Subgroups — C₆₇×#61755 #30741006

Order 17152.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3536	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3344	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3311	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	#562×C₆₇	—	2	2	no	—
21	#556×C₆₇	C₂²	1	2	yes	—
22	#554×C₆₇	C₂²	1	2	yes	—
23	#554×C₆₇	C₂²	1	2	yes	complemented
24	#552×C₆₇	—	2	2	no	—
25	#552×C₆₇	C₂²	1	2	yes	—
26	#552×C₆₇	C₂²	1	2	yes	complemented
27	#551×C₆₇	—	2	2	no	—
28	#548×C₆₇	C₂²	1	2	yes	—
29	#547×C₆₇	C₂²	1	2	yes	—
30	#546×C₆₇	—	2	2	no	—
31	#546×C₆₇	C₂²	1	2	yes	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#543×C₆₇	—	2	1	no	—
34	#542×C₆₇	—	2	1	no	—
35	#542×C₆₇	C₂²	1	2	yes	—
36	#541×C₆₇	—	2	1	no	—
37	#539×C₆₇	—	2	1	no	—
38	#538×C₆₇	—	2	1	no	—
39	#537×C₆₇	—	2	1	no	—
40	#537×C₆₇	C₂²	1	2	yes	—
41	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#533×C₆₇	—	2	1	no	—
43	#529×C₆₇	—	2	1	no	—
44	#525×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
48	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
51	#501×C₆₇	C₂²	1	2	yes	complemented
52	#498×C₆₇	C₂²	1	2	yes	complemented
53	#489×C₆₇	C₂²	1	2	yes	complemented
54	#488×C₆₇	C₂²	1	2	yes	complemented
55	#485×C₆₇	C₂²	1	2	yes	—
56	#485×C₆₇	C₂²	1	2	yes	—
57	#485×C₆₇	C₂²	1	2	yes	complemented
58	#485×C₆₇	C₂²	1	2	yes	complemented
59	#485×C₆₇	C₂²	1	2	yes	complemented
60	#484×C₆₇	C₂²	1	2	yes	complemented
61	#483×C₆₇	C₂²	1	2	yes	—
62	#483×C₆₇	C₂²	1	2	yes	complemented
63	#483×C₆₇	C₂²	1	2	yes	complemented
64	#483×C₆₇	C₂²	1	2	yes	complemented
65	#483×C₆₇	C₂²	1	2	yes	complemented
66	#482×C₆₇	C₂²	1	2	yes	—
67	#482×C₆₇	C₂²	1	2	yes	—
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#481×C₆₇	C₂²	1	2	yes	—
70	#481×C₆₇	C₂²	1	2	yes	—
71	#481×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	—
73	#479×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	complemented
75	#477×C₆₇	C₂²	1	2	yes	complemented
76	#476×C₆₇	C₂²	1	2	yes	complemented
77	#475×C₆₇	C₂²	1	2	yes	complemented
78	#475×C₆₇	C₂²	1	2	yes	complemented
79	#470×C₆₇	C₂²	1	2	yes	—
80	#470×C₆₇	C₂²	1	2	yes	—
81	#470×C₆₇	C₂²	1	2	yes	complemented
82	#468×C₆₇	C₂²	1	2	yes	complemented
83	#467×C₆₇	C₂²	1	2	yes	complemented
84	#465×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#464×C₆₇	C₂²	1	2	yes	complemented
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	complemented
92	#451×C₆₇	C₂²	1	2	yes	complemented
93	#450×C₆₇	C₂²	1	2	yes	—
94	#448×C₆₇	C₂²	1	2	yes	—
95	#441×C₆₇	C₂²	1	2	yes	complemented
96	#440×C₆₇	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
99	#436×C₆₇	C₂²	1	2	yes	—
100	#435×C₆₇	C₂²	1	2	yes	—
101	#435×C₆₇	C₂²	1	2	yes	complemented
102	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
103	#433×C₆₇	C₂²	1	2	yes	complemented
104	#428×C₆₇	C₂²	1	1	yes	characteristic
105	#428×C₆₇	C₂²	1	1	yes	characteristic
106	#428×C₆₇	C₂²	1	2	yes	complemented
107	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
110	#418×C₆₇	C₂²	1	1	yes	characteristic
111	#418×C₆₇	C₂²	1	1	yes	characteristic
112	#417×C₆₇	C₂²	1	2	yes	complemented
113	#416×C₆₇	C₂²	1	2	yes	complemented
114	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
119	C₂×#41×C₆₇	—	2	2	no	—
120	C₂×#41×C₆₇	C₂³	1	2	yes	—
121	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	—	2	1	no	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	—	2	1	no	—
138	C₄⋊Q₈×C₆₇	—	2	1	no	—
139	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
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	#126×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	1	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	C₂³	1	2	yes	—
152	#124×C₆₇	—	2	1	no	—
153	#124×C₆₇	—	2	2	no	—
154	#124×C₆₇	—	2	2	no	—
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	C₂³	1	2	yes	—
157	#123×C₆₇	—	2	2	no	—
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	D₄	1	2	yes	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	1	no	—
167	C₂²⋊Q₈×C₆₇	—	2	1	no	—
168	C₂²⋊Q₈×C₆₇	—	2	1	no	—
169	C₂²⋊Q₈×C₆₇	—	2	1	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	—	2	2	no	—
176	C₂²⋊Q₈×C₆₇	—	2	2	no	—
177	C₂²⋊Q₈×C₆₇	—	2	2	no	—
178	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
179	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
180	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
185	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
187	#121×C₆₇	—	2	2	no	—
188	#121×C₆₇	—	2	2	no	—
189	#121×C₆₇	—	2	2	no	—
190	#121×C₆₇	—	2	2	no	—
191	#121×C₆₇	—	2	1	no	—
192	#121×C₆₇	—	2	1	no	—
193	#121×C₆₇	—	2	2	no	—
194	#121×C₆₇	D₄	1	1	yes	characteristic
195	#121×C₆₇	D₄	1	1	yes	characteristic
196	#121×C₆₇	C₂³	1	2	yes	—
197	#121×C₆₇	C₂³	1	2	yes	—
198	#121×C₆₇	C₂³	1	2	yes	—
199	#120×C₆₇	—	2	2	no	—
200	#120×C₆₇	D₄	1	2	yes	—
201	C₄×Q₈×C₆₇	—	2	1	no	—
202	C₄×Q₈×C₆₇	—	2	1	no	—
203	C₄×Q₈×C₆₇	—	2	1	no	—
204	C₄×Q₈×C₆₇	—	2	2	no	—
205	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
206	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
207	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
208	C₄×D₄×C₆₇	—	2	1	no	—
209	C₄×D₄×C₆₇	—	2	2	no	—
210	C₄×D₄×C₆₇	—	2	2	no	—
211	C₄×D₄×C₆₇	—	2	2	no	—
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	C₂³	1	2	yes	—
214	C₄×D₄×C₆₇	C₂³	1	2	yes	—
215	C₄×D₄×C₆₇	C₂³	1	2	yes	—
216	#117×C₆₇	—	2	1	no	—
217	#117×C₆₇	—	2	1	no	—
218	#117×C₆₇	—	2	2	no	—
219	#117×C₆₇	—	2	2	no	—
220	#117×C₆₇	—	2	2	no	—
221	#117×C₆₇	C₂³	1	1	yes	characteristic
222	#117×C₆₇	C₂³	1	1	yes	characteristic
223	#117×C₆₇	C₂³	1	2	yes	—
224	#117×C₆₇	C₂³	1	1	yes	characteristic
225	#117×C₆₇	C₂³	1	1	yes	characteristic
226	#117×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
228	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
229	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
241	C₂×C₄²×C₆₇	—	2	1	no	—
242	#107×C₆₇	C₂³	1	2	yes	—
243	#107×C₆₇	C₂³	1	2	yes	—
244	#107×C₆₇	C₂³	1	2	yes	—
245	#107×C₆₇	C₂³	1	2	yes	—
246	#106×C₆₇	C₂³	1	2	yes	—
247	#106×C₆₇	C₂³	1	2	yes	—
248	#106×C₆₇	C₂³	1	2	yes	—
249	#106×C₆₇	C₂³	1	2	yes	—
250	#106×C₆₇	C₂³	1	2	yes	—
251	#106×C₆₇	C₂³	1	2	yes	—
252	#106×C₆₇	C₂³	1	2	yes	—
253	#106×C₆₇	C₂³	1	2	yes	—
254	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
256	#103×C₆₇	C₂³	1	2	yes	—
257	#103×C₆₇	C₂³	1	2	yes	—
258	#103×C₆₇	C₂³	1	2	yes	—
259	#103×C₆₇	C₂³	1	2	yes	—
260	#103×C₆₇	C₂³	1	2	yes	—
261	#103×C₆₇	C₂³	1	2	yes	—
262	#103×C₆₇	C₂³	1	2	yes	—
263	#103×C₆₇	C₂³	1	2	yes	—
264	#103×C₆₇	C₂³	1	2	yes	—
265	#103×C₆₇	C₂³	1	2	yes	—
266	#102×C₆₇	C₂³	1	2	yes	—
267	#102×C₆₇	C₂³	1	2	yes	—
268	#102×C₆₇	C₂³	1	2	yes	—
269	#102×C₆₇	C₂³	1	2	yes	—
270	#102×C₆₇	C₂³	1	2	yes	—
271	#102×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	#97×C₆₇	C₂³	1	2	yes	—
279	C₄×C₈×C₆₇	C₂³	1	2	yes	—
280	C₂⁴×C₆₇	—	2	1	no	—
281	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
282	#41×C₆₇	—	4	1	no	—
283	#41×C₆₇	—	4	1	no	—
284	#41×C₆₇	—	4	2	no	—
285	#41×C₆₇	—	4	2	no	—
286	#41×C₆₇	—	8	4	no	—
287	C₂×Q₈×C₆₇	—	2	1	no	—
288	C₂×Q₈×C₆₇	—	2	2	no	—
289	C₂×Q₈×C₆₇	—	2	1	no	—
290	C₂×Q₈×C₆₇	—	2	2	no	—
291	C₂×Q₈×C₆₇	—	4	1	no	—
292	C₂×Q₈×C₆₇	—	4	1	no	—
293	C₂×Q₈×C₆₇	—	4	1	no	—
294	C₂×Q₈×C₆₇	—	4	1	no	—
295	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	2	1	no	—
303	C₂×D₄×C₆₇	—	4	1	no	—
304	C₂×D₄×C₆₇	—	4	1	no	—
305	C₂×D₄×C₆₇	—	8	2	no	—
306	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₇	—	2	1	no	—
312	C₂²×C₄×C₆₇	—	2	1	no	—
313	C₂²×C₄×C₆₇	—	2	1	no	—
314	C₂²×C₄×C₆₇	—	2	1	no	—
315	C₂²×C₄×C₆₇	—	2	1	no	—
316	C₂²×C₄×C₆₇	—	2	1	no	—
317	C₂²×C₄×C₆₇	—	2	1	no	—
318	C₂²×C₄×C₆₇	—	2	2	no	—
319	C₂²×C₄×C₆₇	—	2	2	no	—
320	C₂²×C₄×C₆₇	—	2	2	no	—
321	C₂²×C₄×C₆₇	—	2	2	no	—
322	C₂²×C₄×C₆₇	—	4	1	no	—
323	C₂²×C₄×C₆₇	—	4	1	no	—
324	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	Q₁₆×C₆₇	—	4	2	no	—
332	Q₁₆×C₆₇	—	4	2	no	—
333	SD₁₆×C₆₇	—	4	2	no	—
334	SD₁₆×C₆₇	—	4	2	no	—
335	M₁₆×C₆₇	—	4	2	no	—
336	M₁₆×C₆₇	—	4	1	no	—
337	M₁₆×C₆₇	—	4	1	no	—
338	C₂×C₈×C₆₇	—	4	1	no	—
339	C₂×C₈×C₆₇	—	4	2	no	—
340	C₂×C₈×C₆₇	—	4	1	no	—
341	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
343	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
344	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₇	—	2	2	no	—
346	C₄⋊C₄×C₆₇	—	2	2	no	—
347	C₄⋊C₄×C₆₇	—	2	2	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	1	no	—
350	C₄⋊C₄×C₆₇	—	2	1	no	—
351	C₄⋊C₄×C₆₇	—	2	1	no	—
352	C₄⋊C₄×C₆₇	—	2	2	no	—
353	C₄⋊C₄×C₆₇	—	2	1	no	—
354	C₄⋊C₄×C₆₇	—	2	2	no	—
355	C₄⋊C₄×C₆₇	—	2	1	no	—
356	C₄⋊C₄×C₆₇	—	2	2	no	—
357	C₄⋊C₄×C₆₇	—	2	2	no	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	2	no	—
361	C₄⋊C₄×C₆₇	—	2	2	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	2	no	—
364	C₄⋊C₄×C₆₇	—	2	2	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₂²⋊C₄×C₆₇	—	2	2	no	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	1	no	—
381	C₂²⋊C₄×C₆₇	—	2	1	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	2	no	—
384	C₂²⋊C₄×C₆₇	—	2	2	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	2	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	—	2	2	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	—	2	2	no	—
395	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
400	C₄²×C₆₇	—	2	1	no	—
401	C₄²×C₆₇	—	2	1	no	—
402	C₄²×C₆₇	—	2	1	no	—
403	C₄²×C₆₇	—	2	1	no	—
404	C₄²×C₆₇	—	2	2	no	—
405	C₄²×C₆₇	—	2	2	no	—
406	C₄²×C₆₇	—	2	2	no	—
407	C₄²×C₆₇	—	2	2	no	—
408	C₄²×C₆₇	C₂⁴	1	2	yes	—
409	C₂³×C₆₇	—	2	2	no	—
410	C₂³×C₆₇	—	2	2	no	—
411	C₂³×C₆₇	—	4	1	no	—
412	C₂³×C₆₇	—	4	1	no	—
413	C₂³×C₆₇	—	4	2	no	—
414	C₂³×C₆₇	—	8	1	no	—
415	C₂³×C₆₇	—	8	1	no	—
416	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
419	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₆₇	—	2	2	no	—
421	Q₈×C₆₇	—	2	2	no	—
422	Q₈×C₆₇	—	2	2	no	—
423	Q₈×C₆₇	—	2	2	no	—
424	Q₈×C₆₇	—	4	1	no	—
425	Q₈×C₆₇	—	4	2	no	—
426	Q₈×C₆₇	—	8	2	no	—
427	Q₈×C₆₇	—	8	1	no	—
428	Q₈×C₆₇	—	8	2	no	—
429	D₄×C₆₇	—	2	4	no	—
430	D₄×C₆₇	—	2	2	no	—
431	D₄×C₆₇	—	2	2	no	—
432	D₄×C₆₇	—	4	2	no	—
433	D₄×C₆₇	—	4	1	no	—
434	D₄×C₆₇	—	4	2	no	—
435	D₄×C₆₇	—	4	4	no	—
436	D₄×C₆₇	—	8	1	no	—
437	D₄×C₆₇	—	8	2	no	—
438	D₄×C₆₇	—	8	2	no	—
439	D₄×C₆₇	—	8	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	4	1	no	—
458	C₂×C₄×C₆₇	—	4	1	no	—
459	C₂×C₄×C₆₇	—	4	1	no	—
460	C₂×C₄×C₆₇	—	4	2	no	—
461	C₂×C₄×C₆₇	—	4	2	no	—
462	C₂×C₄×C₆₇	—	4	2	no	—
463	C₂×C₄×C₆₇	—	8	2	no	—
464	C₂×C₄×C₆₇	—	8	2	no	—
465	C₂×C₄×C₆₇	—	8	2	no	—
466	C₂×C₄×C₆₇	—	8	1	no	—
467	C₂×C₄×C₆₇	—	8	1	no	—
468	C₂×C₄×C₆₇	—	8	1	no	—
469	C₂×C₄×C₆₇	—	8	1	no	—
470	C₂×C₄×C₆₇	—	8	2	no	—
471	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
478	C₈×C₆₇	—	2	2	no	—
479	C₈×C₆₇	—	2	2	no	—
480	C₈×C₆₇	—	2	2	no	—
481	C₈×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	1	no	—
483	C₂²×C₆₇	—	2	1	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	1	no	—
486	C₂²×C₆₇	—	2	1	no	—
487	C₂²×C₆₇	—	2	1	no	—
488	C₂²×C₆₇	—	2	1	no	—
489	C₂²×C₆₇	—	2	2	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	1	no	—
492	C₂²×C₆₇	—	2	1	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	—	4	2	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	8	2	no	—
497	C₂²×C₆₇	—	16	2	no	—
498	C₂²×C₆₇	#577	1	2	yes	—
499	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₆₇	—	2	2	no	—
501	C₄×C₆₇	—	2	1	no	—
502	C₄×C₆₇	—	2	1	no	—
503	C₄×C₆₇	—	2	1	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	4	1	no	—
507	C₄×C₆₇	—	4	2	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	2	no	—
510	C₄×C₆₇	—	4	2	no	—
511	C₄×C₆₇	—	4	1	no	—
512	C₄×C₆₇	—	4	1	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	—	4	2	no	—
515	C₄×C₆₇	#585	1	1	yes	characteristic
516	C₄×C₆₇	#585	1	1	yes	characteristic
517	#61755	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂×C₆₇	—	2	2	no	—
519	C₂×C₆₇	—	4	2	no	—
520	C₂×C₆₇	—	4	1	no	—
521	C₂×C₆₇	—	4	1	no	—
522	C₂×C₆₇	—	8	2	no	—
523	C₂×C₆₇	#3485	1	1	yes	characteristic
524	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
525	C₂×C₆₇	#3586	1	1	yes	characteristic
526	#3536	C₂×C₆₇	1	1	yes	characteristic
527	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#3356	C₂×C₆₇	1	2	yes	complemented
529	#3344	C₂×C₆₇	1	2	yes	complemented
530	#3343	C₂×C₆₇	1	2	yes	complemented
531	#3335	C₂×C₆₇	1	2	yes	complemented
532	#3323	C₂×C₆₇	1	2	yes	complemented
533	#3316	C₂×C₆₇	1	2	yes	complemented
534	#3311	C₂×C₆₇	1	2	yes	complemented
535	#3300	C₂×C₆₇	1	2	yes	complemented
536	#3244	C₂×C₆₇	1	2	yes	complemented
537	#3201	C₂×C₆₇	1	2	yes	complemented
538	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#3121	C₂×C₆₇	1	2	yes	complemented
541	#3099	C₂×C₆₇	1	2	yes	complemented
542	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
543	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2976	C₂×C₆₇	1	1	yes	characteristic, complemented
545	C₆₇	#61755	1	1	yes	characteristic, direct product factor, Sylow
546	#562	—	2	2	no	—
547	#556	C₂²×C₆₇	1	2	yes	—
548	#554	C₂²×C₆₇	1	2	yes	—
549	#554	C₂²×C₆₇	1	2	yes	complemented
550	#552	—	2	2	no	—
551	#552	C₂²×C₆₇	1	2	yes	—
552	#552	C₂²×C₆₇	1	2	yes	complemented
553	#551	—	2	2	no	—
554	#548	C₂²×C₆₇	1	2	yes	—
555	#547	C₂²×C₆₇	1	2	yes	—
556	#546	—	2	2	no	—
557	#546	C₂²×C₆₇	1	2	yes	—
558	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	#543	—	2	1	no	—
560	#542	—	2	1	no	—
561	#542	C₂²×C₆₇	1	2	yes	—
562	#541	—	2	1	no	—
563	#539	—	2	1	no	—
564	#538	—	2	1	no	—
565	#537	—	2	1	no	—
566	#537	C₂²×C₆₇	1	2	yes	—
567	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#533	—	2	1	no	—
569	#529	—	2	1	no	—
570	#525	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
572	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
574	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
577	#501	C₂²×C₆₇	1	2	yes	complemented
578	#498	C₂²×C₆₇	1	2	yes	complemented
579	#489	C₂²×C₆₇	1	2	yes	complemented
580	#488	C₂²×C₆₇	1	2	yes	complemented
581	#485	C₂²×C₆₇	1	2	yes	—
582	#485	C₂²×C₆₇	1	2	yes	—
583	#485	C₂²×C₆₇	1	2	yes	complemented
584	#485	C₂²×C₆₇	1	2	yes	complemented
585	#485	C₂²×C₆₇	1	2	yes	complemented
586	#484	C₂²×C₆₇	1	2	yes	complemented
587	#483	C₂²×C₆₇	1	2	yes	—
588	#483	C₂²×C₆₇	1	2	yes	complemented
589	#483	C₂²×C₆₇	1	2	yes	complemented
590	#483	C₂²×C₆₇	1	2	yes	complemented
591	#483	C₂²×C₆₇	1	2	yes	complemented
592	#482	C₂²×C₆₇	1	2	yes	—
593	#482	C₂²×C₆₇	1	2	yes	—
594	#482	C₂²×C₆₇	1	2	yes	complemented
595	#481	C₂²×C₆₇	1	2	yes	—
596	#481	C₂²×C₆₇	1	2	yes	—
597	#481	C₂²×C₆₇	1	2	yes	complemented
598	#480	C₂²×C₆₇	1	2	yes	—
599	#479	C₂²×C₆₇	1	2	yes	complemented
600	#478	C₂²×C₆₇	1	2	yes	complemented
601	#477	C₂²×C₆₇	1	2	yes	complemented
602	#476	C₂²×C₆₇	1	2	yes	complemented
603	#475	C₂²×C₆₇	1	2	yes	complemented
604	#475	C₂²×C₆₇	1	2	yes	complemented
605	#470	C₂²×C₆₇	1	2	yes	—
606	#470	C₂²×C₆₇	1	2	yes	—
607	#470	C₂²×C₆₇	1	2	yes	complemented
608	#468	C₂²×C₆₇	1	2	yes	complemented
609	#467	C₂²×C₆₇	1	2	yes	complemented
610	#465	C₂²×C₆₇	1	2	yes	—
611	#465	C₂²×C₆₇	1	2	yes	—
612	#465	C₂²×C₆₇	1	2	yes	complemented
613	#464	C₂²×C₆₇	1	2	yes	complemented
614	#464	C₂²×C₆₇	1	2	yes	complemented
615	#452	C₂²×C₆₇	1	2	yes	complemented
616	#452	C₂²×C₆₇	1	2	yes	complemented
617	#451	C₂²×C₆₇	1	2	yes	complemented
618	#451	C₂²×C₆₇	1	2	yes	complemented
619	#450	C₂²×C₆₇	1	2	yes	—
620	#448	C₂²×C₆₇	1	2	yes	—
621	#441	C₂²×C₆₇	1	2	yes	complemented
622	#440	C₂²×C₆₇	1	2	yes	complemented
623	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
624	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
625	#436	C₂²×C₆₇	1	2	yes	—
626	#435	C₂²×C₆₇	1	2	yes	—
627	#435	C₂²×C₆₇	1	2	yes	complemented
628	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
629	#433	C₂²×C₆₇	1	2	yes	complemented
630	#428	C₂²×C₆₇	1	1	yes	characteristic
631	#428	C₂²×C₆₇	1	1	yes	characteristic
632	#428	C₂²×C₆₇	1	2	yes	complemented
633	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
636	#418	C₂²×C₆₇	1	1	yes	characteristic
637	#418	C₂²×C₆₇	1	1	yes	characteristic
638	#417	C₂²×C₆₇	1	2	yes	complemented
639	#416	C₂²×C₆₇	1	2	yes	complemented
640	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#408	C₂²×C₆₇	1	2	yes	complemented
643	#407	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
645	C₂×#41	—	2	2	no	—
646	C₂×#41	C₂³×C₆₇	1	2	yes	—
647	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
650	C₂²×D₄	—	2	1	no	—
651	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
655	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
657	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
660	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
661	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
663	C₄⋊Q₈	—	2	1	no	—
664	C₄⋊Q₈	—	2	1	no	—
665	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
666	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	2	no	—
670	#126	—	2	2	no	—
671	#126	—	2	2	no	—
672	#125	—	2	1	no	—
673	#125	—	2	2	no	—
674	#125	—	2	2	no	—
675	#125	—	2	2	no	—
676	#125	—	2	2	no	—
677	#125	C₂³×C₆₇	1	2	yes	—
678	#124	—	2	1	no	—
679	#124	—	2	2	no	—
680	#124	—	2	2	no	—
681	#124	—	2	2	no	—
682	#124	C₂³×C₆₇	1	2	yes	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	D₄×C₆₇	1	2	yes	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	1	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
705	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
706	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
709	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
710	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	1	no	—
718	#121	—	2	1	no	—
719	#121	—	2	2	no	—
720	#121	D₄×C₆₇	1	1	yes	characteristic
721	#121	D₄×C₆₇	1	1	yes	characteristic
722	#121	C₂³×C₆₇	1	2	yes	—
723	#121	C₂³×C₆₇	1	2	yes	—
724	#121	C₂³×C₆₇	1	2	yes	—
725	#120	—	2	2	no	—
726	#120	D₄×C₆₇	1	2	yes	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	2	no	—
731	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
732	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
733	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	C₂³×C₆₇	1	2	yes	—
740	C₄×D₄	C₂³×C₆₇	1	2	yes	—
741	C₄×D₄	C₂³×C₆₇	1	2	yes	—
742	#117	—	2	1	no	—
743	#117	—	2	1	no	—
744	#117	—	2	2	no	—
745	#117	—	2	2	no	—
746	#117	—	2	2	no	—
747	#117	C₂³×C₆₇	1	1	yes	characteristic
748	#117	C₂³×C₆₇	1	1	yes	characteristic
749	#117	C₂³×C₆₇	1	1	yes	characteristic
750	#117	C₂³×C₆₇	1	1	yes	characteristic
751	#117	C₂³×C₆₇	1	2	yes	—
752	#117	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₄⋊C₄	—	2	1	no	—
754	C₂×C₄⋊C₄	—	2	1	no	—
755	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₂²⋊C₄	—	2	1	no	—
763	C₂×C₂²⋊C₄	—	2	1	no	—
764	C₂×C₂²⋊C₄	—	2	1	no	—
765	C₂×C₂²⋊C₄	—	2	1	no	—
766	C₂×C₂²⋊C₄	—	2	2	no	—
767	C₂×C₄²	—	2	1	no	—
768	#107	C₂³×C₆₇	1	2	yes	—
769	#107	C₂³×C₆₇	1	2	yes	—
770	#107	C₂³×C₆₇	1	2	yes	—
771	#107	C₂³×C₆₇	1	2	yes	—
772	#106	C₂³×C₆₇	1	2	yes	—
773	#106	C₂³×C₆₇	1	2	yes	—
774	#106	C₂³×C₆₇	1	2	yes	—
775	#106	C₂³×C₆₇	1	2	yes	—
776	#106	C₂³×C₆₇	1	2	yes	—
777	#106	C₂³×C₆₇	1	2	yes	—
778	#106	C₂³×C₆₇	1	2	yes	—
779	#106	C₂³×C₆₇	1	2	yes	—
780	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
781	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
782	#103	C₂³×C₆₇	1	2	yes	—
783	#103	C₂³×C₆₇	1	2	yes	—
784	#103	C₂³×C₆₇	1	2	yes	—
785	#103	C₂³×C₆₇	1	2	yes	—
786	#103	C₂³×C₆₇	1	2	yes	—
787	#103	C₂³×C₆₇	1	2	yes	—
788	#103	C₂³×C₆₇	1	2	yes	—
789	#103	C₂³×C₆₇	1	2	yes	—
790	#103	C₂³×C₆₇	1	2	yes	—
791	#103	C₂³×C₆₇	1	2	yes	—
792	#102	C₂³×C₆₇	1	2	yes	—
793	#102	C₂³×C₆₇	1	2	yes	—
794	#102	C₂³×C₆₇	1	2	yes	—
795	#102	C₂³×C₆₇	1	2	yes	—
796	#102	C₂³×C₆₇	1	2	yes	—
797	#102	C₂³×C₆₇	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
799	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
800	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
801	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
804	#97	C₂³×C₆₇	1	2	yes	—
805	C₄×C₈	C₂³×C₆₇	1	2	yes	—
806	C₂⁴	—	2	1	no	—
807	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
808	#41	—	4	1	no	—
809	#41	—	4	1	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	8	4	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	4	1	no	—
818	C₂×Q₈	—	4	1	no	—
819	C₂×Q₈	—	4	1	no	—
820	C₂×Q₈	—	4	1	no	—
821	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
822	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
823	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	8	2	no	—
832	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
833	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
834	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
835	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
836	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
851	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
852	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
857	Q₁₆	—	4	2	no	—
858	Q₁₆	—	4	2	no	—
859	SD₁₆	—	4	2	no	—
860	SD₁₆	—	4	2	no	—
861	M₁₆	—	4	2	no	—
862	M₁₆	—	4	1	no	—
863	M₁₆	—	4	1	no	—
864	C₂×C₈	—	4	1	no	—
865	C₂×C₈	—	4	2	no	—
866	C₂×C₈	—	4	1	no	—
867	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
868	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
869	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
870	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
893	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
894	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
895	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	1	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
926	C₄²	—	2	1	no	—
927	C₄²	—	2	1	no	—
928	C₄²	—	2	1	no	—
929	C₄²	—	2	1	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	2	no	—
934	C₄²	C₂⁴×C₆₇	1	2	yes	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	4	1	no	—
938	C₂³	—	4	1	no	—
939	C₂³	—	4	2	no	—
940	C₂³	—	8	1	no	—
941	C₂³	—	8	1	no	—
942	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
943	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
944	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
945	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	2	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	4	1	no	—
951	Q₈	—	4	2	no	—
952	Q₈	—	8	1	no	—
953	Q₈	—	8	2	no	—
954	Q₈	—	8	2	no	—
955	D₄	—	2	4	no	—
956	D₄	—	2	2	no	—
957	D₄	—	2	2	no	—
958	D₄	—	4	1	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	4	no	—
962	D₄	—	8	1	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	4	1	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	8	2	no	—
990	C₂×C₄	—	8	2	no	—
991	C₂×C₄	—	8	1	no	—
992	C₂×C₄	—	8	1	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	1	no	—
996	C₂×C₄	—	8	1	no	—
997	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
998	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1000	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1002	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1003	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	2	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	8	2	no	—
1023	C₂²	—	16	2	no	—
1024	C₂²	#577×C₆₇	1	2	yes	—
1025	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	2	no	—
1041	C₄	#585×C₆₇	1	1	yes	characteristic
1042	C₄	#585×C₆₇	1	1	yes	characteristic
1043	C₂	—	2	2	no	—
1044	C₂	—	4	1	no	—
1045	C₂	—	4	1	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	8	2	no	—
1048	C₂	C₆₇×#3485	1	1	yes	characteristic
1049	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1050	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×#3536	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3495	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3344	C₂	semidirect
5. C₆₇×#3343	C₂	semidirect
6. C₆₇×#3335	C₂	semidirect
7. C₆₇×#3323	C₂	semidirect
8. C₆₇×#3316	C₂	semidirect
9. C₆₇×#3311	C₂	semidirect
10. C₆₇×#3300	C₂	semidirect
11. C₆₇×#3244	C₂	semidirect
12. C₆₇×#3201	C₂	semidirect
13. C₆₇×#3195	C₂	semidirect
14. C₆₇×#3187	C₂	semidirect
15. C₆₇×#3121	C₂	semidirect
16. C₆₇×#3099	C₂	semidirect
17. C₆₇×#3094	C₂	semidirect
18. C₂×#485×C₆₇	C₂	semidirect
19. C₆₇×#2976	C₂	semidirect
23. #554×C₆₇	C₂²	semidirect
26. #552×C₆₇	C₂²	semidirect
32. #544×C₆₇	C₂²	semidirect
41. #536×C₆₇	C₂²	semidirect
48. #520×C₆₇	C₂²	semidirect
49. #519×C₆₇	C₂²	semidirect
51. #501×C₆₇	C₂²	semidirect
52. #498×C₆₇	C₂²	semidirect
53. #489×C₆₇	C₂²	semidirect
54. #488×C₆₇	C₂²	semidirect
57. #485×C₆₇	C₂²	semidirect
58. #485×C₆₇	C₂²	semidirect
59. #485×C₆₇	C₂²	semidirect
60. #484×C₆₇	C₂²	semidirect
62. #483×C₆₇	C₂²	semidirect
63. #483×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
65. #483×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
71. #481×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #478×C₆₇	C₂²	semidirect
75. #477×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #475×C₆₇	C₂²	semidirect
81. #470×C₆₇	C₂²	semidirect
82. #468×C₆₇	C₂²	semidirect
83. #467×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #464×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #452×C₆₇	C₂²	semidirect
91. #451×C₆₇	C₂²	semidirect
92. #451×C₆₇	C₂²	semidirect
95. #441×C₆₇	C₂²	semidirect
96. #440×C₆₇	C₂²	semidirect
97. C₄×Q₁₆×C₆₇	C₂²	semidirect
98. C₄×SD₁₆×C₆₇	C₂²	semidirect
101. #435×C₆₇	C₂²	semidirect
102. C₈×D₄×C₆₇	C₂²	semidirect
103. #433×C₆₇	C₂²	semidirect
106. #428×C₆₇	C₂²	semidirect
107. C₂×#107×C₆₇	C₂²	semidirect
108. C₂×#106×C₆₇	C₂²	semidirect
109. C₂×#106×C₆₇	C₂²	semidirect
112. #417×C₆₇	C₂²	semidirect
113. #416×C₆₇	C₂²	semidirect
114. C₂×#103×C₆₇	C₂²	semidirect
115. C₂×#103×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
517. #61755	C₆₇	direct (N × H)
527. #3495	C₂×C₆₇	semidirect
528. #3356	C₂×C₆₇	semidirect
529. #3344	C₂×C₆₇	semidirect
530. #3343	C₂×C₆₇	semidirect
531. #3335	C₂×C₆₇	semidirect
532. #3323	C₂×C₆₇	semidirect
533. #3316	C₂×C₆₇	semidirect
534. #3311	C₂×C₆₇	semidirect
535. #3300	C₂×C₆₇	semidirect
536. #3244	C₂×C₆₇	semidirect
537. #3201	C₂×C₆₇	semidirect
538. #3195	C₂×C₆₇	semidirect
539. #3187	C₂×C₆₇	semidirect
540. #3121	C₂×C₆₇	semidirect
541. #3099	C₂×C₆₇	semidirect
542. #3094	C₂×C₆₇	semidirect
543. C₂×#485	C₂×C₆₇	semidirect
544. #2976	C₂×C₆₇	semidirect
545. C₆₇	#61755	direct (N × H)
549. #554	C₂²×C₆₇	semidirect
552. #552	C₂²×C₆₇	semidirect
558. #544	C₂²×C₆₇	semidirect
567. #536	C₂²×C₆₇	semidirect
574. #520	C₂²×C₆₇	semidirect
575. #519	C₂²×C₆₇	semidirect
577. #501	C₂²×C₆₇	semidirect
578. #498	C₂²×C₆₇	semidirect
579. #489	C₂²×C₆₇	semidirect
580. #488	C₂²×C₆₇	semidirect
583. #485	C₂²×C₆₇	semidirect
584. #485	C₂²×C₆₇	semidirect
585. #485	C₂²×C₆₇	semidirect
586. #484	C₂²×C₆₇	semidirect
588. #483	C₂²×C₆₇	semidirect
589. #483	C₂²×C₆₇	semidirect
590. #483	C₂²×C₆₇	semidirect
591. #483	C₂²×C₆₇	semidirect
594. #482	C₂²×C₆₇	semidirect
597. #481	C₂²×C₆₇	semidirect
599. #479	C₂²×C₆₇	semidirect
600. #478	C₂²×C₆₇	semidirect
601. #477	C₂²×C₆₇	semidirect
602. #476	C₂²×C₆₇	semidirect
603. #475	C₂²×C₆₇	semidirect
604. #475	C₂²×C₆₇	semidirect
607. #470	C₂²×C₆₇	semidirect
608. #468	C₂²×C₆₇	semidirect
609. #467	C₂²×C₆₇	semidirect
612. #465	C₂²×C₆₇	semidirect
613. #464	C₂²×C₆₇	semidirect
614. #464	C₂²×C₆₇	semidirect
615. #452	C₂²×C₆₇	semidirect
616. #452	C₂²×C₆₇	semidirect
617. #451	C₂²×C₆₇	semidirect
618. #451	C₂²×C₆₇	semidirect
621. #441	C₂²×C₆₇	semidirect
622. #440	C₂²×C₆₇	semidirect
623. C₄×Q₁₆	C₂²×C₆₇	semidirect
624. C₄×SD₁₆	C₂²×C₆₇	semidirect
627. #435	C₂²×C₆₇	semidirect
628. C₈×D₄	C₂²×C₆₇	semidirect
629. #433	C₂²×C₆₇	semidirect
632. #428	C₂²×C₆₇	semidirect
633. C₂×#107	C₂²×C₆₇	semidirect
634. C₂×#106	C₂²×C₆₇	semidirect
635. C₂×#106	C₂²×C₆₇	semidirect
638. #417	C₂²×C₆₇	semidirect
639. #416	C₂²×C₆₇	semidirect
640. C₂×#103	C₂²×C₆₇	semidirect
641. C₂×#103	C₂²×C₆₇	semidirect
642. #408	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×#3536	2
C₆₇×#3495	2
C₆₇×#3356	2
C₆₇×#3344	2
C₆₇×#3343	2
C₆₇×#3335	2
C₆₇×#3323	2
C₆₇×#3316	2
C₆₇×#3311	2
C₆₇×#3300	2
C₆₇×#3244	2
C₆₇×#3201	2
C₆₇×#3195	2
C₆₇×#3187	2
C₆₇×#3121	2
C₆₇×#3099	2
C₆₇×#3094	2
C₂×#485×C₆₇	2
C₆₇×#2976	2
#61755	67

Subgroups — C67×#61755 #30741006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61755 #30741006