Subgroups — C₆₇×#61496 #30740747

Order 17152.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
25	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
26	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	#554×C₆₇	C₂²	1	2	yes	complemented
30	#553×C₆₇	—	2	1	no	—
31	#553×C₆₇	C₂²	1	2	yes	—
32	#552×C₆₇	—	2	1	no	—
33	#551×C₆₇	—	2	2	no	—
34	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#548×C₆₇	—	2	1	no	—
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	—	2	2	no	—
41	#546×C₆₇	C₂²	1	2	yes	complemented
42	D₄²×C₆₇	C₂²	1	2	yes	—
43	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#542×C₆₇	C₂²	1	2	yes	complemented
45	#540×C₆₇	C₂²	1	2	yes	complemented
46	#539×C₆₇	—	2	2	no	—
47	#538×C₆₇	—	2	2	no	—
48	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#529×C₆₇	C₂²	1	1	yes	characteristic
51	#525×C₆₇	—	2	1	no	—
52	#525×C₆₇	—	2	1	no	—
53	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
54	C₂×#121×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	#518×C₆₇	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#501×C₆₇	C₂²	1	2	yes	complemented
60	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#496×C₆₇	C₂²	1	2	yes	complemented
62	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#488×C₆₇	C₂²	1	2	yes	complemented
64	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#486×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	complemented
70	#481×C₆₇	C₂²	1	2	yes	complemented
71	#481×C₆₇	C₂²	1	2	yes	complemented
72	#480×C₆₇	C₂²	1	2	yes	complemented
73	#479×C₆₇	C₂²	1	2	yes	complemented
74	#478×C₆₇	C₂²	1	2	yes	complemented
75	#476×C₆₇	C₂²	1	2	yes	complemented
76	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#474×C₆₇	C₂²	1	2	yes	complemented
80	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#469×C₆₇	C₂²	1	2	yes	complemented
82	#468×C₆₇	C₂²	1	2	yes	complemented
83	#466×C₆₇	C₂²	1	2	yes	complemented
84	#465×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#463×C₆₇	C₂²	1	2	yes	—
88	#463×C₆₇	C₂²	1	2	yes	complemented
89	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#460×C₆₇	C₂²	1	2	yes	complemented
92	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#459×C₆₇	C₂²	1	2	yes	complemented
95	#450×C₆₇	C₂²	1	2	yes	—
96	#450×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#447×C₆₇	C₂²	1	2	yes	—
100	#447×C₆₇	C₂²	1	2	yes	complemented
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	2	yes	—
104	#442×C₆₇	C₂²	1	2	yes	complemented
105	#442×C₆₇	C₂²	1	2	yes	complemented
106	#440×C₆₇	C₂²	1	2	yes	complemented
107	#440×C₆₇	C₂²	1	2	yes	complemented
108	#440×C₆₇	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
117	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#435×C₆₇	C₂²	1	2	yes	complemented
123	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#416×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, 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	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	—	2	2	no	—
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	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	—	2	1	no	—
146	C₂³×C₄×C₆₇	—	2	1	no	—
147	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
148	C₂×SD₁₆×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×D₈×C₆₇	—	2	4	no	—
153	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	1	yes	characteristic
168	#127×C₆₇	C₂³	1	2	yes	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	D₄	1	2	yes	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	D₄	1	1	yes	characteristic
176	#125×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	D₄	1	1	yes	characteristic
181	#124×C₆₇	C₂³	1	2	yes	—
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	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	D₄	1	2	yes	—
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	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	1	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	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	#121×C₆₇	C₂³	1	2	yes	—
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	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
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	1	no	—
236	C₄×D₄×C₆₇	—	2	1	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₇	C₂³	1	2	yes	—
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	—	2	1	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	C₂³	1	2	yes	—
257	#117×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#107×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	2	yes	—
279	#106×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#102×C₆₇	C₂³	1	1	yes	characteristic
289	#102×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	2	yes	—
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂⁴×C₆₇	—	2	1	no	—
315	C₂⁴×C₆₇	—	2	1	no	—
316	C₂⁴×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	4	no	—
318	#41×C₆₇	—	4	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	2	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	—	8	2	no	—
326	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	4	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	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	4	1	no	—
344	C₂×D₄×C₆₇	—	4	1	no	—
345	C₂×D₄×C₆₇	—	4	2	no	—
346	C₂×D₄×C₆₇	—	8	2	no	—
347	C₂×D₄×C₆₇	—	8	4	no	—
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
353	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	—	2	1	no	—
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	1	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	1	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	8	2	no	—
372	C₂²×C₄×C₆₇	—	8	2	no	—
373	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
377	SD₁₆×C₆₇	—	2	4	no	—
378	SD₁₆×C₆₇	—	2	4	no	—
379	SD₁₆×C₆₇	—	4	2	no	—
380	SD₁₆×C₆₇	—	4	2	no	—
381	D₈×C₆₇	—	2	2	no	—
382	D₈×C₆₇	—	2	2	no	—
383	D₈×C₆₇	—	2	4	no	—
384	D₈×C₆₇	—	2	2	no	—
385	D₈×C₆₇	—	4	2	no	—
386	D₈×C₆₇	#41	1	4	yes	complemented
387	M₁₆×C₆₇	—	2	4	no	—
388	C₂×C₈×C₆₇	—	2	2	no	—
389	C₂×C₈×C₆₇	—	4	2	no	—
390	C₂×C₈×C₆₇	—	4	1	no	—
391	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	1	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	1	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	1	no	—
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
449	C₄²×C₆₇	—	2	2	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₇	C₂⁴	1	2	yes	—
456	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	2	1	no	—
459	C₂³×C₆₇	—	2	1	no	—
460	C₂³×C₆₇	—	2	1	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	4	2	no	—
463	C₂³×C₆₇	—	4	2	no	—
464	C₂³×C₆₇	—	4	4	no	—
465	C₂³×C₆₇	—	4	2	no	—
466	C₂³×C₆₇	—	4	2	no	—
467	C₂³×C₆₇	—	8	1	no	—
468	C₂³×C₆₇	—	8	1	no	—
469	C₂³×C₆₇	—	8	2	no	—
470	C₂³×C₆₇	—	8	2	no	—
471	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
472	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	2	no	—
475	Q₈×C₆₇	—	2	2	no	—
476	Q₈×C₆₇	—	4	2	no	—
477	Q₈×C₆₇	—	8	2	no	—
478	Q₈×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	2	4	no	—
480	D₄×C₆₇	—	2	2	no	—
481	D₄×C₆₇	—	2	1	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	2	2	no	—
484	D₄×C₆₇	—	2	1	no	—
485	D₄×C₆₇	—	2	1	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	2	2	no	—
488	D₄×C₆₇	—	2	1	no	—
489	D₄×C₆₇	—	4	4	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	4	no	—
493	D₄×C₆₇	—	4	4	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	8	2	no	—
496	D₄×C₆₇	—	8	2	no	—
497	D₄×C₆₇	—	8	1	no	—
498	D₄×C₆₇	—	8	2	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	C₂×#41	1	2	yes	—
502	D₄×C₆₇	C₂×#41	1	2	yes	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	4	4	no	—
517	C₂×C₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	8	1	no	—
522	C₂×C₄×C₆₇	—	8	1	no	—
523	C₂×C₄×C₆₇	—	8	1	no	—
524	C₂×C₄×C₆₇	—	8	1	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	2	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	8	1	no	—
530	C₂×C₄×C₆₇	—	8	1	no	—
531	C₂×C₄×C₆₇	—	8	2	no	—
532	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
541	C₈×C₆₇	—	2	1	no	—
542	C₈×C₆₇	—	2	2	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	1	no	—
546	C₈×C₆₇	C₂×#41	1	2	yes	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	2	2	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	2	2	no	—
553	C₂²×C₆₇	—	2	2	no	—
554	C₂²×C₆₇	—	4	1	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	2	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	4	1	no	—
563	C₂²×C₆₇	—	4	2	no	—
564	C₂²×C₆₇	—	4	2	no	—
565	C₂²×C₆₇	—	4	1	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	8	4	no	—
568	C₂²×C₆₇	—	8	4	no	—
569	C₂²×C₆₇	—	16	4	no	—
570	C₂²×C₆₇	#577	1	2	yes	—
571	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	1	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	—	2	2	no	—
576	C₄×C₆₇	—	2	1	no	—
577	C₄×C₆₇	—	2	1	no	—
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	—	4	2	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	1	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	—	4	2	no	—
586	C₄×C₆₇	#576	1	2	yes	—
587	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
588	C₄×C₆₇	#585	1	1	yes	characteristic
589	#61496	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
590	C₂×C₆₇	—	2	2	no	—
591	C₂×C₆₇	—	4	2	no	—
592	C₂×C₆₇	—	4	2	no	—
593	C₂×C₆₇	—	4	2	no	—
594	C₂×C₆₇	—	8	1	no	—
595	C₂×C₆₇	—	8	1	no	—
596	C₂×C₆₇	—	8	2	no	—
597	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
598	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
599	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
600	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3397	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3384	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3360	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3358	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3354	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#3346	C₂×C₆₇	1	2	yes	complemented
608	#3303	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#3297	C₂×C₆₇	1	2	yes	complemented
610	#3295	C₂×C₆₇	1	2	yes	complemented
611	#3294	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3272	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3264	C₂×C₆₇	1	2	yes	complemented
614	#3179	C₂×C₆₇	1	2	yes	complemented
615	#3167	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3119	C₂×C₆₇	1	2	yes	complemented
617	#3118	C₂×C₆₇	1	2	yes	complemented
618	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#2946	C₂×C₆₇	1	2	yes	complemented
622	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
623	C₆₇	#61496	1	1	yes	characteristic, direct product factor, Sylow
624	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
625	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
626	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#554	C₂²×C₆₇	1	2	yes	complemented
630	#553	—	2	1	no	—
631	#553	C₂²×C₆₇	1	2	yes	—
632	#552	—	2	1	no	—
633	#551	—	2	2	no	—
634	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#548	—	2	1	no	—
637	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#546	—	2	1	no	—
640	#546	—	2	2	no	—
641	#546	C₂²×C₆₇	1	2	yes	complemented
642	D₄²	C₂²×C₆₇	1	2	yes	—
643	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#542	C₂²×C₆₇	1	2	yes	complemented
645	#540	C₂²×C₆₇	1	2	yes	complemented
646	#539	—	2	2	no	—
647	#538	—	2	2	no	—
648	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	#532	C₂²×C₆₇	1	1	yes	characteristic
650	#529	C₂²×C₆₇	1	1	yes	characteristic
651	#525	—	2	1	no	—
652	#525	—	2	1	no	—
653	C₂×C₂²⋊Q₈	—	2	1	no	—
654	C₂×#121	—	2	1	no	—
655	#520	C₂²×C₆₇	1	2	yes	complemented
656	#518	C₂²×C₆₇	1	2	yes	complemented
657	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
658	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
659	#501	C₂²×C₆₇	1	2	yes	complemented
660	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#496	C₂²×C₆₇	1	2	yes	complemented
662	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#488	C₂²×C₆₇	1	2	yes	complemented
664	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#486	C₂²×C₆₇	1	2	yes	complemented
667	#485	C₂²×C₆₇	1	2	yes	complemented
668	#484	C₂²×C₆₇	1	2	yes	complemented
669	#482	C₂²×C₆₇	1	2	yes	complemented
670	#481	C₂²×C₆₇	1	2	yes	complemented
671	#481	C₂²×C₆₇	1	2	yes	complemented
672	#480	C₂²×C₆₇	1	2	yes	complemented
673	#479	C₂²×C₆₇	1	2	yes	complemented
674	#478	C₂²×C₆₇	1	2	yes	complemented
675	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#476	C₂²×C₆₇	1	2	yes	complemented
678	#474	C₂²×C₆₇	1	2	yes	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	complemented
682	#468	C₂²×C₆₇	1	2	yes	complemented
683	#466	C₂²×C₆₇	1	2	yes	complemented
684	#465	C₂²×C₆₇	1	2	yes	complemented
685	#465	C₂²×C₆₇	1	2	yes	complemented
686	#465	C₂²×C₆₇	1	2	yes	complemented
687	#463	C₂²×C₆₇	1	2	yes	—
688	#463	C₂²×C₆₇	1	2	yes	complemented
689	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#460	C₂²×C₆₇	1	2	yes	complemented
692	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#459	C₂²×C₆₇	1	2	yes	complemented
694	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#450	C₂²×C₆₇	1	2	yes	—
696	#450	C₂²×C₆₇	1	2	yes	complemented
697	#449	C₂²×C₆₇	1	2	yes	complemented
698	#449	C₂²×C₆₇	1	2	yes	complemented
699	#447	C₂²×C₆₇	1	2	yes	—
700	#447	C₂²×C₆₇	1	2	yes	complemented
701	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#442	C₂²×C₆₇	1	2	yes	—
704	#442	C₂²×C₆₇	1	2	yes	complemented
705	#442	C₂²×C₆₇	1	2	yes	complemented
706	#440	C₂²×C₆₇	1	2	yes	complemented
707	#440	C₂²×C₆₇	1	2	yes	complemented
708	#440	C₂²×C₆₇	1	2	yes	complemented
709	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
710	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
711	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
712	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
713	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
714	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
715	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
716	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
719	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	#435	C₂²×C₆₇	1	2	yes	complemented
723	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
725	#433	C₂²×C₆₇	1	2	yes	complemented
726	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#428	C₂²×C₆₇	1	2	yes	complemented
728	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#416	C₂²×C₆₇	1	2	yes	complemented
730	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
731	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
733	#405	C₂²×C₆₇	1	2	yes	complemented
734	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	C₂³×C₆₇	1	2	yes	—
739	C₂²×Q₈	—	2	1	no	—
740	C₂²×D₄	—	2	2	no	—
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
745	C₂³×C₄	—	2	1	no	—
746	C₂³×C₄	—	2	1	no	—
747	AGL(1,ℤ/8)	—	2	8	no	—
748	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×D₈	—	2	4	no	—
753	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×D₈	C₂³×C₆₇	1	2	yes	—
757	C₂×D₈	C₂³×C₆₇	1	2	yes	—
758	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
760	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
761	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
763	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	#127	C₂³×C₆₇	1	1	yes	characteristic
768	#127	C₂³×C₆₇	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	D₄×C₆₇	1	2	yes	—
773	#125	—	2	2	no	—
774	#125	—	2	1	no	—
775	#125	D₄×C₆₇	1	1	yes	characteristic
776	#125	C₂³×C₆₇	1	2	yes	—
777	#124	—	2	2	no	—
778	#124	—	2	2	no	—
779	#124	—	2	1	no	—
780	#124	D₄×C₆₇	1	1	yes	characteristic
781	#124	C₂³×C₆₇	1	2	yes	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	D₄×C₆₇	1	2	yes	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	D₄×C₆₇	1	1	yes	characteristic
815	#121	C₂³×C₆₇	1	2	yes	—
816	#121	C₂³×C₆₇	1	2	yes	—
817	#121	C₂³×C₆₇	1	2	yes	—
818	#121	C₂³×C₆₇	1	2	yes	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
825	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
826	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₇	1	2	yes	—
847	C₄×D₄	C₂³×C₆₇	1	2	yes	—
848	C₄×D₄	C₂³×C₆₇	1	2	yes	—
849	C₄×D₄	C₂³×C₆₇	1	2	yes	—
850	C₄×D₄	C₂³×C₆₇	1	2	yes	—
851	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	C₂³×C₆₇	1	2	yes	—
857	#117	C₂³×C₆₇	1	2	yes	—
858	C₂×C₄⋊C₄	—	2	2	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
870	#107	C₂³×C₆₇	1	1	yes	characteristic
871	#107	C₂³×C₆₇	1	1	yes	characteristic
872	#107	C₂³×C₆₇	1	1	yes	characteristic
873	#107	C₂³×C₆₇	1	1	yes	characteristic
874	#107	C₂³×C₆₇	1	2	yes	—
875	#107	C₂³×C₆₇	1	2	yes	—
876	#106	C₂³×C₆₇	1	2	yes	—
877	#106	C₂³×C₆₇	1	2	yes	—
878	#106	C₂³×C₆₇	1	2	yes	—
879	#106	C₂³×C₆₇	1	2	yes	—
880	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
883	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
884	#103	C₂³×C₆₇	1	2	yes	—
885	#103	C₂³×C₆₇	1	2	yes	—
886	#103	C₂³×C₆₇	1	2	yes	—
887	#103	C₂³×C₆₇	1	2	yes	—
888	#102	C₂³×C₆₇	1	1	yes	characteristic
889	#102	C₂³×C₆₇	1	1	yes	characteristic
890	#102	C₂³×C₆₇	1	1	yes	characteristic
891	#102	C₂³×C₆₇	1	1	yes	characteristic
892	#102	C₂³×C₆₇	1	1	yes	characteristic
893	#102	C₂³×C₆₇	1	1	yes	characteristic
894	#102	C₂³×C₆₇	1	1	yes	characteristic
895	#102	C₂³×C₆₇	1	1	yes	characteristic
896	#102	C₂³×C₆₇	1	2	yes	—
897	#102	C₂³×C₆₇	1	2	yes	—
898	#102	C₂³×C₆₇	1	2	yes	—
899	#102	C₂³×C₆₇	1	2	yes	—
900	#102	C₂³×C₆₇	1	2	yes	—
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
907	#97	C₂³×C₆₇	1	2	yes	—
908	#97	C₂³×C₆₇	1	2	yes	—
909	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₆₇	1	2	yes	—
914	C₂⁴	—	2	1	no	—
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	2	no	—
917	#41	—	2	4	no	—
918	#41	—	4	2	no	—
919	#41	—	8	2	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	8	2	no	—
926	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	1	no	—
945	C₂×D₄	—	4	2	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	—	8	4	no	—
948	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
949	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	8	2	no	—
972	C₂²×C₄	—	8	2	no	—
973	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
977	SD₁₆	—	2	4	no	—
978	SD₁₆	—	2	4	no	—
979	SD₁₆	—	4	2	no	—
980	SD₁₆	—	4	2	no	—
981	D₈	—	2	2	no	—
982	D₈	—	2	2	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	4	2	no	—
986	D₈	#41×C₆₇	1	4	yes	complemented
987	M₁₆	—	2	4	no	—
988	C₂×C₈	—	2	2	no	—
989	C₂×C₈	—	4	2	no	—
990	C₂×C₈	—	4	1	no	—
991	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
995	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
996	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1020	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₆₇	1	2	yes	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	1	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1072	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	8	2	no	—
1078	Q₈	—	8	1	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	C₂×#41×C₆₇	1	2	yes	—
1102	D₄	C₂×#41×C₆₇	1	2	yes	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	—	8	1	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1141	C₈	—	2	1	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×#41×C₆₇	1	2	yes	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	8	4	no	—
1168	C₂²	—	8	4	no	—
1169	C₂²	—	16	4	no	—
1170	C₂²	#577×C₆₇	1	2	yes	—
1171	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	2	no	—
1186	C₄	#576×C₆₇	1	2	yes	—
1187	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1188	C₄	#585×C₆₇	1	1	yes	characteristic
1189	C₂	—	2	2	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	8	1	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1197	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1198	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₆₇×#3519	C₂	semidirect
3. C₆₇×#3397	C₂	semidirect
4. C₆₇×#3384	C₂	semidirect
5. C₆₇×#3360	C₂	semidirect
6. C₆₇×#3358	C₂	semidirect
7. C₆₇×#3354	C₂	semidirect
8. C₆₇×#3346	C₂	semidirect
9. C₆₇×#3303	C₂	semidirect
10. C₆₇×#3297	C₂	semidirect
11. C₆₇×#3295	C₂	semidirect
12. C₆₇×#3294	C₂	semidirect
13. C₆₇×#3272	C₂	semidirect
14. C₆₇×#3264	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3167	C₂	semidirect
17. C₆₇×#3119	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3110	C₂	semidirect
20. C₆₇×#3109	C₂	semidirect
21. C₆₇×#2966	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₂×C₄×D₈×C₆₇	C₂	semidirect
26. #556×C₆₇	C₂²	semidirect
27. #555×C₆₇	C₂²	semidirect
28. #554×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
34. #550×C₆₇	C₂²	semidirect
35. D₄×Q₈×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
41. #546×C₆₇	C₂²	semidirect
43. D₄²×C₆₇	C₂²	semidirect
44. #542×C₆₇	C₂²	semidirect
45. #540×C₆₇	C₂²	semidirect
48. #533×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
56. #518×C₆₇	C₂²	semidirect
58. C₂×C₄×D₄×C₆₇	C₂²	semidirect
59. #501×C₆₇	C₂²	semidirect
60. #498×C₆₇	C₂²	semidirect
61. #496×C₆₇	C₂²	semidirect
62. #492×C₆₇	C₂²	semidirect
63. #488×C₆₇	C₂²	semidirect
64. #487×C₆₇	C₂²	semidirect
65. #486×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #484×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #481×C₆₇	C₂²	semidirect
71. #481×C₆₇	C₂²	semidirect
72. #480×C₆₇	C₂²	semidirect
73. #479×C₆₇	C₂²	semidirect
74. #478×C₆₇	C₂²	semidirect
75. #476×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #474×C₆₇	C₂²	semidirect
79. #474×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
81. #469×C₆₇	C₂²	semidirect
82. #468×C₆₇	C₂²	semidirect
83. #466×C₆₇	C₂²	semidirect
84. #465×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
88. #463×C₆₇	C₂²	semidirect
89. #461×C₆₇	C₂²	semidirect
90. #461×C₆₇	C₂²	semidirect
91. #460×C₆₇	C₂²	semidirect
92. #459×C₆₇	C₂²	semidirect
93. #459×C₆₇	C₂²	semidirect
94. #459×C₆₇	C₂²	semidirect
96. #450×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
100. #447×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
104. #442×C₆₇	C₂²	semidirect
105. #442×C₆₇	C₂²	semidirect
106. #440×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. C₄×SD₁₆×C₆₇	C₂²	semidirect
110. C₄×SD₁₆×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
116. C₄×D₈×C₆₇	C₂²	semidirect
117. C₄×D₈×C₆₇	C₂²	semidirect
118. C₄×D₈×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #435×C₆₇	C₂²	semidirect
123. C₈×D₄×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
126. #432×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. C₂×#107×C₆₇	C₂²	semidirect
129. #416×C₆₇	C₂²	semidirect
131. C₂×#102×C₆₇	C₂²	semidirect
132. C₂×#102×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
386. D₈×C₆₇	#41	semidirect
589. #61496	C₆₇	direct (N × H)
600. #3520	C₂×C₆₇	semidirect
601. #3519	C₂×C₆₇	semidirect
602. #3397	C₂×C₆₇	semidirect
603. #3384	C₂×C₆₇	semidirect
604. #3360	C₂×C₆₇	semidirect
605. #3358	C₂×C₆₇	semidirect
606. #3354	C₂×C₆₇	semidirect
607. #3346	C₂×C₆₇	semidirect
608. #3303	C₂×C₆₇	semidirect
609. #3297	C₂×C₆₇	semidirect
610. #3295	C₂×C₆₇	semidirect
611. #3294	C₂×C₆₇	semidirect
612. #3272	C₂×C₆₇	semidirect
613. #3264	C₂×C₆₇	semidirect
614. #3179	C₂×C₆₇	semidirect
615. #3167	C₂×C₆₇	semidirect
616. #3119	C₂×C₆₇	semidirect
617. #3118	C₂×C₆₇	semidirect
618. #3110	C₂×C₆₇	semidirect
619. #3109	C₂×C₆₇	semidirect
620. #2966	C₂×C₆₇	semidirect
621. #2946	C₂×C₆₇	semidirect
622. C₂×C₄×D₈	C₂×C₆₇	semidirect
623. C₆₇	#61496	direct (N × H)
626. #556	C₂²×C₆₇	semidirect
627. #555	C₂²×C₆₇	semidirect
628. #554	C₂²×C₆₇	semidirect
629. #554	C₂²×C₆₇	semidirect
634. #550	C₂²×C₆₇	semidirect
635. D₄×Q₈	C₂²×C₆₇	semidirect
637. #547	C₂²×C₆₇	semidirect
638. #547	C₂²×C₆₇	semidirect
641. #546	C₂²×C₆₇	semidirect
643. D₄²	C₂²×C₆₇	semidirect
644. #542	C₂²×C₆₇	semidirect
645. #540	C₂²×C₆₇	semidirect
648. #533	C₂²×C₆₇	semidirect
655. #520	C₂²×C₆₇	semidirect
656. #518	C₂²×C₆₇	semidirect
658. C₂×C₄×D₄	C₂²×C₆₇	semidirect
659. #501	C₂²×C₆₇	semidirect
660. #498	C₂²×C₆₇	semidirect
661. #496	C₂²×C₆₇	semidirect
662. #492	C₂²×C₆₇	semidirect
663. #488	C₂²×C₆₇	semidirect
664. #487	C₂²×C₆₇	semidirect
665. #486	C₂²×C₆₇	semidirect
666. #486	C₂²×C₆₇	semidirect
667. #485	C₂²×C₆₇	semidirect
668. #484	C₂²×C₆₇	semidirect
669. #482	C₂²×C₆₇	semidirect
670. #481	C₂²×C₆₇	semidirect
671. #481	C₂²×C₆₇	semidirect
672. #480	C₂²×C₆₇	semidirect
673. #479	C₂²×C₆₇	semidirect
674. #478	C₂²×C₆₇	semidirect
675. #476	C₂²×C₆₇	semidirect
676. #476	C₂²×C₆₇	semidirect
677. #476	C₂²×C₆₇	semidirect
678. #474	C₂²×C₆₇	semidirect
679. #474	C₂²×C₆₇	semidirect
680. #474	C₂²×C₆₇	semidirect
681. #469	C₂²×C₆₇	semidirect
682. #468	C₂²×C₆₇	semidirect
683. #466	C₂²×C₆₇	semidirect
684. #465	C₂²×C₆₇	semidirect
685. #465	C₂²×C₆₇	semidirect
686. #465	C₂²×C₆₇	semidirect
688. #463	C₂²×C₆₇	semidirect
689. #461	C₂²×C₆₇	semidirect
690. #461	C₂²×C₆₇	semidirect
691. #460	C₂²×C₆₇	semidirect
692. #459	C₂²×C₆₇	semidirect
693. #459	C₂²×C₆₇	semidirect
694. #459	C₂²×C₆₇	semidirect
696. #450	C₂²×C₆₇	semidirect
697. #449	C₂²×C₆₇	semidirect
698. #449	C₂²×C₆₇	semidirect
700. #447	C₂²×C₆₇	semidirect
701. #446	C₂²×C₆₇	semidirect
702. C₈×Q₈	C₂²×C₆₇	semidirect
704. #442	C₂²×C₆₇	semidirect
705. #442	C₂²×C₆₇	semidirect
706. #440	C₂²×C₆₇	semidirect
707. #440	C₂²×C₆₇	semidirect
708. #440	C₂²×C₆₇	semidirect
709. C₄×SD₁₆	C₂²×C₆₇	semidirect
710. C₄×SD₁₆	C₂²×C₆₇	semidirect
711. C₄×SD₁₆	C₂²×C₆₇	semidirect
716. C₄×D₈	C₂²×C₆₇	semidirect
717. C₄×D₈	C₂²×C₆₇	semidirect
718. C₄×D₈	C₂²×C₆₇	semidirect
719. C₄×D₈	C₂²×C₆₇	semidirect
720. C₄×D₈	C₂²×C₆₇	semidirect
721. #436	C₂²×C₆₇	semidirect
722. #435	C₂²×C₆₇	semidirect
723. C₈×D₄	C₂²×C₆₇	semidirect
724. C₈×D₄	C₂²×C₆₇	semidirect
725. #433	C₂²×C₆₇	semidirect
726. #432	C₂²×C₆₇	semidirect
727. #428	C₂²×C₆₇	semidirect
728. C₂×#107	C₂²×C₆₇	semidirect
729. #416	C₂²×C₆₇	semidirect
731. C₂×#102	C₂²×C₆₇	semidirect
732. C₂×#102	C₂²×C₆₇	semidirect
733. #405	C₂²×C₆₇	semidirect
734. C₂×C₄×C₈	C₂²×C₆₇	semidirect
986. D₈	#41×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3520	2
C₆₇×#3519	2
C₆₇×#3397	2
C₆₇×#3384	2
C₆₇×#3360	2
C₆₇×#3358	2
C₆₇×#3354	2
C₆₇×#3346	2
C₆₇×#3303	2
C₆₇×#3297	2
C₆₇×#3295	2
C₆₇×#3294	2
C₆₇×#3272	2
C₆₇×#3264	2
C₆₇×#3179	2
C₆₇×#3167	2
C₆₇×#3119	2
C₆₇×#3118	2
C₆₇×#3110	2
C₆₇×#3109	2
C₆₇×#2966	2
C₆₇×#2946	2
C₂×C₄×D₈×C₆₇	2
#61496	67

Subgroups — C67×#61496 #30740747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61496 #30740747