Subgroups — C₆₇×#61784 #30741035

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3355	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3339	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3199	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#560×C₆₇	—	2	2	no	—
25	#559×C₆₇	—	2	2	no	—
26	#556×C₆₇	—	2	1	no	—
27	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#555×C₆₇	C₂²	1	1	yes	characteristic
29	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#553×C₆₇	C₂²	1	2	yes	complemented
31	#553×C₆₇	C₂²	1	2	yes	complemented
32	#553×C₆₇	C₂²	1	2	yes	complemented
33	#550×C₆₇	—	2	1	no	—
34	#550×C₆₇	—	2	1	no	—
35	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#547×C₆₇	C₂²	1	1	yes	characteristic
37	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	2	yes	complemented
41	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#542×C₆₇	—	2	1	no	—
43	#538×C₆₇	—	2	2	no	—
44	#538×C₆₇	—	2	2	no	—
45	#537×C₆₇	C₂²	1	2	yes	—
46	#535×C₆₇	—	2	1	no	—
47	#535×C₆₇	C₂²	1	2	yes	—
48	#535×C₆₇	C₂²	1	2	yes	complemented
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#529×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	1	no	—
54	#525×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#499×C₆₇	C₂²	1	2	yes	complemented
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#488×C₆₇	C₂²	1	2	yes	complemented
61	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#484×C₆₇	C₂²	1	2	yes	complemented
66	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#482×C₆₇	C₂²	1	2	yes	—
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#482×C₆₇	C₂²	1	2	yes	complemented
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#481×C₆₇	C₂²	1	1	yes	characteristic
76	#481×C₆₇	C₂²	1	2	yes	complemented
77	#481×C₆₇	C₂²	1	2	yes	complemented
78	#480×C₆₇	C₂²	1	2	yes	complemented
79	#480×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#478×C₆₇	C₂²	1	2	yes	complemented
84	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#469×C₆₇	C₂²	1	2	yes	—
93	#469×C₆₇	C₂²	1	2	yes	—
94	#469×C₆₇	C₂²	1	2	yes	complemented
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#466×C₆₇	C₂²	1	2	yes	—
97	#466×C₆₇	C₂²	1	2	yes	—
98	#466×C₆₇	C₂²	1	2	yes	complemented
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#463×C₆₇	C₂²	1	1	yes	characteristic
101	#463×C₆₇	C₂²	1	1	yes	characteristic
102	#459×C₆₇	C₂²	1	1	yes	characteristic
103	#459×C₆₇	C₂²	1	1	yes	characteristic
104	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#449×C₆₇	C₂²	1	2	yes	complemented
106	#449×C₆₇	C₂²	1	2	yes	complemented
107	#447×C₆₇	C₂²	1	2	yes	—
108	#447×C₆₇	C₂²	1	2	yes	—
109	#447×C₆₇	C₂²	1	1	yes	characteristic
110	#447×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
116	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
117	#436×C₆₇	C₂²	1	2	yes	complemented
118	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
122	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#428×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	2	yes	complemented
127	#427×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	2	yes	complemented
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
133	#408×C₆₇	C₂²	1	2	yes	complemented
134	#408×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₇	—	2	1	no	—
142	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	—	2	1	no	—
145	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₇	C₂³	1	2	yes	—
148	C₂×D₈×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	#127×C₆₇	—	2	1	no	—
160	#127×C₆₇	—	2	2	no	—
161	#127×C₆₇	—	2	2	no	—
162	#127×C₆₇	D₄	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	1	yes	characteristic
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	1	no	—
169	#125×C₆₇	C₂³	1	2	yes	—
170	#125×C₆₇	C₂³	1	1	yes	characteristic
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	—	2	1	no	—
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	—	2	2	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	D₄	1	2	yes	—
178	#124×C₆₇	C₂³	1	1	yes	characteristic
179	#123×C₆₇	—	2	1	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	#121×C₆₇	—	2	1	no	—
196	#121×C₆₇	—	2	1	no	—
197	#121×C₆₇	—	2	2	no	—
198	#121×C₆₇	—	2	2	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	D₄	1	1	yes	characteristic
208	#121×C₆₇	D₄	1	1	yes	characteristic
209	#121×C₆₇	D₄	1	2	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#121×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	C₂³	1	2	yes	—
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#121×C₆₇	C₂³	1	1	yes	characteristic
219	#120×C₆₇	—	2	2	no	—
220	#120×C₆₇	—	2	2	no	—
221	#120×C₆₇	—	2	2	no	—
222	#120×C₆₇	—	2	2	no	—
223	#120×C₆₇	—	2	2	no	—
224	#120×C₆₇	—	2	2	no	—
225	C₄×Q₈×C₆₇	—	2	2	no	—
226	C₄×Q₈×C₆₇	—	2	1	no	—
227	C₄×Q₈×C₆₇	—	2	1	no	—
228	C₄×Q₈×C₆₇	—	2	1	no	—
229	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	2	yes	—
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	1	no	—
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	2	yes	—
255	#117×C₆₇	C₂³	1	2	yes	—
256	#117×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
263	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
264	#107×C₆₇	C₂³	1	2	yes	—
265	#107×C₆₇	C₂³	1	2	yes	—
266	#107×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	2	yes	—
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#106×C₆₇	C₂³	1	2	yes	—
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#103×C₆₇	C₂³	1	2	yes	—
283	#103×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	1	yes	characteristic
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#102×C₆₇	C₂³	1	2	yes	—
287	#102×C₆₇	C₂³	1	2	yes	—
288	#102×C₆₇	C₂³	1	1	yes	characteristic
289	#102×C₆₇	C₂³	1	1	yes	characteristic
290	#102×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	1	yes	characteristic
293	#102×C₆₇	C₂³	1	1	yes	characteristic
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	1	yes	characteristic
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₂⁴×C₆₇	—	2	1	no	—
313	C₂⁴×C₆₇	—	2	2	no	—
314	#41×C₆₇	—	4	2	no	—
315	#41×C₆₇	—	4	2	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	8	2	no	—
319	#41×C₆₇	—	8	2	no	—
320	#41×C₆₇	—	8	2	no	—
321	#41×C₆₇	—	8	2	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	1	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₆₇	—	2	1	no	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	1	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	4	1	no	—
342	C₂×D₄×C₆₇	—	4	1	no	—
343	C₂×D₄×C₆₇	—	4	2	no	—
344	C₂×D₄×C₆₇	—	4	2	no	—
345	C₂×D₄×C₆₇	—	8	2	no	—
346	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₆₇	—	2	1	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	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	8	2	no	—
368	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
373	SD₁₆×C₆₇	—	4	1	no	—
374	SD₁₆×C₆₇	—	4	1	no	—
375	D₈×C₆₇	—	4	2	no	—
376	D₈×C₆₇	—	4	1	no	—
377	D₈×C₆₇	—	4	2	no	—
378	D₈×C₆₇	—	4	1	no	—
379	M₁₆×C₆₇	—	4	2	no	—
380	M₁₆×C₆₇	—	4	2	no	—
381	C₂×C₈×C₆₇	—	4	2	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	1	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₄²×C₆₇	—	2	2	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	—	2	2	no	—
453	C₂³×C₆₇	—	4	2	no	—
454	C₂³×C₆₇	—	8	1	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	—	8	2	no	—
457	C₂³×C₆₇	—	8	2	no	—
458	C₂³×C₆₇	—	8	2	no	—
459	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	2	1	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	4	2	no	—
466	Q₈×C₆₇	—	4	2	no	—
467	Q₈×C₆₇	—	8	1	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	2	no	—
470	D₄×C₆₇	—	2	1	no	—
471	D₄×C₆₇	—	2	1	no	—
472	D₄×C₆₇	—	2	1	no	—
473	D₄×C₆₇	—	2	1	no	—
474	D₄×C₆₇	—	2	1	no	—
475	D₄×C₆₇	—	2	1	no	—
476	D₄×C₆₇	—	2	2	no	—
477	D₄×C₆₇	—	2	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	2	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	2	no	—
484	D₄×C₆₇	—	8	1	no	—
485	D₄×C₆₇	—	8	2	no	—
486	D₄×C₆₇	—	8	1	no	—
487	D₄×C₆₇	—	8	2	no	—
488	D₄×C₆₇	—	8	2	no	—
489	D₄×C₆₇	—	8	2	no	—
490	D₄×C₆₇	—	8	2	no	—
491	D₄×C₆₇	—	8	2	no	—
492	D₄×C₆₇	—	8	2	no	—
493	D₄×C₆₇	—	8	2	no	—
494	D₄×C₆₇	—	8	2	no	—
495	D₄×C₆₇	—	8	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	4	1	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	4	2	no	—
514	C₂×C₄×C₆₇	—	4	2	no	—
515	C₂×C₄×C₆₇	—	8	1	no	—
516	C₂×C₄×C₆₇	—	8	1	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	8	1	no	—
520	C₂×C₄×C₆₇	—	8	2	no	—
521	C₂×C₄×C₆₇	—	8	2	no	—
522	C₂×C₄×C₆₇	—	8	2	no	—
523	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	2	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	—	2	1	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	—	4	2	no	—
549	C₂²×C₆₇	—	4	1	no	—
550	C₂²×C₆₇	—	4	2	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	1	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	2	no	—
558	C₂²×C₆₇	—	8	4	no	—
559	C₂²×C₆₇	—	16	4	no	—
560	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	1	no	—
567	C₄×C₆₇	—	4	1	no	—
568	C₄×C₆₇	—	4	2	no	—
569	C₄×C₆₇	—	4	1	no	—
570	C₄×C₆₇	—	4	1	no	—
571	C₄×C₆₇	—	4	1	no	—
572	C₄×C₆₇	—	4	1	no	—
573	C₄×C₆₇	—	4	2	no	—
574	C₄×C₆₇	—	4	2	no	—
575	C₄×C₆₇	#576	1	2	yes	—
576	C₄×C₆₇	#585	1	1	yes	characteristic
577	C₄×C₆₇	#585	1	1	yes	characteristic
578	#61784	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	1	no	—
581	C₂×C₆₇	—	4	2	no	—
582	C₂×C₆₇	—	8	1	no	—
583	C₂×C₆₇	—	8	1	no	—
584	C₂×C₆₇	—	8	2	no	—
585	C₂×C₆₇	—	8	1	no	—
586	C₂×C₆₇	#3485	1	1	yes	characteristic
587	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
588	C₂×C₆₇	#3584	1	1	yes	characteristic
589	#3546	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3355	C₂×C₆₇	1	2	yes	complemented
592	#3354	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3340	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3339	C₂×C₆₇	1	2	yes	complemented
596	#3334	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#3332	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#3325	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3322	C₂×C₆₇	1	2	yes	complemented
600	#3305	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3297	C₂×C₆₇	1	2	yes	complemented
602	#3294	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3228	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3199	C₂×C₆₇	1	2	yes	complemented
606	#3198	C₂×C₆₇	1	2	yes	complemented
607	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#3098	C₂×C₆₇	1	2	yes	complemented
610	#3096	C₂×C₆₇	1	2	yes	complemented
611	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
612	C₆₇	#61784	1	1	yes	characteristic, direct product factor, Sylow
613	#560	—	2	2	no	—
614	#559	—	2	2	no	—
615	#556	—	2	1	no	—
616	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	#555	C₂²×C₆₇	1	1	yes	characteristic
618	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#553	C₂²×C₆₇	1	2	yes	complemented
620	#553	C₂²×C₆₇	1	2	yes	complemented
621	#553	C₂²×C₆₇	1	2	yes	complemented
622	#550	—	2	1	no	—
623	#550	—	2	1	no	—
624	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#547	C₂²×C₆₇	1	1	yes	characteristic
626	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#546	—	2	1	no	—
629	#546	C₂²×C₆₇	1	2	yes	complemented
630	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#542	—	2	1	no	—
632	#538	—	2	2	no	—
633	#538	—	2	2	no	—
634	#537	C₂²×C₆₇	1	2	yes	—
635	#535	—	2	1	no	—
636	#535	C₂²×C₆₇	1	2	yes	—
637	#535	C₂²×C₆₇	1	2	yes	complemented
638	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#532	C₂²×C₆₇	1	1	yes	characteristic
640	#532	C₂²×C₆₇	1	1	yes	characteristic
641	#529	C₂²×C₆₇	1	1	yes	characteristic
642	#525	—	2	1	no	—
643	#525	—	2	1	no	—
644	#520	C₂²×C₆₇	1	2	yes	complemented
645	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#499	C₂²×C₆₇	1	2	yes	complemented
648	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#488	C₂²×C₆₇	1	2	yes	complemented
650	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	#485	C₂²×C₆₇	1	2	yes	complemented
653	#485	C₂²×C₆₇	1	2	yes	complemented
654	#484	C₂²×C₆₇	1	2	yes	complemented
655	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#482	C₂²×C₆₇	1	2	yes	—
657	#482	C₂²×C₆₇	1	2	yes	complemented
658	#482	C₂²×C₆₇	1	2	yes	complemented
659	#482	C₂²×C₆₇	1	2	yes	complemented
660	#482	C₂²×C₆₇	1	2	yes	complemented
661	#482	C₂²×C₆₇	1	2	yes	complemented
662	#482	C₂²×C₆₇	1	2	yes	complemented
663	#482	C₂²×C₆₇	1	2	yes	complemented
664	#481	C₂²×C₆₇	1	1	yes	characteristic
665	#481	C₂²×C₆₇	1	2	yes	complemented
666	#481	C₂²×C₆₇	1	2	yes	complemented
667	#480	C₂²×C₆₇	1	2	yes	complemented
668	#480	C₂²×C₆₇	1	2	yes	complemented
669	#480	C₂²×C₆₇	1	2	yes	complemented
670	#480	C₂²×C₆₇	1	2	yes	complemented
671	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#478	C₂²×C₆₇	1	2	yes	complemented
673	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	#478	C₂²×C₆₇	1	2	yes	complemented
675	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	#469	C₂²×C₆₇	1	2	yes	—
682	#469	C₂²×C₆₇	1	2	yes	—
683	#469	C₂²×C₆₇	1	2	yes	complemented
684	#468	C₂²×C₆₇	1	2	yes	complemented
685	#466	C₂²×C₆₇	1	2	yes	—
686	#466	C₂²×C₆₇	1	2	yes	—
687	#466	C₂²×C₆₇	1	2	yes	complemented
688	#465	C₂²×C₆₇	1	2	yes	complemented
689	#463	C₂²×C₆₇	1	1	yes	characteristic
690	#463	C₂²×C₆₇	1	1	yes	characteristic
691	#459	C₂²×C₆₇	1	1	yes	characteristic
692	#459	C₂²×C₆₇	1	1	yes	characteristic
693	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#449	C₂²×C₆₇	1	2	yes	complemented
695	#449	C₂²×C₆₇	1	2	yes	complemented
696	#447	C₂²×C₆₇	1	1	yes	characteristic
697	#447	C₂²×C₆₇	1	2	yes	—
698	#447	C₂²×C₆₇	1	2	yes	—
699	#447	C₂²×C₆₇	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
705	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
706	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#436	C₂²×C₆₇	1	2	yes	complemented
709	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
711	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#428	C₂²×C₆₇	1	2	yes	complemented
715	#428	C₂²×C₆₇	1	2	yes	complemented
716	#427	C₂²×C₆₇	1	2	yes	complemented
717	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
718	#418	C₂²×C₆₇	1	2	yes	complemented
719	#417	C₂²×C₆₇	1	2	yes	complemented
720	#416	C₂²×C₆₇	1	2	yes	complemented
721	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
722	#408	C₂²×C₆₇	1	2	yes	complemented
723	#408	C₂²×C₆₇	1	2	yes	complemented
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	—	2	1	no	—
728	C₂×#41	C₂³×C₆₇	1	2	yes	—
729	C₂×#41	C₂³×C₆₇	1	2	yes	—
730	C₂²×D₄	—	2	1	no	—
731	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
733	C₂³×C₄	—	2	1	no	—
734	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₆₇	1	2	yes	—
739	C₂×D₈	C₂³×C₆₇	1	2	yes	—
740	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
743	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
744	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
748	#127	—	2	1	no	—
749	#127	—	2	2	no	—
750	#127	—	2	2	no	—
751	#127	D₄×C₆₇	1	1	yes	characteristic
752	#127	C₂³×C₆₇	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#125	C₂³×C₆₇	1	1	yes	characteristic
759	#125	C₂³×C₆₇	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	D₄×C₆₇	1	2	yes	—
767	#124	C₂³×C₆₇	1	1	yes	characteristic
768	#123	—	2	1	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	D₄×C₆₇	1	1	yes	characteristic
797	#121	D₄×C₆₇	1	1	yes	characteristic
798	#121	D₄×C₆₇	1	2	yes	—
799	#121	C₂³×C₆₇	1	1	yes	characteristic
800	#121	C₂³×C₆₇	1	2	yes	—
801	#121	C₂³×C₆₇	1	2	yes	—
802	#121	C₂³×C₆₇	1	2	yes	—
803	#121	C₂³×C₆₇	1	2	yes	—
804	#121	C₂³×C₆₇	1	2	yes	—
805	#121	C₂³×C₆₇	1	2	yes	—
806	#121	C₂³×C₆₇	1	2	yes	—
807	#121	C₂³×C₆₇	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	C₄×Q₈	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₆₇	1	2	yes	—
838	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₆₇	1	2	yes	—
843	#117	C₂³×C₆₇	1	2	yes	—
844	#117	C₂³×C₆₇	1	2	yes	—
845	#117	C₂³×C₆₇	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
848	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
849	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
853	#107	C₂³×C₆₇	1	1	yes	characteristic
854	#107	C₂³×C₆₇	1	2	yes	—
855	#107	C₂³×C₆₇	1	2	yes	—
856	#107	C₂³×C₆₇	1	2	yes	—
857	#107	C₂³×C₆₇	1	2	yes	—
858	#107	C₂³×C₆₇	1	1	yes	characteristic
859	#107	C₂³×C₆₇	1	2	yes	—
860	#107	C₂³×C₆₇	1	2	yes	—
861	#106	C₂³×C₆₇	1	1	yes	characteristic
862	#106	C₂³×C₆₇	1	2	yes	—
863	#106	C₂³×C₆₇	1	1	yes	characteristic
864	#106	C₂³×C₆₇	1	2	yes	—
865	#106	C₂³×C₆₇	1	2	yes	—
866	#106	C₂³×C₆₇	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
871	#103	C₂³×C₆₇	1	1	yes	characteristic
872	#103	C₂³×C₆₇	1	2	yes	—
873	#103	C₂³×C₆₇	1	1	yes	characteristic
874	#103	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	1	yes	characteristic
876	#102	C₂³×C₆₇	1	2	yes	—
877	#102	C₂³×C₆₇	1	2	yes	—
878	#102	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	2	yes	—
880	#102	C₂³×C₆₇	1	2	yes	—
881	#102	C₂³×C₆₇	1	2	yes	—
882	#102	C₂³×C₆₇	1	1	yes	characteristic
883	#102	C₂³×C₆₇	1	2	yes	—
884	#102	C₂³×C₆₇	1	2	yes	—
885	#102	C₂³×C₆₇	1	1	yes	characteristic
886	#102	C₂³×C₆₇	1	1	yes	characteristic
887	#102	C₂³×C₆₇	1	2	yes	—
888	#102	C₂³×C₆₇	1	2	yes	—
889	#102	C₂³×C₆₇	1	1	yes	characteristic
890	#102	C₂³×C₆₇	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
898	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₆₇	1	2	yes	—
901	C₂⁴	—	2	1	no	—
902	C₂⁴	—	2	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	4	1	no	—
931	C₂×D₄	—	4	1	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	8	2	no	—
935	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
936	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
938	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
941	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
943	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	8	2	no	—
957	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
962	SD₁₆	—	4	1	no	—
963	SD₁₆	—	4	1	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	1	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	1	no	—
968	M₁₆	—	4	2	no	—
969	M₁₆	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
976	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	8	1	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1049	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	—	16	4	no	—
1149	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	#576×C₆₇	1	2	yes	—
1165	C₄	#585×C₆₇	1	1	yes	characteristic
1166	C₄	#585×C₆₇	1	1	yes	characteristic
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	2	no	—
1174	C₂	C₆₇×#3485	1	1	yes	characteristic
1175	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1176	C₂	C₆₇×#3584	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3546	C₂	semidirect
2. C₆₇×#3506	C₂	semidirect
3. C₆₇×#3355	C₂	semidirect
4. C₆₇×#3354	C₂	semidirect
5. C₆₇×#3353	C₂	semidirect
6. C₆₇×#3340	C₂	semidirect
7. C₆₇×#3339	C₂	semidirect
8. C₆₇×#3334	C₂	semidirect
9. C₆₇×#3332	C₂	semidirect
10. C₆₇×#3325	C₂	semidirect
11. C₆₇×#3322	C₂	semidirect
12. C₆₇×#3305	C₂	semidirect
13. C₆₇×#3297	C₂	semidirect
14. C₆₇×#3294	C₂	semidirect
15. C₆₇×#3233	C₂	semidirect
16. C₆₇×#3228	C₂	semidirect
17. C₆₇×#3199	C₂	semidirect
18. C₆₇×#3198	C₂	semidirect
19. C₆₇×#3105	C₂	semidirect
20. C₆₇×#3100	C₂	semidirect
21. C₆₇×#3098	C₂	semidirect
22. C₆₇×#3096	C₂	semidirect
23. C₆₇×#2979	C₂	semidirect
27. #556×C₆₇	C₂²	semidirect
29. #555×C₆₇	C₂²	semidirect
30. #553×C₆₇	C₂²	semidirect
31. #553×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
35. #550×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
40. #546×C₆₇	C₂²	semidirect
41. D₄²×C₆₇	C₂²	semidirect
48. #535×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
56. C₂×C₄×D₄×C₆₇	C₂²	semidirect
57. #500×C₆₇	C₂²	semidirect
58. #499×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #488×C₆₇	C₂²	semidirect
61. #486×C₆₇	C₂²	semidirect
62. #486×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #484×C₆₇	C₂²	semidirect
66. #484×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
76. #481×C₆₇	C₂²	semidirect
77. #481×C₆₇	C₂²	semidirect
78. #480×C₆₇	C₂²	semidirect
79. #480×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #478×C₆₇	C₂²	semidirect
84. #478×C₆₇	C₂²	semidirect
85. #478×C₆₇	C₂²	semidirect
86. #477×C₆₇	C₂²	semidirect
87. #476×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #474×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
94. #469×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
98. #466×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
104. #450×C₆₇	C₂²	semidirect
105. #449×C₆₇	C₂²	semidirect
106. #449×C₆₇	C₂²	semidirect
110. #447×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
112. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×D₈×C₆₇	C₂²	semidirect
116. C₄×D₈×C₆₇	C₂²	semidirect
117. #436×C₆₇	C₂²	semidirect
118. #436×C₆₇	C₂²	semidirect
119. #436×C₆₇	C₂²	semidirect
120. C₈×D₄×C₆₇	C₂²	semidirect
121. C₈×D₄×C₆₇	C₂²	semidirect
122. C₈×D₄×C₆₇	C₂²	semidirect
123. #431×C₆₇	C₂²	semidirect
124. #431×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #427×C₆₇	C₂²	semidirect
128. C₂×#107×C₆₇	C₂²	semidirect
129. #418×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#102×C₆₇	C₂²	semidirect
133. #408×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
578. #61784	C₆₇	direct (N × H)
589. #3546	C₂×C₆₇	semidirect
590. #3506	C₂×C₆₇	semidirect
591. #3355	C₂×C₆₇	semidirect
592. #3354	C₂×C₆₇	semidirect
593. #3353	C₂×C₆₇	semidirect
594. #3340	C₂×C₆₇	semidirect
595. #3339	C₂×C₆₇	semidirect
596. #3334	C₂×C₆₇	semidirect
597. #3332	C₂×C₆₇	semidirect
598. #3325	C₂×C₆₇	semidirect
599. #3322	C₂×C₆₇	semidirect
600. #3305	C₂×C₆₇	semidirect
601. #3297	C₂×C₆₇	semidirect
602. #3294	C₂×C₆₇	semidirect
603. #3233	C₂×C₆₇	semidirect
604. #3228	C₂×C₆₇	semidirect
605. #3199	C₂×C₆₇	semidirect
606. #3198	C₂×C₆₇	semidirect
607. #3105	C₂×C₆₇	semidirect
608. #3100	C₂×C₆₇	semidirect
609. #3098	C₂×C₆₇	semidirect
610. #3096	C₂×C₆₇	semidirect
611. #2979	C₂×C₆₇	semidirect
612. C₆₇	#61784	direct (N × H)
616. #556	C₂²×C₆₇	semidirect
618. #555	C₂²×C₆₇	semidirect
619. #553	C₂²×C₆₇	semidirect
620. #553	C₂²×C₆₇	semidirect
621. #553	C₂²×C₆₇	semidirect
624. #550	C₂²×C₆₇	semidirect
626. #547	C₂²×C₆₇	semidirect
627. #547	C₂²×C₆₇	semidirect
629. #546	C₂²×C₆₇	semidirect
630. D₄²	C₂²×C₆₇	semidirect
637. #535	C₂²×C₆₇	semidirect
638. #533	C₂²×C₆₇	semidirect
644. #520	C₂²×C₆₇	semidirect
645. C₂×C₄×D₄	C₂²×C₆₇	semidirect
646. #500	C₂²×C₆₇	semidirect
647. #499	C₂²×C₆₇	semidirect
648. #498	C₂²×C₆₇	semidirect
649. #488	C₂²×C₆₇	semidirect
650. #486	C₂²×C₆₇	semidirect
651. #486	C₂²×C₆₇	semidirect
652. #485	C₂²×C₆₇	semidirect
653. #485	C₂²×C₆₇	semidirect
654. #484	C₂²×C₆₇	semidirect
655. #484	C₂²×C₆₇	semidirect
657. #482	C₂²×C₆₇	semidirect
658. #482	C₂²×C₆₇	semidirect
659. #482	C₂²×C₆₇	semidirect
660. #482	C₂²×C₆₇	semidirect
661. #482	C₂²×C₆₇	semidirect
662. #482	C₂²×C₆₇	semidirect
663. #482	C₂²×C₆₇	semidirect
665. #481	C₂²×C₆₇	semidirect
666. #481	C₂²×C₆₇	semidirect
667. #480	C₂²×C₆₇	semidirect
668. #480	C₂²×C₆₇	semidirect
669. #480	C₂²×C₆₇	semidirect
670. #480	C₂²×C₆₇	semidirect
671. #478	C₂²×C₆₇	semidirect
672. #478	C₂²×C₆₇	semidirect
673. #478	C₂²×C₆₇	semidirect
674. #478	C₂²×C₆₇	semidirect
675. #477	C₂²×C₆₇	semidirect
676. #476	C₂²×C₆₇	semidirect
677. #475	C₂²×C₆₇	semidirect
678. #474	C₂²×C₆₇	semidirect
679. #474	C₂²×C₆₇	semidirect
680. #474	C₂²×C₆₇	semidirect
683. #469	C₂²×C₆₇	semidirect
684. #468	C₂²×C₆₇	semidirect
687. #466	C₂²×C₆₇	semidirect
688. #465	C₂²×C₆₇	semidirect
693. #450	C₂²×C₆₇	semidirect
694. #449	C₂²×C₆₇	semidirect
695. #449	C₂²×C₆₇	semidirect
699. #447	C₂²×C₆₇	semidirect
700. C₄×SD₁₆	C₂²×C₆₇	semidirect
701. C₄×SD₁₆	C₂²×C₆₇	semidirect
704. C₄×D₈	C₂²×C₆₇	semidirect
705. C₄×D₈	C₂²×C₆₇	semidirect
706. #436	C₂²×C₆₇	semidirect
707. #436	C₂²×C₆₇	semidirect
708. #436	C₂²×C₆₇	semidirect
709. C₈×D₄	C₂²×C₆₇	semidirect
710. C₈×D₄	C₂²×C₆₇	semidirect
711. C₈×D₄	C₂²×C₆₇	semidirect
712. #431	C₂²×C₆₇	semidirect
713. #431	C₂²×C₆₇	semidirect
714. #428	C₂²×C₆₇	semidirect
715. #428	C₂²×C₆₇	semidirect
716. #427	C₂²×C₆₇	semidirect
717. C₂×#107	C₂²×C₆₇	semidirect
718. #418	C₂²×C₆₇	semidirect
719. #417	C₂²×C₆₇	semidirect
720. #416	C₂²×C₆₇	semidirect
721. C₂×#102	C₂²×C₆₇	semidirect
722. #408	C₂²×C₆₇	semidirect
723. #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×#3546	2
C₆₇×#3506	2
C₆₇×#3355	2
C₆₇×#3354	2
C₆₇×#3353	2
C₆₇×#3340	2
C₆₇×#3339	2
C₆₇×#3334	2
C₆₇×#3332	2
C₆₇×#3325	2
C₆₇×#3322	2
C₆₇×#3305	2
C₆₇×#3297	2
C₆₇×#3294	2
C₆₇×#3233	2
C₆₇×#3228	2
C₆₇×#3199	2
C₆₇×#3198	2
C₆₇×#3105	2
C₆₇×#3100	2
C₆₇×#3098	2
C₆₇×#3096	2
C₆₇×#2979	2
#61784	67

Subgroups — C67×#61784 #30741035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61784 #30741035