Subgroups — C₆₇×#61285 #30740536

Order 17152.

1818 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3351	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3337	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3097	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3057	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2912	C₂	1	2	yes	maximal, complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	—	2	1	no	—
21	#559×C₆₇	—	2	2	no	—
22	#557×C₆₇	—	2	1	no	—
23	#556×C₆₇	—	2	1	no	—
24	#556×C₆₇	—	2	2	no	—
25	#556×C₆₇	C₂²	1	2	yes	complemented
26	#555×C₆₇	C₂²	1	2	yes	—
27	#554×C₆₇	C₂²	1	2	yes	complemented
28	#553×C₆₇	C₂²	1	4	yes	—
29	#552×C₆₇	C₂²	1	4	yes	complemented
30	#550×C₆₇	—	2	1	no	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#539×C₆₇	—	2	2	no	—
33	#538×C₆₇	—	2	2	no	—
34	#536×C₆₇	C₂²	1	2	yes	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	—	2	2	no	—
40	#525×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	—
42	#520×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#499×C₆₇	C₂²	1	2	yes	complemented
48	#499×C₆₇	C₂²	1	2	yes	complemented
49	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#485×C₆₇	C₂²	1	4	yes	complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#484×C₆₇	C₂²	1	4	yes	complemented
54	#483×C₆₇	C₂²	1	4	yes	complemented
55	#482×C₆₇	C₂²	1	4	yes	—
56	#482×C₆₇	C₂²	1	4	yes	—
57	#481×C₆₇	C₂²	1	4	yes	—
58	#480×C₆₇	C₂²	1	4	yes	—
59	#479×C₆₇	C₂²	1	4	yes	complemented
60	#478×C₆₇	C₂²	1	4	yes	—
61	#477×C₆₇	C₂²	1	2	yes	complemented
62	#476×C₆₇	C₂²	1	2	yes	—
63	#475×C₆₇	C₂²	1	2	yes	complemented
64	#474×C₆₇	C₂²	1	2	yes	—
65	#468×C₆₇	C₂²	1	4	yes	—
66	#468×C₆₇	C₂²	1	4	yes	—
67	#465×C₆₇	C₂²	1	4	yes	—
68	#465×C₆₇	C₂²	1	4	yes	—
69	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
70	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
73	#436×C₆₇	C₂²	1	2	yes	complemented
74	#436×C₆₇	C₂²	1	2	yes	complemented
75	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
76	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
77	#428×C₆₇	C₂²	1	2	yes	—
78	#428×C₆₇	C₂²	1	2	yes	—
79	#428×C₆₇	C₂²	1	4	yes	complemented
80	#428×C₆₇	C₂²	1	4	yes	complemented
81	#427×C₆₇	C₂²	1	2	yes	—
82	#427×C₆₇	C₂²	1	2	yes	—
83	#427×C₆₇	C₂²	1	4	yes	complemented
84	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×#106×C₆₇	C₂²	1	4	yes	complemented
86	#423×C₆₇	C₂²	1	1	yes	characteristic
87	#419×C₆₇	C₂²	1	2	yes	—
88	#418×C₆₇	C₂²	1	2	yes	—
89	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
91	#408×C₆₇	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	—	2	1	no	—
98	C₂×SD₁₆×C₆₇	—	2	4	no	—
99	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
101	#131×C₆₇	—	2	8	no	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
109	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	#127×C₆₇	—	2	2	no	—
114	#127×C₆₇	D₄	1	1	yes	characteristic
115	#126×C₆₇	—	2	4	no	—
116	#126×C₆₇	—	2	4	no	—
117	#126×C₆₇	—	2	4	no	—
118	#125×C₆₇	—	2	2	no	—
119	#125×C₆₇	—	2	4	no	—
120	#125×C₆₇	C₂³	1	2	yes	—
121	#125×C₆₇	C₂³	1	2	yes	—
122	#124×C₆₇	—	2	2	no	—
123	#124×C₆₇	—	2	2	no	—
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	—	2	4	no	—
126	#124×C₆₇	D₄	1	2	yes	—
127	#123×C₆₇	—	2	4	no	—
128	#123×C₆₇	—	2	4	no	—
129	#123×C₆₇	—	2	4	no	—
130	#123×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	C₂²⋊Q₈×C₆₇	—	2	1	no	—
134	C₂²⋊Q₈×C₆₇	—	2	1	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	—	2	2	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	D₄	1	2	yes	—
142	#121×C₆₇	D₄	1	2	yes	—
143	#121×C₆₇	C₂³	1	4	yes	—
144	#121×C₆₇	C₂³	1	4	yes	—
145	#120×C₆₇	—	2	4	no	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	—	2	1	no	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄×D₄×C₆₇	—	2	4	no	—
158	C₄×D₄×C₆₇	—	2	4	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	#117×C₆₇	—	2	2	no	—
170	#117×C₆₇	—	2	4	no	—
171	#117×C₆₇	C₂³	1	4	yes	—
172	#117×C₆₇	C₂³	1	4	yes	—
173	#117×C₆₇	C₂³	1	2	yes	—
174	#117×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
181	C₂×C₄²×C₆₇	—	2	1	no	—
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	#107×C₆₇	C₂³	1	2	yes	—
184	#107×C₆₇	C₂³	1	2	yes	—
185	#107×C₆₇	C₂³	1	4	yes	—
186	#107×C₆₇	C₂³	1	4	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	4	yes	—
192	#106×C₆₇	C₂³	1	4	yes	—
193	#106×C₆₇	C₂³	1	2	yes	—
194	#106×C₆₇	C₂³	1	2	yes	—
195	#106×C₆₇	C₂³	1	2	yes	—
196	#106×C₆₇	C₂³	1	2	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
198	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
209	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂⁴×C₆₇	—	2	1	no	—
214	#41×C₆₇	—	2	4	no	—
215	#41×C₆₇	—	2	4	no	—
216	#41×C₆₇	—	8	4	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	—	2	1	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	2	2	no	—
223	C₂×Q₈×C₆₇	—	2	2	no	—
224	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	2	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	8	2	no	—
244	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₆₇	—	2	4	no	—
249	SD₁₆×C₆₇	—	2	4	no	—
250	M₁₆×C₆₇	—	2	4	no	—
251	M₁₆×C₆₇	—	2	8	no	—
252	C₂×C₈×C₆₇	—	2	2	no	—
253	C₂×C₈×C₆₇	—	2	8	no	—
254	C₂×C₈×C₆₇	#41	1	4	yes	complemented
255	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
256	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	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	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	—	2	4	no	—
299	C₄²×C₆₇	—	2	4	no	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	—	2	2	no	—
302	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	4	2	no	—
308	C₂³×C₆₇	—	8	1	no	—
309	C₂³×C₆₇	—	8	1	no	—
310	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
311	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₆₇	—	2	4	no	—
313	Q₈×C₆₇	—	2	2	no	—
314	Q₈×C₆₇	—	2	2	no	—
315	Q₈×C₆₇	—	4	2	no	—
316	Q₈×C₆₇	—	4	2	no	—
317	Q₈×C₆₇	—	4	2	no	—
318	Q₈×C₆₇	—	8	1	no	—
319	Q₈×C₆₇	—	8	1	no	—
320	D₄×C₆₇	—	2	8	no	—
321	D₄×C₆₇	—	2	4	no	—
322	D₄×C₆₇	—	2	4	no	—
323	D₄×C₆₇	—	2	2	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	4	2	no	—
326	D₄×C₆₇	—	4	2	no	—
327	D₄×C₆₇	—	8	4	no	—
328	D₄×C₆₇	—	8	4	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	2	4	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	4	1	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	4	4	no	—
342	C₂×C₄×C₆₇	—	8	2	no	—
343	C₂×C₄×C₆₇	—	8	1	no	—
344	C₂×C₄×C₆₇	—	8	4	no	—
345	C₂×C₄×C₆₇	—	8	1	no	—
346	C₂×C₄×C₆₇	—	8	4	no	—
347	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
354	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
355	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
356	C₈×C₆₇	—	2	4	no	—
357	C₈×C₆₇	—	2	1	no	—
358	C₈×C₆₇	—	2	1	no	—
359	C₈×C₆₇	C₂×#41	1	2	yes	—
360	C₈×C₆₇	C₂×#41	1	2	yes	—
361	C₂²×C₆₇	—	2	1	no	—
362	C₂²×C₆₇	—	2	1	no	—
363	C₂²×C₆₇	—	2	4	no	—
364	C₂²×C₆₇	—	2	4	no	—
365	C₂²×C₆₇	—	2	4	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	8	4	no	—
370	C₂²×C₆₇	#547	1	2	yes	—
371	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₆₇	—	2	1	no	—
373	C₄×C₆₇	—	2	1	no	—
374	C₄×C₆₇	—	2	4	no	—
375	C₄×C₆₇	—	2	1	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	#547	1	2	yes	—
384	C₄×C₆₇	#577	1	2	yes	—
385	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
386	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
387	#61285	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₆₇	—	2	2	no	—
389	C₂×C₆₇	—	4	4	no	—
390	C₂×C₆₇	—	8	2	no	—
391	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
392	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
393	C₂×C₆₇	#3584	1	1	yes	characteristic
394	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#3506	C₂×C₆₇	1	1	yes	characteristic
396	#3357	C₂×C₆₇	1	2	yes	complemented
397	#3353	C₂×C₆₇	1	2	yes	complemented
398	#3351	C₂×C₆₇	1	4	yes	complemented
399	#3340	C₂×C₆₇	1	2	yes	complemented
400	#3337	C₂×C₆₇	1	4	yes	complemented
401	#3335	C₂×C₆₇	1	2	yes	complemented
402	#3160	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#3097	C₂×C₆₇	1	2	yes	complemented
404	#3096	C₂×C₆₇	1	2	yes	complemented
405	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#3057	C₂×C₆₇	1	2	yes	complemented
408	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#2912	C₂×C₆₇	1	2	yes	complemented
411	C₆₇	#61285	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
413	C₂×#131	C₂²×C₆₇	1	2	yes	—
414	#559	—	2	1	no	—
415	#559	—	2	2	no	—
416	#557	—	2	1	no	—
417	#556	—	2	1	no	—
418	#556	—	2	2	no	—
419	#556	C₂²×C₆₇	1	2	yes	complemented
420	#555	C₂²×C₆₇	1	2	yes	—
421	#554	C₂²×C₆₇	1	2	yes	complemented
422	#553	C₂²×C₆₇	1	4	yes	—
423	#552	C₂²×C₆₇	1	4	yes	complemented
424	#550	—	2	1	no	—
425	#547	C₂²×C₆₇	1	2	yes	—
426	#539	—	2	2	no	—
427	#538	—	2	2	no	—
428	#536	C₂²×C₆₇	1	2	yes	—
429	#535	C₂²×C₆₇	1	2	yes	—
430	#533	C₂²×C₆₇	1	1	yes	characteristic
431	#533	C₂²×C₆₇	1	1	yes	characteristic
432	#532	C₂²×C₆₇	1	1	yes	characteristic
433	#529	—	2	2	no	—
434	#525	—	2	2	no	—
435	#520	C₂²×C₆₇	1	2	yes	—
436	#520	C₂²×C₆₇	1	2	yes	—
437	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
439	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
441	#499	C₂²×C₆₇	1	2	yes	complemented
442	#499	C₂²×C₆₇	1	2	yes	complemented
443	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
444	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
445	#485	C₂²×C₆₇	1	4	yes	complemented
446	#485	C₂²×C₆₇	1	4	yes	complemented
447	#484	C₂²×C₆₇	1	4	yes	complemented
448	#483	C₂²×C₆₇	1	4	yes	complemented
449	#482	C₂²×C₆₇	1	4	yes	—
450	#482	C₂²×C₆₇	1	4	yes	—
451	#481	C₂²×C₆₇	1	4	yes	—
452	#480	C₂²×C₆₇	1	4	yes	—
453	#479	C₂²×C₆₇	1	4	yes	complemented
454	#478	C₂²×C₆₇	1	4	yes	—
455	#477	C₂²×C₆₇	1	2	yes	complemented
456	#476	C₂²×C₆₇	1	2	yes	—
457	#475	C₂²×C₆₇	1	2	yes	complemented
458	#474	C₂²×C₆₇	1	2	yes	—
459	#468	C₂²×C₆₇	1	4	yes	—
460	#468	C₂²×C₆₇	1	4	yes	—
461	#465	C₂²×C₆₇	1	4	yes	—
462	#465	C₂²×C₆₇	1	4	yes	—
463	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
464	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
465	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
466	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
467	#436	C₂²×C₆₇	1	2	yes	complemented
468	#436	C₂²×C₆₇	1	2	yes	complemented
469	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
470	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
471	#428	C₂²×C₆₇	1	2	yes	—
472	#428	C₂²×C₆₇	1	2	yes	—
473	#428	C₂²×C₆₇	1	4	yes	complemented
474	#428	C₂²×C₆₇	1	4	yes	complemented
475	#427	C₂²×C₆₇	1	2	yes	—
476	#427	C₂²×C₆₇	1	2	yes	—
477	#427	C₂²×C₆₇	1	4	yes	complemented
478	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#106	C₂²×C₆₇	1	4	yes	complemented
480	#423	C₂²×C₆₇	1	1	yes	characteristic
481	#419	C₂²×C₆₇	1	2	yes	—
482	#418	C₂²×C₆₇	1	2	yes	—
483	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
484	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
485	#408	C₂²×C₆₇	1	2	yes	—
486	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×#41	—	2	2	no	—
488	C₂×#41	C₂³×C₆₇	1	2	yes	—
489	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	C₂×SD₁₆	—	2	4	no	—
493	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
495	#131	—	2	8	no	—
496	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
497	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
498	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
499	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
507	#127	—	2	2	no	—
508	#127	D₄×C₆₇	1	1	yes	characteristic
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#125	—	2	2	no	—
513	#125	—	2	4	no	—
514	#125	C₂³×C₆₇	1	2	yes	—
515	#125	C₂³×C₆₇	1	2	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	#124	—	2	4	no	—
520	#124	D₄×C₆₇	1	2	yes	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
532	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
533	#121	—	2	2	no	—
534	#121	—	2	4	no	—
535	#121	D₄×C₆₇	1	2	yes	—
536	#121	D₄×C₆₇	1	2	yes	—
537	#121	C₂³×C₆₇	1	4	yes	—
538	#121	C₂³×C₆₇	1	4	yes	—
539	#120	—	2	4	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
550	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	4	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	C₂³×C₆₇	1	2	yes	—
560	C₄×D₄	C₂³×C₆₇	1	2	yes	—
561	C₄×D₄	C₂³×C₆₇	1	2	yes	—
562	C₄×D₄	C₂³×C₆₇	1	2	yes	—
563	#117	—	2	2	no	—
564	#117	—	2	4	no	—
565	#117	C₂³×C₆₇	1	2	yes	—
566	#117	C₂³×C₆₇	1	2	yes	—
567	#117	C₂³×C₆₇	1	4	yes	—
568	#117	C₂³×C₆₇	1	4	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
577	#107	C₂³×C₆₇	1	2	yes	—
578	#107	C₂³×C₆₇	1	2	yes	—
579	#107	C₂³×C₆₇	1	2	yes	—
580	#107	C₂³×C₆₇	1	2	yes	—
581	#107	C₂³×C₆₇	1	4	yes	—
582	#107	C₂³×C₆₇	1	4	yes	—
583	#106	C₂³×C₆₇	1	2	yes	—
584	#106	C₂³×C₆₇	1	2	yes	—
585	#106	C₂³×C₆₇	1	2	yes	—
586	#106	C₂³×C₆₇	1	4	yes	—
587	#106	C₂³×C₆₇	1	4	yes	—
588	#106	C₂³×C₆₇	1	2	yes	—
589	#106	C₂³×C₆₇	1	2	yes	—
590	#106	C₂³×C₆₇	1	2	yes	—
591	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
592	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
593	#103	C₂³×C₆₇	1	2	yes	—
594	#103	C₂³×C₆₇	1	2	yes	—
595	#103	C₂³×C₆₇	1	4	yes	—
596	#103	C₂³×C₆₇	1	4	yes	—
597	#102	C₂³×C₆₇	1	2	yes	—
598	#102	C₂³×C₆₇	1	2	yes	—
599	#102	C₂³×C₆₇	1	4	yes	—
600	#102	C₂³×C₆₇	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
603	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
605	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
607	C₂⁴	—	2	1	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	8	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
628	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
629	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	8	2	no	—
638	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
642	SD₁₆	—	2	4	no	—
643	SD₁₆	—	2	4	no	—
644	M₁₆	—	2	4	no	—
645	M₁₆	—	2	8	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	8	no	—
648	C₂×C₈	#41×C₆₇	1	4	yes	complemented
649	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
650	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
652	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
689	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
697	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
698	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂³	—	2	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	8	1	no	—
703	C₂³	—	8	1	no	—
704	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
705	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
706	Q₈	—	2	4	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	1	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	8	4	no	—
722	D₄	—	8	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
748	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
749	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₂×#41×C₆₇	1	2	yes	—
754	C₈	C₂×#41×C₆₇	1	2	yes	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	4	no	—
764	C₂²	#547×C₆₇	1	2	yes	—
765	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	#547×C₆₇	1	2	yes	—
778	C₄	#577×C₆₇	1	2	yes	—
779	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
780	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
781	C₂	—	2	2	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
785	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
786	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3507	C₂	semidirect
3. C₆₇×#3357	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3351	C₂	semidirect
6. C₆₇×#3340	C₂	semidirect
7. C₆₇×#3337	C₂	semidirect
8. C₆₇×#3335	C₂	semidirect
9. C₆₇×#3160	C₂	semidirect
10. C₆₇×#3097	C₂	semidirect
11. C₆₇×#3096	C₂	semidirect
12. C₆₇×#3078	C₂	semidirect
13. C₆₇×#3077	C₂	semidirect
14. C₆₇×#3057	C₂	semidirect
15. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
16. C₆₇×#2931	C₂	semidirect
17. C₆₇×#2912	C₂	semidirect
25. #556×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
29. #552×C₆₇	C₂²	semidirect
45. #500×C₆₇	C₂²	semidirect
46. #500×C₆₇	C₂²	semidirect
47. #499×C₆₇	C₂²	semidirect
48. #499×C₆₇	C₂²	semidirect
49. #498×C₆₇	C₂²	semidirect
50. #498×C₆₇	C₂²	semidirect
51. #485×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
59. #479×C₆₇	C₂²	semidirect
61. #477×C₆₇	C₂²	semidirect
63. #475×C₆₇	C₂²	semidirect
73. #436×C₆₇	C₂²	semidirect
74. #436×C₆₇	C₂²	semidirect
75. C₈×D₄×C₆₇	C₂²	semidirect
76. C₈×D₄×C₆₇	C₂²	semidirect
79. #428×C₆₇	C₂²	semidirect
80. #428×C₆₇	C₂²	semidirect
83. #427×C₆₇	C₂²	semidirect
85. C₂×#106×C₆₇	C₂²	semidirect
254. C₂×C₈×C₆₇	#41	semidirect
387. #61285	C₆₇	direct (N × H)
394. #3507	C₂×C₆₇	semidirect
396. #3357	C₂×C₆₇	semidirect
397. #3353	C₂×C₆₇	semidirect
398. #3351	C₂×C₆₇	semidirect
399. #3340	C₂×C₆₇	semidirect
400. #3337	C₂×C₆₇	semidirect
401. #3335	C₂×C₆₇	semidirect
402. #3160	C₂×C₆₇	semidirect
403. #3097	C₂×C₆₇	semidirect
404. #3096	C₂×C₆₇	semidirect
405. #3078	C₂×C₆₇	semidirect
406. #3077	C₂×C₆₇	semidirect
407. #3057	C₂×C₆₇	semidirect
408. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
409. #2931	C₂×C₆₇	semidirect
410. #2912	C₂×C₆₇	semidirect
411. C₆₇	#61285	direct (N × H)
419. #556	C₂²×C₆₇	semidirect
421. #554	C₂²×C₆₇	semidirect
423. #552	C₂²×C₆₇	semidirect
439. #500	C₂²×C₆₇	semidirect
440. #500	C₂²×C₆₇	semidirect
441. #499	C₂²×C₆₇	semidirect
442. #499	C₂²×C₆₇	semidirect
443. #498	C₂²×C₆₇	semidirect
444. #498	C₂²×C₆₇	semidirect
445. #485	C₂²×C₆₇	semidirect
446. #485	C₂²×C₆₇	semidirect
447. #484	C₂²×C₆₇	semidirect
448. #483	C₂²×C₆₇	semidirect
453. #479	C₂²×C₆₇	semidirect
455. #477	C₂²×C₆₇	semidirect
457. #475	C₂²×C₆₇	semidirect
467. #436	C₂²×C₆₇	semidirect
468. #436	C₂²×C₆₇	semidirect
469. C₈×D₄	C₂²×C₆₇	semidirect
470. C₈×D₄	C₂²×C₆₇	semidirect
473. #428	C₂²×C₆₇	semidirect
474. #428	C₂²×C₆₇	semidirect
477. #427	C₂²×C₆₇	semidirect
479. C₂×#106	C₂²×C₆₇	semidirect
648. C₂×C₈	#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×#3507	2
C₆₇×#3506	2
C₆₇×#3357	2
C₆₇×#3353	2
C₆₇×#3351	2
C₆₇×#3340	2
C₆₇×#3337	2
C₆₇×#3335	2
C₆₇×#3160	2
C₆₇×#3097	2
C₆₇×#3096	2
C₆₇×#3078	2
C₆₇×#3077	2
C₆₇×#3057	2
C₂×C₄×SD₁₆×C₆₇	2
C₆₇×#2931	2
C₆₇×#2912	2
#61285	67

Subgroups — C67×#61285 #30740536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61285 #30740536