Subgroups — C₆₇×#61650 #30740901

Order 17152.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1144 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×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3332	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	#562×C₆₇	—	2	2	no	—
27	#554×C₆₇	C₂²	1	2	yes	complemented
28	#550×C₆₇	—	2	1	no	—
29	#550×C₆₇	—	2	1	no	—
30	#550×C₆₇	C₂²	1	2	yes	—
31	#550×C₆₇	C₂²	1	2	yes	complemented
32	#548×C₆₇	—	2	1	no	—
33	#548×C₆₇	—	2	1	no	—
34	#548×C₆₇	C₂²	1	2	yes	—
35	#548×C₆₇	C₂²	1	2	yes	complemented
36	#548×C₆₇	C₂²	1	2	yes	complemented
37	#547×C₆₇	C₂²	1	2	yes	complemented
38	#546×C₆₇	—	2	2	no	—
39	#546×C₆₇	C₂²	1	2	yes	complemented
40	#543×C₆₇	—	2	1	no	—
41	#542×C₆₇	C₂²	1	2	yes	—
42	#539×C₆₇	—	2	1	no	—
43	#538×C₆₇	—	2	1	no	—
44	#537×C₆₇	—	2	1	no	—
45	#537×C₆₇	C₂²	1	2	yes	—
46	#535×C₆₇	—	2	2	no	—
47	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#525×C₆₇	—	2	2	no	—
50	#525×C₆₇	C₂²	1	1	yes	characteristic
51	#525×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
54	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#496×C₆₇	C₂²	1	2	yes	complemented
56	#495×C₆₇	C₂²	1	2	yes	complemented
57	#489×C₆₇	C₂²	1	2	yes	complemented
58	#486×C₆₇	C₂²	1	2	yes	complemented
59	#485×C₆₇	C₂²	1	2	yes	complemented
60	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#482×C₆₇	C₂²	1	2	yes	—
63	#481×C₆₇	C₂²	1	2	yes	complemented
64	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#480×C₆₇	C₂²	1	2	yes	complemented
66	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#477×C₆₇	C₂²	1	2	yes	complemented
68	#475×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#469×C₆₇	C₂²	1	2	yes	complemented
71	#469×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#468×C₆₇	C₂²	1	2	yes	complemented
74	#468×C₆₇	C₂²	1	2	yes	complemented
75	#466×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#460×C₆₇	C₂²	1	2	yes	complemented
82	#459×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#452×C₆₇	C₂²	1	2	yes	complemented
87	#451×C₆₇	C₂²	1	2	yes	complemented
88	#451×C₆₇	C₂²	1	2	yes	complemented
89	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#450×C₆₇	C₂²	1	2	yes	complemented
92	#449×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#448×C₆₇	C₂²	1	2	yes	—
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#447×C₆₇	C₂²	1	2	yes	—
102	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#441×C₆₇	C₂²	1	2	yes	complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
107	#436×C₆₇	C₂²	1	2	yes	complemented
108	#436×C₆₇	C₂²	1	2	yes	complemented
109	#435×C₆₇	C₂²	1	2	yes	complemented
110	#435×C₆₇	C₂²	1	2	yes	complemented
111	#433×C₆₇	C₂²	1	2	yes	complemented
112	#417×C₆₇	C₂²	1	2	yes	—
113	#417×C₆₇	C₂²	1	2	yes	complemented
114	#417×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic
118	#407×C₆₇	C₂²	1	1	yes	characteristic
119	2₋¹⁺⁴×C₆₇	—	4	4	no	—
120	C₂×#41×C₆₇	—	2	2	no	—
121	C₂×#41×C₆₇	—	2	1	no	—
122	C₂×#41×C₆₇	—	2	2	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	2	1	no	—
125	C₂×#41×C₆₇	—	4	4	no	—
126	C₂×#41×C₆₇	C₂³	1	2	yes	—
127	C₂×#41×C₆₇	C₂³	1	2	yes	—
128	C₂×#41×C₆₇	C₂³	1	2	yes	—
129	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×#41×C₆₇	C₂³	1	2	yes	—
131	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	—	2	1	no	—
133	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	—	2	1	no	—
137	C₂²×D₄×C₆₇	—	2	1	no	—
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	—	2	1	no	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	#137×C₆₇	—	4	4	no	—
143	#137×C₆₇	—	4	4	no	—
144	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
145	#135×C₆₇	—	4	4	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
163	#127×C₆₇	—	2	2	no	—
164	#127×C₆₇	—	2	2	no	—
165	#127×C₆₇	—	2	1	no	—
166	#127×C₆₇	C₂³	1	2	yes	—
167	#126×C₆₇	—	2	2	no	—
168	#125×C₆₇	—	2	2	no	—
169	#124×C₆₇	—	2	1	no	—
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	C₂³	1	2	yes	—
175	#124×C₆₇	C₂³	1	2	yes	—
176	#123×C₆₇	—	2	1	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	—	2	1	no	—
184	C₂²⋊Q₈×C₆₇	—	2	1	no	—
185	C₂²⋊Q₈×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
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	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	D₄	1	1	yes	characteristic
215	#121×C₆₇	D₄	1	1	yes	characteristic
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#121×C₆₇	C₂³	1	1	yes	characteristic
219	#121×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	C₂³	1	2	yes	—
221	#121×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	C₂³	1	1	yes	characteristic
223	#120×C₆₇	—	2	1	no	—
224	#120×C₆₇	—	2	2	no	—
225	#120×C₆₇	—	2	2	no	—
226	#120×C₆₇	—	2	2	no	—
227	#120×C₆₇	D₄	1	2	yes	—
228	C₄×Q₈×C₆₇	—	2	1	no	—
229	C₄×Q₈×C₆₇	—	2	1	no	—
230	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	C₂³	1	1	yes	characteristic
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
248	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
254	#107×C₆₇	C₂³	1	2	yes	—
255	#107×C₆₇	C₂³	1	2	yes	—
256	#106×C₆₇	C₂³	1	2	yes	—
257	#106×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×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	#103×C₆₇	C₂³	1	2	yes	—
267	#103×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	#102×C₆₇	C₂³	1	2	yes	—
273	#102×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
284	#97×C₆₇	C₂³	1	2	yes	—
285	C₄×C₈×C₆₇	C₂³	1	2	yes	—
286	C₂⁴×C₆₇	—	2	1	no	—
287	C₂⁴×C₆₇	—	2	1	no	—
288	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
289	#41×C₆₇	—	2	4	no	—
290	#41×C₆₇	—	2	4	no	—
291	#41×C₆₇	—	2	4	no	—
292	#41×C₆₇	—	4	2	no	—
293	#41×C₆₇	—	4	2	no	—
294	#41×C₆₇	—	4	2	no	—
295	#41×C₆₇	—	4	2	no	—
296	#41×C₆₇	—	4	2	no	—
297	#41×C₆₇	—	4	8	no	—
298	#41×C₆₇	—	4	2	no	—
299	#41×C₆₇	—	4	2	no	—
300	#41×C₆₇	—	4	4	no	—
301	#41×C₆₇	—	4	4	no	—
302	#41×C₆₇	—	4	4	no	—
303	#41×C₆₇	—	8	4	no	—
304	C₂×Q₈×C₆₇	—	2	4	no	—
305	C₂×Q₈×C₆₇	—	2	1	no	—
306	C₂×Q₈×C₆₇	—	2	2	no	—
307	C₂×Q₈×C₆₇	—	2	1	no	—
308	C₂×Q₈×C₆₇	—	2	2	no	—
309	C₂×Q₈×C₆₇	—	2	4	no	—
310	C₂×Q₈×C₆₇	—	4	2	no	—
311	C₂×Q₈×C₆₇	—	4	2	no	—
312	C₂×Q₈×C₆₇	—	4	4	no	—
313	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
317	C₂×D₄×C₆₇	—	2	2	no	—
318	C₂×D₄×C₆₇	—	2	1	no	—
319	C₂×D₄×C₆₇	—	2	2	no	—
320	C₂×D₄×C₆₇	—	2	2	no	—
321	C₂×D₄×C₆₇	—	2	2	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	2	2	no	—
324	C₂×D₄×C₆₇	—	2	1	no	—
325	C₂×D₄×C₆₇	—	2	1	no	—
326	C₂×D₄×C₆₇	—	2	2	no	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	1	no	—
330	C₂×D₄×C₆₇	—	2	2	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	1	no	—
333	C₂×D₄×C₆₇	—	4	2	no	—
334	C₂×D₄×C₆₇	—	4	2	no	—
335	C₂×D₄×C₆₇	—	4	4	no	—
336	C₂×D₄×C₆₇	—	8	2	no	—
337	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
342	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	1	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	1	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	4	2	no	—
357	C₂²×C₄×C₆₇	—	4	4	no	—
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₆₇	—	2	4	no	—
366	Q₁₆×C₆₇	—	2	4	no	—
367	Q₁₆×C₆₇	—	4	2	no	—
368	SD₁₆×C₆₇	—	2	4	no	—
369	SD₁₆×C₆₇	—	2	4	no	—
370	SD₁₆×C₆₇	—	4	2	no	—
371	SD₁₆×C₆₇	—	4	2	no	—
372	SD₁₆×C₆₇	—	4	2	no	—
373	SD₁₆×C₆₇	—	4	2	no	—
374	D₈×C₆₇	—	4	2	no	—
375	D₈×C₆₇	—	4	2	no	—
376	D₈×C₆₇	—	4	2	no	—
377	M₁₆×C₆₇	—	4	2	no	—
378	M₁₆×C₆₇	—	4	2	no	—
379	M₁₆×C₆₇	—	4	2	no	—
380	C₂×C₈×C₆₇	—	4	2	no	—
381	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
382	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
383	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
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	1	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₆₇	—	2	2	no	—
406	C₂²⋊C₄×C₆₇	—	2	2	no	—
407	C₂²⋊C₄×C₆₇	—	2	1	no	—
408	C₂²⋊C₄×C₆₇	—	2	1	no	—
409	C₂²⋊C₄×C₆₇	—	2	1	no	—
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	1	no	—
416	C₂²⋊C₄×C₆₇	—	2	1	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
428	C₄²×C₆₇	—	2	2	no	—
429	C₄²×C₆₇	—	2	2	no	—
430	C₄²×C₆₇	—	2	1	no	—
431	C₄²×C₆₇	—	2	2	no	—
432	C₄²×C₆₇	C₂⁴	1	2	yes	—
433	C₂³×C₆₇	—	2	2	no	—
434	C₂³×C₆₇	—	2	2	no	—
435	C₂³×C₆₇	—	2	1	no	—
436	C₂³×C₆₇	—	4	1	no	—
437	C₂³×C₆₇	—	4	1	no	—
438	C₂³×C₆₇	—	4	1	no	—
439	C₂³×C₆₇	—	4	2	no	—
440	C₂³×C₆₇	—	4	2	no	—
441	C₂³×C₆₇	—	8	1	no	—
442	C₂³×C₆₇	—	8	1	no	—
443	C₂³×C₆₇	—	8	1	no	—
444	C₂³×C₆₇	—	8	1	no	—
445	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
446	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
449	Q₈×C₆₇	—	2	4	no	—
450	Q₈×C₆₇	—	2	2	no	—
451	Q₈×C₆₇	—	2	2	no	—
452	Q₈×C₆₇	—	2	2	no	—
453	Q₈×C₆₇	—	2	2	no	—
454	Q₈×C₆₇	—	4	1	no	—
455	Q₈×C₆₇	—	4	4	no	—
456	Q₈×C₆₇	—	8	1	no	—
457	Q₈×C₆₇	—	8	2	no	—
458	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
459	D₄×C₆₇	—	2	2	no	—
460	D₄×C₆₇	—	2	2	no	—
461	D₄×C₆₇	—	2	2	no	—
462	D₄×C₆₇	—	2	2	no	—
463	D₄×C₆₇	—	2	2	no	—
464	D₄×C₆₇	—	4	2	no	—
465	D₄×C₆₇	—	4	1	no	—
466	D₄×C₆₇	—	4	2	no	—
467	D₄×C₆₇	—	4	2	no	—
468	D₄×C₆₇	—	4	4	no	—
469	D₄×C₆₇	—	4	4	no	—
470	D₄×C₆₇	—	4	4	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	4	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	8	2	no	—
475	D₄×C₆₇	—	8	2	no	—
476	D₄×C₆₇	—	8	1	no	—
477	D₄×C₆₇	—	8	2	no	—
478	D₄×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	8	2	no	—
480	D₄×C₆₇	—	8	1	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	2	no	—
484	C₂×C₄×C₆₇	—	2	4	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	4	1	no	—
498	C₂×C₄×C₆₇	—	4	1	no	—
499	C₂×C₄×C₆₇	—	4	1	no	—
500	C₂×C₄×C₆₇	—	4	4	no	—
501	C₂×C₄×C₆₇	—	4	4	no	—
502	C₂×C₄×C₆₇	—	4	4	no	—
503	C₂×C₄×C₆₇	—	4	4	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	8	2	no	—
507	C₂×C₄×C₆₇	—	8	2	no	—
508	C₂×C₄×C₆₇	—	8	1	no	—
509	C₂×C₄×C₆₇	—	8	1	no	—
510	C₂×C₄×C₆₇	—	8	2	no	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₇	—	2	2	no	—
519	C₈×C₆₇	—	2	2	no	—
520	C₈×C₆₇	—	2	2	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	2	1	no	—
523	C₂²×C₆₇	—	2	2	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	1	no	—
527	C₂²×C₆₇	—	2	2	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	1	no	—
534	C₂²×C₆₇	—	4	2	no	—
535	C₂²×C₆₇	—	4	1	no	—
536	C₂²×C₆₇	—	4	2	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	4	2	no	—
540	C₂²×C₆₇	—	4	1	no	—
541	C₂²×C₆₇	—	4	2	no	—
542	C₂²×C₆₇	—	4	2	no	—
543	C₂²×C₆₇	—	8	2	no	—
544	C₂²×C₆₇	—	8	4	no	—
545	C₂²×C₆₇	—	16	2	no	—
546	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₆₇	—	2	2	no	—
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	4	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	1	no	—
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	2	no	—
554	C₄×C₆₇	—	4	2	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
561	#61650	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
562	C₂×C₆₇	—	4	2	no	—
563	C₂×C₆₇	—	4	1	no	—
564	C₂×C₆₇	—	4	1	no	—
565	C₂×C₆₇	—	4	1	no	—
566	C₂×C₆₇	—	8	1	no	—
567	C₂×C₆₇	—	8	2	no	—
568	C₂×C₆₇	—	8	2	no	—
569	C₂×C₆₇	#3484	1	1	yes	characteristic
570	C₂×C₆₇	#3585	1	1	yes	characteristic
571	C₂×C₆₇	#3586	1	1	yes	characteristic
572	#3536	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3333	C₂×C₆₇	1	2	yes	complemented
575	#3332	C₂×C₆₇	1	2	yes	complemented
576	#3316	C₂×C₆₇	1	2	yes	complemented
577	#3308	C₂×C₆₇	1	2	yes	complemented
578	#3277	C₂×C₆₇	1	2	yes	complemented
579	#3275	C₂×C₆₇	1	2	yes	complemented
580	#3271	C₂×C₆₇	1	2	yes	complemented
581	#3268	C₂×C₆₇	1	2	yes	complemented
582	#3224	C₂×C₆₇	1	2	yes	complemented
583	#3198	C₂×C₆₇	1	2	yes	complemented
584	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3121	C₂×C₆₇	1	2	yes	complemented
587	#3013	C₂×C₆₇	1	2	yes	complemented
588	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
591	C₆₇	#61650	1	1	yes	characteristic, direct product factor, Sylow
592	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
594	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
595	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
596	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
597	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
598	#562	—	2	2	no	—
599	#554	C₂²×C₆₇	1	2	yes	complemented
600	#550	—	2	1	no	—
601	#550	—	2	1	no	—
602	#550	C₂²×C₆₇	1	2	yes	—
603	#550	C₂²×C₆₇	1	2	yes	complemented
604	#548	—	2	1	no	—
605	#548	—	2	1	no	—
606	#548	C₂²×C₆₇	1	2	yes	—
607	#548	C₂²×C₆₇	1	2	yes	complemented
608	#548	C₂²×C₆₇	1	2	yes	complemented
609	#547	C₂²×C₆₇	1	2	yes	complemented
610	#546	—	2	2	no	—
611	#546	C₂²×C₆₇	1	2	yes	complemented
612	#543	—	2	1	no	—
613	#542	C₂²×C₆₇	1	2	yes	—
614	#539	—	2	1	no	—
615	#538	—	2	1	no	—
616	#537	—	2	1	no	—
617	#537	C₂²×C₆₇	1	2	yes	—
618	#535	—	2	2	no	—
619	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#525	—	2	2	no	—
622	#525	C₂²×C₆₇	1	1	yes	characteristic
623	#525	C₂²×C₆₇	1	1	yes	characteristic
624	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
625	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
626	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#496	C₂²×C₆₇	1	2	yes	complemented
628	#495	C₂²×C₆₇	1	2	yes	complemented
629	#489	C₂²×C₆₇	1	2	yes	complemented
630	#486	C₂²×C₆₇	1	2	yes	complemented
631	#485	C₂²×C₆₇	1	2	yes	complemented
632	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#482	C₂²×C₆₇	1	2	yes	—
635	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#481	C₂²×C₆₇	1	2	yes	complemented
637	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#480	C₂²×C₆₇	1	2	yes	complemented
639	#477	C₂²×C₆₇	1	2	yes	complemented
640	#475	C₂²×C₆₇	1	2	yes	complemented
641	#470	C₂²×C₆₇	1	2	yes	complemented
642	#469	C₂²×C₆₇	1	2	yes	complemented
643	#469	C₂²×C₆₇	1	2	yes	complemented
644	#468	C₂²×C₆₇	1	2	yes	complemented
645	#468	C₂²×C₆₇	1	2	yes	complemented
646	#468	C₂²×C₆₇	1	2	yes	complemented
647	#466	C₂²×C₆₇	1	2	yes	complemented
648	#465	C₂²×C₆₇	1	2	yes	complemented
649	#464	C₂²×C₆₇	1	2	yes	complemented
650	#464	C₂²×C₆₇	1	2	yes	complemented
651	#464	C₂²×C₆₇	1	2	yes	complemented
652	#463	C₂²×C₆₇	1	2	yes	complemented
653	#460	C₂²×C₆₇	1	2	yes	complemented
654	#459	C₂²×C₆₇	1	2	yes	complemented
655	#452	C₂²×C₆₇	1	2	yes	—
656	#452	C₂²×C₆₇	1	2	yes	—
657	#452	C₂²×C₆₇	1	2	yes	complemented
658	#452	C₂²×C₆₇	1	2	yes	complemented
659	#451	C₂²×C₆₇	1	2	yes	complemented
660	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#451	C₂²×C₆₇	1	2	yes	complemented
662	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#450	C₂²×C₆₇	1	2	yes	complemented
664	#449	C₂²×C₆₇	1	2	yes	—
665	#449	C₂²×C₆₇	1	2	yes	—
666	#449	C₂²×C₆₇	1	2	yes	—
667	#449	C₂²×C₆₇	1	2	yes	complemented
668	#449	C₂²×C₆₇	1	2	yes	complemented
669	#449	C₂²×C₆₇	1	2	yes	complemented
670	#448	C₂²×C₆₇	1	2	yes	—
671	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#448	C₂²×C₆₇	1	2	yes	complemented
673	#447	C₂²×C₆₇	1	2	yes	—
674	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#441	C₂²×C₆₇	1	2	yes	complemented
676	#440	C₂²×C₆₇	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
679	#436	C₂²×C₆₇	1	2	yes	complemented
680	#436	C₂²×C₆₇	1	2	yes	complemented
681	#435	C₂²×C₆₇	1	2	yes	complemented
682	#435	C₂²×C₆₇	1	2	yes	complemented
683	#433	C₂²×C₆₇	1	2	yes	complemented
684	#417	C₂²×C₆₇	1	2	yes	—
685	#417	C₂²×C₆₇	1	2	yes	complemented
686	#417	C₂²×C₆₇	1	2	yes	complemented
687	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
688	#408	C₂²×C₆₇	1	2	yes	complemented
689	#407	C₂²×C₆₇	1	1	yes	characteristic
690	#407	C₂²×C₆₇	1	1	yes	characteristic
691	2₋¹⁺⁴	—	4	4	no	—
692	C₂×#41	—	2	2	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	2	2	no	—
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	2	1	no	—
697	C₂×#41	—	4	4	no	—
698	C₂×#41	C₂³×C₆₇	1	2	yes	—
699	C₂×#41	C₂³×C₆₇	1	2	yes	—
700	C₂×#41	C₂³×C₆₇	1	2	yes	—
701	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×#41	C₂³×C₆₇	1	2	yes	—
703	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²×Q₈	—	2	1	no	—
705	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
707	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂³×C₄	—	2	1	no	—
713	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
714	#137	—	4	4	no	—
715	#137	—	4	4	no	—
716	AGL(1,ℤ/8)	—	4	4	no	—
717	#135	—	4	4	no	—
718	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
727	C₂×D₈	C₂³×C₆₇	1	2	yes	—
728	C₂×D₈	C₂³×C₆₇	1	2	yes	—
729	C₂×D₈	C₂³×C₆₇	1	2	yes	—
730	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
731	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
734	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
735	#127	—	2	2	no	—
736	#127	—	2	2	no	—
737	#127	—	2	1	no	—
738	#127	C₂³×C₆₇	1	2	yes	—
739	#126	—	2	2	no	—
740	#125	—	2	2	no	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	C₂³×C₆₇	1	2	yes	—
747	#124	C₂³×C₆₇	1	2	yes	—
748	#123	—	2	1	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	D₄×C₆₇	1	2	yes	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
765	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₆₇	1	1	yes	characteristic
787	#121	D₄×C₆₇	1	1	yes	characteristic
788	#121	C₂³×C₆₇	1	2	yes	—
789	#121	C₂³×C₆₇	1	2	yes	—
790	#121	C₂³×C₆₇	1	1	yes	characteristic
791	#121	C₂³×C₆₇	1	1	yes	characteristic
792	#121	C₂³×C₆₇	1	2	yes	—
793	#121	C₂³×C₆₇	1	2	yes	—
794	#121	C₂³×C₆₇	1	2	yes	—
795	#120	—	2	1	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	D₄×C₆₇	1	2	yes	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	C₂³×C₆₇	1	2	yes	—
814	C₄×D₄	C₂³×C₆₇	1	2	yes	—
815	C₄×D₄	C₂³×C₆₇	1	2	yes	—
816	#117	—	2	2	no	—
817	#117	C₂³×C₆₇	1	1	yes	characteristic
818	#117	C₂³×C₆₇	1	1	yes	characteristic
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	#107	C₂³×C₆₇	1	2	yes	—
827	#107	C₂³×C₆₇	1	2	yes	—
828	#106	C₂³×C₆₇	1	2	yes	—
829	#106	C₂³×C₆₇	1	2	yes	—
830	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
831	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
832	#103	C₂³×C₆₇	1	2	yes	—
833	#103	C₂³×C₆₇	1	2	yes	—
834	#103	C₂³×C₆₇	1	2	yes	—
835	#103	C₂³×C₆₇	1	2	yes	—
836	#103	C₂³×C₆₇	1	2	yes	—
837	#103	C₂³×C₆₇	1	2	yes	—
838	#103	C₂³×C₆₇	1	2	yes	—
839	#103	C₂³×C₆₇	1	2	yes	—
840	#102	C₂³×C₆₇	1	2	yes	—
841	#102	C₂³×C₆₇	1	2	yes	—
842	#102	C₂³×C₆₇	1	2	yes	—
843	#102	C₂³×C₆₇	1	2	yes	—
844	#102	C₂³×C₆₇	1	2	yes	—
845	#102	C₂³×C₆₇	1	2	yes	—
846	#102	C₂³×C₆₇	1	2	yes	—
847	#102	C₂³×C₆₇	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
856	#97	C₂³×C₆₇	1	2	yes	—
857	C₄×C₈	C₂³×C₆₇	1	2	yes	—
858	C₂⁴	—	2	1	no	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
861	#41	—	2	4	no	—
862	#41	—	2	4	no	—
863	#41	—	2	4	no	—
864	#41	—	4	2	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	8	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	4	no	—
873	#41	—	4	4	no	—
874	#41	—	4	4	no	—
875	#41	—	8	4	no	—
876	C₂×Q₈	—	2	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	4	no	—
882	C₂×Q₈	—	4	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	4	4	no	—
885	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	4	no	—
908	C₂×D₄	—	8	2	no	—
909	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
911	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
912	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
914	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	4	no	—
930	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
937	Q₁₆	—	2	4	no	—
938	Q₁₆	—	2	4	no	—
939	Q₁₆	—	4	2	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	2	no	—
946	D₈	—	4	2	no	—
947	D₈	—	4	2	no	—
948	D₈	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	C₂×C₈	—	4	2	no	—
953	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
954	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
955	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
956	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂⁴×C₆₇	1	2	yes	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	1	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1018	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1020	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1021	Q₈	—	2	4	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	1	no	—
1027	Q₈	—	4	4	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	1	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	8	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	1	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	1	no	—
1056	C₂×C₄	—	2	4	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	4	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1089	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1090	C₈	—	2	2	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	2	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	8	2	no	—
1116	C₂²	—	8	4	no	—
1117	C₂²	—	16	2	no	—
1118	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1119	C₄	—	2	2	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	4	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1133	C₂	—	4	1	no	—
1134	C₂	—	4	1	no	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	8	2	no	—
1138	C₂	—	8	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₆₇×#3484	1	1	yes	characteristic
1141	C₂	C₆₇×#3585	1	1	yes	characteristic
1142	C₂	C₆₇×#3586	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×#3487	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3332	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3308	C₂	semidirect
7. C₆₇×#3277	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3268	C₂	semidirect
11. C₆₇×#3224	C₂	semidirect
12. C₆₇×#3198	C₂	semidirect
13. C₆₇×#3196	C₂	semidirect
14. C₆₇×#3194	C₂	semidirect
15. C₆₇×#3121	C₂	semidirect
16. C₆₇×#3013	C₂	semidirect
17. C₆₇×#3007	C₂	semidirect
18. C₆₇×#3006	C₂	semidirect
19. C₆₇×#2978	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
31. #550×C₆₇	C₂²	semidirect
35. #548×C₆₇	C₂²	semidirect
36. #548×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
39. #546×C₆₇	C₂²	semidirect
47. #535×C₆₇	C₂²	semidirect
48. #535×C₆₇	C₂²	semidirect
54. #519×C₆₇	C₂²	semidirect
55. #496×C₆₇	C₂²	semidirect
56. #495×C₆₇	C₂²	semidirect
57. #489×C₆₇	C₂²	semidirect
58. #486×C₆₇	C₂²	semidirect
59. #485×C₆₇	C₂²	semidirect
60. #484×C₆₇	C₂²	semidirect
61. #483×C₆₇	C₂²	semidirect
63. #481×C₆₇	C₂²	semidirect
64. #481×C₆₇	C₂²	semidirect
65. #480×C₆₇	C₂²	semidirect
66. #480×C₆₇	C₂²	semidirect
67. #477×C₆₇	C₂²	semidirect
68. #475×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #469×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #468×C₆₇	C₂²	semidirect
74. #468×C₆₇	C₂²	semidirect
75. #466×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #460×C₆₇	C₂²	semidirect
82. #459×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #452×C₆₇	C₂²	semidirect
87. #451×C₆₇	C₂²	semidirect
88. #451×C₆₇	C₂²	semidirect
89. #451×C₆₇	C₂²	semidirect
90. #450×C₆₇	C₂²	semidirect
91. #450×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
102. #447×C₆₇	C₂²	semidirect
103. #441×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. C₄×Q₁₆×C₆₇	C₂²	semidirect
106. C₄×SD₁₆×C₆₇	C₂²	semidirect
107. #436×C₆₇	C₂²	semidirect
108. #436×C₆₇	C₂²	semidirect
109. #435×C₆₇	C₂²	semidirect
110. #435×C₆₇	C₂²	semidirect
111. #433×C₆₇	C₂²	semidirect
113. #417×C₆₇	C₂²	semidirect
114. #417×C₆₇	C₂²	semidirect
115. C₂×#103×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
561. #61650	C₆₇	direct (N × H)
572. #3536	C₂×C₆₇	semidirect
573. #3487	C₂×C₆₇	semidirect
574. #3333	C₂×C₆₇	semidirect
575. #3332	C₂×C₆₇	semidirect
576. #3316	C₂×C₆₇	semidirect
577. #3308	C₂×C₆₇	semidirect
578. #3277	C₂×C₆₇	semidirect
579. #3275	C₂×C₆₇	semidirect
580. #3271	C₂×C₆₇	semidirect
581. #3268	C₂×C₆₇	semidirect
582. #3224	C₂×C₆₇	semidirect
583. #3198	C₂×C₆₇	semidirect
584. #3196	C₂×C₆₇	semidirect
585. #3194	C₂×C₆₇	semidirect
586. #3121	C₂×C₆₇	semidirect
587. #3013	C₂×C₆₇	semidirect
588. #3007	C₂×C₆₇	semidirect
589. #3006	C₂×C₆₇	semidirect
590. #2978	C₂×C₆₇	semidirect
591. C₆₇	#61650	direct (N × H)
592. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
594. C₂×#137	C₂²×C₆₇	semidirect
595. C₂×#137	C₂²×C₆₇	semidirect
597. C₂×#135	C₂²×C₆₇	semidirect
599. #554	C₂²×C₆₇	semidirect
603. #550	C₂²×C₆₇	semidirect
607. #548	C₂²×C₆₇	semidirect
608. #548	C₂²×C₆₇	semidirect
609. #547	C₂²×C₆₇	semidirect
611. #546	C₂²×C₆₇	semidirect
619. #535	C₂²×C₆₇	semidirect
620. #535	C₂²×C₆₇	semidirect
626. #519	C₂²×C₆₇	semidirect
627. #496	C₂²×C₆₇	semidirect
628. #495	C₂²×C₆₇	semidirect
629. #489	C₂²×C₆₇	semidirect
630. #486	C₂²×C₆₇	semidirect
631. #485	C₂²×C₆₇	semidirect
632. #484	C₂²×C₆₇	semidirect
633. #483	C₂²×C₆₇	semidirect
635. #481	C₂²×C₆₇	semidirect
636. #481	C₂²×C₆₇	semidirect
637. #480	C₂²×C₆₇	semidirect
638. #480	C₂²×C₆₇	semidirect
639. #477	C₂²×C₆₇	semidirect
640. #475	C₂²×C₆₇	semidirect
641. #470	C₂²×C₆₇	semidirect
642. #469	C₂²×C₆₇	semidirect
643. #469	C₂²×C₆₇	semidirect
644. #468	C₂²×C₆₇	semidirect
645. #468	C₂²×C₆₇	semidirect
646. #468	C₂²×C₆₇	semidirect
647. #466	C₂²×C₆₇	semidirect
648. #465	C₂²×C₆₇	semidirect
649. #464	C₂²×C₆₇	semidirect
650. #464	C₂²×C₆₇	semidirect
651. #464	C₂²×C₆₇	semidirect
652. #463	C₂²×C₆₇	semidirect
653. #460	C₂²×C₆₇	semidirect
654. #459	C₂²×C₆₇	semidirect
657. #452	C₂²×C₆₇	semidirect
658. #452	C₂²×C₆₇	semidirect
659. #451	C₂²×C₆₇	semidirect
660. #451	C₂²×C₆₇	semidirect
661. #451	C₂²×C₆₇	semidirect
662. #450	C₂²×C₆₇	semidirect
663. #450	C₂²×C₆₇	semidirect
667. #449	C₂²×C₆₇	semidirect
668. #449	C₂²×C₆₇	semidirect
669. #449	C₂²×C₆₇	semidirect
671. #448	C₂²×C₆₇	semidirect
672. #448	C₂²×C₆₇	semidirect
674. #447	C₂²×C₆₇	semidirect
675. #441	C₂²×C₆₇	semidirect
676. #440	C₂²×C₆₇	semidirect
677. C₄×Q₁₆	C₂²×C₆₇	semidirect
678. C₄×SD₁₆	C₂²×C₆₇	semidirect
679. #436	C₂²×C₆₇	semidirect
680. #436	C₂²×C₆₇	semidirect
681. #435	C₂²×C₆₇	semidirect
682. #435	C₂²×C₆₇	semidirect
683. #433	C₂²×C₆₇	semidirect
685. #417	C₂²×C₆₇	semidirect
686. #417	C₂²×C₆₇	semidirect
687. C₂×#103	C₂²×C₆₇	semidirect
688. #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×#3487	2
C₆₇×#3333	2
C₆₇×#3332	2
C₆₇×#3316	2
C₆₇×#3308	2
C₆₇×#3277	2
C₆₇×#3275	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3224	2
C₆₇×#3198	2
C₆₇×#3196	2
C₆₇×#3194	2
C₆₇×#3121	2
C₆₇×#3013	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#2978	2
#61650	67

Subgroups — C67×#61650 #30740901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61650 #30740901