Subgroups — C₆₇×#60886 #30740137

Order 17152.

1678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3244	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3243	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3237	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3236	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3235	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3234	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#501×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3084	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3083	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	#557×C₆₇	—	2	1	no	—
19	#557×C₆₇	—	2	1	no	—
20	#556×C₆₇	—	2	1	no	—
21	#555×C₆₇	—	2	1	no	—
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	1	no	—
24	#554×C₆₇	—	2	2	no	—
25	#554×C₆₇	—	2	2	no	—
26	#554×C₆₇	—	2	1	no	—
27	#553×C₆₇	—	2	2	no	—
28	#548×C₆₇	—	2	2	no	—
29	#547×C₆₇	—	2	1	no	—
30	#544×C₆₇	C₂²	1	1	yes	characteristic
31	#544×C₆₇	C₂²	1	1	yes	characteristic
32	#544×C₆₇	C₂²	1	2	yes	—
33	#544×C₆₇	C₂²	1	2	yes	—
34	#542×C₆₇	C₂²	1	4	yes	—
35	#537×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	2	yes	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#533×C₆₇	C₂²	1	2	yes	—
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#125×C₆₇	C₂²	1	2	yes	—
44	#520×C₆₇	C₂²	1	2	yes	—
45	#520×C₆₇	C₂²	1	1	yes	characteristic
46	#520×C₆₇	C₂²	1	1	yes	characteristic
47	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
48	#501×C₆₇	C₂²	1	2	yes	—
49	#501×C₆₇	C₂²	1	2	yes	—
50	#501×C₆₇	C₂²	1	4	yes	—
51	#501×C₆₇	C₂²	1	2	yes	—
52	#501×C₆₇	C₂²	1	2	yes	—
53	#500×C₆₇	C₂²	1	2	yes	—
54	#498×C₆₇	C₂²	1	2	yes	—
55	#491×C₆₇	C₂²	1	1	yes	characteristic
56	#491×C₆₇	C₂²	1	1	yes	characteristic
57	#491×C₆₇	C₂²	1	2	yes	—
58	#490×C₆₇	C₂²	1	1	yes	characteristic
59	#490×C₆₇	C₂²	1	1	yes	characteristic
60	#490×C₆₇	C₂²	1	2	yes	—
61	#489×C₆₇	C₂²	1	2	yes	—
62	#489×C₆₇	C₂²	1	2	yes	—
63	#488×C₆₇	C₂²	1	4	yes	—
64	#485×C₆₇	C₂²	1	4	yes	—
65	#485×C₆₇	C₂²	1	4	yes	—
66	#484×C₆₇	C₂²	1	4	yes	—
67	#483×C₆₇	C₂²	1	4	yes	—
68	#482×C₆₇	C₂²	1	4	yes	—
69	#482×C₆₇	C₂²	1	4	yes	—
70	#481×C₆₇	C₂²	1	4	yes	—
71	#480×C₆₇	C₂²	1	4	yes	—
72	#479×C₆₇	C₂²	1	4	yes	—
73	#479×C₆₇	C₂²	1	4	yes	—
74	#478×C₆₇	C₂²	1	4	yes	—
75	#478×C₆₇	C₂²	1	4	yes	—
76	#477×C₆₇	C₂²	1	4	yes	—
77	#476×C₆₇	C₂²	1	4	yes	—
78	#475×C₆₇	C₂²	1	4	yes	—
79	#474×C₆₇	C₂²	1	4	yes	—
80	#433×C₆₇	C₂²	1	4	yes	—
81	#432×C₆₇	C₂²	1	2	yes	—
82	#432×C₆₇	C₂²	1	2	yes	—
83	#428×C₆₇	C₂²	1	2	yes	—
84	#428×C₆₇	C₂²	1	2	yes	—
85	C₂×#107×C₆₇	C₂²	1	2	yes	—
86	C₂×#106×C₆₇	C₂²	1	2	yes	—
87	#424×C₆₇	C₂²	1	2	yes	—
88	#417×C₆₇	C₂²	1	2	yes	—
89	#417×C₆₇	C₂²	1	2	yes	—
90	#416×C₆₇	C₂²	1	2	yes	—
91	#416×C₆₇	C₂²	1	2	yes	—
92	#408×C₆₇	C₂²	1	2	yes	—
93	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
94	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₆₇	—	2	1	no	—
99	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
101	C₄⋊Q₈×C₆₇	—	2	1	no	—
102	C₄⋊Q₈×C₆₇	—	2	1	no	—
103	C₄⋊Q₈×C₆₇	—	2	2	no	—
104	C₄⋊Q₈×C₆₇	—	2	2	no	—
105	C₄⋊Q₈×C₆₇	—	2	1	no	—
106	C₄⋊Q₈×C₆₇	—	2	1	no	—
107	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
114	#127×C₆₇	C₂³	1	1	yes	characteristic
115	#126×C₆₇	—	2	4	no	—
116	#125×C₆₇	—	2	1	no	—
117	#125×C₆₇	—	2	1	no	—
118	#125×C₆₇	—	2	2	no	—
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	1	no	—
122	#125×C₆₇	—	2	1	no	—
123	#125×C₆₇	—	2	2	no	—
124	#125×C₆₇	—	2	2	no	—
125	#125×C₆₇	C₂³	1	2	yes	—
126	#125×C₆₇	C₂³	1	2	yes	—
127	#125×C₆₇	C₂³	1	2	yes	—
128	#125×C₆₇	C₂³	1	1	yes	characteristic
129	#125×C₆₇	C₂³	1	2	yes	—
130	#125×C₆₇	C₂³	1	1	yes	characteristic
131	#124×C₆₇	—	2	4	no	—
132	#124×C₆₇	—	2	2	no	—
133	#124×C₆₇	C₂³	1	2	yes	—
134	#123×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×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	4	yes	—
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	1	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₇	—	2	1	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	—	2	2	no	—
158	C₄×Q₈×C₆₇	—	2	2	no	—
159	C₄×Q₈×C₆₇	—	2	1	no	—
160	C₄×Q₈×C₆₇	—	2	1	no	—
161	C₄×Q₈×C₆₇	—	2	2	no	—
162	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	—	2	4	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	D₄	1	2	yes	—
176	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	4	yes	—
178	#117×C₆₇	—	2	2	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	C₂³	1	2	yes	—
181	#117×C₆₇	C₂³	1	2	yes	—
182	#117×C₆₇	C₂³	1	1	yes	characteristic
183	#117×C₆₇	C₂³	1	1	yes	characteristic
184	#117×C₆₇	C₂³	1	1	yes	characteristic
185	#117×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
187	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
188	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	#107×C₆₇	C₂³	1	4	yes	—
200	#107×C₆₇	C₂³	1	4	yes	—
201	#107×C₆₇	C₂³	1	4	yes	—
202	#107×C₆₇	C₂³	1	4	yes	—
203	#106×C₆₇	C₂³	1	4	yes	—
204	#106×C₆₇	C₂³	1	4	yes	—
205	#106×C₆₇	C₂³	1	4	yes	—
206	#106×C₆₇	C₂³	1	4	yes	—
207	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
209	#103×C₆₇	C₂³	1	2	yes	—
210	#103×C₆₇	C₂³	1	4	yes	—
211	#103×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#102×C₆₇	C₂³	1	2	yes	—
216	#102×C₆₇	C₂³	1	4	yes	—
217	#102×C₆₇	C₂³	1	2	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
223	#97×C₆₇	C₂³	1	2	yes	—
224	#97×C₆₇	C₂³	1	1	yes	characteristic
225	#97×C₆₇	C₂³	1	1	yes	characteristic
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	#41×C₆₇	—	2	4	no	—
229	#41×C₆₇	—	2	8	no	—
230	#41×C₆₇	—	8	4	no	—
231	C₂×Q₈×C₆₇	—	2	2	no	—
232	C₂×Q₈×C₆₇	—	2	2	no	—
233	C₂×Q₈×C₆₇	—	2	1	no	—
234	C₂×Q₈×C₆₇	—	2	1	no	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	2	2	no	—
237	C₂×Q₈×C₆₇	—	8	2	no	—
238	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	1	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	1	no	—
250	C₂²×C₄×C₆₇	—	2	1	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	M₁₆×C₆₇	—	2	4	no	—
261	C₂×C₈×C₆₇	—	2	4	no	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	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	2	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₄⋊C₄×C₆₇	—	2	1	no	—
283	C₄⋊C₄×C₆₇	—	2	1	no	—
284	C₄⋊C₄×C₆₇	—	2	1	no	—
285	C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	1	no	—
307	C₂²⋊C₄×C₆₇	—	2	1	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₄²×C₆₇	—	2	4	no	—
316	C₄²×C₆₇	—	2	2	no	—
317	C₄²×C₆₇	—	2	2	no	—
318	C₄²×C₆₇	—	2	1	no	—
319	C₄²×C₆₇	—	2	1	no	—
320	C₄²×C₆₇	C₂×D₄	1	2	yes	—
321	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₆₇	C₂×D₄	1	2	yes	—
324	C₄²×C₆₇	C₂⁴	1	2	yes	—
325	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₆₇	—	2	2	no	—
331	Q₈×C₆₇	—	2	4	no	—
332	Q₈×C₆₇	—	4	4	no	—
333	Q₈×C₆₇	—	8	2	no	—
334	Q₈×C₆₇	—	8	1	no	—
335	Q₈×C₆₇	—	8	2	no	—
336	Q₈×C₆₇	—	8	1	no	—
337	Q₈×C₆₇	—	8	2	no	—
338	D₄×C₆₇	—	2	4	no	—
339	D₄×C₆₇	—	2	2	no	—
340	D₄×C₆₇	—	2	4	no	—
341	D₄×C₆₇	—	4	2	no	—
342	D₄×C₆₇	—	4	2	no	—
343	D₄×C₆₇	—	4	4	no	—
344	D₄×C₆₇	—	8	4	no	—
345	C₂×C₄×C₆₇	—	2	4	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	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	4	1	no	—
355	C₂×C₄×C₆₇	—	4	2	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	4	2	no	—
358	C₂×C₄×C₆₇	—	4	4	no	—
359	C₂×C₄×C₆₇	—	8	4	no	—
360	C₂×C₄×C₆₇	—	8	1	no	—
361	C₂×C₄×C₆₇	—	8	2	no	—
362	C₂×C₄×C₆₇	—	8	1	no	—
363	C₂×C₄×C₆₇	—	8	2	no	—
364	C₂×C₄×C₆₇	—	8	2	no	—
365	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
374	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
375	C₈×C₆₇	—	2	2	no	—
376	C₈×C₆₇	—	2	2	no	—
377	C₈×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	1	no	—
379	C₂²×C₆₇	—	2	1	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	#536	1	2	yes	—
387	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₆₇	—	2	1	no	—
389	C₄×C₆₇	—	2	2	no	—
390	C₄×C₆₇	—	2	1	no	—
391	C₄×C₆₇	—	2	1	no	—
392	C₄×C₆₇	—	2	2	no	—
393	C₄×C₆₇	—	2	1	no	—
394	C₄×C₆₇	—	2	2	no	—
395	C₄×C₆₇	—	4	4	no	—
396	C₄×C₆₇	—	4	2	no	—
397	C₄×C₆₇	—	4	1	no	—
398	C₄×C₆₇	—	4	1	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	1	no	—
401	C₄×C₆₇	—	4	1	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	#536	1	2	yes	—
404	C₄×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
405	#60886	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂×C₆₇	—	2	2	no	—
407	C₂×C₆₇	—	4	2	no	—
408	C₂×C₆₇	—	8	2	no	—
409	C₂×C₆₇	C₂×#536	1	1	yes	characteristic
410	C₂×C₆₇	#3585	1	1	yes	characteristic
411	C₂×C₆₇	#3586	1	1	yes	characteristic
412	#3511	C₂×C₆₇	1	1	yes	characteristic
413	#3504	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#3244	C₂×C₆₇	1	4	yes	complemented
415	#3243	C₂×C₆₇	1	4	yes	complemented
416	#3237	C₂×C₆₇	1	2	yes	complemented
417	#3236	C₂×C₆₇	1	2	yes	complemented
418	#3235	C₂×C₆₇	1	2	yes	complemented
419	#3234	C₂×C₆₇	1	2	yes	complemented
420	#3165	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#501	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3142	C₂×C₆₇	1	1	yes	characteristic, complemented
423	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
424	#3099	C₂×C₆₇	1	2	yes	complemented
425	#3098	C₂×C₆₇	1	2	yes	complemented
426	#3084	C₂×C₆₇	1	2	yes	complemented
427	#3083	C₂×C₆₇	1	2	yes	complemented
428	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
429	C₆₇	#60886	1	1	yes	characteristic, direct product factor, Sylow
430	#557	—	2	1	no	—
431	#557	—	2	1	no	—
432	#556	—	2	1	no	—
433	#555	—	2	1	no	—
434	#554	—	2	1	no	—
435	#554	—	2	1	no	—
436	#554	—	2	2	no	—
437	#554	—	2	2	no	—
438	#554	—	2	1	no	—
439	#553	—	2	2	no	—
440	#548	—	2	2	no	—
441	#547	—	2	1	no	—
442	#544	C₂²×C₆₇	1	1	yes	characteristic
443	#544	C₂²×C₆₇	1	1	yes	characteristic
444	#544	C₂²×C₆₇	1	2	yes	—
445	#544	C₂²×C₆₇	1	2	yes	—
446	#542	C₂²×C₆₇	1	4	yes	—
447	#537	C₂²×C₆₇	1	2	yes	—
448	#533	C₂²×C₆₇	1	2	yes	—
449	#533	C₂²×C₆₇	1	1	yes	characteristic
450	#533	C₂²×C₆₇	1	2	yes	—
451	#532	C₂²×C₆₇	1	1	yes	characteristic
452	#532	C₂²×C₆₇	1	2	yes	—
453	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#125	C₂²×C₆₇	1	2	yes	—
456	#520	C₂²×C₆₇	1	2	yes	—
457	#520	C₂²×C₆₇	1	1	yes	characteristic
458	#520	C₂²×C₆₇	1	1	yes	characteristic
459	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
460	#501	C₂²×C₆₇	1	2	yes	—
461	#501	C₂²×C₆₇	1	2	yes	—
462	#501	C₂²×C₆₇	1	4	yes	—
463	#501	C₂²×C₆₇	1	2	yes	—
464	#501	C₂²×C₆₇	1	2	yes	—
465	#500	C₂²×C₆₇	1	2	yes	—
466	#498	C₂²×C₆₇	1	2	yes	—
467	#491	C₂²×C₆₇	1	1	yes	characteristic
468	#491	C₂²×C₆₇	1	1	yes	characteristic
469	#491	C₂²×C₆₇	1	2	yes	—
470	#490	C₂²×C₆₇	1	1	yes	characteristic
471	#490	C₂²×C₆₇	1	1	yes	characteristic
472	#490	C₂²×C₆₇	1	2	yes	—
473	#489	C₂²×C₆₇	1	2	yes	—
474	#489	C₂²×C₆₇	1	2	yes	—
475	#488	C₂²×C₆₇	1	4	yes	—
476	#485	C₂²×C₆₇	1	4	yes	—
477	#485	C₂²×C₆₇	1	4	yes	—
478	#484	C₂²×C₆₇	1	4	yes	—
479	#483	C₂²×C₆₇	1	4	yes	—
480	#482	C₂²×C₆₇	1	4	yes	—
481	#482	C₂²×C₆₇	1	4	yes	—
482	#481	C₂²×C₆₇	1	4	yes	—
483	#480	C₂²×C₆₇	1	4	yes	—
484	#479	C₂²×C₆₇	1	4	yes	—
485	#479	C₂²×C₆₇	1	4	yes	—
486	#478	C₂²×C₆₇	1	4	yes	—
487	#478	C₂²×C₆₇	1	4	yes	—
488	#477	C₂²×C₆₇	1	4	yes	—
489	#476	C₂²×C₆₇	1	4	yes	—
490	#475	C₂²×C₆₇	1	4	yes	—
491	#474	C₂²×C₆₇	1	4	yes	—
492	#433	C₂²×C₆₇	1	4	yes	—
493	#432	C₂²×C₆₇	1	2	yes	—
494	#432	C₂²×C₆₇	1	2	yes	—
495	#428	C₂²×C₆₇	1	2	yes	—
496	#428	C₂²×C₆₇	1	2	yes	—
497	C₂×#107	C₂²×C₆₇	1	2	yes	—
498	C₂×#106	C₂²×C₆₇	1	2	yes	—
499	#424	C₂²×C₆₇	1	2	yes	—
500	#417	C₂²×C₆₇	1	2	yes	—
501	#417	C₂²×C₆₇	1	2	yes	—
502	#416	C₂²×C₆₇	1	2	yes	—
503	#416	C₂²×C₆₇	1	2	yes	—
504	#408	C₂²×C₆₇	1	2	yes	—
505	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×#41	—	2	2	no	—
508	C₂×#41	C₂³×C₆₇	1	2	yes	—
509	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×Q₈	—	2	1	no	—
511	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
512	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
524	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
526	#127	C₂³×C₆₇	1	1	yes	characteristic
527	#126	—	2	4	no	—
528	#125	—	2	1	no	—
529	#125	—	2	1	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	2	no	—
533	#125	—	2	1	no	—
534	#125	—	2	1	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	C₂³×C₆₇	1	2	yes	—
538	#125	C₂³×C₆₇	1	1	yes	characteristic
539	#125	C₂³×C₆₇	1	2	yes	—
540	#125	C₂³×C₆₇	1	2	yes	—
541	#125	C₂³×C₆₇	1	2	yes	—
542	#125	C₂³×C₆₇	1	1	yes	characteristic
543	#124	—	2	4	no	—
544	#124	—	2	2	no	—
545	#124	C₂³×C₆₇	1	2	yes	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
561	#121	—	2	2	no	—
562	#121	—	2	4	no	—
563	#121	—	2	1	no	—
564	#121	—	2	1	no	—
565	#121	—	2	2	no	—
566	#121	C₂³×C₆₇	1	4	yes	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
575	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	4	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
586	C₄×D₄	D₄×C₆₇	1	2	yes	—
587	C₄×D₄	D₄×C₆₇	1	2	yes	—
588	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
589	C₄×D₄	C₂³×C₆₇	1	4	yes	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	C₂³×C₆₇	1	1	yes	characteristic
593	#117	C₂³×C₆₇	1	1	yes	characteristic
594	#117	C₂³×C₆₇	1	2	yes	—
595	#117	C₂³×C₆₇	1	2	yes	—
596	#117	C₂³×C₆₇	1	1	yes	characteristic
597	#117	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	2	no	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
611	#107	C₂³×C₆₇	1	4	yes	—
612	#107	C₂³×C₆₇	1	4	yes	—
613	#107	C₂³×C₆₇	1	4	yes	—
614	#107	C₂³×C₆₇	1	4	yes	—
615	#106	C₂³×C₆₇	1	4	yes	—
616	#106	C₂³×C₆₇	1	4	yes	—
617	#106	C₂³×C₆₇	1	4	yes	—
618	#106	C₂³×C₆₇	1	4	yes	—
619	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
620	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
621	#103	C₂³×C₆₇	1	2	yes	—
622	#103	C₂³×C₆₇	1	2	yes	—
623	#103	C₂³×C₆₇	1	2	yes	—
624	#103	C₂³×C₆₇	1	2	yes	—
625	#103	C₂³×C₆₇	1	4	yes	—
626	#103	C₂³×C₆₇	1	4	yes	—
627	#102	C₂³×C₆₇	1	2	yes	—
628	#102	C₂³×C₆₇	1	2	yes	—
629	#102	C₂³×C₆₇	1	2	yes	—
630	#102	C₂³×C₆₇	1	2	yes	—
631	#102	C₂³×C₆₇	1	4	yes	—
632	#102	C₂³×C₆₇	1	4	yes	—
633	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
634	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
635	#97	C₂³×C₆₇	1	1	yes	characteristic
636	#97	C₂³×C₆₇	1	1	yes	characteristic
637	#97	C₂³×C₆₇	1	2	yes	—
638	#97	C₂³×C₆₇	1	2	yes	—
639	C₄×C₈	C₂³×C₆₇	1	2	yes	—
640	#41	—	2	4	no	—
641	#41	—	2	8	no	—
642	#41	—	8	4	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	8	2	no	—
650	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
651	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
657	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
658	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
668	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	M₁₆	—	2	4	no	—
673	C₂×C₈	—	2	4	no	—
674	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
675	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
676	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	4	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	C₂×D₄×C₆₇	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
706	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
707	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
711	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
725	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
726	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	1	no	—
731	C₄²	—	2	1	no	—
732	C₄²	C₂×D₄×C₆₇	1	2	yes	—
733	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₆₇	1	2	yes	—
736	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
738	C₄²	C₂⁴×C₆₇	1	2	yes	—
739	C₂³	—	2	2	no	—
740	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
741	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
742	Q₈	—	2	2	no	—
743	Q₈	—	2	4	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	8	2	no	—
746	Q₈	—	8	2	no	—
747	Q₈	—	8	1	no	—
748	Q₈	—	8	2	no	—
749	Q₈	—	8	1	no	—
750	D₄	—	2	4	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	8	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
785	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
786	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	#536×C₆₇	1	2	yes	—
799	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
800	C₄	—	2	1	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	#536×C₆₇	1	2	yes	—
816	C₄	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
817	C₂	—	2	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×#536×C₆₇	1	1	yes	characteristic
821	C₂	C₆₇×#3585	1	1	yes	characteristic
822	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3504	C₂	semidirect
3. C₆₇×#3244	C₂	semidirect
4. C₆₇×#3243	C₂	semidirect
5. C₆₇×#3237	C₂	semidirect
6. C₆₇×#3236	C₂	semidirect
7. C₆₇×#3235	C₂	semidirect
8. C₆₇×#3234	C₂	semidirect
9. C₆₇×#3165	C₂	semidirect
10. C₂×#501×C₆₇	C₂	semidirect
11. C₆₇×#3142	C₂	semidirect
12. C₆₇×#3135	C₂	semidirect
13. C₆₇×#3099	C₂	semidirect
14. C₆₇×#3098	C₂	semidirect
15. C₆₇×#3084	C₂	semidirect
16. C₆₇×#3083	C₂	semidirect
17. C₆₇×#2923	C₂	semidirect
405. #60886	C₆₇	direct (N × H)
413. #3504	C₂×C₆₇	semidirect
414. #3244	C₂×C₆₇	semidirect
415. #3243	C₂×C₆₇	semidirect
416. #3237	C₂×C₆₇	semidirect
417. #3236	C₂×C₆₇	semidirect
418. #3235	C₂×C₆₇	semidirect
419. #3234	C₂×C₆₇	semidirect
420. #3165	C₂×C₆₇	semidirect
421. C₂×#501	C₂×C₆₇	semidirect
422. #3142	C₂×C₆₇	semidirect
423. #3135	C₂×C₆₇	semidirect
424. #3099	C₂×C₆₇	semidirect
425. #3098	C₂×C₆₇	semidirect
426. #3084	C₂×C₆₇	semidirect
427. #3083	C₂×C₆₇	semidirect
428. #2923	C₂×C₆₇	semidirect
429. C₆₇	#60886	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₆₇×#3504	2
C₆₇×#3244	2
C₆₇×#3243	2
C₆₇×#3237	2
C₆₇×#3236	2
C₆₇×#3235	2
C₆₇×#3234	2
C₆₇×#3165	2
C₂×#501×C₆₇	2
C₆₇×#3142	2
C₆₇×#3135	2
C₆₇×#3099	2
C₆₇×#3098	2
C₆₇×#3084	2
C₆₇×#3083	2
C₆₇×#2923	2
#60886	67

Subgroups — C67×#60886 #30740137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60886 #30740137