Subgroups — C₆₇×#61765 #30741016

Order 17152.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1050 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, complemented
2	C₆₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3345	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3344	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3204	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
17	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	#562×C₆₇	—	2	2	no	—
21	#554×C₆₇	—	2	1	no	—
22	#554×C₆₇	C₂²	1	2	yes	—
23	#554×C₆₇	C₂²	1	2	yes	complemented
24	#553×C₆₇	—	2	1	no	—
25	#553×C₆₇	C₂²	1	2	yes	complemented
26	#552×C₆₇	—	2	1	no	—
27	#552×C₆₇	C₂²	1	2	yes	—
28	#548×C₆₇	C₂²	1	2	yes	—
29	#547×C₆₇	—	2	1	no	—
30	#547×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#546×C₆₇	—	2	2	no	—
33	#546×C₆₇	C₂²	1	2	yes	—
34	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#543×C₆₇	—	2	1	no	—
36	#542×C₆₇	C₂²	1	2	yes	—
37	#539×C₆₇	—	2	2	no	—
38	#539×C₆₇	—	2	1	no	—
39	#538×C₆₇	—	2	1	no	—
40	#537×C₆₇	—	2	1	no	—
41	#537×C₆₇	C₂²	1	2	yes	—
42	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#525×C₆₇	—	2	2	no	—
44	#525×C₆₇	C₂²	1	1	yes	characteristic
45	#525×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	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×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	complemented
56	#485×C₆₇	C₂²	1	2	yes	complemented
57	#484×C₆₇	C₂²	1	1	yes	characteristic
58	#483×C₆₇	C₂²	1	2	yes	—
59	#483×C₆₇	C₂²	1	2	yes	—
60	#483×C₆₇	C₂²	1	2	yes	complemented
61	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	#482×C₆₇	C₂²	1	2	yes	—
66	#482×C₆₇	C₂²	1	2	yes	complemented
67	#481×C₆₇	C₂²	1	2	yes	—
68	#481×C₆₇	C₂²	1	2	yes	—
69	#481×C₆₇	C₂²	1	1	yes	characteristic
70	#481×C₆₇	C₂²	1	2	yes	—
71	#481×C₆₇	C₂²	1	2	yes	—
72	#481×C₆₇	C₂²	1	2	yes	complemented
73	#481×C₆₇	C₂²	1	2	yes	complemented
74	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#476×C₆₇	C₂²	1	2	yes	complemented
78	#476×C₆₇	C₂²	1	2	yes	complemented
79	#475×C₆₇	C₂²	1	2	yes	complemented
80	#475×C₆₇	C₂²	1	2	yes	complemented
81	#470×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#467×C₆₇	C₂²	1	2	yes	—
84	#466×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#465×C₆₇	C₂²	1	2	yes	—
87	#465×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#464×C₆₇	C₂²	1	2	yes	complemented
90	#463×C₆₇	C₂²	1	2	yes	complemented
91	#452×C₆₇	C₂²	1	2	yes	complemented
92	#452×C₆₇	C₂²	1	2	yes	complemented
93	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#450×C₆₇	C₂²	1	1	yes	characteristic
95	#449×C₆₇	C₂²	1	2	yes	—
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#447×C₆₇	C₂²	1	1	yes	characteristic
99	#442×C₆₇	C₂²	1	2	yes	complemented
100	#441×C₆₇	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	#435×C₆₇	C₂²	1	2	yes	—
104	#435×C₆₇	C₂²	1	2	yes	complemented
105	C₈×D₄×C₆₇	C₂²	1	2	yes	—
106	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
107	#433×C₆₇	C₂²	1	2	yes	complemented
108	#428×C₆₇	C₂²	1	2	yes	complemented
109	C₂×#106×C₆₇	C₂²	1	2	yes	—
110	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
111	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
112	#417×C₆₇	C₂²	1	2	yes	complemented
113	#416×C₆₇	C₂²	1	2	yes	complemented
114	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#102×C₆₇	C₂²	1	2	yes	—
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₈×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	—	2	2	no	—
121	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×#41×C₆₇	C₂³	1	2	yes	—
123	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	—	2	1	no	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	—	2	1	no	—
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×D₈×C₆₇	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
135	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
136	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	—	2	1	no	—
138	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#125×C₆₇	—	2	2	no	—
144	#125×C₆₇	—	2	2	no	—
145	#125×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	1	no	—
147	#125×C₆₇	C₂³	1	2	yes	—
148	#124×C₆₇	—	2	2	no	—
149	#124×C₆₇	—	2	2	no	—
150	#124×C₆₇	C₂³	1	2	yes	—
151	#123×C₆₇	—	2	2	no	—
152	#123×C₆₇	—	2	1	no	—
153	#123×C₆₇	—	2	2	no	—
154	#123×C₆₇	—	2	2	no	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	2	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	D₄	1	2	yes	—
161	C₂²⋊Q₈×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	1	no	—
163	C₂²⋊Q₈×C₆₇	—	2	1	no	—
164	C₂²⋊Q₈×C₆₇	—	2	1	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	D₄	1	1	yes	characteristic
175	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
176	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	—	2	2	no	—
183	#121×C₆₇	—	2	2	no	—
184	#121×C₆₇	—	2	2	no	—
185	#121×C₆₇	—	2	2	no	—
186	#121×C₆₇	—	2	2	no	—
187	#121×C₆₇	—	2	2	no	—
188	#121×C₆₇	—	2	1	no	—
189	#121×C₆₇	—	2	1	no	—
190	#121×C₆₇	—	2	1	no	—
191	#121×C₆₇	—	2	2	no	—
192	#121×C₆₇	D₄	1	1	yes	characteristic
193	#121×C₆₇	D₄	1	1	yes	characteristic
194	#121×C₆₇	C₂³	1	1	yes	characteristic
195	#121×C₆₇	C₂³	1	2	yes	—
196	#121×C₆₇	C₂³	1	2	yes	—
197	#121×C₆₇	C₂³	1	1	yes	characteristic
198	#121×C₆₇	C₂³	1	2	yes	—
199	#121×C₆₇	C₂³	1	2	yes	—
200	#120×C₆₇	—	2	1	no	—
201	#120×C₆₇	—	2	2	no	—
202	#120×C₆₇	D₄	1	2	yes	—
203	C₄×Q₈×C₆₇	—	2	1	no	—
204	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
205	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	—	2	2	no	—
207	C₄×D₄×C₆₇	—	2	1	no	—
208	C₄×D₄×C₆₇	—	2	2	no	—
209	C₄×D₄×C₆₇	—	2	2	no	—
210	C₄×D₄×C₆₇	—	2	1	no	—
211	C₄×D₄×C₆₇	—	2	1	no	—
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	—	2	2	no	—
214	C₄×D₄×C₆₇	—	2	2	no	—
215	C₄×D₄×C₆₇	C₂³	1	2	yes	—
216	C₄×D₄×C₆₇	C₂³	1	2	yes	—
217	C₄×D₄×C₆₇	C₂³	1	2	yes	—
218	C₄×D₄×C₆₇	C₂³	1	2	yes	—
219	#117×C₆₇	—	2	1	no	—
220	#117×C₆₇	—	2	2	no	—
221	#117×C₆₇	C₂³	1	1	yes	characteristic
222	#117×C₆₇	C₂³	1	2	yes	—
223	#117×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
225	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
226	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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	2	yes	—
235	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
240	#107×C₆₇	C₂³	1	2	yes	—
241	#107×C₆₇	C₂³	1	2	yes	—
242	#106×C₆₇	C₂³	1	2	yes	—
243	#106×C₆₇	C₂³	1	2	yes	—
244	#106×C₆₇	C₂³	1	2	yes	—
245	#106×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	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
254	#103×C₆₇	C₂³	1	2	yes	—
255	#103×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	#102×C₆₇	C₂³	1	2	yes	—
263	#102×C₆₇	C₂³	1	2	yes	—
264	#102×C₆₇	C₂³	1	2	yes	—
265	#102×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	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
275	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	2	no	—
283	#41×C₆₇	—	4	2	no	—
284	#41×C₆₇	—	4	2	no	—
285	#41×C₆₇	—	4	2	no	—
286	#41×C₆₇	—	8	4	no	—
287	#41×C₆₇	—	8	4	no	—
288	C₂×Q₈×C₆₇	—	2	1	no	—
289	C₂×Q₈×C₆₇	—	2	2	no	—
290	C₂×Q₈×C₆₇	—	2	2	no	—
291	C₂×Q₈×C₆₇	—	4	2	no	—
292	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₆₇	—	2	1	no	—
296	C₂×D₄×C₆₇	—	2	1	no	—
297	C₂×D₄×C₆₇	—	2	1	no	—
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	2	no	—
303	C₂×D₄×C₆₇	—	2	1	no	—
304	C₂×D₄×C₆₇	—	4	2	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	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	—	2	1	no	—
313	C₂²×C₄×C₆₇	—	2	2	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	2	no	—
318	C₂²×C₄×C₆₇	—	2	1	no	—
319	C₂²×C₄×C₆₇	—	2	2	no	—
320	C₂²×C₄×C₆₇	—	2	2	no	—
321	C₂²×C₄×C₆₇	—	2	1	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	4	2	no	—
326	C₂²×C₄×C₆₇	—	8	2	no	—
327	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
334	Q₁₆×C₆₇	—	4	2	no	—
335	SD₁₆×C₆₇	—	4	2	no	—
336	SD₁₆×C₆₇	—	4	2	no	—
337	D₈×C₆₇	—	4	2	no	—
338	M₁₆×C₆₇	—	4	2	no	—
339	C₂×C₈×C₆₇	—	4	2	no	—
340	C₂×C₈×C₆₇	—	4	2	no	—
341	C₂×C₈×C₆₇	—	4	2	no	—
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	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₆₇	—	2	1	no	—
347	C₄⋊C₄×C₆₇	—	2	1	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	2	2	no	—
351	C₄⋊C₄×C₆₇	—	2	2	no	—
352	C₄⋊C₄×C₆₇	—	2	2	no	—
353	C₄⋊C₄×C₆₇	—	2	2	no	—
354	C₄⋊C₄×C₆₇	—	2	1	no	—
355	C₄⋊C₄×C₆₇	—	2	2	no	—
356	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
361	C₄⋊C₄×C₆₇	—	2	2	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	1	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	2	yes	—
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	2	yes	—
375	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	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	1	no	—
392	C₂²⋊C₄×C₆₇	—	2	1	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	C₄²×C₆₇	—	2	2	no	—
400	C₄²×C₆₇	—	2	2	no	—
401	C₄²×C₆₇	—	2	1	no	—
402	C₄²×C₆₇	—	2	2	no	—
403	C₄²×C₆₇	C₂⁴	1	2	yes	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	4	1	no	—
409	C₂³×C₆₇	—	4	2	no	—
410	C₂³×C₆₇	—	8	1	no	—
411	C₂³×C₆₇	—	8	1	no	—
412	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
414	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
416	Q₈×C₆₇	—	2	2	no	—
417	Q₈×C₆₇	—	2	2	no	—
418	Q₈×C₆₇	—	2	2	no	—
419	Q₈×C₆₇	—	4	1	no	—
420	Q₈×C₆₇	—	8	1	no	—
421	Q₈×C₆₇	—	8	2	no	—
422	Q₈×C₆₇	—	8	2	no	—
423	D₄×C₆₇	—	2	4	no	—
424	D₄×C₆₇	—	2	4	no	—
425	D₄×C₆₇	—	2	2	no	—
426	D₄×C₆₇	—	2	2	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	4	1	no	—
429	D₄×C₆₇	—	4	2	no	—
430	D₄×C₆₇	—	4	2	no	—
431	D₄×C₆₇	—	4	2	no	—
432	D₄×C₆₇	—	4	4	no	—
433	D₄×C₆₇	—	4	2	no	—
434	D₄×C₆₇	—	8	1	no	—
435	D₄×C₆₇	—	8	2	no	—
436	D₄×C₆₇	—	8	2	no	—
437	D₄×C₆₇	—	8	2	no	—
438	D₄×C₆₇	—	8	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	4	1	no	—
453	C₂×C₄×C₆₇	—	4	1	no	—
454	C₂×C₄×C₆₇	—	4	1	no	—
455	C₂×C₄×C₆₇	—	4	2	no	—
456	C₂×C₄×C₆₇	—	4	4	no	—
457	C₂×C₄×C₆₇	—	4	2	no	—
458	C₂×C₄×C₆₇	—	8	2	no	—
459	C₂×C₄×C₆₇	—	8	2	no	—
460	C₂×C₄×C₆₇	—	8	2	no	—
461	C₂×C₄×C₆₇	—	8	1	no	—
462	C₂×C₄×C₆₇	—	8	2	no	—
463	C₂×C₄×C₆₇	—	8	1	no	—
464	C₂×C₄×C₆₇	—	8	1	no	—
465	C₂×C₄×C₆₇	—	8	1	no	—
466	C₂×C₄×C₆₇	—	8	2	no	—
467	C₂×C₄×C₆₇	—	8	2	no	—
468	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
475	C₈×C₆₇	—	2	2	no	—
476	C₈×C₆₇	—	2	2	no	—
477	C₈×C₆₇	—	2	2	no	—
478	C₈×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	1	no	—
480	C₂²×C₆₇	—	2	1	no	—
481	C₂²×C₆₇	—	2	1	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	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	1	no	—
489	C₂²×C₆₇	—	4	4	no	—
490	C₂²×C₆₇	—	4	1	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	4	1	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	—	4	1	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	16	2	no	—
497	C₂²×C₆₇	#577	1	2	yes	—
498	C₂²×C₆₇	#577	1	2	yes	—
499	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₆₇	—	2	1	no	—
501	C₄×C₆₇	—	2	1	no	—
502	C₄×C₆₇	—	2	1	no	—
503	C₄×C₆₇	—	2	2	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	2	no	—
509	C₄×C₆₇	—	4	2	no	—
510	C₄×C₆₇	—	4	2	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	1	no	—
513	C₄×C₆₇	—	4	1	no	—
514	C₄×C₆₇	#585	1	2	yes	—
515	#61765	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₆₇	—	2	2	no	—
517	C₂×C₆₇	—	2	2	no	—
518	C₂×C₆₇	—	4	2	no	—
519	C₂×C₆₇	—	4	1	no	—
520	C₂×C₆₇	—	8	1	no	—
521	C₂×C₆₇	—	8	2	no	—
522	C₂×C₆₇	#3485	1	1	yes	characteristic
523	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
524	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
525	#3536	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#3492	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#3345	C₂×C₆₇	1	2	yes	complemented
528	#3344	C₂×C₆₇	1	2	yes	complemented
529	#3335	C₂×C₆₇	1	2	yes	complemented
530	#3335	C₂×C₆₇	1	2	yes	complemented
531	#3316	C₂×C₆₇	1	2	yes	complemented
532	#3306	C₂×C₆₇	1	2	yes	complemented
533	#3301	C₂×C₆₇	1	2	yes	complemented
534	#3296	C₂×C₆₇	1	2	yes	complemented
535	#3244	C₂×C₆₇	1	2	yes	complemented
536	#3204	C₂×C₆₇	1	2	yes	complemented
537	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#3188	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#3125	C₂×C₆₇	1	2	yes	complemented
540	#3099	C₂×C₆₇	1	2	yes	complemented
541	C₂×#481	C₂×C₆₇	1	1	yes	characteristic, complemented
542	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₆₇	#61765	1	1	yes	characteristic, direct product factor, Sylow
545	#562	—	2	2	no	—
546	#554	—	2	1	no	—
547	#554	C₂²×C₆₇	1	2	yes	—
548	#554	C₂²×C₆₇	1	2	yes	complemented
549	#553	—	2	1	no	—
550	#553	C₂²×C₆₇	1	2	yes	complemented
551	#552	—	2	1	no	—
552	#552	C₂²×C₆₇	1	2	yes	—
553	#548	C₂²×C₆₇	1	2	yes	—
554	#547	—	2	1	no	—
555	#547	C₂²×C₆₇	1	2	yes	—
556	#547	C₂²×C₆₇	1	2	yes	—
557	#546	—	2	2	no	—
558	#546	C₂²×C₆₇	1	2	yes	—
559	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	#543	—	2	1	no	—
561	#542	C₂²×C₆₇	1	2	yes	—
562	#539	—	2	2	no	—
563	#539	—	2	1	no	—
564	#538	—	2	1	no	—
565	#537	—	2	1	no	—
566	#537	C₂²×C₆₇	1	2	yes	—
567	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#525	—	2	2	no	—
569	#525	C₂²×C₆₇	1	1	yes	characteristic
570	#525	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
572	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
573	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
576	#501	C₂²×C₆₇	1	2	yes	complemented
577	#498	C₂²×C₆₇	1	2	yes	complemented
578	#489	C₂²×C₆₇	1	2	yes	complemented
579	#488	C₂²×C₆₇	1	2	yes	complemented
580	#485	C₂²×C₆₇	1	2	yes	complemented
581	#485	C₂²×C₆₇	1	2	yes	complemented
582	#484	C₂²×C₆₇	1	1	yes	characteristic
583	#483	C₂²×C₆₇	1	2	yes	—
584	#483	C₂²×C₆₇	1	2	yes	—
585	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	#483	C₂²×C₆₇	1	2	yes	complemented
587	#483	C₂²×C₆₇	1	2	yes	complemented
588	#483	C₂²×C₆₇	1	2	yes	complemented
589	#483	C₂²×C₆₇	1	2	yes	complemented
590	#482	C₂²×C₆₇	1	2	yes	—
591	#482	C₂²×C₆₇	1	2	yes	complemented
592	#481	C₂²×C₆₇	1	1	yes	characteristic
593	#481	C₂²×C₆₇	1	2	yes	—
594	#481	C₂²×C₆₇	1	2	yes	—
595	#481	C₂²×C₆₇	1	2	yes	—
596	#481	C₂²×C₆₇	1	2	yes	—
597	#481	C₂²×C₆₇	1	2	yes	complemented
598	#481	C₂²×C₆₇	1	2	yes	complemented
599	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
600	#479	C₂²×C₆₇	1	2	yes	complemented
601	#478	C₂²×C₆₇	1	2	yes	complemented
602	#476	C₂²×C₆₇	1	2	yes	complemented
603	#476	C₂²×C₆₇	1	2	yes	complemented
604	#475	C₂²×C₆₇	1	2	yes	complemented
605	#475	C₂²×C₆₇	1	2	yes	complemented
606	#470	C₂²×C₆₇	1	2	yes	complemented
607	#469	C₂²×C₆₇	1	2	yes	complemented
608	#467	C₂²×C₆₇	1	2	yes	—
609	#466	C₂²×C₆₇	1	2	yes	—
610	#465	C₂²×C₆₇	1	2	yes	—
611	#465	C₂²×C₆₇	1	2	yes	—
612	#465	C₂²×C₆₇	1	2	yes	complemented
613	#465	C₂²×C₆₇	1	2	yes	complemented
614	#464	C₂²×C₆₇	1	2	yes	complemented
615	#463	C₂²×C₆₇	1	2	yes	complemented
616	#452	C₂²×C₆₇	1	2	yes	complemented
617	#452	C₂²×C₆₇	1	2	yes	complemented
618	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#450	C₂²×C₆₇	1	1	yes	characteristic
620	#449	C₂²×C₆₇	1	2	yes	—
621	#449	C₂²×C₆₇	1	2	yes	complemented
622	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#447	C₂²×C₆₇	1	1	yes	characteristic
624	#442	C₂²×C₆₇	1	2	yes	complemented
625	#441	C₂²×C₆₇	1	2	yes	complemented
626	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
627	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
628	#435	C₂²×C₆₇	1	2	yes	—
629	#435	C₂²×C₆₇	1	2	yes	complemented
630	C₈×D₄	C₂²×C₆₇	1	2	yes	—
631	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
632	#433	C₂²×C₆₇	1	2	yes	complemented
633	#428	C₂²×C₆₇	1	2	yes	complemented
634	C₂×#106	C₂²×C₆₇	1	2	yes	—
635	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
636	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
637	#417	C₂²×C₆₇	1	2	yes	complemented
638	#416	C₂²×C₆₇	1	2	yes	complemented
639	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
640	C₂×#102	C₂²×C₆₇	1	2	yes	—
641	#408	C₂²×C₆₇	1	2	yes	complemented
642	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
643	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×#41	—	2	2	no	—
645	C₂×#41	—	2	2	no	—
646	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×#41	C₂³×C₆₇	1	2	yes	—
648	C₂×#41	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	—	2	1	no	—
653	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
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×D₈	C₂³×C₆₇	1	2	yes	—
658	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
659	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
660	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
661	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
662	C₄⋊Q₈	—	2	1	no	—
663	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
665	#126	—	2	2	no	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	2	no	—
670	#125	—	2	2	no	—
671	#125	—	2	1	no	—
672	#125	C₂³×C₆₇	1	2	yes	—
673	#124	—	2	2	no	—
674	#124	—	2	2	no	—
675	#124	C₂³×C₆₇	1	2	yes	—
676	#123	—	2	2	no	—
677	#123	—	2	1	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	D₄×C₆₇	1	2	yes	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
700	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	1	no	—
716	#121	—	2	2	no	—
717	#121	D₄×C₆₇	1	1	yes	characteristic
718	#121	D₄×C₆₇	1	1	yes	characteristic
719	#121	C₂³×C₆₇	1	2	yes	—
720	#121	C₂³×C₆₇	1	2	yes	—
721	#121	C₂³×C₆₇	1	1	yes	characteristic
722	#121	C₂³×C₆₇	1	1	yes	characteristic
723	#121	C₂³×C₆₇	1	2	yes	—
724	#121	C₂³×C₆₇	1	2	yes	—
725	#120	—	2	1	no	—
726	#120	—	2	2	no	—
727	#120	D₄×C₆₇	1	2	yes	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
730	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	C₂³×C₆₇	1	2	yes	—
741	C₄×D₄	C₂³×C₆₇	1	2	yes	—
742	C₄×D₄	C₂³×C₆₇	1	2	yes	—
743	C₄×D₄	C₂³×C₆₇	1	2	yes	—
744	#117	—	2	1	no	—
745	#117	—	2	2	no	—
746	#117	C₂³×C₆₇	1	1	yes	characteristic
747	#117	C₂³×C₆₇	1	2	yes	—
748	#117	C₂³×C₆₇	1	1	yes	characteristic
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	—	2	1	no	—
751	C₂×C₄⋊C₄	—	2	1	no	—
752	C₂×C₄⋊C₄	—	2	1	no	—
753	C₂×C₄⋊C₄	—	2	1	no	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	no	—
765	#107	C₂³×C₆₇	1	2	yes	—
766	#107	C₂³×C₆₇	1	2	yes	—
767	#106	C₂³×C₆₇	1	2	yes	—
768	#106	C₂³×C₆₇	1	2	yes	—
769	#106	C₂³×C₆₇	1	2	yes	—
770	#106	C₂³×C₆₇	1	2	yes	—
771	#106	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	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
778	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
779	#103	C₂³×C₆₇	1	2	yes	—
780	#103	C₂³×C₆₇	1	2	yes	—
781	#103	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	#102	C₂³×C₆₇	1	2	yes	—
788	#102	C₂³×C₆₇	1	2	yes	—
789	#102	C₂³×C₆₇	1	2	yes	—
790	#102	C₂³×C₆₇	1	2	yes	—
791	#102	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	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
796	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
798	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
803	#97	C₂³×C₆₇	1	2	yes	—
804	C₄×C₈	C₂³×C₆₇	1	2	yes	—
805	C₂⁴	—	2	1	no	—
806	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	8	4	no	—
812	#41	—	8	4	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	4	2	no	—
817	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
819	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	2	no	—
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	2	no	—
830	C₂×D₄	—	8	2	no	—
831	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
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	1	yes	characteristic
835	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
836	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	8	2	no	—
852	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
853	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
854	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
859	Q₁₆	—	4	2	no	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	D₈	—	4	2	no	—
863	M₁₆	—	4	2	no	—
864	C₂×C₈	—	4	2	no	—
865	C₂×C₈	—	4	2	no	—
866	C₂×C₈	—	4	2	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	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	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	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
892	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
893	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
895	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
897	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	1	no	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	1	no	—
907	C₂²⋊C₄	—	2	2	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	1	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
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	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	1	no	—
927	C₄²	—	2	2	no	—
928	C₄²	C₂⁴×C₆₇	1	2	yes	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	2	no	—
935	C₂³	—	8	1	no	—
936	C₂³	—	8	1	no	—
937	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
938	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
939	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
940	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
941	Q₈	—	2	2	no	—
942	Q₈	—	2	2	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	4	1	no	—
945	Q₈	—	8	1	no	—
946	Q₈	—	8	2	no	—
947	Q₈	—	8	2	no	—
948	D₄	—	2	4	no	—
949	D₄	—	2	4	no	—
950	D₄	—	2	2	no	—
951	D₄	—	2	2	no	—
952	D₄	—	2	2	no	—
953	D₄	—	4	1	no	—
954	D₄	—	4	2	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	2	no	—
958	D₄	—	4	2	no	—
959	D₄	—	8	1	no	—
960	D₄	—	8	2	no	—
961	D₄	—	8	2	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	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	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	4	1	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	8	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	1	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	—	8	1	no	—
989	C₂×C₄	—	8	1	no	—
990	C₂×C₄	—	8	1	no	—
991	C₂×C₄	—	8	2	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
996	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
997	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
999	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1000	C₈	—	2	2	no	—
1001	C₈	—	2	2	no	—
1002	C₈	—	2	2	no	—
1003	C₈	—	2	2	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	16	2	no	—
1022	C₂²	#577×C₆₇	1	2	yes	—
1023	C₂²	#577×C₆₇	1	2	yes	—
1024	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	#585×C₆₇	1	2	yes	—
1040	C₂	—	2	2	no	—
1041	C₂	—	2	2	no	—
1042	C₂	—	4	1	no	—
1043	C₂	—	4	2	no	—
1044	C₂	—	8	2	no	—
1045	C₂	—	8	1	no	—
1046	C₂	C₆₇×#3485	1	1	yes	characteristic
1047	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1048	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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
1. C₆₇×#3536	C₂	semidirect
2. C₆₇×#3492	C₂	semidirect
3. C₆₇×#3345	C₂	semidirect
4. C₆₇×#3344	C₂	semidirect
5. C₆₇×#3335	C₂	semidirect
6. C₆₇×#3335	C₂	semidirect
7. C₆₇×#3316	C₂	semidirect
8. C₆₇×#3306	C₂	semidirect
9. C₆₇×#3301	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₆₇×#3244	C₂	semidirect
12. C₆₇×#3204	C₂	semidirect
13. C₆₇×#3190	C₂	semidirect
14. C₆₇×#3188	C₂	semidirect
15. C₆₇×#3125	C₂	semidirect
16. C₆₇×#3099	C₂	semidirect
17. C₂×#481×C₆₇	C₂	semidirect
18. C₂×#483×C₆₇	C₂	semidirect
19. C₆₇×#2977	C₂	semidirect
23. #554×C₆₇	C₂²	semidirect
25. #553×C₆₇	C₂²	semidirect
34. #544×C₆₇	C₂²	semidirect
42. #537×C₆₇	C₂²	semidirect
48. #520×C₆₇	C₂²	semidirect
49. #520×C₆₇	C₂²	semidirect
51. #501×C₆₇	C₂²	semidirect
52. #498×C₆₇	C₂²	semidirect
53. #489×C₆₇	C₂²	semidirect
54. #488×C₆₇	C₂²	semidirect
55. #485×C₆₇	C₂²	semidirect
56. #485×C₆₇	C₂²	semidirect
60. #483×C₆₇	C₂²	semidirect
61. #483×C₆₇	C₂²	semidirect
62. #483×C₆₇	C₂²	semidirect
63. #483×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
72. #481×C₆₇	C₂²	semidirect
73. #481×C₆₇	C₂²	semidirect
74. #480×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #476×C₆₇	C₂²	semidirect
79. #475×C₆₇	C₂²	semidirect
80. #475×C₆₇	C₂²	semidirect
81. #470×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
87. #465×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #464×C₆₇	C₂²	semidirect
90. #463×C₆₇	C₂²	semidirect
91. #452×C₆₇	C₂²	semidirect
92. #452×C₆₇	C₂²	semidirect
93. #451×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #448×C₆₇	C₂²	semidirect
99. #442×C₆₇	C₂²	semidirect
100. #441×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. #435×C₆₇	C₂²	semidirect
106. C₈×D₄×C₆₇	C₂²	semidirect
107. #433×C₆₇	C₂²	semidirect
108. #428×C₆₇	C₂²	semidirect
110. C₂×#106×C₆₇	C₂²	semidirect
111. C₂×#106×C₆₇	C₂²	semidirect
112. #417×C₆₇	C₂²	semidirect
113. #416×C₆₇	C₂²	semidirect
114. C₂×#103×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
515. #61765	C₆₇	direct (N × H)
525. #3536	C₂×C₆₇	semidirect
526. #3492	C₂×C₆₇	semidirect
527. #3345	C₂×C₆₇	semidirect
528. #3344	C₂×C₆₇	semidirect
529. #3335	C₂×C₆₇	semidirect
530. #3335	C₂×C₆₇	semidirect
531. #3316	C₂×C₆₇	semidirect
532. #3306	C₂×C₆₇	semidirect
533. #3301	C₂×C₆₇	semidirect
534. #3296	C₂×C₆₇	semidirect
535. #3244	C₂×C₆₇	semidirect
536. #3204	C₂×C₆₇	semidirect
537. #3190	C₂×C₆₇	semidirect
538. #3188	C₂×C₆₇	semidirect
539. #3125	C₂×C₆₇	semidirect
540. #3099	C₂×C₆₇	semidirect
541. C₂×#481	C₂×C₆₇	semidirect
542. C₂×#483	C₂×C₆₇	semidirect
543. #2977	C₂×C₆₇	semidirect
544. C₆₇	#61765	direct (N × H)
548. #554	C₂²×C₆₇	semidirect
550. #553	C₂²×C₆₇	semidirect
559. #544	C₂²×C₆₇	semidirect
567. #537	C₂²×C₆₇	semidirect
573. #520	C₂²×C₆₇	semidirect
574. #520	C₂²×C₆₇	semidirect
576. #501	C₂²×C₆₇	semidirect
577. #498	C₂²×C₆₇	semidirect
578. #489	C₂²×C₆₇	semidirect
579. #488	C₂²×C₆₇	semidirect
580. #485	C₂²×C₆₇	semidirect
581. #485	C₂²×C₆₇	semidirect
585. #483	C₂²×C₆₇	semidirect
586. #483	C₂²×C₆₇	semidirect
587. #483	C₂²×C₆₇	semidirect
588. #483	C₂²×C₆₇	semidirect
589. #483	C₂²×C₆₇	semidirect
591. #482	C₂²×C₆₇	semidirect
597. #481	C₂²×C₆₇	semidirect
598. #481	C₂²×C₆₇	semidirect
599. #480	C₂²×C₆₇	semidirect
600. #479	C₂²×C₆₇	semidirect
601. #478	C₂²×C₆₇	semidirect
602. #476	C₂²×C₆₇	semidirect
603. #476	C₂²×C₆₇	semidirect
604. #475	C₂²×C₆₇	semidirect
605. #475	C₂²×C₆₇	semidirect
606. #470	C₂²×C₆₇	semidirect
607. #469	C₂²×C₆₇	semidirect
612. #465	C₂²×C₆₇	semidirect
613. #465	C₂²×C₆₇	semidirect
614. #464	C₂²×C₆₇	semidirect
615. #463	C₂²×C₆₇	semidirect
616. #452	C₂²×C₆₇	semidirect
617. #452	C₂²×C₆₇	semidirect
618. #451	C₂²×C₆₇	semidirect
621. #449	C₂²×C₆₇	semidirect
622. #448	C₂²×C₆₇	semidirect
624. #442	C₂²×C₆₇	semidirect
625. #441	C₂²×C₆₇	semidirect
626. C₄×SD₁₆	C₂²×C₆₇	semidirect
627. C₄×SD₁₆	C₂²×C₆₇	semidirect
629. #435	C₂²×C₆₇	semidirect
631. C₈×D₄	C₂²×C₆₇	semidirect
632. #433	C₂²×C₆₇	semidirect
633. #428	C₂²×C₆₇	semidirect
635. C₂×#106	C₂²×C₆₇	semidirect
636. C₂×#106	C₂²×C₆₇	semidirect
637. #417	C₂²×C₆₇	semidirect
638. #416	C₂²×C₆₇	semidirect
639. C₂×#103	C₂²×C₆₇	semidirect
641. #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×#3492	2
C₆₇×#3345	2
C₆₇×#3344	2
C₆₇×#3335	2
C₆₇×#3316	2
C₆₇×#3306	2
C₆₇×#3301	2
C₆₇×#3296	2
C₆₇×#3244	2
C₆₇×#3204	2
C₆₇×#3190	2
C₆₇×#3188	2
C₆₇×#3125	2
C₆₇×#3099	2
C₂×#481×C₆₇	2
C₂×#483×C₆₇	2
C₆₇×#2977	2
#61765	67

Subgroups — C67×#61765 #30741016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61765 #30741016