	—
351	C₂×C₄×C₆₇	—	4	2	no	—
352	C₂×C₄×C₆₇	—	4	2	no	—
353	C₂×C₄×C₆₇	—	8	4	no	—
354	C₂×C₄×C₆₇	—	8	4	no	—
355	C₂×C₄×C₆₇	—	8	1	no	—
356	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
359	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
364	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
366	C₈×C₆₇	—	2	2	no	—
367	C₈×C₆₇	—	2	2	no	—
368	C₈×C₆₇	—	2	2	no	—
369	C₈×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	2	1	no	—
371	C₂²×C₆₇	—	2	1	no	—
372	C₂²×C₆₇	—	4	1	no	—
373	C₂²×C₆₇	—	4	4	no	—
374	C₂²×C₆₇	—	4	1	no	—
375	C₂²×C₆₇	—	4	4	no	—
376	C₂²×C₆₇	—	4	1	no	—
377	C₂²×C₆₇	—	4	4	no	—
378	C₂²×C₆₇	—	16	4	no	—
379	C₂²×C₆₇	#548	1	2	yes	—
380	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₆₇	—	2	1	no	—
382	C₄×C₆₇	—	2	1	no	—
383	C₄×C₆₇	—	2	4	no	—
384	C₄×C₆₇	—	2	4	no	—
385	C₄×C₆₇	—	2	1	no	—
386	C₄×C₆₇	—	2	4	no	—
387	C₄×C₆₇	—	4	1	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	1	no	—
391	C₄×C₆₇	—	4	1	no	—
392	C₄×C₆₇	—	4	2	no	—
393	C₄×C₆₇	#548	1	2	yes	—
394	C₄×C₆₇	#577	1	2	yes	—
395	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
396	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	#61341	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂×C₆₇	—	2	2	no	—
399	C₂×C₆₇	—	8	1	no	—
400	C₂×C₆₇	—	8	4	no	—
401	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
402	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
403	C₂×C₆₇	#3585	1	1	yes	characteristic
404	#3508	C₂×C₆₇	1	1	yes	characteristic
405	#3502	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#3375	C₂×C₆₇	1	2	yes	complemented
407	#3371	C₂×C₆₇	1	4	yes	complemented
408	#3368	C₂×C₆₇	1	2	yes	complemented
409	#3368	C₂×C₆₇	1	4	yes	complemented
410	#3365	C₂×C₆₇	1	2	yes	complemented
411	#3362	C₂×C₆₇	1	2	yes	complemented
412	#3138	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#3136	C₂×C₆₇	1	2	yes	complemented
414	#3081	C₂×C₆₇	1	2	yes	complemented
415	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#3043	C₂×C₆₇	1	2	yes	complemented
417	C₂×#460	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#2949	C₂×C₆₇	1	2	yes	complemented
420	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₆₇	#61341	1	1	yes	characteristic, direct product factor, Sylow
422	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
423	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
424	#559	C₂²×C₆₇	1	2	yes	—
425	#559	C₂²×C₆₇	1	2	yes	—
426	Q₈²	—	2	1	no	—
427	Q₈²	C₂²×C₆₇	1	2	yes	complemented
428	#557	—	2	1	no	—
429	#557	—	2	2	no	—
430	#557	C₂²×C₆₇	1	2	yes	complemented
431	#557	C₂²×C₆₇	1	4	yes	complemented
432	#550	C₂²×C₆₇	1	2	yes	—
433	#550	C₂²×C₆₇	1	2	yes	—
434	#546	—	2	2	no	—
435	#546	—	2	2	no	—
436	#544	—	2	2	no	—
437	#544	C₂²×C₆₇	1	2	yes	—
438	#540	—	2	2	no	—
439	#535	C₂²×C₆₇	1	2	yes	—
440	#533	—	2	2	no	—
441	#533	C₂²×C₆₇	1	1	yes	characteristic
442	#533	C₂²×C₆₇	1	1	yes	characteristic
443	#532	—	2	1	no	—
444	#532	—	2	1	no	—
445	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
446	#519	C₂²×C₆₇	1	2	yes	—
447	#518	C₂²×C₆₇	1	2	yes	—
448	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
450	#490	C₂²×C₆₇	1	4	yes	—
451	#490	C₂²×C₆₇	1	4	yes	complemented
452	#489	C₂²×C₆₇	1	4	yes	complemented
453	#488	C₂²×C₆₇	1	4	yes	complemented
454	#486	C₂²×C₆₇	1	2	yes	—
455	#486	C₂²×C₆₇	1	2	yes	—
456	#486	C₂²×C₆₇	1	4	yes	complemented
457	#479	C₂²×C₆₇	1	2	yes	complemented
458	#478	C₂²×C₆₇	1	2	yes	complemented
459	#478	C₂²×C₆₇	1	4	yes	complemented
460	#478	C₂²×C₆₇	1	4	yes	complemented
461	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	#476	C₂²×C₆₇	1	4	yes	complemented
464	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
465	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	#474	C₂²×C₆₇	1	4	yes	complemented
467	#464	C₂²×C₆₇	1	4	yes	complemented
468	#464	C₂²×C₆₇	1	4	yes	complemented
469	#460	C₂²×C₆₇	1	2	yes	—
470	#460	C₂²×C₆₇	1	4	yes	—
471	#460	C₂²×C₆₇	1	2	yes	—
472	#460	C₂²×C₆₇	1	4	yes	complemented
473	#460	C₂²×C₆₇	1	4	yes	complemented
474	#446	C₂²×C₆₇	1	4	yes	complemented
475	#446	C₂²×C₆₇	1	2	yes	complemented
476	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
477	#441	C₂²×C₆₇	1	2	yes	complemented
478	#440	C₂²×C₆₇	1	2	yes	complemented
479	#440	C₂²×C₆₇	1	4	yes	complemented
480	#440	C₂²×C₆₇	1	4	yes	complemented
481	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
482	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
483	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
484	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
485	#428	C₂²×C₆₇	1	1	yes	characteristic
486	#427	C₂²×C₆₇	1	2	yes	—
487	#424	C₂²×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
489	#419	C₂²×C₆₇	1	1	yes	characteristic
490	#418	C₂²×C₆₇	1	2	yes	—
491	#418	C₂²×C₆₇	1	2	yes	—
492	#417	C₂²×C₆₇	1	1	yes	characteristic
493	#416	C₂²×C₆₇	1	2	yes	—
494	C₂×#102	C₂²×C₆₇	1	2	yes	—
495	#405	C₂²×C₆₇	1	2	yes	—
496	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
504	#137	—	2	4	no	—
505	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
506	C₂×SD₁₆	—	2	8	no	—
507	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
510	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
513	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	—	2	4	no	—
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	4	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
519	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
523	#127	—	2	1	no	—
524	#127	—	2	1	no	—
525	#127	C₂³×C₆₇	1	2	yes	—
526	#127	C₂³×C₆₇	1	2	yes	—
527	#127	C₂³×C₆₇	1	4	yes	—
528	#125	—	2	4	no	—
529	#125	—	2	4	no	—
530	#125	—	2	4	no	—
531	#125	—	2	2	no	—
532	#125	D₄×C₆₇	1	2	yes	—
533	#125	C₂³×C₆₇	1	2	yes	—
534	#125	C₂³×C₆₇	1	4	yes	—
535	#124	—	2	2	no	—
536	#124	—	2	2	no	—
537	#124	C₂³×C₆₇	1	4	yes	—
538	#123	—	2	4	no	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
544	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	4	no	—
550	#121	—	2	4	no	—
551	#120	—	2	4	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	4	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
562	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
563	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
564	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
566	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
567	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
568	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₄×D₄	C₂³×C₆₇	1	4	yes	—
578	C₄×D₄	C₂³×C₆₇	1	4	yes	—
579	#117	—	2	4	no	—
580	#117	—	2	1	no	—
581	#117	C₂³×C₆₇	1	1	yes	characteristic
582	#117	C₂³×C₆₇	1	2	yes	—
583	#117	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	—	2	4	no	—
587	C₂×C₄²	—	2	1	no	—
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
590	#107	C₂³×C₆₇	1	2	yes	—
591	#107	C₂³×C₆₇	1	2	yes	—
592	#107	C₂³×C₆₇	1	2	yes	—
593	#106	C₂³×C₆₇	1	2	yes	—
594	#106	C₂³×C₆₇	1	2	yes	—
595	#106	C₂³×C₆₇	1	2	yes	—
596	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
597	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
598	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
599	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
600	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
601	#103	C₂³×C₆₇	1	2	yes	—
602	#103	C₂³×C₆₇	1	2	yes	—
603	#103	C₂³×C₆₇	1	2	yes	—
604	#103	C₂³×C₆₇	1	2	yes	—
605	#103	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	4	yes	—
607	#102	C₂³×C₆₇	1	4	yes	—
608	#102	C₂³×C₆₇	1	2	yes	—
609	#102	C₂³×C₆₇	1	2	yes	—
610	#102	C₂³×C₆₇	1	2	yes	—
611	#102	C₂³×C₆₇	1	4	yes	—
612	#102	C₂³×C₆₇	1	4	yes	—
613	#102	C₂³×C₆₇	1	4	yes	—
614	#102	C₂³×C₆₇	1	4	yes	—
615	#97	C₂³×C₆₇	1	2	yes	—
616	#97	C₂³×C₆₇	1	4	yes	—
617	C₄×C₈	C₂³×C₆₇	1	2	yes	—
618	C₄×C₈	C₂³×C₆₇	1	4	yes	—
619	C₂⁴	—	2	2	no	—
620	#41	—	2	2	no	—
621	#41	—	2	2	no	—
622	#41	—	8	4	no	—
623	#41	—	8	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
631	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
632	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
633	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	8	2	no	—
645	C₂×D₄	—	8	2	no	—
646	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
647	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
658	Q₁₆	—	2	4	no	—
659	SD₁₆	—	2	8	no	—
660	SD₁₆	—	2	8	no	—
661	SD₁₆	—	2	4	no	—
662	M₁₆	—	2	2	no	—
663	M₁₆	—	2	2	no	—
664	C₂×C₈	—	2	4	no	—
665	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
666	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
667	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
668	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
687	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
688	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
693	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	2	no	—
711	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
713	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₄²	C₂⁴×C₆₇	1	4	yes	—
715	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
716	C₂³	—	2	4	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	4	4	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	2	no	—
721	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
722	Q₈	—	2	4	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	Q₈	—	8	4	no	—
731	Q₈	C₂×#41×C₆₇	1	4	yes	—
732	D₄	—	2	4	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	2	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
764	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
767	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
768	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
769	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	16	4	no	—
783	C₂²	#548×C₆₇	1	2	yes	—
784	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
785	C₄	—	2	1	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	#548×C₆₇	1	2	yes	—
798	C₄	#577×C₆₇	1	2	yes	—
799	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
800	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	8	4	no	—
803	C₂	—	8	1	no	—
804	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
805	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
806	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3502	C₂	semidirect
3. C₆₇×#3375	C₂	semidirect
4. C₆₇×#3371	C₂	semidirect
5. C₆₇×#3368	C₂	semidirect
6. C₆₇×#3368	C₂	semidirect
7. C₆₇×#3365	C₂	semidirect
8. C₆₇×#3362	C₂	semidirect
9. C₆₇×#3138	C₂	semidirect
10. C₆₇×#3136	C₂	semidirect
11. C₆₇×#3081	C₂	semidirect
12. C₆₇×#3076	C₂	semidirect
13. C₆₇×#3043	C₂	semidirect
14. C₂×#460×C₆₇	C₂	semidirect
15. C₆₇×#2962	C₂	semidirect
16. C₆₇×#2949	C₂	semidirect
17. C₄×#137×C₆₇	C₂	semidirect
23. Q₈²×C₆₇	C₂²	semidirect
26. #557×C₆₇	C₂²	semidirect
27. #557×C₆₇	C₂²	semidirect
47. #490×C₆₇	C₂²	semidirect
48. #489×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #479×C₆₇	C₂²	semidirect
54. #478×C₆₇	C₂²	semidirect
55. #478×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
58. #476×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #474×C₆₇	C₂²	semidirect
62. #474×C₆₇	C₂²	semidirect
63. #464×C₆₇	C₂²	semidirect
64. #464×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #460×C₆₇	C₂²	semidirect
70. #446×C₆₇	C₂²	semidirect
71. #446×C₆₇	C₂²	semidirect
72. C₈×Q₈×C₆₇	C₂²	semidirect
73. #441×C₆₇	C₂²	semidirect
74. #440×C₆₇	C₂²	semidirect
75. #440×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. C₄×Q₁₆×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
227. C₂×Q₈×C₆₇	#41	semidirect
397. #61341	C₆₇	direct (N × H)
405. #3502	C₂×C₆₇	semidirect
406. #3375	C₂×C₆₇	semidirect
407. #3371	C₂×C₆₇	semidirect
408. #3368	C₂×C₆₇	semidirect
409. #3368	C₂×C₆₇	semidirect
410. #3365	C₂×C₆₇	semidirect
411. #3362	C₂×C₆₇	semidirect
412. #3138	C₂×C₆₇	semidirect
413. #3136	C₂×C₆₇	semidirect
414. #3081	C₂×C₆₇	semidirect
415. #3076	C₂×C₆₇	semidirect
416. #3043	C₂×C₆₇	semidirect
417. C₂×#460	C₂×C₆₇	semidirect
418. #2962	C₂×C₆₇	semidirect
419. #2949	C₂×C₆₇	semidirect
420. C₄×#137	C₂×C₆₇	semidirect
421. C₆₇	#61341	direct (N × H)
427. Q₈²	C₂²×C₆₇	semidirect
430. #557	C₂²×C₆₇	semidirect
431. #557	C₂²×C₆₇	semidirect
451. #490	C₂²×C₆₇	semidirect
452. #489	C₂²×C₆₇	semidirect
453. #488	C₂²×C₆₇	semidirect
456. #486	C₂²×C₆₇	semidirect
457. #479	C₂²×C₆₇	semidirect
458. #478	C₂²×C₆₇	semidirect
459. #478	C₂²×C₆₇	semidirect
460. #478	C₂²×C₆₇	semidirect
461. #477	C₂²×C₆₇	semidirect
462. #476	C₂²×C₆₇	semidirect
463. #476	C₂²×C₆₇	semidirect
464. #475	C₂²×C₆₇	semidirect
465. #474	C₂²×C₆₇	semidirect
466. #474	C₂²×C₆₇	semidirect
467. #464	C₂²×C₆₇	semidirect
468. #464	C₂²×C₆₇	semidirect
472. #460	C₂²×C₆₇	semidirect
473. #460	C₂²×C₆₇	semidirect
474. #446	C₂²×C₆₇	semidirect
475. #446	C₂²×C₆₇	semidirect
476. C₈×Q₈	C₂²×C₆₇	semidirect
477. #441	C₂²×C₆₇	semidirect
478. #440	C₂²×C₆₇	semidirect
479. #440	C₂²×C₆₇	semidirect
480. #440	C₂²×C₆₇	semidirect
481. C₄×Q₁₆	C₂²×C₆₇	semidirect
482. C₄×SD₁₆	C₂²×C₆₇	semidirect
483. C₄×SD₁₆	C₂²×C₆₇	semidirect
484. C₄×SD₁₆	C₂²×C₆₇	semidirect
631. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3508	2
C₆₇×#3502	2
C₆₇×#3375	2
C₆₇×#3371	2
C₆₇×#3368	2
C₆₇×#3365	2
C₆₇×#3362	2
C₆₇×#3138	2
C₆₇×#3136	2
C₆₇×#3081	2
C₆₇×#3076	2
C₆₇×#3043	2
C₂×#460×C₆₇	2
C₆₇×#2962	2
C₆₇×#2949	2
C₄×#137×C₆₇	2
#61341	67

Subgroups — C67×#61341 #30740592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61341 #30740592