Subgroups — C₆₇×#60342 #30739593

Order 17152.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3482	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2987	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2970	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, 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	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#557×C₆₇	C₄	1	1	yes	characteristic
25	#556×C₆₇	C₄	1	2	yes	—
26	#556×C₆₇	C₄	1	1	yes	characteristic
27	#552×C₆₇	C₄	1	1	yes	characteristic
28	#552×C₆₇	C₄	1	2	yes	—
29	#552×C₆₇	C₄	1	1	yes	characteristic
30	#552×C₆₇	C₄	1	2	yes	—
31	D₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
32	#548×C₆₇	C₄	1	1	yes	characteristic
33	#548×C₆₇	C₄	1	1	yes	characteristic
34	#547×C₆₇	C₄	1	1	yes	characteristic
35	#547×C₆₇	C₄	1	2	yes	—
36	#533×C₆₇	C₂²	1	2	yes	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#529×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	C₂²	1	2	yes	—
40	#529×C₆₇	C₂²	1	2	yes	—
41	#529×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
43	C₄×#41×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×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	1	yes	characteristic
52	#446×C₆₇	C₂²	1	2	yes	—
53	#446×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
58	#446×C₆₇	C₂²	1	2	yes	—
59	#446×C₆₇	C₂²	1	2	yes	—
60	#446×C₆₇	C₂²	1	1	yes	characteristic
61	#446×C₆₇	C₂²	1	2	yes	—
62	#446×C₆₇	C₂²	1	1	yes	characteristic
63	#446×C₆₇	C₂²	1	2	yes	—
64	#446×C₆₇	C₂²	1	1	yes	characteristic
65	#446×C₆₇	C₂²	1	1	yes	characteristic
66	#446×C₆₇	C₂²	1	2	yes	—
67	#446×C₆₇	C₂²	1	2	yes	—
68	#446×C₆₇	C₂²	1	1	yes	characteristic
69	#446×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
79	#436×C₆₇	C₂²	1	2	yes	—
80	#435×C₆₇	C₂²	1	1	yes	characteristic
81	#435×C₆₇	C₂²	1	1	yes	characteristic
82	#435×C₆₇	C₂²	1	1	yes	characteristic
83	#435×C₆₇	C₂²	1	1	yes	characteristic
84	#435×C₆₇	C₂²	1	2	yes	—
85	#435×C₆₇	C₂²	1	2	yes	—
86	#435×C₆₇	C₂²	1	2	yes	—
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	C₈×D₄×C₆₇	C₂²	1	2	yes	—
95	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
96	C₈×D₄×C₆₇	C₂²	1	2	yes	—
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	#432×C₆₇	C₂²	1	1	yes	characteristic
106	#432×C₆₇	C₂²	1	2	yes	—
107	#432×C₆₇	C₂²	1	2	yes	—
108	#432×C₆₇	C₂²	1	2	yes	—
109	#432×C₆₇	C₂²	1	1	yes	characteristic
110	#432×C₆₇	C₂²	1	2	yes	—
111	#432×C₆₇	C₂²	1	2	yes	—
112	#431×C₆₇	C₂²	1	1	yes	characteristic
113	#431×C₆₇	C₂²	1	1	yes	characteristic
114	#431×C₆₇	C₂²	1	1	yes	characteristic
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	#423×C₆₇	C₂²	1	2	yes	—
121	#423×C₆₇	C₂²	1	2	yes	—
122	#423×C₆₇	C₂²	1	1	yes	characteristic
123	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
124	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
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	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
131	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
132	C₂×#97×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	2	yes	—
137	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
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	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
164	#125×C₆₇	C₂×C₄	1	2	yes	—
165	#125×C₆₇	C₂×C₄	1	2	yes	—
166	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
167	#125×C₆₇	C₂×C₄	1	2	yes	—
168	#125×C₆₇	C₂×C₄	1	2	yes	—
169	#125×C₆₇	C₂×C₄	1	2	yes	—
170	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
171	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
172	#124×C₆₇	C₂×C₄	1	2	yes	—
173	#124×C₆₇	C₂×C₄	1	2	yes	—
174	#123×C₆₇	C₂×C₄	1	2	yes	—
175	#123×C₆₇	C₂×C₄	1	2	yes	—
176	#123×C₆₇	C₂×C₄	1	2	yes	—
177	#123×C₆₇	C₂×C₄	1	2	yes	—
178	#123×C₆₇	C₂×C₄	1	2	yes	—
179	#123×C₆₇	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
183	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
186	C₂²⋊Q₈×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	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
192	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
193	#121×C₆₇	C₂×C₄	1	2	yes	—
194	#121×C₆₇	C₂×C₄	1	2	yes	—
195	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
196	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
199	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
200	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
201	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
202	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
203	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
204	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
208	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
209	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
211	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
213	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
217	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
219	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₆₇	C₂³	1	2	yes	—
222	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₆₇	C₂³	1	2	yes	—
224	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₇	C₂³	1	2	yes	—
226	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
227	#117×C₆₇	C₂×C₄	1	2	yes	—
228	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
229	#117×C₆₇	C₂×C₄	1	2	yes	—
230	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
231	#117×C₆₇	C₂×C₄	1	2	yes	—
232	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
233	#117×C₆₇	C₂×C₄	1	2	yes	—
234	#117×C₆₇	C₂³	1	2	yes	—
235	#117×C₆₇	C₂³	1	2	yes	—
236	#117×C₆₇	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
239	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
241	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
243	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
274	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	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	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	#97×C₆₇	C₂³	1	2	yes	—
286	#97×C₆₇	C₂³	1	1	yes	characteristic
287	#97×C₆₇	C₂³	1	2	yes	—
288	#97×C₆₇	C₂³	1	2	yes	—
289	#97×C₆₇	C₂³	1	2	yes	—
290	#97×C₆₇	C₂³	1	2	yes	—
291	#97×C₆₇	C₂³	1	2	yes	—
292	#97×C₆₇	C₂³	1	1	yes	characteristic
293	#97×C₆₇	C₂³	1	1	yes	characteristic
294	#97×C₆₇	C₂³	1	2	yes	—
295	#97×C₆₇	C₂³	1	1	yes	characteristic
296	#97×C₆₇	C₂³	1	2	yes	—
297	#97×C₆₇	C₂³	1	2	yes	—
298	#97×C₆₇	C₂³	1	2	yes	—
299	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
300	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
302	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₆₇	C₂³	1	2	yes	—
304	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
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	4	no	—
312	#41×C₆₇	—	4	2	no	—
313	C₂×Q₈×C₆₇	—	4	2	no	—
314	C₂×Q₈×C₆₇	—	4	2	no	—
315	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
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×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
325	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
328	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
329	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
331	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
337	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
339	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	M₁₆×C₆₇	—	2	2	no	—
346	M₁₆×C₆₇	—	2	2	no	—
347	M₁₆×C₆₇	—	4	1	no	—
348	M₁₆×C₆₇	—	4	2	no	—
349	M₁₆×C₆₇	—	4	2	no	—
350	M₁₆×C₆₇	—	4	2	no	—
351	M₁₆×C₆₇	—	4	1	no	—
352	C₂×C₈×C₆₇	—	2	2	no	—
353	C₂×C₈×C₆₇	—	2	4	no	—
354	C₂×C₈×C₆₇	—	4	2	no	—
355	C₂×C₈×C₆₇	—	4	2	no	—
356	C₂×C₈×C₆₇	—	4	2	no	—
357	C₂×C₈×C₆₇	—	4	1	no	—
358	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
363	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
364	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
366	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
377	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
378	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
380	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
382	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
384	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
391	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
401	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
411	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
421	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
424	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
432	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₄²×C₆₇	C₂⁴	1	2	yes	—
434	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄²×C₆₇	C₂⁴	1	2	yes	—
437	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₆₇	C₂⁴	1	2	yes	—
439	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
440	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
441	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
442	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
443	Q₈×C₆₇	—	2	2	no	—
444	Q₈×C₆₇	—	2	2	no	—
445	Q₈×C₆₇	—	2	2	no	—
446	Q₈×C₆₇	—	4	2	no	—
447	Q₈×C₆₇	—	4	2	no	—
448	Q₈×C₆₇	—	4	1	no	—
449	Q₈×C₆₇	—	4	2	no	—
450	D₄×C₆₇	—	2	2	no	—
451	D₄×C₆₇	—	2	4	no	—
452	D₄×C₆₇	—	2	2	no	—
453	D₄×C₆₇	—	2	2	no	—
454	D₄×C₆₇	—	4	1	no	—
455	D₄×C₆₇	—	4	2	no	—
456	D₄×C₆₇	—	4	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	4	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	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	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	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	—	4	1	no	—
474	C₂×C₄×C₆₇	—	4	2	no	—
475	C₂×C₄×C₆₇	—	4	1	no	—
476	C₂×C₄×C₆₇	—	4	2	no	—
477	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
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	1	yes	characteristic
481	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
483	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
484	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
491	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
493	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
496	C₈×C₆₇	—	2	1	no	—
497	C₈×C₆₇	—	2	2	no	—
498	C₈×C₆₇	—	2	1	no	—
499	C₈×C₆₇	—	2	1	no	—
500	C₈×C₆₇	—	2	2	no	—
501	C₈×C₆₇	—	2	2	no	—
502	C₈×C₆₇	—	2	1	no	—
503	C₈×C₆₇	—	2	2	no	—
504	C₈×C₆₇	—	2	1	no	—
505	C₈×C₆₇	—	2	1	no	—
506	C₈×C₆₇	—	2	1	no	—
507	C₈×C₆₇	2₋¹⁺⁴	1	2	yes	—
508	C₂²×C₆₇	—	2	1	no	—
509	C₂²×C₆₇	—	2	1	no	—
510	C₂²×C₆₇	—	2	2	no	—
511	C₂²×C₆₇	—	2	1	no	—
512	C₂²×C₆₇	—	2	1	no	—
513	C₂²×C₆₇	—	2	1	no	—
514	C₂²×C₆₇	—	2	1	no	—
515	C₂²×C₆₇	—	2	1	no	—
516	C₂²×C₆₇	—	2	1	no	—
517	C₂²×C₆₇	—	2	2	no	—
518	C₂²×C₆₇	—	2	2	no	—
519	C₂²×C₆₇	#568	1	2	yes	—
520	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
521	C₄×C₆₇	—	2	1	no	—
522	C₄×C₆₇	—	2	2	no	—
523	C₄×C₆₇	—	2	1	no	—
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	2	1	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	1	no	—
531	C₄×C₆₇	—	2	1	no	—
532	C₄×C₆₇	—	2	1	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	1	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	#568	1	2	yes	—
539	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄×C₆₇	#585	1	1	yes	characteristic
541	#60342	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
542	C₂×C₆₇	—	2	2	no	—
543	C₂×C₆₇	—	4	1	no	—
544	C₂×C₆₇	—	4	1	no	—
545	C₂×C₆₇	—	4	2	no	—
546	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
547	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
548	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
549	#3482	C₂×C₆₇	1	1	yes	characteristic
550	#2995	C₂×C₆₇	1	2	yes	complemented
551	#2994	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2993	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#2992	C₂×C₆₇	1	2	yes	complemented
554	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#2989	C₂×C₆₇	1	2	yes	complemented
556	#2989	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#2987	C₂×C₆₇	1	2	yes	complemented
558	#2985	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#2984	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#2983	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#2970	C₂×C₆₇	1	2	yes	complemented
562	#2970	C₂×C₆₇	1	1	yes	characteristic, complemented
563	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#2968	C₂×C₆₇	1	2	yes	complemented
565	#2967	C₂×C₆₇	1	2	yes	complemented
566	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
568	Q₈×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2961	C₂×C₆₇	1	2	yes	complemented
571	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
572	C₆₇	#60342	1	1	yes	characteristic, direct product factor, Sylow
573	#557	C₄×C₆₇	1	1	yes	characteristic
574	#556	C₄×C₆₇	1	2	yes	—
575	#556	C₄×C₆₇	1	1	yes	characteristic
576	#552	C₄×C₆₇	1	1	yes	characteristic
577	#552	C₄×C₆₇	1	2	yes	—
578	#552	C₄×C₆₇	1	1	yes	characteristic
579	#552	C₄×C₆₇	1	2	yes	—
580	D₄×Q₈	C₄×C₆₇	1	1	yes	characteristic
581	#548	C₄×C₆₇	1	1	yes	characteristic
582	#548	C₄×C₆₇	1	1	yes	characteristic
583	#547	C₄×C₆₇	1	1	yes	characteristic
584	#547	C₄×C₆₇	1	2	yes	—
585	#533	C₂²×C₆₇	1	2	yes	—
586	#533	C₂²×C₆₇	1	1	yes	characteristic
587	#529	C₂²×C₆₇	1	1	yes	characteristic
588	#529	C₂²×C₆₇	1	2	yes	—
589	#529	C₂²×C₆₇	1	2	yes	—
590	#529	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
592	C₄×#41	C₂²×C₆₇	1	2	yes	—
593	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
594	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
596	#446	C₂²×C₆₇	1	2	yes	—
597	#446	C₂²×C₆₇	1	1	yes	characteristic
598	#446	C₂²×C₆₇	1	1	yes	characteristic
599	#446	C₂²×C₆₇	1	1	yes	characteristic
600	#446	C₂²×C₆₇	1	1	yes	characteristic
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	2	yes	—
605	#446	C₂²×C₆₇	1	2	yes	—
606	#446	C₂²×C₆₇	1	2	yes	—
607	#446	C₂²×C₆₇	1	2	yes	—
608	#446	C₂²×C₆₇	1	2	yes	—
609	#446	C₂²×C₆₇	1	1	yes	characteristic
610	#446	C₂²×C₆₇	1	2	yes	—
611	#446	C₂²×C₆₇	1	1	yes	characteristic
612	#446	C₂²×C₆₇	1	2	yes	—
613	#446	C₂²×C₆₇	1	1	yes	characteristic
614	#446	C₂²×C₆₇	1	1	yes	characteristic
615	#446	C₂²×C₆₇	1	2	yes	—
616	#446	C₂²×C₆₇	1	2	yes	—
617	#446	C₂²×C₆₇	1	1	yes	characteristic
618	#446	C₂²×C₆₇	1	2	yes	—
619	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
620	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
621	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
622	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
623	#436	C₂²×C₆₇	1	1	yes	characteristic
624	#436	C₂²×C₆₇	1	1	yes	characteristic
625	#436	C₂²×C₆₇	1	1	yes	characteristic
626	#436	C₂²×C₆₇	1	2	yes	—
627	#436	C₂²×C₆₇	1	1	yes	characteristic
628	#436	C₂²×C₆₇	1	2	yes	—
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	1	yes	characteristic
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	#435	C₂²×C₆₇	1	2	yes	—
641	#435	C₂²×C₆₇	1	2	yes	—
642	#435	C₂²×C₆₇	1	2	yes	—
643	C₈×D₄	C₂²×C₆₇	1	2	yes	—
644	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
645	C₈×D₄	C₂²×C₆₇	1	2	yes	—
646	C₈×D₄	C₂²×C₆₇	1	2	yes	—
647	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
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	#433	C₂²×C₆₇	1	2	yes	—
653	#433	C₂²×C₆₇	1	2	yes	—
654	#432	C₂²×C₆₇	1	1	yes	characteristic
655	#432	C₂²×C₆₇	1	2	yes	—
656	#432	C₂²×C₆₇	1	2	yes	—
657	#432	C₂²×C₆₇	1	2	yes	—
658	#432	C₂²×C₆₇	1	1	yes	characteristic
659	#432	C₂²×C₆₇	1	2	yes	—
660	#432	C₂²×C₆₇	1	2	yes	—
661	#431	C₂²×C₆₇	1	1	yes	characteristic
662	#431	C₂²×C₆₇	1	1	yes	characteristic
663	#431	C₂²×C₆₇	1	1	yes	characteristic
664	#431	C₂²×C₆₇	1	2	yes	—
665	#431	C₂²×C₆₇	1	1	yes	characteristic
666	#424	C₂²×C₆₇	1	2	yes	—
667	#424	C₂²×C₆₇	1	2	yes	—
668	#424	C₂²×C₆₇	1	2	yes	—
669	#423	C₂²×C₆₇	1	2	yes	—
670	#423	C₂²×C₆₇	1	2	yes	—
671	#423	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
673	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
674	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
675	#405	C₂²×C₆₇	1	2	yes	—
676	#405	C₂²×C₆₇	1	2	yes	—
677	#405	C₂²×C₆₇	1	2	yes	—
678	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
679	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
680	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
681	C₂×#97	C₂²×C₆₇	1	2	yes	—
682	C₂×#97	C₂²×C₆₇	1	2	yes	—
683	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
684	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
685	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
686	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
687	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
688	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
689	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
692	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
695	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
696	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
697	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
698	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
700	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
701	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
702	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
703	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
705	C₄⋊Q₈	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	#126	C₂×C₄×C₆₇	1	2	yes	—
711	#126	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	2	yes	—
715	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
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	#123	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	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
730	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
731	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
732	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
733	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
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	1	yes	characteristic
737	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
739	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
740	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
741	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
742	#121	C₂×C₄×C₆₇	1	2	yes	—
743	#121	C₂×C₄×C₆₇	1	2	yes	—
744	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
745	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
746	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
747	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
748	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
749	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
750	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
751	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
752	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
753	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
757	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
758	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
760	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
761	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
762	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
763	C₄×D₄	C₂×C₄×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	2	yes	—
768	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₆₇	1	2	yes	—
771	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₆₇	1	2	yes	—
773	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
774	C₄×D₄	C₂³×C₆₇	1	2	yes	—
775	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
776	#117	C₂×C₄×C₆₇	1	2	yes	—
777	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
778	#117	C₂×C₄×C₆₇	1	2	yes	—
779	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
780	#117	C₂×C₄×C₆₇	1	2	yes	—
781	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
782	#117	C₂×C₄×C₆₇	1	2	yes	—
783	#117	C₂³×C₆₇	1	2	yes	—
784	#117	C₂³×C₆₇	1	2	yes	—
785	#117	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
790	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
794	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
796	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
814	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
817	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
821	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
827	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
829	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
834	#97	C₂³×C₆₇	1	2	yes	—
835	#97	C₂³×C₆₇	1	1	yes	characteristic
836	#97	C₂³×C₆₇	1	2	yes	—
837	#97	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
842	#97	C₂³×C₆₇	1	1	yes	characteristic
843	#97	C₂³×C₆₇	1	2	yes	—
844	#97	C₂³×C₆₇	1	1	yes	characteristic
845	#97	C₂³×C₆₇	1	2	yes	—
846	#97	C₂³×C₆₇	1	2	yes	—
847	#97	C₂³×C₆₇	1	2	yes	—
848	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₆₇	1	2	yes	—
853	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₆₇	1	2	yes	—
856	C₄×C₈	C₂³×C₆₇	1	2	yes	—
857	C₄×C₈	C₂³×C₆₇	1	2	yes	—
858	C₄×C₈	C₂³×C₆₇	1	2	yes	—
859	#41	—	4	2	no	—
860	#41	—	4	4	no	—
861	#41	—	4	2	no	—
862	C₂×Q₈	—	4	2	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
865	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
866	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
867	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
868	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
869	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
870	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
871	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
872	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
873	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
874	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
875	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
876	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
877	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
880	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
884	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
885	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
886	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
887	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
888	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
889	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
894	M₁₆	—	2	2	no	—
895	M₁₆	—	2	2	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	4	2	no	—
898	M₁₆	—	4	2	no	—
899	M₁₆	—	4	2	no	—
900	M₁₆	—	4	1	no	—
901	C₂×C₈	—	2	2	no	—
902	C₂×C₈	—	2	4	no	—
903	C₂×C₈	—	4	2	no	—
904	C₂×C₈	—	4	2	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	—	4	1	no	—
907	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
912	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
915	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
917	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
918	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
920	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
922	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
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	2	yes	—
926	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
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	1	yes	characteristic
932	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
933	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
940	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
948	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
949	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
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	1	yes	characteristic
953	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
960	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
961	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
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	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
969	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
970	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
971	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
972	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
973	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
974	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
975	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
976	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
977	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
978	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
979	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
980	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
981	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₄²	C₂⁴×C₆₇	1	2	yes	—
984	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₄²	C₂⁴×C₆₇	1	2	yes	—
986	C₄²	C₂⁴×C₆₇	1	2	yes	—
987	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
989	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
990	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
991	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	1	no	—
998	Q₈	—	4	2	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	4	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	4	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	4	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1027	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
1035	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1036	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1037	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1038	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1039	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1040	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1041	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1042	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1043	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1044	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1045	C₈	—	2	1	no	—
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	2	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	2	2	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	2₋¹⁺⁴×C₆₇	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	#568×C₆₇	1	2	yes	—
1069	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	#568×C₆₇	1	2	yes	—
1088	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1089	C₄	#585×C₆₇	1	1	yes	characteristic
1090	C₂	—	2	2	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1095	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1096	C₂	C₂×#568×C₆₇	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	C₆₇×#3482	C₂
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×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2990	C₂	semidirect
7. C₆₇×#2989	C₂	semidirect
8. C₆₇×#2989	C₂	semidirect
9. C₆₇×#2987	C₂	semidirect
10. C₆₇×#2985	C₂	semidirect
11. C₆₇×#2984	C₂	semidirect
12. C₆₇×#2983	C₂	semidirect
13. C₆₇×#2970	C₂	semidirect
14. C₆₇×#2970	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. C₂×#446×C₆₇	C₂	semidirect
541. #60342	C₆₇	direct (N × H)
550. #2995	C₂×C₆₇	semidirect
551. #2994	C₂×C₆₇	semidirect
552. #2993	C₂×C₆₇	semidirect
553. #2992	C₂×C₆₇	semidirect
554. #2990	C₂×C₆₇	semidirect
555. #2989	C₂×C₆₇	semidirect
556. #2989	C₂×C₆₇	semidirect
557. #2987	C₂×C₆₇	semidirect
558. #2985	C₂×C₆₇	semidirect
559. #2984	C₂×C₆₇	semidirect
560. #2983	C₂×C₆₇	semidirect
561. #2970	C₂×C₆₇	semidirect
562. #2970	C₂×C₆₇	semidirect
563. #2969	C₂×C₆₇	semidirect
564. #2968	C₂×C₆₇	semidirect
565. #2967	C₂×C₆₇	semidirect
566. #2966	C₂×C₆₇	semidirect
567. #2965	C₂×C₆₇	semidirect
568. Q₈×M₁₆	C₂×C₆₇	semidirect
569. #2962	C₂×C₆₇	semidirect
570. #2961	C₂×C₆₇	semidirect
571. C₂×#446	C₂×C₆₇	semidirect
572. C₆₇	#60342	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×#3482	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2987	2
C₆₇×#2985	2
C₆₇×#2984	2
C₆₇×#2983	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
C₂×#446×C₆₇	2
#60342	67

Subgroups — C67×#60342 #30739593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60342 #30739593