Subgroups — C₆₇×#61002 #30740253

Order 17152.

1682 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3248	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3191	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3181	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#556×C₆₇	—	2	2	no	—
21	#554×C₆₇	—	2	2	no	—
22	#552×C₆₇	—	2	2	no	—
23	#552×C₆₇	—	2	2	no	—
24	#552×C₆₇	—	2	2	no	—
25	#552×C₆₇	—	2	2	no	—
26	#551×C₆₇	—	2	2	no	—
27	#551×C₆₇	—	2	2	no	—
28	#544×C₆₇	C₂²	1	2	yes	—
29	#542×C₆₇	C₂²	1	2	yes	—
30	#542×C₆₇	C₂²	1	2	yes	—
31	#541×C₆₇	C₂²	1	2	yes	—
32	#541×C₆₇	C₂²	1	2	yes	—
33	#536×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	C₂²	1	2	yes	—
35	#533×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#525×C₆₇	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	2	yes	—
41	#519×C₆₇	C₂²	1	2	yes	—
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#497×C₆₇	C₂²	1	2	yes	complemented
47	#495×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#491×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#488×C₆₇	C₂²	1	2	yes	complemented
52	#487×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	—
54	#485×C₆₇	C₂²	1	2	yes	—
55	#485×C₆₇	C₂²	1	2	yes	—
56	#484×C₆₇	C₂²	1	2	yes	—
57	#484×C₆₇	C₂²	1	2	yes	—
58	#483×C₆₇	C₂²	1	2	yes	—
59	#482×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	2	yes	complemented
62	#479×C₆₇	C₂²	1	2	yes	complemented
63	#479×C₆₇	C₂²	1	2	yes	complemented
64	#478×C₆₇	C₂²	1	2	yes	complemented
65	#477×C₆₇	C₂²	1	2	yes	complemented
66	#477×C₆₇	C₂²	1	2	yes	complemented
67	#475×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#467×C₆₇	C₂²	1	1	yes	characteristic
70	#467×C₆₇	C₂²	1	1	yes	characteristic
71	#467×C₆₇	C₂²	1	2	yes	—
72	#467×C₆₇	C₂²	1	1	yes	characteristic
73	#467×C₆₇	C₂²	1	2	yes	—
74	#467×C₆₇	C₂²	1	2	yes	—
75	#466×C₆₇	C₂²	1	1	yes	characteristic
76	#465×C₆₇	C₂²	1	2	yes	—
77	#465×C₆₇	C₂²	1	2	yes	—
78	#465×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#464×C₆₇	C₂²	1	2	yes	complemented
81	#464×C₆₇	C₂²	1	2	yes	complemented
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#462×C₆₇	C₂²	1	2	yes	complemented
84	#462×C₆₇	C₂²	1	2	yes	complemented
85	#462×C₆₇	C₂²	1	2	yes	complemented
86	#461×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	2	yes	—
91	#451×C₆₇	C₂²	1	2	yes	—
92	#451×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#448×C₆₇	C₂²	1	2	yes	—
95	#441×C₆₇	C₂²	1	2	yes	complemented
96	#441×C₆₇	C₂²	1	2	yes	complemented
97	#440×C₆₇	C₂²	1	2	yes	complemented
98	#440×C₆₇	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#433×C₆₇	C₂²	1	2	yes	—
106	#433×C₆₇	C₂²	1	2	yes	—
107	#433×C₆₇	C₂²	1	2	yes	—
108	#433×C₆₇	C₂²	1	2	yes	—
109	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
110	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
111	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
112	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₇	C₂³	1	2	yes	—
116	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₆₇	—	2	2	no	—
133	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	#126×C₆₇	—	2	2	no	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#125×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	2	no	—
147	#125×C₆₇	—	2	2	no	—
148	#125×C₆₇	—	2	2	no	—
149	#125×C₆₇	—	2	2	no	—
150	#125×C₆₇	—	2	2	no	—
151	#125×C₆₇	—	2	2	no	—
152	#125×C₆₇	C₂³	1	2	yes	—
153	#125×C₆₇	C₂³	1	2	yes	—
154	#124×C₆₇	—	2	2	no	—
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	C₂³	1	2	yes	—
157	#124×C₆₇	C₂³	1	2	yes	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	—	2	2	no	—
172	C₂²⋊Q₈×C₆₇	—	2	2	no	—
173	C₂²⋊Q₈×C₆₇	—	2	2	no	—
174	C₂²⋊Q₈×C₆₇	—	2	2	no	—
175	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#120×C₆₇	—	2	2	no	—
184	C₄×Q₈×C₆₇	—	2	2	no	—
185	C₄×Q₈×C₆₇	—	2	2	no	—
186	C₄×Q₈×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	—	2	2	no	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
190	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
192	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	#117×C₆₇	—	2	2	no	—
203	#117×C₆₇	—	2	2	no	—
204	#117×C₆₇	—	2	2	no	—
205	#117×C₆₇	—	2	2	no	—
206	#117×C₆₇	—	2	2	no	—
207	#117×C₆₇	—	2	2	no	—
208	#117×C₆₇	—	2	2	no	—
209	#117×C₆₇	D₄	1	2	yes	—
210	#117×C₆₇	D₄	1	2	yes	—
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	2	yes	—
213	#117×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
215	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	#107×C₆₇	C₂³	1	1	yes	characteristic
225	#107×C₆₇	C₂³	1	2	yes	—
226	#107×C₆₇	C₂³	1	2	yes	—
227	#107×C₆₇	C₂³	1	2	yes	—
228	#107×C₆₇	C₂³	1	1	yes	characteristic
229	#107×C₆₇	C₂³	1	1	yes	characteristic
230	#107×C₆₇	C₂³	1	1	yes	characteristic
231	#106×C₆₇	C₂³	1	2	yes	—
232	#106×C₆₇	C₂³	1	2	yes	—
233	#106×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#103×C₆₇	C₂³	1	2	yes	—
243	#103×C₆₇	C₂³	1	2	yes	—
244	#103×C₆₇	C₂³	1	2	yes	—
245	#103×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#103×C₆₇	C₂³	1	2	yes	—
249	#103×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	#97×C₆₇	C₂³	1	2	yes	—
259	#97×C₆₇	C₂³	1	2	yes	—
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
264	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
265	#41×C₆₇	—	4	2	no	—
266	#41×C₆₇	—	4	2	no	—
267	C₂×Q₈×C₆₇	—	2	2	no	—
268	C₂×Q₈×C₆₇	—	2	2	no	—
269	C₂×Q₈×C₆₇	—	2	2	no	—
270	C₂×Q₈×C₆₇	—	4	2	no	—
271	C₂×Q₈×C₆₇	—	4	2	no	—
272	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	4	1	no	—
285	C₂²×C₄×C₆₇	—	4	1	no	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	Q₁₆×C₆₇	—	4	1	no	—
295	Q₁₆×C₆₇	—	4	2	no	—
296	Q₁₆×C₆₇	—	4	2	no	—
297	Q₁₆×C₆₇	—	4	1	no	—
298	Q₁₆×C₆₇	—	4	2	no	—
299	Q₁₆×C₆₇	—	4	1	no	—
300	SD₁₆×C₆₇	—	4	2	no	—
301	SD₁₆×C₆₇	—	4	2	no	—
302	SD₁₆×C₆₇	—	4	2	no	—
303	D₈×C₆₇	—	4	1	no	—
304	C₂×C₈×C₆₇	—	4	1	no	—
305	C₂×C₈×C₆₇	—	4	1	no	—
306	C₂×C₈×C₆₇	—	4	1	no	—
307	C₂×C₈×C₆₇	—	4	1	no	—
308	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
311	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
312	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₄²×C₆₇	—	2	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₆₇	C₂×D₄	1	2	yes	—
373	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₆₇	C₂⁴	1	2	yes	—
375	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	4	1	no	—
380	C₂³×C₆₇	—	4	1	no	—
381	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
382	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₆₇	—	2	2	no	—
384	Q₈×C₆₇	—	2	2	no	—
385	Q₈×C₆₇	—	2	2	no	—
386	Q₈×C₆₇	—	2	2	no	—
387	Q₈×C₆₇	—	2	2	no	—
388	Q₈×C₆₇	—	2	2	no	—
389	Q₈×C₆₇	—	4	4	no	—
390	Q₈×C₆₇	—	8	2	no	—
391	Q₈×C₆₇	—	8	2	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	2	no	—
394	D₄×C₆₇	—	4	4	no	—
395	D₄×C₆₇	—	4	4	no	—
396	D₄×C₆₇	—	8	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	4	1	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	—	4	1	no	—
413	C₂×C₄×C₆₇	—	4	1	no	—
414	C₂×C₄×C₆₇	—	4	4	no	—
415	C₂×C₄×C₆₇	—	4	4	no	—
416	C₂×C₄×C₆₇	—	8	2	no	—
417	C₂×C₄×C₆₇	—	8	2	no	—
418	C₂×C₄×C₆₇	—	8	2	no	—
419	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
428	C₈×C₆₇	—	2	1	no	—
429	C₈×C₆₇	—	2	1	no	—
430	C₈×C₆₇	—	2	2	no	—
431	C₈×C₆₇	—	2	2	no	—
432	C₈×C₆₇	—	2	1	no	—
433	C₈×C₆₇	—	2	1	no	—
434	C₂²×C₆₇	—	2	1	no	—
435	C₂²×C₆₇	—	2	1	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	8	2	no	—
443	C₂²×C₆₇	#578	1	2	yes	—
444	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	2	2	no	—
447	C₄×C₆₇	—	2	1	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	1	no	—
450	C₄×C₆₇	—	2	1	no	—
451	C₄×C₆₇	—	2	2	no	—
452	C₄×C₆₇	—	2	1	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	2	no	—
457	C₄×C₆₇	—	4	2	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	—	4	2	no	—
460	C₄×C₆₇	#585	1	1	yes	characteristic
461	C₄×C₆₇	#585	1	1	yes	characteristic
462	#61002	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂×C₆₇	—	2	2	no	—
464	C₂×C₆₇	—	4	2	no	—
465	C₂×C₆₇	—	8	2	no	—
466	C₂×C₆₇	#3449	1	1	yes	characteristic
467	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
468	C₂×C₆₇	#3584	1	1	yes	characteristic
469	#3495	C₂×C₆₇	1	2	yes	complemented
470	#3250	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#3249	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3248	C₂×C₆₇	1	2	yes	complemented
473	#3243	C₂×C₆₇	1	2	yes	complemented
474	#3242	C₂×C₆₇	1	2	yes	complemented
475	#3225	C₂×C₆₇	1	2	yes	complemented
476	#3223	C₂×C₆₇	1	2	yes	complemented
477	#3191	C₂×C₆₇	1	1	yes	characteristic
478	#3190	C₂×C₆₇	1	2	yes	complemented
479	#3189	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#3181	C₂×C₆₇	1	2	yes	complemented
481	#3170	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#3168	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#3127	C₂×C₆₇	1	2	yes	complemented
484	#3124	C₂×C₆₇	1	2	yes	complemented
485	#3121	C₂×C₆₇	1	2	yes	complemented
486	#3120	C₂×C₆₇	1	2	yes	complemented
487	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
488	C₆₇	#61002	1	1	yes	characteristic, direct product factor, Sylow
489	#556	—	2	2	no	—
490	#554	—	2	2	no	—
491	#552	—	2	2	no	—
492	#552	—	2	2	no	—
493	#552	—	2	2	no	—
494	#552	—	2	2	no	—
495	#551	—	2	2	no	—
496	#551	—	2	2	no	—
497	#544	C₂²×C₆₇	1	2	yes	—
498	#542	C₂²×C₆₇	1	2	yes	—
499	#542	C₂²×C₆₇	1	2	yes	—
500	#541	C₂²×C₆₇	1	2	yes	—
501	#541	C₂²×C₆₇	1	2	yes	—
502	#536	C₂²×C₆₇	1	2	yes	—
503	#533	C₂²×C₆₇	1	2	yes	—
504	#533	C₂²×C₆₇	1	2	yes	—
505	#529	C₂²×C₆₇	1	2	yes	—
506	#529	C₂²×C₆₇	1	2	yes	—
507	#525	C₂²×C₆₇	1	2	yes	—
508	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
509	#520	C₂²×C₆₇	1	2	yes	—
510	#519	C₂²×C₆₇	1	2	yes	—
511	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
512	#501	C₂²×C₆₇	1	2	yes	complemented
513	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	#497	C₂²×C₆₇	1	2	yes	complemented
516	#495	C₂²×C₆₇	1	1	yes	characteristic, complemented
517	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	#491	C₂²×C₆₇	1	2	yes	complemented
519	#489	C₂²×C₆₇	1	2	yes	complemented
520	#488	C₂²×C₆₇	1	2	yes	complemented
521	#487	C₂²×C₆₇	1	2	yes	complemented
522	#485	C₂²×C₆₇	1	2	yes	—
523	#485	C₂²×C₆₇	1	2	yes	—
524	#485	C₂²×C₆₇	1	2	yes	—
525	#484	C₂²×C₆₇	1	2	yes	—
526	#484	C₂²×C₆₇	1	2	yes	—
527	#483	C₂²×C₆₇	1	2	yes	—
528	#482	C₂²×C₆₇	1	2	yes	—
529	#480	C₂²×C₆₇	1	2	yes	—
530	#479	C₂²×C₆₇	1	2	yes	complemented
531	#479	C₂²×C₆₇	1	2	yes	complemented
532	#479	C₂²×C₆₇	1	2	yes	complemented
533	#478	C₂²×C₆₇	1	2	yes	complemented
534	#477	C₂²×C₆₇	1	2	yes	complemented
535	#477	C₂²×C₆₇	1	2	yes	complemented
536	#475	C₂²×C₆₇	1	2	yes	complemented
537	#474	C₂²×C₆₇	1	2	yes	complemented
538	#467	C₂²×C₆₇	1	1	yes	characteristic
539	#467	C₂²×C₆₇	1	1	yes	characteristic
540	#467	C₂²×C₆₇	1	2	yes	—
541	#467	C₂²×C₆₇	1	1	yes	characteristic
542	#467	C₂²×C₆₇	1	2	yes	—
543	#467	C₂²×C₆₇	1	2	yes	—
544	#466	C₂²×C₆₇	1	1	yes	characteristic
545	#465	C₂²×C₆₇	1	2	yes	—
546	#465	C₂²×C₆₇	1	2	yes	—
547	#465	C₂²×C₆₇	1	2	yes	—
548	#464	C₂²×C₆₇	1	2	yes	complemented
549	#464	C₂²×C₆₇	1	2	yes	complemented
550	#464	C₂²×C₆₇	1	2	yes	complemented
551	#463	C₂²×C₆₇	1	2	yes	complemented
552	#462	C₂²×C₆₇	1	2	yes	complemented
553	#462	C₂²×C₆₇	1	2	yes	complemented
554	#462	C₂²×C₆₇	1	2	yes	complemented
555	#461	C₂²×C₆₇	1	2	yes	complemented
556	#452	C₂²×C₆₇	1	2	yes	—
557	#452	C₂²×C₆₇	1	2	yes	—
558	#452	C₂²×C₆₇	1	2	yes	—
559	#451	C₂²×C₆₇	1	2	yes	—
560	#451	C₂²×C₆₇	1	2	yes	—
561	#451	C₂²×C₆₇	1	2	yes	—
562	#449	C₂²×C₆₇	1	2	yes	—
563	#448	C₂²×C₆₇	1	2	yes	—
564	#441	C₂²×C₆₇	1	2	yes	complemented
565	#441	C₂²×C₆₇	1	2	yes	complemented
566	#440	C₂²×C₆₇	1	2	yes	complemented
567	#440	C₂²×C₆₇	1	2	yes	complemented
568	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
571	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
573	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	#433	C₂²×C₆₇	1	2	yes	—
575	#433	C₂²×C₆₇	1	2	yes	—
576	#433	C₂²×C₆₇	1	2	yes	—
577	#433	C₂²×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
579	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
580	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
581	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
582	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
584	C₂×#41	C₂³×C₆₇	1	2	yes	—
585	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
586	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
590	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
605	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	C₂³×C₆₇	1	2	yes	—
622	#125	C₂³×C₆₇	1	2	yes	—
623	#124	—	2	2	no	—
624	#124	—	2	2	no	—
625	#124	C₂³×C₆₇	1	2	yes	—
626	#124	C₂³×C₆₇	1	2	yes	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
650	#121	C₂³×C₆₇	1	2	yes	—
651	#121	C₂³×C₆₇	1	2	yes	—
652	#120	—	2	2	no	—
653	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	—	2	2	no	—
657	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
658	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
659	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
660	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
661	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
662	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	C₂³×C₆₇	1	2	yes	—
670	C₄×D₄	C₂³×C₆₇	1	2	yes	—
671	#117	—	2	2	no	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	D₄×C₆₇	1	2	yes	—
679	#117	D₄×C₆₇	1	2	yes	—
680	#117	C₂³×C₆₇	1	2	yes	—
681	#117	C₂³×C₆₇	1	2	yes	—
682	#117	C₂³×C₆₇	1	2	yes	—
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	—	2	2	no	—
685	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
686	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	—	2	2	no	—
689	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
693	#107	C₂³×C₆₇	1	1	yes	characteristic
694	#107	C₂³×C₆₇	1	1	yes	characteristic
695	#107	C₂³×C₆₇	1	2	yes	—
696	#107	C₂³×C₆₇	1	1	yes	characteristic
697	#107	C₂³×C₆₇	1	1	yes	characteristic
698	#107	C₂³×C₆₇	1	2	yes	—
699	#107	C₂³×C₆₇	1	2	yes	—
700	#106	C₂³×C₆₇	1	2	yes	—
701	#106	C₂³×C₆₇	1	2	yes	—
702	#106	C₂³×C₆₇	1	2	yes	—
703	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
704	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
705	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
706	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
707	#103	C₂³×C₆₇	1	2	yes	—
708	#103	C₂³×C₆₇	1	2	yes	—
709	#103	C₂³×C₆₇	1	2	yes	—
710	#103	C₂³×C₆₇	1	2	yes	—
711	#103	C₂³×C₆₇	1	2	yes	—
712	#103	C₂³×C₆₇	1	2	yes	—
713	#103	C₂³×C₆₇	1	2	yes	—
714	#103	C₂³×C₆₇	1	2	yes	—
715	#103	C₂³×C₆₇	1	2	yes	—
716	#103	C₂³×C₆₇	1	2	yes	—
717	#103	C₂³×C₆₇	1	2	yes	—
718	#103	C₂³×C₆₇	1	2	yes	—
719	#102	C₂³×C₆₇	1	2	yes	—
720	#102	C₂³×C₆₇	1	2	yes	—
721	#102	C₂³×C₆₇	1	2	yes	—
722	#102	C₂³×C₆₇	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
727	#97	C₂³×C₆₇	1	2	yes	—
728	#97	C₂³×C₆₇	1	2	yes	—
729	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
731	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
733	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
734	#41	—	4	2	no	—
735	#41	—	4	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	4	2	no	—
740	C₂×Q₈	—	4	2	no	—
741	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
743	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
758	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
760	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
763	Q₁₆	—	4	1	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	2	no	—
766	Q₁₆	—	4	1	no	—
767	Q₁₆	—	4	2	no	—
768	Q₁₆	—	4	1	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	SD₁₆	—	4	2	no	—
772	D₈	—	4	1	no	—
773	C₂×C₈	—	4	1	no	—
774	C₂×C₈	—	4	1	no	—
775	C₂×C₈	—	4	1	no	—
776	C₂×C₈	—	4	1	no	—
777	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
782	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
807	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
841	C₄²	C₂×D₄×C₆₇	1	2	yes	—
842	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
843	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
845	C₄²	C₂⁴×C₆₇	1	2	yes	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
851	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	8	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	8	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
896	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
897	C₈	—	2	1	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	1	no	—
902	C₈	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	8	2	no	—
912	C₂²	#578×C₆₇	1	2	yes	—
913	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	#585×C₆₇	1	1	yes	characteristic
930	C₄	#585×C₆₇	1	1	yes	characteristic
931	C₂	—	2	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₆₇×#3449	1	1	yes	characteristic
935	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
936	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×#3191	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3495	C₂	semidirect
2. C₆₇×#3250	C₂	semidirect
3. C₆₇×#3249	C₂	semidirect
4. C₆₇×#3248	C₂	semidirect
5. C₆₇×#3243	C₂	semidirect
6. C₆₇×#3242	C₂	semidirect
7. C₆₇×#3225	C₂	semidirect
8. C₆₇×#3223	C₂	semidirect
10. C₆₇×#3190	C₂	semidirect
11. C₆₇×#3189	C₂	semidirect
12. C₆₇×#3181	C₂	semidirect
13. C₆₇×#3170	C₂	semidirect
14. C₆₇×#3168	C₂	semidirect
15. C₆₇×#3127	C₂	semidirect
16. C₆₇×#3124	C₂	semidirect
17. C₆₇×#3121	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₂×#433×C₆₇	C₂	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #500×C₆₇	C₂²	semidirect
45. #499×C₆₇	C₂²	semidirect
46. #497×C₆₇	C₂²	semidirect
47. #495×C₆₇	C₂²	semidirect
48. #494×C₆₇	C₂²	semidirect
49. #491×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
52. #487×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #479×C₆₇	C₂²	semidirect
63. #479×C₆₇	C₂²	semidirect
64. #478×C₆₇	C₂²	semidirect
65. #477×C₆₇	C₂²	semidirect
66. #477×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #464×C₆₇	C₂²	semidirect
81. #464×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
83. #462×C₆₇	C₂²	semidirect
84. #462×C₆₇	C₂²	semidirect
85. #462×C₆₇	C₂²	semidirect
86. #461×C₆₇	C₂²	semidirect
95. #441×C₆₇	C₂²	semidirect
96. #441×C₆₇	C₂²	semidirect
97. #440×C₆₇	C₂²	semidirect
98. #440×C₆₇	C₂²	semidirect
99. C₄×Q₁₆×C₆₇	C₂²	semidirect
100. C₄×Q₁₆×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
102. C₄×Q₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
462. #61002	C₆₇	direct (N × H)
469. #3495	C₂×C₆₇	semidirect
470. #3250	C₂×C₆₇	semidirect
471. #3249	C₂×C₆₇	semidirect
472. #3248	C₂×C₆₇	semidirect
473. #3243	C₂×C₆₇	semidirect
474. #3242	C₂×C₆₇	semidirect
475. #3225	C₂×C₆₇	semidirect
476. #3223	C₂×C₆₇	semidirect
478. #3190	C₂×C₆₇	semidirect
479. #3189	C₂×C₆₇	semidirect
480. #3181	C₂×C₆₇	semidirect
481. #3170	C₂×C₆₇	semidirect
482. #3168	C₂×C₆₇	semidirect
483. #3127	C₂×C₆₇	semidirect
484. #3124	C₂×C₆₇	semidirect
485. #3121	C₂×C₆₇	semidirect
486. #3120	C₂×C₆₇	semidirect
487. C₂×#433	C₂×C₆₇	semidirect
488. C₆₇	#61002	direct (N × H)
512. #501	C₂²×C₆₇	semidirect
513. #500	C₂²×C₆₇	semidirect
514. #499	C₂²×C₆₇	semidirect
515. #497	C₂²×C₆₇	semidirect
516. #495	C₂²×C₆₇	semidirect
517. #494	C₂²×C₆₇	semidirect
518. #491	C₂²×C₆₇	semidirect
519. #489	C₂²×C₆₇	semidirect
520. #488	C₂²×C₆₇	semidirect
521. #487	C₂²×C₆₇	semidirect
530. #479	C₂²×C₆₇	semidirect
531. #479	C₂²×C₆₇	semidirect
532. #479	C₂²×C₆₇	semidirect
533. #478	C₂²×C₆₇	semidirect
534. #477	C₂²×C₆₇	semidirect
535. #477	C₂²×C₆₇	semidirect
536. #475	C₂²×C₆₇	semidirect
537. #474	C₂²×C₆₇	semidirect
548. #464	C₂²×C₆₇	semidirect
549. #464	C₂²×C₆₇	semidirect
550. #464	C₂²×C₆₇	semidirect
551. #463	C₂²×C₆₇	semidirect
552. #462	C₂²×C₆₇	semidirect
553. #462	C₂²×C₆₇	semidirect
554. #462	C₂²×C₆₇	semidirect
555. #461	C₂²×C₆₇	semidirect
564. #441	C₂²×C₆₇	semidirect
565. #441	C₂²×C₆₇	semidirect
566. #440	C₂²×C₆₇	semidirect
567. #440	C₂²×C₆₇	semidirect
568. C₄×Q₁₆	C₂²×C₆₇	semidirect
569. C₄×Q₁₆	C₂²×C₆₇	semidirect
570. C₄×Q₁₆	C₂²×C₆₇	semidirect
571. C₄×Q₁₆	C₂²×C₆₇	semidirect
572. C₄×SD₁₆	C₂²×C₆₇	semidirect
573. C₄×D₈	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×#3495	2
C₆₇×#3250	2
C₆₇×#3249	2
C₆₇×#3248	2
C₆₇×#3243	2
C₆₇×#3242	2
C₆₇×#3225	2
C₆₇×#3223	2
C₆₇×#3191	2
C₆₇×#3190	2
C₆₇×#3189	2
C₆₇×#3181	2
C₆₇×#3170	2
C₆₇×#3168	2
C₆₇×#3127	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3120	2
C₂×#433×C₆₇	2
#61002	67

Subgroups — C67×#61002 #30740253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61002 #30740253