Subgroups — C₆₇×#60344 #30739595

Order 17152.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3461	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2985	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2968	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2961	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
24	#544×C₆₇	C₄	1	1	yes	characteristic
25	#542×C₆₇	C₄	1	1	yes	characteristic
26	#542×C₆₇	C₄	1	1	yes	characteristic
27	#542×C₆₇	C₄	1	2	yes	—
28	#541×C₆₇	C₄	1	1	yes	characteristic
29	#541×C₆₇	C₄	1	1	yes	characteristic
30	#541×C₆₇	C₄	1	2	yes	—
31	#539×C₆₇	C₄	1	2	yes	—
32	#539×C₆₇	C₄	1	2	yes	—
33	#537×C₆₇	C₄	1	1	yes	characteristic
34	#536×C₆₇	C₄	1	1	yes	characteristic
35	#536×C₆₇	C₄	1	1	yes	characteristic
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#533×C₆₇	C₂²	1	2	yes	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	C₂²	1	1	yes	characteristic
40	#529×C₆₇	C₂²	1	2	yes	—
41	#529×C₆₇	C₂²	1	2	yes	—
42	#529×C₆₇	C₂²	1	1	yes	characteristic
43	#529×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
47	#446×C₆₇	C₂²	1	2	yes	—
48	#446×C₆₇	C₂²	1	1	yes	characteristic
49	#446×C₆₇	C₂²	1	1	yes	characteristic
50	#446×C₆₇	C₂²	1	1	yes	characteristic
51	#446×C₆₇	C₂²	1	2	yes	—
52	#446×C₆₇	C₂²	1	2	yes	—
53	#446×C₆₇	C₂²	1	2	yes	—
54	#446×C₆₇	C₂²	1	2	yes	—
55	#446×C₆₇	C₂²	1	2	yes	—
56	#446×C₆₇	C₂²	1	2	yes	—
57	#446×C₆₇	C₂²	1	1	yes	characteristic
58	#446×C₆₇	C₂²	1	2	yes	—
59	#446×C₆₇	C₂²	1	1	yes	characteristic
60	#446×C₆₇	C₂²	1	2	yes	—
61	#446×C₆₇	C₂²	1	1	yes	characteristic
62	#446×C₆₇	C₂²	1	1	yes	characteristic
63	#446×C₆₇	C₂²	1	2	yes	—
64	#446×C₆₇	C₂²	1	2	yes	—
65	#446×C₆₇	C₂²	1	1	yes	characteristic
66	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
67	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
68	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
69	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
70	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
71	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
72	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
73	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
74	#436×C₆₇	C₂²	1	1	yes	characteristic
75	#436×C₆₇	C₂²	1	1	yes	characteristic
76	#436×C₆₇	C₂²	1	1	yes	characteristic
77	#436×C₆₇	C₂²	1	2	yes	—
78	#436×C₆₇	C₂²	1	2	yes	—
79	#436×C₆₇	C₂²	1	1	yes	characteristic
80	#436×C₆₇	C₂²	1	2	yes	—
81	#436×C₆₇	C₂²	1	2	yes	—
82	#436×C₆₇	C₂²	1	2	yes	—
83	#435×C₆₇	C₂²	1	1	yes	characteristic
84	#435×C₆₇	C₂²	1	1	yes	characteristic
85	#435×C₆₇	C₂²	1	1	yes	characteristic
86	#435×C₆₇	C₂²	1	1	yes	characteristic
87	#435×C₆₇	C₂²	1	2	yes	—
88	#435×C₆₇	C₂²	1	2	yes	—
89	#435×C₆₇	C₂²	1	2	yes	—
90	#435×C₆₇	C₂²	1	2	yes	—
91	#435×C₆₇	C₂²	1	2	yes	—
92	#435×C₆₇	C₂²	1	2	yes	—
93	#435×C₆₇	C₂²	1	2	yes	—
94	#435×C₆₇	C₂²	1	2	yes	—
95	C₈×D₄×C₆₇	C₂²	1	2	yes	—
96	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₈×D₄×C₆₇	C₂²	1	2	yes	—
98	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
99	#433×C₆₇	C₂²	1	2	yes	—
100	#433×C₆₇	C₂²	1	2	yes	—
101	#433×C₆₇	C₂²	1	2	yes	—
102	#433×C₆₇	C₂²	1	2	yes	—
103	#433×C₆₇	C₂²	1	2	yes	—
104	#433×C₆₇	C₂²	1	2	yes	—
105	#433×C₆₇	C₂²	1	2	yes	—
106	#433×C₆₇	C₂²	1	2	yes	—
107	#432×C₆₇	C₂²	1	1	yes	characteristic
108	#432×C₆₇	C₂²	1	2	yes	—
109	#432×C₆₇	C₂²	1	1	yes	characteristic
110	#432×C₆₇	C₂²	1	2	yes	—
111	#431×C₆₇	C₂²	1	1	yes	characteristic
112	#431×C₆₇	C₂²	1	1	yes	characteristic
113	#431×C₆₇	C₂²	1	1	yes	characteristic
114	#431×C₆₇	C₂²	1	2	yes	—
115	#431×C₆₇	C₂²	1	2	yes	—
116	#431×C₆₇	C₂²	1	1	yes	characteristic
117	#424×C₆₇	C₂²	1	2	yes	—
118	#424×C₆₇	C₂²	1	2	yes	—
119	#424×C₆₇	C₂²	1	2	yes	—
120	#424×C₆₇	C₂²	1	2	yes	—
121	#423×C₆₇	C₂²	1	1	yes	characteristic
122	#423×C₆₇	C₂²	1	2	yes	—
123	#423×C₆₇	C₂²	1	1	yes	characteristic
124	#423×C₆₇	C₂²	1	2	yes	—
125	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
126	#405×C₆₇	C₂²	1	2	yes	—
127	#405×C₆₇	C₂²	1	2	yes	—
128	#405×C₆₇	C₂²	1	2	yes	—
129	#405×C₆₇	C₂²	1	2	yes	—
130	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
131	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
133	C₂×#97×C₆₇	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
154	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
156	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
157	#126×C₆₇	C₂×C₄	1	2	yes	—
158	#126×C₆₇	C₂×C₄	1	2	yes	—
159	#126×C₆₇	C₂×C₄	1	2	yes	—
160	#126×C₆₇	C₂×C₄	1	2	yes	—
161	#126×C₆₇	C₂×C₄	1	2	yes	—
162	#126×C₆₇	C₂×C₄	1	2	yes	—
163	#126×C₆₇	C₂×C₄	1	2	yes	—
164	#126×C₆₇	C₂×C₄	1	2	yes	—
165	#125×C₆₇	C₂×C₄	1	2	yes	—
166	#125×C₆₇	C₂×C₄	1	2	yes	—
167	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#125×C₆₇	C₂×C₄	1	2	yes	—
169	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
170	#125×C₆₇	C₂×C₄	1	2	yes	—
171	#125×C₆₇	C₂×C₄	1	2	yes	—
172	#125×C₆₇	C₂×C₄	1	2	yes	—
173	#125×C₆₇	C₂×C₄	1	2	yes	—
174	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
175	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
176	#124×C₆₇	C₂×C₄	1	2	yes	—
177	#124×C₆₇	C₂×C₄	1	2	yes	—
178	#124×C₆₇	C₂×C₄	1	2	yes	—
179	#123×C₆₇	C₂×C₄	1	2	yes	—
180	#123×C₆₇	C₂×C₄	1	2	yes	—
181	#123×C₆₇	C₂×C₄	1	2	yes	—
182	#123×C₆₇	C₂×C₄	1	2	yes	—
183	#123×C₆₇	C₂×C₄	1	2	yes	—
184	#123×C₆₇	C₂×C₄	1	2	yes	—
185	#123×C₆₇	C₂×C₄	1	2	yes	—
186	#123×C₆₇	C₂×C₄	1	2	yes	—
187	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
190	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
191	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
202	#121×C₆₇	C₂×C₄	1	2	yes	—
203	#121×C₆₇	C₂×C₄	1	2	yes	—
204	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
205	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
206	#121×C₆₇	C₂×C₄	1	2	yes	—
207	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
208	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
209	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
210	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
211	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
212	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
215	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₆₇	C₂³	1	2	yes	—
229	C₄×D₄×C₆₇	C₂³	1	2	yes	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
232	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
233	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
234	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
235	#117×C₆₇	C₂×C₄	1	2	yes	—
236	#117×C₆₇	C₂³	1	2	yes	—
237	#117×C₆₇	C₂³	1	2	yes	—
238	#117×C₆₇	C₂³	1	2	yes	—
239	#117×C₆₇	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
242	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
244	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
246	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
247	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
250	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
251	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
253	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
260	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
263	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
267	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
268	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
270	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
271	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
275	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	#97×C₆₇	C₂³	1	1	yes	characteristic
286	#97×C₆₇	C₂³	1	2	yes	—
287	#97×C₆₇	C₂³	1	2	yes	—
288	#97×C₆₇	C₂³	1	2	yes	—
289	#97×C₆₇	C₂³	1	1	yes	characteristic
290	#97×C₆₇	C₂³	1	2	yes	—
291	#97×C₆₇	C₂³	1	1	yes	characteristic
292	#97×C₆₇	C₂³	1	1	yes	characteristic
293	#97×C₆₇	C₂³	1	2	yes	—
294	#97×C₆₇	C₂³	1	2	yes	—
295	#97×C₆₇	C₂³	1	2	yes	—
296	#97×C₆₇	C₂³	1	2	yes	—
297	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
300	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₆₇	C₂³	1	2	yes	—
302	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₄×C₈×C₆₇	C₂³	1	2	yes	—
305	C₄×C₈×C₆₇	C₂³	1	2	yes	—
306	C₄×C₈×C₆₇	C₂³	1	2	yes	—
307	C₄×C₈×C₆₇	C₂³	1	2	yes	—
308	C₄×C₈×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	2	yes	—
310	#41×C₆₇	—	4	2	no	—
311	#41×C₆₇	—	4	2	no	—
312	C₂×Q₈×C₆₇	—	4	2	no	—
313	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
314	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
315	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
317	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
319	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
320	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
321	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
326	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
327	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
328	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
332	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	M₁₆×C₆₇	—	2	2	no	—
342	M₁₆×C₆₇	—	2	2	no	—
343	M₁₆×C₆₇	—	4	1	no	—
344	M₁₆×C₆₇	—	4	2	no	—
345	M₁₆×C₆₇	—	4	2	no	—
346	M₁₆×C₆₇	—	4	1	no	—
347	M₁₆×C₆₇	—	4	2	no	—
348	M₁₆×C₆₇	—	4	2	no	—
349	C₂×C₈×C₆₇	—	2	2	no	—
350	C₂×C₈×C₆₇	—	2	4	no	—
351	C₂×C₈×C₆₇	—	4	2	no	—
352	C₂×C₈×C₆₇	—	4	2	no	—
353	C₂×C₈×C₆₇	—	4	1	no	—
354	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
360	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
363	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
369	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
390	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
391	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
392	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
394	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
397	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
399	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
403	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
410	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
411	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
413	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
421	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
423	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
424	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
426	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
427	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
428	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
429	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
430	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄²×C₆₇	C₂⁴	1	2	yes	—
434	C₄²×C₆₇	C₂⁴	1	2	yes	—
435	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄²×C₆₇	C₂⁴	1	2	yes	—
437	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
438	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
439	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
440	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
441	Q₈×C₆₇	—	2	2	no	—
442	Q₈×C₆₇	—	2	2	no	—
443	Q₈×C₆₇	—	2	2	no	—
444	Q₈×C₆₇	—	4	2	no	—
445	Q₈×C₆₇	—	4	2	no	—
446	Q₈×C₆₇	—	4	2	no	—
447	Q₈×C₆₇	—	4	1	no	—
448	D₄×C₆₇	—	2	2	no	—
449	D₄×C₆₇	—	4	2	no	—
450	D₄×C₆₇	—	4	2	no	—
451	D₄×C₆₇	—	4	1	no	—
452	D₄×C₆₇	—	4	1	no	—
453	D₄×C₆₇	—	4	1	no	—
454	D₄×C₆₇	—	4	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	4	1	no	—
467	C₂×C₄×C₆₇	—	4	1	no	—
468	C₂×C₄×C₆₇	—	4	2	no	—
469	C₂×C₄×C₆₇	—	4	1	no	—
470	C₂×C₄×C₆₇	—	4	2	no	—
471	C₂×C₄×C₆₇	—	4	2	no	—
472	C₂×C₄×C₆₇	—	4	2	no	—
473	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
478	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
480	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
485	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
488	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
490	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
492	C₈×C₆₇	—	2	1	no	—
493	C₈×C₆₇	—	2	2	no	—
494	C₈×C₆₇	—	2	1	no	—
495	C₈×C₆₇	—	2	1	no	—
496	C₈×C₆₇	—	2	1	no	—
497	C₈×C₆₇	—	2	2	no	—
498	C₈×C₆₇	—	2	2	no	—
499	C₈×C₆₇	—	2	1	no	—
500	C₈×C₆₇	—	2	1	no	—
501	C₈×C₆₇	—	2	2	no	—
502	C₈×C₆₇	—	2	1	no	—
503	C₈×C₆₇	2₋¹⁺⁴	1	2	yes	—
504	C₂²×C₆₇	—	2	1	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	2	1	no	—
507	C₂²×C₆₇	—	2	1	no	—
508	C₂²×C₆₇	—	2	1	no	—
509	C₂²×C₆₇	—	2	1	no	—
510	C₂²×C₆₇	—	2	1	no	—
511	C₂²×C₆₇	—	2	2	no	—
512	C₂²×C₆₇	—	2	1	no	—
513	C₂²×C₆₇	—	2	1	no	—
514	C₂²×C₆₇	—	2	1	no	—
515	C₂²×C₆₇	—	2	2	no	—
516	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
517	C₄×C₆₇	—	2	1	no	—
518	C₄×C₆₇	—	2	2	no	—
519	C₄×C₆₇	—	2	1	no	—
520	C₄×C₆₇	—	2	1	no	—
521	C₄×C₆₇	—	2	1	no	—
522	C₄×C₆₇	—	2	1	no	—
523	C₄×C₆₇	—	2	1	no	—
524	C₄×C₆₇	—	2	2	no	—
525	C₄×C₆₇	—	2	2	no	—
526	C₄×C₆₇	—	2	2	no	—
527	C₄×C₆₇	—	2	1	no	—
528	C₄×C₆₇	—	2	1	no	—
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	2	no	—
531	C₄×C₆₇	—	2	1	no	—
532	C₄×C₆₇	—	2	2	no	—
533	C₄×C₆₇	—	2	1	no	—
534	C₄×C₆₇	#568	1	2	yes	—
535	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₄×C₆₇	#585	1	1	yes	characteristic
537	#60344	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂×C₆₇	—	4	1	no	—
539	C₂×C₆₇	—	4	1	no	—
540	C₂×C₆₇	—	4	1	no	—
541	C₂×C₆₇	—	4	2	no	—
542	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
543	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
544	C₂×C₆₇	#3573	1	1	yes	characteristic
545	#3461	C₂×C₆₇	1	1	yes	characteristic
546	#2995	C₂×C₆₇	1	2	yes	complemented
547	#2995	C₂×C₆₇	1	2	yes	complemented
548	#2994	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#2993	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#2993	C₂×C₆₇	1	2	yes	complemented
551	#2991	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2989	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#2986	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2985	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#2985	C₂×C₆₇	1	2	yes	complemented
556	#2984	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#2970	C₂×C₆₇	1	1	yes	characteristic, complemented
558	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#2969	C₂×C₆₇	1	2	yes	complemented
560	#2968	C₂×C₆₇	1	2	yes	complemented
561	#2967	C₂×C₆₇	1	2	yes	complemented
562	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
563	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
564	Q₈×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2961	C₂×C₆₇	1	2	yes	complemented
567	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
568	C₆₇	#60344	1	1	yes	characteristic, direct product factor, Sylow
569	#544	C₄×C₆₇	1	1	yes	characteristic
570	#542	C₄×C₆₇	1	1	yes	characteristic
571	#542	C₄×C₆₇	1	1	yes	characteristic
572	#542	C₄×C₆₇	1	2	yes	—
573	#541	C₄×C₆₇	1	1	yes	characteristic
574	#541	C₄×C₆₇	1	1	yes	characteristic
575	#541	C₄×C₆₇	1	2	yes	—
576	#539	C₄×C₆₇	1	2	yes	—
577	#539	C₄×C₆₇	1	2	yes	—
578	#537	C₄×C₆₇	1	1	yes	characteristic
579	#536	C₄×C₆₇	1	1	yes	characteristic
580	#536	C₄×C₆₇	1	1	yes	characteristic
581	#533	C₂²×C₆₇	1	1	yes	characteristic
582	#533	C₂²×C₆₇	1	2	yes	—
583	#533	C₂²×C₆₇	1	1	yes	characteristic
584	#529	C₂²×C₆₇	1	1	yes	characteristic
585	#529	C₂²×C₆₇	1	2	yes	—
586	#529	C₂²×C₆₇	1	2	yes	—
587	#529	C₂²×C₆₇	1	1	yes	characteristic
588	#529	C₂²×C₆₇	1	2	yes	—
589	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
590	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
591	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
592	#446	C₂²×C₆₇	1	2	yes	—
593	#446	C₂²×C₆₇	1	1	yes	characteristic
594	#446	C₂²×C₆₇	1	1	yes	characteristic
595	#446	C₂²×C₆₇	1	1	yes	characteristic
596	#446	C₂²×C₆₇	1	2	yes	—
597	#446	C₂²×C₆₇	1	2	yes	—
598	#446	C₂²×C₆₇	1	2	yes	—
599	#446	C₂²×C₆₇	1	2	yes	—
600	#446	C₂²×C₆₇	1	2	yes	—
601	#446	C₂²×C₆₇	1	2	yes	—
602	#446	C₂²×C₆₇	1	1	yes	characteristic
603	#446	C₂²×C₆₇	1	2	yes	—
604	#446	C₂²×C₆₇	1	1	yes	characteristic
605	#446	C₂²×C₆₇	1	2	yes	—
606	#446	C₂²×C₆₇	1	1	yes	characteristic
607	#446	C₂²×C₆₇	1	1	yes	characteristic
608	#446	C₂²×C₆₇	1	2	yes	—
609	#446	C₂²×C₆₇	1	2	yes	—
610	#446	C₂²×C₆₇	1	1	yes	characteristic
611	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
612	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
613	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
614	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
615	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
616	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
617	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
618	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
619	#436	C₂²×C₆₇	1	1	yes	characteristic
620	#436	C₂²×C₆₇	1	1	yes	characteristic
621	#436	C₂²×C₆₇	1	1	yes	characteristic
622	#436	C₂²×C₆₇	1	2	yes	—
623	#436	C₂²×C₆₇	1	2	yes	—
624	#436	C₂²×C₆₇	1	1	yes	characteristic
625	#436	C₂²×C₆₇	1	2	yes	—
626	#436	C₂²×C₆₇	1	2	yes	—
627	#436	C₂²×C₆₇	1	2	yes	—
628	#435	C₂²×C₆₇	1	1	yes	characteristic
629	#435	C₂²×C₆₇	1	1	yes	characteristic
630	#435	C₂²×C₆₇	1	1	yes	characteristic
631	#435	C₂²×C₆₇	1	1	yes	characteristic
632	#435	C₂²×C₆₇	1	2	yes	—
633	#435	C₂²×C₆₇	1	2	yes	—
634	#435	C₂²×C₆₇	1	2	yes	—
635	#435	C₂²×C₆₇	1	2	yes	—
636	#435	C₂²×C₆₇	1	2	yes	—
637	#435	C₂²×C₆₇	1	2	yes	—
638	#435	C₂²×C₆₇	1	2	yes	—
639	#435	C₂²×C₆₇	1	2	yes	—
640	C₈×D₄	C₂²×C₆₇	1	2	yes	—
641	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₈×D₄	C₂²×C₆₇	1	2	yes	—
643	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
644	#433	C₂²×C₆₇	1	2	yes	—
645	#433	C₂²×C₆₇	1	2	yes	—
646	#433	C₂²×C₆₇	1	2	yes	—
647	#433	C₂²×C₆₇	1	2	yes	—
648	#433	C₂²×C₆₇	1	2	yes	—
649	#433	C₂²×C₆₇	1	2	yes	—
650	#433	C₂²×C₆₇	1	2	yes	—
651	#433	C₂²×C₆₇	1	2	yes	—
652	#432	C₂²×C₆₇	1	1	yes	characteristic
653	#432	C₂²×C₆₇	1	2	yes	—
654	#432	C₂²×C₆₇	1	1	yes	characteristic
655	#432	C₂²×C₆₇	1	2	yes	—
656	#431	C₂²×C₆₇	1	1	yes	characteristic
657	#431	C₂²×C₆₇	1	1	yes	characteristic
658	#431	C₂²×C₆₇	1	1	yes	characteristic
659	#431	C₂²×C₆₇	1	2	yes	—
660	#431	C₂²×C₆₇	1	2	yes	—
661	#431	C₂²×C₆₇	1	1	yes	characteristic
662	#424	C₂²×C₆₇	1	2	yes	—
663	#424	C₂²×C₆₇	1	2	yes	—
664	#424	C₂²×C₆₇	1	2	yes	—
665	#424	C₂²×C₆₇	1	2	yes	—
666	#423	C₂²×C₆₇	1	1	yes	characteristic
667	#423	C₂²×C₆₇	1	2	yes	—
668	#423	C₂²×C₆₇	1	1	yes	characteristic
669	#423	C₂²×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
671	#405	C₂²×C₆₇	1	2	yes	—
672	#405	C₂²×C₆₇	1	2	yes	—
673	#405	C₂²×C₆₇	1	2	yes	—
674	#405	C₂²×C₆₇	1	2	yes	—
675	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
678	C₂×#97	C₂²×C₆₇	1	2	yes	—
679	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
680	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
681	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
682	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
687	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
689	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
690	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
691	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
693	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
695	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
696	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
697	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
698	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
699	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
701	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
702	#126	C₂×C₄×C₆₇	1	2	yes	—
703	#126	C₂×C₄×C₆₇	1	2	yes	—
704	#126	C₂×C₄×C₆₇	1	2	yes	—
705	#126	C₂×C₄×C₆₇	1	2	yes	—
706	#126	C₂×C₄×C₆₇	1	2	yes	—
707	#126	C₂×C₄×C₆₇	1	2	yes	—
708	#126	C₂×C₄×C₆₇	1	2	yes	—
709	#126	C₂×C₄×C₆₇	1	2	yes	—
710	#125	C₂×C₄×C₆₇	1	2	yes	—
711	#125	C₂×C₄×C₆₇	1	2	yes	—
712	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
713	#125	C₂×C₄×C₆₇	1	2	yes	—
714	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
715	#125	C₂×C₄×C₆₇	1	2	yes	—
716	#125	C₂×C₄×C₆₇	1	2	yes	—
717	#125	C₂×C₄×C₆₇	1	2	yes	—
718	#125	C₂×C₄×C₆₇	1	2	yes	—
719	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
720	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
721	#124	C₂×C₄×C₆₇	1	2	yes	—
722	#124	C₂×C₄×C₆₇	1	2	yes	—
723	#124	C₂×C₄×C₆₇	1	2	yes	—
724	#123	C₂×C₄×C₆₇	1	2	yes	—
725	#123	C₂×C₄×C₆₇	1	2	yes	—
726	#123	C₂×C₄×C₆₇	1	2	yes	—
727	#123	C₂×C₄×C₆₇	1	2	yes	—
728	#123	C₂×C₄×C₆₇	1	2	yes	—
729	#123	C₂×C₄×C₆₇	1	2	yes	—
730	#123	C₂×C₄×C₆₇	1	2	yes	—
731	#123	C₂×C₄×C₆₇	1	2	yes	—
732	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
735	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
736	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
737	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
740	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
743	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
744	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
745	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
746	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
747	#121	C₂×C₄×C₆₇	1	2	yes	—
748	#121	C₂×C₄×C₆₇	1	2	yes	—
749	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
750	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
751	#121	C₂×C₄×C₆₇	1	2	yes	—
752	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
753	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
754	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
755	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
756	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
760	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
763	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
764	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
765	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
766	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
767	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
768	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₆₇	1	2	yes	—
774	C₄×D₄	C₂³×C₆₇	1	2	yes	—
775	C₄×D₄	C₂³×C₆₇	1	2	yes	—
776	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
777	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
778	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
779	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
780	#117	C₂×C₄×C₆₇	1	2	yes	—
781	#117	C₂³×C₆₇	1	2	yes	—
782	#117	C₂³×C₆₇	1	2	yes	—
783	#117	C₂³×C₆₇	1	2	yes	—
784	#117	C₂³×C₆₇	1	2	yes	—
785	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
789	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
791	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
792	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
793	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
794	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
795	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
797	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
799	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
800	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
801	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
802	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
804	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
805	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
808	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
809	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
810	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
813	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
816	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
818	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
819	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
820	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
822	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
828	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
830	#97	C₂³×C₆₇	1	1	yes	characteristic
831	#97	C₂³×C₆₇	1	2	yes	—
832	#97	C₂³×C₆₇	1	2	yes	—
833	#97	C₂³×C₆₇	1	2	yes	—
834	#97	C₂³×C₆₇	1	1	yes	characteristic
835	#97	C₂³×C₆₇	1	2	yes	—
836	#97	C₂³×C₆₇	1	1	yes	characteristic
837	#97	C₂³×C₆₇	1	1	yes	characteristic
838	#97	C₂³×C₆₇	1	2	yes	—
839	#97	C₂³×C₆₇	1	2	yes	—
840	#97	C₂³×C₆₇	1	2	yes	—
841	#97	C₂³×C₆₇	1	2	yes	—
842	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₆₇	1	2	yes	—
847	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₆₇	1	2	yes	—
850	C₄×C₈	C₂³×C₆₇	1	2	yes	—
851	C₄×C₈	C₂³×C₆₇	1	2	yes	—
852	C₄×C₈	C₂³×C₆₇	1	2	yes	—
853	C₄×C₈	C₂³×C₆₇	1	2	yes	—
854	C₄×C₈	C₂³×C₆₇	1	2	yes	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
859	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
860	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
861	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
862	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
863	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
864	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
865	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
866	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
867	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
868	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
869	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
870	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
871	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
872	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
873	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
874	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
875	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
876	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
877	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
879	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
880	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
881	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
886	M₁₆	—	2	2	no	—
887	M₁₆	—	2	2	no	—
888	M₁₆	—	4	1	no	—
889	M₁₆	—	4	2	no	—
890	M₁₆	—	4	2	no	—
891	M₁₆	—	4	1	no	—
892	M₁₆	—	4	2	no	—
893	M₁₆	—	4	2	no	—
894	C₂×C₈	—	2	2	no	—
895	C₂×C₈	—	2	4	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	—	4	2	no	—
898	C₂×C₈	—	4	1	no	—
899	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
904	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
905	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
908	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
910	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
912	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
914	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
915	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
916	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
917	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
918	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
922	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
923	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
927	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
928	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
929	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
932	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
933	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
934	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
935	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
936	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
937	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
940	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
941	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
943	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
944	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
945	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
946	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
947	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
948	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
949	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
950	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
951	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
952	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
957	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
958	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
959	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
960	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
961	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
962	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
965	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
966	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
967	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
968	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
969	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
970	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
971	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
972	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
973	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
974	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
975	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₄²	C₂⁴×C₆₇	1	2	yes	—
978	C₄²	C₂⁴×C₆₇	1	2	yes	—
979	C₄²	C₂⁴×C₆₇	1	2	yes	—
980	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
983	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
984	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
985	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	1	no	—
991	Q₈	—	4	2	no	—
992	Q₈	—	4	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	4	1	no	—
995	D₄	—	4	1	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	1	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	4	1	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1019	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1020	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1021	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1022	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1023	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1024	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1025	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1026	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1027	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1028	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1029	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1030	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1031	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1032	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1034	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1035	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1036	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1037	C₈	—	2	1	no	—
1038	C₈	—	2	2	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	2	2	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	2₋¹⁺⁴×C₆₇	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	#568×C₆₇	1	2	yes	—
1080	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1081	C₄	#585×C₆₇	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1087	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1088	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	#537×C₆₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2995	C₂	semidirect
4. C₆₇×#2994	C₂	semidirect
5. C₆₇×#2993	C₂	semidirect
6. C₆₇×#2993	C₂	semidirect
7. C₆₇×#2991	C₂	semidirect
8. C₆₇×#2989	C₂	semidirect
9. C₆₇×#2986	C₂	semidirect
10. C₆₇×#2985	C₂	semidirect
11. C₆₇×#2985	C₂	semidirect
12. C₆₇×#2984	C₂	semidirect
13. C₆₇×#2970	C₂	semidirect
14. C₆₇×#2969	C₂	semidirect
15. C₆₇×#2969	C₂	semidirect
16. C₆₇×#2968	C₂	semidirect
17. C₆₇×#2967	C₂	semidirect
18. C₆₇×#2966	C₂	semidirect
19. C₆₇×#2965	C₂	semidirect
20. Q₈×M₁₆×C₆₇	C₂	semidirect
21. C₆₇×#2962	C₂	semidirect
22. C₆₇×#2961	C₂	semidirect
23. C₆₇×#2960	C₂	semidirect
537. #60344	C₆₇	direct (N × H)
546. #2995	C₂×C₆₇	semidirect
547. #2995	C₂×C₆₇	semidirect
548. #2994	C₂×C₆₇	semidirect
549. #2993	C₂×C₆₇	semidirect
550. #2993	C₂×C₆₇	semidirect
551. #2991	C₂×C₆₇	semidirect
552. #2989	C₂×C₆₇	semidirect
553. #2986	C₂×C₆₇	semidirect
554. #2985	C₂×C₆₇	semidirect
555. #2985	C₂×C₆₇	semidirect
556. #2984	C₂×C₆₇	semidirect
557. #2970	C₂×C₆₇	semidirect
558. #2969	C₂×C₆₇	semidirect
559. #2969	C₂×C₆₇	semidirect
560. #2968	C₂×C₆₇	semidirect
561. #2967	C₂×C₆₇	semidirect
562. #2966	C₂×C₆₇	semidirect
563. #2965	C₂×C₆₇	semidirect
564. Q₈×M₁₆	C₂×C₆₇	semidirect
565. #2962	C₂×C₆₇	semidirect
566. #2961	C₂×C₆₇	semidirect
567. #2960	C₂×C₆₇	semidirect
568. C₆₇	#60344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3461	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2991	2
C₆₇×#2989	2
C₆₇×#2986	2
C₆₇×#2985	2
C₆₇×#2984	2
C₆₇×#2970	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2965	2
Q₈×M₁₆×C₆₇	2
C₆₇×#2962	2
C₆₇×#2961	2
C₆₇×#2960	2
#60344	67

Subgroups — C67×#60344 #30739595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60344 #30739595