Subgroups — C₆₇×#60298 #30739549

Order 17152.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	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×#2988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2977	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2972	C₂	1	1	yes	maximal, characteristic, 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×#2966	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2924	C₂	1	2	yes	maximal, complemented
22	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#433×C₆₇	C₂	1	2	yes	maximal, complemented
24	#556×C₆₇	C₄	1	1	yes	characteristic
25	#555×C₆₇	C₄	1	1	yes	characteristic
26	#554×C₆₇	C₄	1	1	yes	characteristic
27	#553×C₆₇	C₄	1	2	yes	—
28	#552×C₆₇	C₄	1	2	yes	—
29	#552×C₆₇	C₄	1	1	yes	characteristic
30	#552×C₆₇	C₄	1	1	yes	characteristic
31	#551×C₆₇	C₄	1	2	yes	—
32	#551×C₆₇	C₄	1	2	yes	—
33	#547×C₆₇	C₄	1	1	yes	characteristic
34	#546×C₆₇	C₄	1	1	yes	characteristic
35	#546×C₆₇	C₄	1	1	yes	characteristic
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	C₂²	1	2	yes	—
38	#529×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	C₂²	1	2	yes	—
40	#529×C₆₇	C₂²	1	1	yes	characteristic
41	#525×C₆₇	C₂²	1	2	yes	—
42	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
43	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#117×C₆₇	C₂²	1	2	yes	—
47	#446×C₆₇	C₂²	1	2	yes	complemented
48	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#446×C₆₇	C₂²	1	2	yes	complemented
50	#446×C₆₇	C₂²	1	2	yes	complemented
51	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
58	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#436×C₆₇	C₂²	1	1	yes	characteristic
60	#436×C₆₇	C₂²	1	1	yes	characteristic
61	#436×C₆₇	C₂²	1	2	yes	complemented
62	#436×C₆₇	C₂²	1	2	yes	complemented
63	#435×C₆₇	C₂²	1	2	yes	—
64	#435×C₆₇	C₂²	1	2	yes	—
65	#435×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	2	yes	complemented
67	#435×C₆₇	C₂²	1	2	yes	complemented
68	#435×C₆₇	C₂²	1	2	yes	complemented
69	#435×C₆₇	C₂²	1	2	yes	complemented
70	#435×C₆₇	C₂²	1	2	yes	complemented
71	#435×C₆₇	C₂²	1	2	yes	complemented
72	#435×C₆₇	C₂²	1	2	yes	complemented
73	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
74	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
75	C₈×D₄×C₆₇	C₂²	1	2	yes	—
76	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₆₇	C₂²	1	2	yes	—
78	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	#433×C₆₇	C₂²	1	1	yes	characteristic
88	#433×C₆₇	C₂²	1	2	yes	—
89	#433×C₆₇	C₂²	1	2	yes	—
90	#433×C₆₇	C₂²	1	2	yes	—
91	#433×C₆₇	C₂²	1	1	yes	characteristic
92	#433×C₆₇	C₂²	1	2	yes	—
93	#433×C₆₇	C₂²	1	2	yes	—
94	#433×C₆₇	C₂²	1	2	yes	complemented
95	#433×C₆₇	C₂²	1	2	yes	complemented
96	#433×C₆₇	C₂²	1	2	yes	complemented
97	#433×C₆₇	C₂²	1	2	yes	complemented
98	#433×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#433×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#433×C₆₇	C₂²	1	2	yes	complemented
101	#432×C₆₇	C₂²	1	1	yes	characteristic
102	#432×C₆₇	C₂²	1	2	yes	complemented
103	#432×C₆₇	C₂²	1	2	yes	complemented
104	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#431×C₆₇	C₂²	1	1	yes	characteristic
106	#431×C₆₇	C₂²	1	1	yes	characteristic
107	#431×C₆₇	C₂²	1	1	yes	characteristic
108	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#431×C₆₇	C₂²	1	2	yes	complemented
111	#431×C₆₇	C₂²	1	2	yes	complemented
112	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#424×C₆₇	C₂²	1	2	yes	complemented
116	#424×C₆₇	C₂²	1	2	yes	complemented
117	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
120	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#408×C₆₇	C₂²	1	1	yes	characteristic
122	#408×C₆₇	C₂²	1	1	yes	characteristic
123	#408×C₆₇	C₂²	1	2	yes	—
124	#407×C₆₇	C₂²	1	2	yes	—
125	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
126	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
127	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
128	#405×C₆₇	C₂²	1	2	yes	complemented
129	#405×C₆₇	C₂²	1	2	yes	complemented
130	#405×C₆₇	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
133	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
144	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
156	#126×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	#125×C₆₇	C₂×C₄	1	2	yes	—
163	#125×C₆₇	C₂×C₄	1	2	yes	—
164	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
165	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
166	#125×C₆₇	C₂×C₄	1	2	yes	—
167	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
169	#124×C₆₇	C₂×C₄	1	2	yes	—
170	#124×C₆₇	C₂×C₄	1	2	yes	—
171	#123×C₆₇	C₂×C₄	1	2	yes	—
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	#123×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	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
187	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
188	#121×C₆₇	C₂×C₄	1	2	yes	—
189	#121×C₆₇	C₂×C₄	1	2	yes	—
190	#121×C₆₇	C₂×C₄	1	2	yes	—
191	#121×C₆₇	C₂×C₄	1	2	yes	—
192	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
193	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
194	#120×C₆₇	C₂×C₄	1	2	yes	—
195	#120×C₆₇	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
200	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
203	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
204	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
205	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
206	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
207	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
208	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
211	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
214	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₆₇	C₂³	1	2	yes	—
218	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₆₇	C₂³	1	2	yes	—
220	C₄×D₄×C₆₇	C₂³	1	2	yes	—
221	C₄×D₄×C₆₇	C₂³	1	2	yes	—
222	C₄×D₄×C₆₇	C₂³	1	2	yes	—
223	#117×C₆₇	C₂×C₄	1	2	yes	—
224	#117×C₆₇	C₂×C₄	1	2	yes	—
225	#117×C₆₇	C₂×C₄	1	2	yes	—
226	#117×C₆₇	C₂×C₄	1	2	yes	—
227	#117×C₆₇	C₂×C₄	1	2	yes	—
228	#117×C₆₇	C₂×C₄	1	2	yes	—
229	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
230	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
231	#117×C₆₇	C₂³	1	1	yes	characteristic
232	#117×C₆₇	C₂³	1	2	yes	—
233	#117×C₆₇	C₂³	1	2	yes	—
234	#117×C₆₇	C₂³	1	2	yes	—
235	#117×C₆₇	C₂³	1	1	yes	characteristic
236	#117×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
238	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
239	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
240	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
241	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
242	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
243	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
244	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
245	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄²×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	1	yes	characteristic
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	1	yes	characteristic
259	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
265	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
267	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
268	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
269	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊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	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
290	#97×C₆₇	C₂³	1	1	yes	characteristic
291	#97×C₆₇	C₂³	1	2	yes	—
292	#97×C₆₇	C₂³	1	2	yes	—
293	#97×C₆₇	C₂³	1	2	yes	—
294	#97×C₆₇	C₂³	1	1	yes	characteristic
295	#97×C₆₇	C₂³	1	2	yes	—
296	#97×C₆₇	C₂³	1	2	yes	—
297	#97×C₆₇	C₂³	1	2	yes	—
298	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
299	C₄×C₈×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
305	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
311	#41×C₆₇	—	2	4	no	—
312	#41×C₆₇	—	2	4	no	—
313	#41×C₆₇	—	4	1	no	—
314	#41×C₆₇	—	4	1	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×D₄×C₆₇	—	2	4	no	—
320	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
321	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
323	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	—	4	2	no	—
331	C₂²×C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
344	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
345	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
350	M₁₆×C₆₇	—	4	1	no	—
351	M₁₆×C₆₇	—	4	2	no	—
352	M₁₆×C₆₇	—	4	2	no	—
353	M₁₆×C₆₇	—	4	1	no	—
354	M₁₆×C₆₇	—	4	2	no	—
355	C₂×C₈×C₆₇	—	4	2	no	—
356	C₂×C₈×C₆₇	—	4	1	no	—
357	C₂×C₈×C₆₇	—	4	2	no	—
358	C₂×C₈×C₆₇	—	4	2	no	—
359	C₂×C₈×C₆₇	—	4	2	no	—
360	C₂×C₈×C₆₇	—	4	2	no	—
361	C₂×C₈×C₆₇	—	4	1	no	—
362	C₂×C₈×C₆₇	—	4	2	no	—
363	C₂×C₈×C₆₇	—	4	2	no	—
364	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
365	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
372	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	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	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	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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
394	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
395	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	2	yes	—
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	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	1	yes	characteristic
419	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
420	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
426	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
427	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
433	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
434	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
435	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
436	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄²×C₆₇	C₂⁴	1	2	yes	—
440	C₄²×C₆₇	C₂⁴	1	2	yes	—
441	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₂³×C₆₇	—	2	4	no	—
443	C₂³×C₆₇	—	4	2	no	—
444	C₂³×C₆₇	—	4	2	no	—
445	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
446	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
447	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
448	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
449	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
450	Q₈×C₆₇	—	2	2	no	—
451	Q₈×C₆₇	—	2	2	no	—
452	Q₈×C₆₇	—	4	2	no	—
453	Q₈×C₆₇	—	4	1	no	—
454	D₄×C₆₇	—	2	4	no	—
455	D₄×C₆₇	—	2	4	no	—
456	D₄×C₆₇	—	2	4	no	—
457	D₄×C₆₇	—	2	2	no	—
458	D₄×C₆₇	—	4	2	no	—
459	D₄×C₆₇	—	4	2	no	—
460	D₄×C₆₇	—	4	1	no	—
461	D₄×C₆₇	—	4	1	no	—
462	D₄×C₆₇	—	4	1	no	—
463	D₄×C₆₇	#131	1	4	yes	—
464	C₂×C₄×C₆₇	—	2	4	no	—
465	C₂×C₄×C₆₇	—	2	4	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	4	2	no	—
480	C₂×C₄×C₆₇	—	4	2	no	—
481	C₂×C₄×C₆₇	—	4	2	no	—
482	C₂×C₄×C₆₇	—	4	1	no	—
483	C₂×C₄×C₆₇	—	4	1	no	—
484	C₂×C₄×C₆₇	—	4	2	no	—
485	C₂×C₄×C₆₇	—	4	2	no	—
486	C₂×C₄×C₆₇	—	4	1	no	—
487	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
488	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
502	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
503	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
504	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
505	C₈×C₆₇	—	2	1	no	—
506	C₈×C₆₇	—	2	2	no	—
507	C₈×C₆₇	—	2	1	no	—
508	C₈×C₆₇	—	2	1	no	—
509	C₈×C₆₇	—	2	2	no	—
510	C₈×C₆₇	—	2	1	no	—
511	C₈×C₆₇	—	2	1	no	—
512	C₈×C₆₇	—	2	2	no	—
513	C₈×C₆₇	—	2	1	no	—
514	C₈×C₆₇	—	2	1	no	—
515	C₈×C₆₇	—	2	2	no	—
516	C₈×C₆₇	—	2	1	no	—
517	C₂²×C₆₇	—	2	2	no	—
518	C₂²×C₆₇	—	2	2	no	—
519	C₂²×C₆₇	—	2	1	no	—
520	C₂²×C₆₇	—	2	2	no	—
521	C₂²×C₆₇	—	2	1	no	—
522	C₂²×C₆₇	—	2	1	no	—
523	C₂²×C₆₇	—	2	1	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	2	no	—
531	C₂²×C₆₇	—	8	4	no	—
532	C₂²×C₆₇	C₂×#131	1	4	yes	—
533	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
534	C₄×C₆₇	—	2	1	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	1	no	—
540	C₄×C₆₇	—	2	1	no	—
541	C₄×C₆₇	—	2	1	no	—
542	C₄×C₆₇	—	2	2	no	—
543	C₄×C₆₇	—	2	2	no	—
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	1	no	—
546	C₄×C₆₇	—	2	1	no	—
547	C₄×C₆₇	—	2	2	no	—
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	1	no	—
550	C₄×C₆₇	C₂×#131	1	2	yes	—
551	C₄×C₆₇	#585	1	1	yes	characteristic
552	C₄×C₆₇	#585	1	1	yes	characteristic
553	#60298	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
554	C₂×C₆₇	—	2	4	no	—
555	C₂×C₆₇	—	4	1	no	—
556	C₂×C₆₇	—	4	1	no	—
557	C₂×C₆₇	—	4	2	no	—
558	C₂×C₆₇	—	4	1	no	—
559	C₂×C₆₇	#3428	1	1	yes	characteristic
560	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
561	C₂×C₆₇	#3573	1	1	yes	characteristic
562	#3475	C₂×C₆₇	1	1	yes	characteristic
563	#2994	C₂×C₆₇	1	2	yes	complemented
564	#2994	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#2993	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2992	C₂×C₆₇	1	2	yes	complemented
567	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#2988	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2986	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2985	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2977	C₂×C₆₇	1	2	yes	complemented
572	#2976	C₂×C₆₇	1	2	yes	complemented
573	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#2972	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2970	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2968	C₂×C₆₇	1	2	yes	complemented
578	#2966	C₂×C₆₇	1	2	yes	complemented
579	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
580	C₈×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2924	C₂×C₆₇	1	2	yes	complemented
583	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
584	C₂×#433	C₂×C₆₇	1	2	yes	complemented
585	C₆₇	#60298	1	1	yes	characteristic, direct product factor, Sylow
586	#556	C₄×C₆₇	1	1	yes	characteristic
587	#555	C₄×C₆₇	1	1	yes	characteristic
588	#554	C₄×C₆₇	1	1	yes	characteristic
589	#553	C₄×C₆₇	1	2	yes	—
590	#552	C₄×C₆₇	1	2	yes	—
591	#552	C₄×C₆₇	1	1	yes	characteristic
592	#552	C₄×C₆₇	1	1	yes	characteristic
593	#551	C₄×C₆₇	1	2	yes	—
594	#551	C₄×C₆₇	1	2	yes	—
595	#547	C₄×C₆₇	1	1	yes	characteristic
596	#546	C₄×C₆₇	1	1	yes	characteristic
597	#546	C₄×C₆₇	1	1	yes	characteristic
598	#533	C₂²×C₆₇	1	1	yes	characteristic
599	#529	C₂²×C₆₇	1	2	yes	—
600	#529	C₂²×C₆₇	1	1	yes	characteristic
601	#529	C₂²×C₆₇	1	2	yes	—
602	#529	C₂²×C₆₇	1	1	yes	characteristic
603	#525	C₂²×C₆₇	1	2	yes	—
604	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
605	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
606	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
608	C₂×#117	C₂²×C₆₇	1	2	yes	—
609	#446	C₂²×C₆₇	1	2	yes	complemented
610	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#446	C₂²×C₆₇	1	2	yes	complemented
612	#446	C₂²×C₆₇	1	2	yes	complemented
613	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
614	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
615	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
620	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#436	C₂²×C₆₇	1	1	yes	characteristic
622	#436	C₂²×C₆₇	1	1	yes	characteristic
623	#436	C₂²×C₆₇	1	2	yes	complemented
624	#436	C₂²×C₆₇	1	2	yes	complemented
625	#435	C₂²×C₆₇	1	2	yes	—
626	#435	C₂²×C₆₇	1	2	yes	—
627	#435	C₂²×C₆₇	1	2	yes	complemented
628	#435	C₂²×C₆₇	1	2	yes	complemented
629	#435	C₂²×C₆₇	1	2	yes	complemented
630	#435	C₂²×C₆₇	1	2	yes	complemented
631	#435	C₂²×C₆₇	1	2	yes	complemented
632	#435	C₂²×C₆₇	1	2	yes	complemented
633	#435	C₂²×C₆₇	1	2	yes	complemented
634	#435	C₂²×C₆₇	1	2	yes	complemented
635	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
636	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
637	C₈×D₄	C₂²×C₆₇	1	2	yes	—
638	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₈×D₄	C₂²×C₆₇	1	2	yes	—
640	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
641	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
643	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
644	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
645	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
646	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
647	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
648	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
649	#433	C₂²×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
654	#433	C₂²×C₆₇	1	2	yes	—
655	#433	C₂²×C₆₇	1	2	yes	—
656	#433	C₂²×C₆₇	1	2	yes	complemented
657	#433	C₂²×C₆₇	1	2	yes	complemented
658	#433	C₂²×C₆₇	1	2	yes	complemented
659	#433	C₂²×C₆₇	1	2	yes	complemented
660	#433	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#433	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#433	C₂²×C₆₇	1	2	yes	complemented
663	#432	C₂²×C₆₇	1	1	yes	characteristic
664	#432	C₂²×C₆₇	1	2	yes	complemented
665	#432	C₂²×C₆₇	1	2	yes	complemented
666	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#431	C₂²×C₆₇	1	1	yes	characteristic
668	#431	C₂²×C₆₇	1	1	yes	characteristic
669	#431	C₂²×C₆₇	1	1	yes	characteristic
670	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#431	C₂²×C₆₇	1	2	yes	complemented
673	#431	C₂²×C₆₇	1	2	yes	complemented
674	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	#424	C₂²×C₆₇	1	2	yes	complemented
678	#424	C₂²×C₆₇	1	2	yes	complemented
679	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
681	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
682	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#408	C₂²×C₆₇	1	1	yes	characteristic
684	#408	C₂²×C₆₇	1	1	yes	characteristic
685	#408	C₂²×C₆₇	1	2	yes	—
686	#407	C₂²×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
690	#405	C₂²×C₆₇	1	2	yes	complemented
691	#405	C₂²×C₆₇	1	2	yes	complemented
692	#405	C₂²×C₆₇	1	2	yes	complemented
693	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
695	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
696	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
698	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
699	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
700	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
706	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
707	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
708	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
709	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
712	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
713	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
714	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
715	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
716	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
717	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
718	#126	C₂×C₄×C₆₇	1	2	yes	—
719	#126	C₂×C₄×C₆₇	1	2	yes	—
720	#126	C₂×C₄×C₆₇	1	2	yes	—
721	#126	C₂×C₄×C₆₇	1	2	yes	—
722	#126	C₂×C₄×C₆₇	1	2	yes	—
723	#126	C₂×C₄×C₆₇	1	2	yes	—
724	#125	C₂×C₄×C₆₇	1	2	yes	—
725	#125	C₂×C₄×C₆₇	1	2	yes	—
726	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
727	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
728	#125	C₂×C₄×C₆₇	1	2	yes	—
729	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
730	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
731	#124	C₂×C₄×C₆₇	1	2	yes	—
732	#124	C₂×C₄×C₆₇	1	2	yes	—
733	#123	C₂×C₄×C₆₇	1	2	yes	—
734	#123	C₂×C₄×C₆₇	1	2	yes	—
735	#123	C₂×C₄×C₆₇	1	2	yes	—
736	#123	C₂×C₄×C₆₇	1	2	yes	—
737	#123	C₂×C₄×C₆₇	1	2	yes	—
738	#123	C₂×C₄×C₆₇	1	2	yes	—
739	#123	C₂×C₄×C₆₇	1	2	yes	—
740	#123	C₂×C₄×C₆₇	1	2	yes	—
741	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
742	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
743	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
745	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
746	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
747	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
748	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
750	#121	C₂×C₄×C₆₇	1	2	yes	—
751	#121	C₂×C₄×C₆₇	1	2	yes	—
752	#121	C₂×C₄×C₆₇	1	2	yes	—
753	#121	C₂×C₄×C₆₇	1	2	yes	—
754	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
755	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
756	#120	C₂×C₄×C₆₇	1	2	yes	—
757	#120	C₂×C₄×C₆₇	1	2	yes	—
758	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
759	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
760	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
761	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
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	C₂×C₄×C₆₇	1	1	yes	characteristic
770	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
771	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
772	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
773	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
774	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
775	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
776	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
777	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₆₇	1	2	yes	—
780	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₆₇	1	2	yes	—
782	C₄×D₄	C₂³×C₆₇	1	2	yes	—
783	C₄×D₄	C₂³×C₆₇	1	2	yes	—
784	C₄×D₄	C₂³×C₆₇	1	2	yes	—
785	#117	C₂×C₄×C₆₇	1	2	yes	—
786	#117	C₂×C₄×C₆₇	1	2	yes	—
787	#117	C₂×C₄×C₆₇	1	2	yes	—
788	#117	C₂×C₄×C₆₇	1	2	yes	—
789	#117	C₂×C₄×C₆₇	1	2	yes	—
790	#117	C₂×C₄×C₆₇	1	2	yes	—
791	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
792	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
793	#117	C₂³×C₆₇	1	1	yes	characteristic
794	#117	C₂³×C₆₇	1	2	yes	—
795	#117	C₂³×C₆₇	1	2	yes	—
796	#117	C₂³×C₆₇	1	2	yes	—
797	#117	C₂³×C₆₇	1	1	yes	characteristic
798	#117	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
800	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
801	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
805	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
806	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
807	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
812	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
818	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
819	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
820	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
829	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
830	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
831	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
835	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
836	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
852	#97	C₂³×C₆₇	1	1	yes	characteristic
853	#97	C₂³×C₆₇	1	2	yes	—
854	#97	C₂³×C₆₇	1	2	yes	—
855	#97	C₂³×C₆₇	1	2	yes	—
856	#97	C₂³×C₆₇	1	1	yes	characteristic
857	#97	C₂³×C₆₇	1	2	yes	—
858	#97	C₂³×C₆₇	1	2	yes	—
859	#97	C₂³×C₆₇	1	2	yes	—
860	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₆₇	1	2	yes	—
862	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₆₇	1	2	yes	—
866	C₄×C₈	C₂³×C₆₇	1	2	yes	—
867	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₆₇	1	2	yes	—
870	C₄×C₈	C₂³×C₆₇	1	2	yes	—
871	C₄×C₈	C₂³×C₆₇	1	2	yes	—
872	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
873	#41	—	2	4	no	—
874	#41	—	2	4	no	—
875	#41	—	4	1	no	—
876	#41	—	4	1	no	—
877	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
878	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
879	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
880	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
883	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
884	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
885	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
886	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
887	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
888	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
889	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
890	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
891	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	—	4	2	no	—
894	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
895	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
896	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
897	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
898	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
900	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
901	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
902	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
903	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
904	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
905	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
906	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
912	M₁₆	—	4	1	no	—
913	M₁₆	—	4	2	no	—
914	M₁₆	—	4	2	no	—
915	M₁₆	—	4	1	no	—
916	M₁₆	—	4	2	no	—
917	C₂×C₈	—	4	2	no	—
918	C₂×C₈	—	4	1	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	2	no	—
922	C₂×C₈	—	4	2	no	—
923	C₂×C₈	—	4	1	no	—
924	C₂×C₈	—	4	2	no	—
925	C₂×C₈	—	4	2	no	—
926	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
927	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
930	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
933	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
937	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
948	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
949	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
952	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
953	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
954	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
955	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
960	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
961	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
962	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
963	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
965	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
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	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
970	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
971	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
972	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
973	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
974	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
975	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
976	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
978	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
981	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
982	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
983	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
984	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
985	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
986	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
987	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
988	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
989	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
990	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
991	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
992	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
993	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
994	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
995	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
996	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
997	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
998	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
999	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₆₇	1	2	yes	—
1002	C₄²	C₂⁴×C₆₇	1	2	yes	—
1003	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂³	—	2	4	no	—
1005	C₂³	—	4	2	no	—
1006	C₂³	—	4	2	no	—
1007	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1008	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1009	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1010	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1011	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	2	no	—
1016	D₄	—	2	4	no	—
1017	D₄	—	2	4	no	—
1018	D₄	—	2	4	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	#131×C₆₇	1	4	yes	—
1026	C₂×C₄	—	2	4	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1050	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1051	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1052	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1053	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1054	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1055	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1056	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1057	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1058	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1059	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1060	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1061	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1062	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1063	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1064	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1065	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1066	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	8	4	no	—
1094	C₂²	C₂×#131×C₆₇	1	4	yes	—
1095	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	C₂×#131×C₆₇	1	2	yes	—
1113	C₄	#585×C₆₇	1	1	yes	characteristic
1114	C₄	#585×C₆₇	1	1	yes	characteristic
1115	C₂	—	2	4	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	1	no	—
1120	C₂	C₆₇×#3428	1	1	yes	characteristic
1121	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
1122	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	C₆₇×#3475	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×#2994	C₂	semidirect
3. C₆₇×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2990	C₂	semidirect
7. C₆₇×#2988	C₂	semidirect
8. C₆₇×#2986	C₂	semidirect
9. C₆₇×#2985	C₂	semidirect
10. C₆₇×#2977	C₂	semidirect
11. C₆₇×#2976	C₂	semidirect
12. C₆₇×#2974	C₂	semidirect
13. C₆₇×#2972	C₂	semidirect
14. C₆₇×#2970	C₂	semidirect
15. C₆₇×#2969	C₂	semidirect
16. C₆₇×#2968	C₂	semidirect
17. C₆₇×#2966	C₂	semidirect
18. C₆₇×#2966	C₂	semidirect
19. C₈×#41×C₆₇	C₂	semidirect
20. C₆₇×#2925	C₂	semidirect
21. C₆₇×#2924	C₂	semidirect
22. C₆₇×#2922	C₂	semidirect
23. C₂×#433×C₆₇	C₂	semidirect
47. #446×C₆₇	C₂²	semidirect
48. #446×C₆₇	C₂²	semidirect
49. #446×C₆₇	C₂²	semidirect
50. #446×C₆₇	C₂²	semidirect
51. #446×C₆₇	C₂²	semidirect
52. #446×C₆₇	C₂²	semidirect
53. #446×C₆₇	C₂²	semidirect
54. C₈×Q₈×C₆₇	C₂²	semidirect
55. C₈×Q₈×C₆₇	C₂²	semidirect
56. C₈×Q₈×C₆₇	C₂²	semidirect
57. C₈×Q₈×C₆₇	C₂²	semidirect
58. C₈×Q₈×C₆₇	C₂²	semidirect
61. #436×C₆₇	C₂²	semidirect
62. #436×C₆₇	C₂²	semidirect
65. #435×C₆₇	C₂²	semidirect
66. #435×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #435×C₆₇	C₂²	semidirect
71. #435×C₆₇	C₂²	semidirect
72. #435×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₈×D₄×C₆₇	C₂²	semidirect
84. C₈×D₄×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
94. #433×C₆₇	C₂²	semidirect
95. #433×C₆₇	C₂²	semidirect
96. #433×C₆₇	C₂²	semidirect
97. #433×C₆₇	C₂²	semidirect
98. #433×C₆₇	C₂²	semidirect
99. #433×C₆₇	C₂²	semidirect
100. #433×C₆₇	C₂²	semidirect
102. #432×C₆₇	C₂²	semidirect
103. #432×C₆₇	C₂²	semidirect
104. #432×C₆₇	C₂²	semidirect
108. #431×C₆₇	C₂²	semidirect
109. #431×C₆₇	C₂²	semidirect
110. #431×C₆₇	C₂²	semidirect
111. #431×C₆₇	C₂²	semidirect
112. #431×C₆₇	C₂²	semidirect
113. #424×C₆₇	C₂²	semidirect
114. #424×C₆₇	C₂²	semidirect
115. #424×C₆₇	C₂²	semidirect
116. #424×C₆₇	C₂²	semidirect
117. #423×C₆₇	C₂²	semidirect
118. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
119. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
120. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
128. #405×C₆₇	C₂²	semidirect
129. #405×C₆₇	C₂²	semidirect
130. #405×C₆₇	C₂²	semidirect
131. C₄×M₁₆×C₆₇	C₂²	semidirect
132. C₂×#97×C₆₇	C₂²	semidirect
133. C₂×C₄×C₈×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
553. #60298	C₆₇	direct (N × H)
563. #2994	C₂×C₆₇	semidirect
564. #2994	C₂×C₆₇	semidirect
565. #2993	C₂×C₆₇	semidirect
566. #2992	C₂×C₆₇	semidirect
567. #2990	C₂×C₆₇	semidirect
568. #2988	C₂×C₆₇	semidirect
569. #2986	C₂×C₆₇	semidirect
570. #2985	C₂×C₆₇	semidirect
571. #2977	C₂×C₆₇	semidirect
572. #2976	C₂×C₆₇	semidirect
573. #2974	C₂×C₆₇	semidirect
574. #2972	C₂×C₆₇	semidirect
575. #2970	C₂×C₆₇	semidirect
576. #2969	C₂×C₆₇	semidirect
577. #2968	C₂×C₆₇	semidirect
578. #2966	C₂×C₆₇	semidirect
579. #2966	C₂×C₆₇	semidirect
580. C₈×#41	C₂×C₆₇	semidirect
581. #2925	C₂×C₆₇	semidirect
582. #2924	C₂×C₆₇	semidirect
583. #2922	C₂×C₆₇	semidirect
584. C₂×#433	C₂×C₆₇	semidirect
585. C₆₇	#60298	direct (N × H)
609. #446	C₂²×C₆₇	semidirect
610. #446	C₂²×C₆₇	semidirect
611. #446	C₂²×C₆₇	semidirect
612. #446	C₂²×C₆₇	semidirect
613. #446	C₂²×C₆₇	semidirect
614. #446	C₂²×C₆₇	semidirect
615. #446	C₂²×C₆₇	semidirect
616. C₈×Q₈	C₂²×C₆₇	semidirect
617. C₈×Q₈	C₂²×C₆₇	semidirect
618. C₈×Q₈	C₂²×C₆₇	semidirect
619. C₈×Q₈	C₂²×C₆₇	semidirect
620. C₈×Q₈	C₂²×C₆₇	semidirect
623. #436	C₂²×C₆₇	semidirect
624. #436	C₂²×C₆₇	semidirect
627. #435	C₂²×C₆₇	semidirect
628. #435	C₂²×C₆₇	semidirect
629. #435	C₂²×C₆₇	semidirect
630. #435	C₂²×C₆₇	semidirect
631. #435	C₂²×C₆₇	semidirect
632. #435	C₂²×C₆₇	semidirect
633. #435	C₂²×C₆₇	semidirect
634. #435	C₂²×C₆₇	semidirect
643. C₈×D₄	C₂²×C₆₇	semidirect
644. C₈×D₄	C₂²×C₆₇	semidirect
645. C₈×D₄	C₂²×C₆₇	semidirect
646. C₈×D₄	C₂²×C₆₇	semidirect
647. C₈×D₄	C₂²×C₆₇	semidirect
648. C₈×D₄	C₂²×C₆₇	semidirect
656. #433	C₂²×C₆₇	semidirect
657. #433	C₂²×C₆₇	semidirect
658. #433	C₂²×C₆₇	semidirect
659. #433	C₂²×C₆₇	semidirect
660. #433	C₂²×C₆₇	semidirect
661. #433	C₂²×C₆₇	semidirect
662. #433	C₂²×C₆₇	semidirect
664. #432	C₂²×C₆₇	semidirect
665. #432	C₂²×C₆₇	semidirect
666. #432	C₂²×C₆₇	semidirect
670. #431	C₂²×C₆₇	semidirect
671. #431	C₂²×C₆₇	semidirect
672. #431	C₂²×C₆₇	semidirect
673. #431	C₂²×C₆₇	semidirect
674. #431	C₂²×C₆₇	semidirect
675. #424	C₂²×C₆₇	semidirect
676. #424	C₂²×C₆₇	semidirect
677. #424	C₂²×C₆₇	semidirect
678. #424	C₂²×C₆₇	semidirect
679. #423	C₂²×C₆₇	semidirect
680. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
681. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
682. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
690. #405	C₂²×C₆₇	semidirect
691. #405	C₂²×C₆₇	semidirect
692. #405	C₂²×C₆₇	semidirect
693. C₄×M₁₆	C₂²×C₆₇	semidirect
694. C₂×#97	C₂²×C₆₇	semidirect
695. C₂×C₄×C₈	C₂²×C₆₇	semidirect
696. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2988	2
C₆₇×#2986	2
C₆₇×#2985	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2972	2
C₆₇×#2970	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2966	2
C₈×#41×C₆₇	2
C₆₇×#2925	2
C₆₇×#2924	2
C₆₇×#2922	2
C₂×#433×C₆₇	2
#60298	67

Subgroups — C67×#60298 #30739549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60298 #30739549