Subgroups — C₆₇×#60995 #30740246

Order 17152.

1662 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3461	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3248	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3242	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3202	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3201	C₂	1	2	yes	maximal
15	C₆₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3177	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#557×C₆₇	—	2	1	no	—
25	#557×C₆₇	—	2	1	no	—
26	#556×C₆₇	—	2	1	no	—
27	#556×C₆₇	—	2	1	no	—
28	#552×C₆₇	—	2	1	no	—
29	#552×C₆₇	—	2	1	no	—
30	#552×C₆₇	—	2	1	no	—
31	#552×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic
33	#542×C₆₇	—	2	1	no	—
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#542×C₆₇	C₂²	1	1	yes	characteristic
36	#541×C₆₇	—	2	1	no	—
37	#541×C₆₇	C₂²	1	1	yes	characteristic
38	#541×C₆₇	C₂²	1	1	yes	characteristic
39	#541×C₆₇	C₂²	1	2	yes	—
40	#541×C₆₇	C₂²	1	2	yes	—
41	#539×C₆₇	—	2	1	no	—
42	#539×C₆₇	—	2	1	no	—
43	#537×C₆₇	C₂²	1	1	yes	characteristic
44	#536×C₆₇	C₂²	1	1	yes	characteristic
45	#536×C₆₇	C₂²	1	2	yes	—
46	#536×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	—	2	1	no	—
48	#533×C₆₇	C₂²	1	1	yes	characteristic
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic
51	#533×C₆₇	C₂²	1	1	yes	characteristic
52	#533×C₆₇	C₂²	1	1	yes	characteristic
53	#533×C₆₇	C₂²	1	1	yes	characteristic
54	#533×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
56	#529×C₆₇	—	2	1	no	—
57	#529×C₆₇	—	2	1	no	—
58	#529×C₆₇	—	2	1	no	—
59	#529×C₆₇	C₂²	1	1	yes	characteristic
60	#529×C₆₇	C₂²	1	1	yes	characteristic
61	#519×C₆₇	C₂²	1	2	yes	—
62	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
65	#501×C₆₇	C₂²	1	2	yes	—
66	#499×C₆₇	C₂²	1	2	yes	—
67	#497×C₆₇	C₂²	1	2	yes	—
68	#494×C₆₇	C₂²	1	2	yes	—
69	#491×C₆₇	C₂²	1	2	yes	—
70	#491×C₆₇	C₂²	1	2	yes	—
71	#488×C₆₇	C₂²	1	2	yes	—
72	#487×C₆₇	C₂²	1	2	yes	—
73	#485×C₆₇	C₂²	1	2	yes	—
74	#485×C₆₇	C₂²	1	2	yes	—
75	#485×C₆₇	C₂²	1	2	yes	—
76	#485×C₆₇	C₂²	1	2	yes	—
77	#485×C₆₇	C₂²	1	2	yes	—
78	#484×C₆₇	C₂²	1	2	yes	—
79	#483×C₆₇	C₂²	1	2	yes	—
80	#482×C₆₇	C₂²	1	2	yes	—
81	#479×C₆₇	C₂²	1	2	yes	—
82	#479×C₆₇	C₂²	1	2	yes	—
83	#477×C₆₇	C₂²	1	1	yes	characteristic
84	#477×C₆₇	C₂²	1	1	yes	characteristic
85	#477×C₆₇	C₂²	1	1	yes	characteristic
86	#477×C₆₇	C₂²	1	2	yes	—
87	#476×C₆₇	C₂²	1	1	yes	characteristic
88	#475×C₆₇	C₂²	1	1	yes	characteristic
89	#475×C₆₇	C₂²	1	1	yes	characteristic
90	#475×C₆₇	C₂²	1	1	yes	characteristic
91	#475×C₆₇	C₂²	1	2	yes	—
92	#474×C₆₇	C₂²	1	1	yes	characteristic
93	#470×C₆₇	C₂²	1	2	yes	—
94	#470×C₆₇	C₂²	1	2	yes	—
95	#470×C₆₇	C₂²	1	2	yes	—
96	#468×C₆₇	C₂²	1	2	yes	—
97	#467×C₆₇	C₂²	1	2	yes	—
98	#467×C₆₇	C₂²	1	2	yes	—
99	#467×C₆₇	C₂²	1	2	yes	—
100	#465×C₆₇	C₂²	1	2	yes	—
101	#464×C₆₇	C₂²	1	2	yes	—
102	#464×C₆₇	C₂²	1	2	yes	—
103	#462×C₆₇	C₂²	1	1	yes	characteristic
104	#462×C₆₇	C₂²	1	1	yes	characteristic
105	#462×C₆₇	C₂²	1	1	yes	characteristic
106	#462×C₆₇	C₂²	1	1	yes	characteristic
107	#462×C₆₇	C₂²	1	1	yes	characteristic
108	#462×C₆₇	C₂²	1	1	yes	characteristic
109	#462×C₆₇	C₂²	1	2	yes	—
110	#462×C₆₇	C₂²	1	2	yes	—
111	#461×C₆₇	C₂²	1	1	yes	characteristic
112	#461×C₆₇	C₂²	1	1	yes	characteristic
113	#452×C₆₇	C₂²	1	2	yes	—
114	#452×C₆₇	C₂²	1	2	yes	—
115	#451×C₆₇	C₂²	1	2	yes	—
116	#451×C₆₇	C₂²	1	2	yes	—
117	#451×C₆₇	C₂²	1	2	yes	—
118	#451×C₆₇	C₂²	1	2	yes	—
119	#451×C₆₇	C₂²	1	2	yes	—
120	#448×C₆₇	C₂²	1	2	yes	—
121	#441×C₆₇	C₂²	1	2	yes	—
122	#441×C₆₇	C₂²	1	2	yes	—
123	#441×C₆₇	C₂²	1	2	yes	—
124	#440×C₆₇	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
126	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
127	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
129	#433×C₆₇	C₂²	1	2	yes	—
130	#433×C₆₇	C₂²	1	2	yes	—
131	#432×C₆₇	C₂²	1	1	yes	characteristic
132	#432×C₆₇	C₂²	1	1	yes	characteristic
133	#431×C₆₇	C₂²	1	1	yes	characteristic
134	#431×C₆₇	C₂²	1	1	yes	characteristic
135	#423×C₆₇	C₂²	1	1	yes	characteristic
136	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
137	#408×C₆₇	C₂²	1	2	yes	—
138	#405×C₆₇	C₂²	1	2	yes	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₆₇	—	2	1	no	—
154	C₄⋊Q₈×C₆₇	—	2	2	no	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#126×C₆₇	—	2	1	no	—
168	#126×C₆₇	—	2	1	no	—
169	#126×C₆₇	—	2	1	no	—
170	#126×C₆₇	—	2	1	no	—
171	#126×C₆₇	—	2	1	no	—
172	#126×C₆₇	—	2	1	no	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#126×C₆₇	—	2	1	no	—
178	#126×C₆₇	—	2	1	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	—	2	1	no	—
181	#125×C₆₇	—	2	1	no	—
182	#125×C₆₇	—	2	1	no	—
183	#125×C₆₇	—	2	1	no	—
184	#125×C₆₇	—	2	2	no	—
185	#125×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	2	no	—
187	#125×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	—	2	1	no	—
190	#125×C₆₇	—	2	1	no	—
191	#125×C₆₇	—	2	1	no	—
192	#125×C₆₇	—	2	1	no	—
193	#125×C₆₇	—	2	1	no	—
194	#125×C₆₇	C₂³	1	1	yes	characteristic
195	#125×C₆₇	C₂³	1	2	yes	—
196	#125×C₆₇	C₂³	1	1	yes	characteristic
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	—	2	2	no	—
199	#124×C₆₇	—	2	1	no	—
200	#124×C₆₇	—	2	1	no	—
201	#124×C₆₇	C₂³	1	1	yes	characteristic
202	#124×C₆₇	C₂³	1	1	yes	characteristic
203	#123×C₆₇	—	2	1	no	—
204	#123×C₆₇	—	2	1	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	2	no	—
207	#123×C₆₇	—	2	1	no	—
208	#123×C₆₇	—	2	1	no	—
209	#123×C₆₇	—	2	1	no	—
210	#123×C₆₇	—	2	1	no	—
211	#123×C₆₇	—	2	1	no	—
212	#123×C₆₇	—	2	1	no	—
213	C₂²⋊Q₈×C₆₇	—	2	1	no	—
214	C₂²⋊Q₈×C₆₇	—	2	1	no	—
215	C₂²⋊Q₈×C₆₇	—	2	1	no	—
216	C₂²⋊Q₈×C₆₇	—	2	1	no	—
217	C₂²⋊Q₈×C₆₇	—	2	1	no	—
218	C₂²⋊Q₈×C₆₇	—	2	1	no	—
219	C₂²⋊Q₈×C₆₇	—	2	1	no	—
220	C₂²⋊Q₈×C₆₇	—	2	1	no	—
221	C₂²⋊Q₈×C₆₇	—	2	1	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	—	2	1	no	—
224	C₂²⋊Q₈×C₆₇	—	2	1	no	—
225	C₂²⋊Q₈×C₆₇	—	2	1	no	—
226	C₂²⋊Q₈×C₆₇	—	2	1	no	—
227	C₂²⋊Q₈×C₆₇	—	2	1	no	—
228	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
232	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
233	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
234	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
235	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
238	#121×C₆₇	—	2	1	no	—
239	#121×C₆₇	—	2	1	no	—
240	#121×C₆₇	—	2	1	no	—
241	#121×C₆₇	C₂³	1	1	yes	characteristic
242	#121×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₆₇	—	2	2	no	—
244	C₄×Q₈×C₆₇	—	2	2	no	—
245	C₄×Q₈×C₆₇	—	2	1	no	—
246	C₄×Q₈×C₆₇	—	2	1	no	—
247	C₄×Q₈×C₆₇	—	2	1	no	—
248	C₄×Q₈×C₆₇	—	2	1	no	—
249	C₄×Q₈×C₆₇	—	2	1	no	—
250	C₄×Q₈×C₆₇	—	2	1	no	—
251	C₄×Q₈×C₆₇	—	2	1	no	—
252	C₄×Q₈×C₆₇	—	2	1	no	—
253	C₄×Q₈×C₆₇	—	2	1	no	—
254	C₄×Q₈×C₆₇	—	2	1	no	—
255	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
261	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
262	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
266	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
267	C₄×D₄×C₆₇	—	2	1	no	—
268	C₄×D₄×C₆₇	—	2	1	no	—
269	C₄×D₄×C₆₇	—	2	1	no	—
270	C₄×D₄×C₆₇	—	2	1	no	—
271	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
272	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
273	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
274	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
275	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
276	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
277	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
279	#117×C₆₇	—	2	1	no	—
280	#117×C₆₇	—	2	1	no	—
281	#117×C₆₇	—	2	1	no	—
282	#117×C₆₇	—	2	1	no	—
283	#117×C₆₇	—	2	1	no	—
284	#117×C₆₇	—	2	1	no	—
285	#117×C₆₇	—	2	2	no	—
286	#117×C₆₇	—	2	2	no	—
287	#117×C₆₇	—	2	1	no	—
288	#117×C₆₇	—	2	1	no	—
289	#117×C₆₇	—	2	1	no	—
290	#117×C₆₇	C₂³	1	2	yes	—
291	#117×C₆₇	C₂³	1	1	yes	characteristic
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	2	yes	—
326	#103×C₆₇	C₂³	1	2	yes	—
327	#103×C₆₇	C₂³	1	2	yes	—
328	#103×C₆₇	C₂³	1	2	yes	—
329	#103×C₆₇	C₂³	1	2	yes	—
330	#103×C₆₇	C₂³	1	2	yes	—
331	#103×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	#97×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	#41×C₆₇	—	4	1	no	—
343	#41×C₆₇	—	4	1	no	—
344	#41×C₆₇	—	4	1	no	—
345	#41×C₆₇	—	4	1	no	—
346	C₂×Q₈×C₆₇	—	2	1	no	—
347	C₂×Q₈×C₆₇	—	2	1	no	—
348	C₂×Q₈×C₆₇	—	2	1	no	—
349	C₂×Q₈×C₆₇	—	2	2	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	2	1	no	—
352	C₂×Q₈×C₆₇	—	4	2	no	—
353	C₂×Q₈×C₆₇	—	4	2	no	—
354	C₂×Q₈×C₆₇	—	4	1	no	—
355	C₂×Q₈×C₆₇	—	4	1	no	—
356	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
360	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
361	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	1	no	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	Q₁₆×C₆₇	—	4	2	no	—
385	Q₁₆×C₆₇	—	4	2	no	—
386	Q₁₆×C₆₇	—	4	2	no	—
387	Q₁₆×C₆₇	—	4	2	no	—
388	Q₁₆×C₆₇	—	4	2	no	—
389	Q₁₆×C₆₇	—	4	2	no	—
390	SD₁₆×C₆₇	—	4	2	no	—
391	SD₁₆×C₆₇	—	4	2	no	—
392	M₁₆×C₆₇	—	4	2	no	—
393	C₂×C₈×C₆₇	—	4	2	no	—
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
396	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
397	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	1	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	1	no	—
409	C₄⋊C₄×C₆₇	—	2	1	no	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	2	no	—
434	C₄⋊C₄×C₆₇	—	2	2	no	—
435	C₄⋊C₄×C₆₇	—	2	2	no	—
436	C₄⋊C₄×C₆₇	—	2	2	no	—
437	C₄⋊C₄×C₆₇	—	2	2	no	—
438	C₄⋊C₄×C₆₇	—	2	2	no	—
439	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₆₇	—	2	1	no	—
478	C₄²×C₆₇	—	2	1	no	—
479	C₄²×C₆₇	—	2	1	no	—
480	C₄²×C₆₇	—	2	1	no	—
481	C₄²×C₆₇	—	2	1	no	—
482	C₄²×C₆₇	—	2	1	no	—
483	C₄²×C₆₇	—	2	1	no	—
484	C₄²×C₆₇	—	2	2	no	—
485	C₄²×C₆₇	—	2	2	no	—
486	C₄²×C₆₇	—	2	2	no	—
487	C₄²×C₆₇	—	2	2	no	—
488	C₄²×C₆₇	—	2	2	no	—
489	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	1	no	—
500	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	Q₈×C₆₇	—	2	2	no	—
504	Q₈×C₆₇	—	2	2	no	—
505	Q₈×C₆₇	—	2	1	no	—
506	Q₈×C₆₇	—	2	1	no	—
507	Q₈×C₆₇	—	2	1	no	—
508	Q₈×C₆₇	—	2	1	no	—
509	Q₈×C₆₇	—	2	2	no	—
510	Q₈×C₆₇	—	2	2	no	—
511	Q₈×C₆₇	—	2	1	no	—
512	Q₈×C₆₇	—	2	1	no	—
513	Q₈×C₆₇	—	4	1	no	—
514	Q₈×C₆₇	—	4	2	no	—
515	Q₈×C₆₇	—	4	2	no	—
516	Q₈×C₆₇	—	4	4	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	Q₈×C₆₇	—	8	1	no	—
519	Q₈×C₆₇	—	8	1	no	—
520	D₄×C₆₇	—	2	1	no	—
521	D₄×C₆₇	—	2	1	no	—
522	D₄×C₆₇	—	4	1	no	—
523	D₄×C₆₇	—	4	1	no	—
524	D₄×C₆₇	—	4	1	no	—
525	D₄×C₆₇	—	4	2	no	—
526	D₄×C₆₇	—	8	1	no	—
527	D₄×C₆₇	—	8	1	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	4	1	no	—
549	C₂×C₄×C₆₇	—	4	1	no	—
550	C₂×C₄×C₆₇	—	4	1	no	—
551	C₂×C₄×C₆₇	—	4	2	no	—
552	C₂×C₄×C₆₇	—	4	4	no	—
553	C₂×C₄×C₆₇	—	4	2	no	—
554	C₂×C₄×C₆₇	—	4	2	no	—
555	C₂×C₄×C₆₇	—	8	1	no	—
556	C₂×C₄×C₆₇	—	8	1	no	—
557	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
569	C₈×C₆₇	—	2	2	no	—
570	C₈×C₆₇	—	2	2	no	—
571	C₈×C₆₇	—	2	2	no	—
572	C₈×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	2	1	no	—
574	C₂²×C₆₇	—	2	1	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	2	1	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	1	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	4	1	no	—
583	C₂²×C₆₇	—	4	1	no	—
584	C₂²×C₆₇	—	4	1	no	—
585	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	1	no	—
588	C₄×C₆₇	—	2	1	no	—
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	2	1	no	—
591	C₄×C₆₇	—	2	1	no	—
592	C₄×C₆₇	—	2	1	no	—
593	C₄×C₆₇	—	2	1	no	—
594	C₄×C₆₇	—	2	1	no	—
595	C₄×C₆₇	—	2	1	no	—
596	C₄×C₆₇	—	4	1	no	—
597	C₄×C₆₇	—	4	1	no	—
598	C₄×C₆₇	—	4	1	no	—
599	C₄×C₆₇	—	4	2	no	—
600	C₄×C₆₇	—	4	1	no	—
601	C₄×C₆₇	—	4	1	no	—
602	C₄×C₆₇	—	4	1	no	—
603	C₄×C₆₇	—	4	2	no	—
604	C₄×C₆₇	—	4	2	no	—
605	C₄×C₆₇	—	4	1	no	—
606	C₄×C₆₇	—	4	2	no	—
607	C₄×C₆₇	#578	1	2	yes	—
608	C₄×C₆₇	#585	1	1	yes	characteristic
609	C₄×C₆₇	#585	1	1	yes	characteristic
610	#60995	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
611	C₂×C₆₇	—	4	1	no	—
612	C₂×C₆₇	—	4	1	no	—
613	C₂×C₆₇	—	4	1	no	—
614	C₂×C₆₇	—	8	1	no	—
615	C₂×C₆₇	#3449	1	1	yes	characteristic
616	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
617	C₂×C₆₇	#3586	1	1	yes	characteristic
618	#3509	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3461	C₂×C₆₇	1	1	yes	characteristic
620	#3255	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3252	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3249	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3248	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3242	C₂×C₆₇	1	2	yes	complemented
625	#3237	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3223	C₂×C₆₇	1	2	yes	complemented
628	#3218	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3209	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3202	C₂×C₆₇	1	2	yes	complemented
631	#3201	C₂×C₆₇	1	2	yes	—
632	#3178	C₂×C₆₇	1	2	yes	complemented
633	#3177	C₂×C₆₇	1	2	yes	complemented
634	#3127	C₂×C₆₇	1	2	yes	complemented
635	#3121	C₂×C₆₇	1	2	yes	complemented
636	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
641	C₆₇	#60995	1	1	yes	characteristic, direct product factor, Sylow
642	#557	—	2	1	no	—
643	#557	—	2	1	no	—
644	#556	—	2	1	no	—
645	#556	—	2	1	no	—
646	#552	—	2	1	no	—
647	#552	—	2	1	no	—
648	#552	—	2	1	no	—
649	#552	—	2	1	no	—
650	#544	C₂²×C₆₇	1	1	yes	characteristic
651	#542	—	2	1	no	—
652	#542	C₂²×C₆₇	1	1	yes	characteristic
653	#542	C₂²×C₆₇	1	1	yes	characteristic
654	#541	—	2	1	no	—
655	#541	C₂²×C₆₇	1	1	yes	characteristic
656	#541	C₂²×C₆₇	1	1	yes	characteristic
657	#541	C₂²×C₆₇	1	2	yes	—
658	#541	C₂²×C₆₇	1	2	yes	—
659	#539	—	2	1	no	—
660	#539	—	2	1	no	—
661	#537	C₂²×C₆₇	1	1	yes	characteristic
662	#536	C₂²×C₆₇	1	1	yes	characteristic
663	#536	C₂²×C₆₇	1	2	yes	—
664	#536	C₂²×C₆₇	1	1	yes	characteristic
665	#533	—	2	1	no	—
666	#533	C₂²×C₆₇	1	1	yes	characteristic
667	#533	C₂²×C₆₇	1	1	yes	characteristic
668	#533	C₂²×C₆₇	1	1	yes	characteristic
669	#533	C₂²×C₆₇	1	1	yes	characteristic
670	#533	C₂²×C₆₇	1	1	yes	characteristic
671	#533	C₂²×C₆₇	1	1	yes	characteristic
672	#533	C₂²×C₆₇	1	1	yes	characteristic
673	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
674	#529	—	2	1	no	—
675	#529	—	2	1	no	—
676	#529	—	2	1	no	—
677	#529	C₂²×C₆₇	1	1	yes	characteristic
678	#529	C₂²×C₆₇	1	1	yes	characteristic
679	#519	C₂²×C₆₇	1	2	yes	—
680	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
681	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
683	#501	C₂²×C₆₇	1	2	yes	—
684	#499	C₂²×C₆₇	1	2	yes	—
685	#497	C₂²×C₆₇	1	2	yes	—
686	#494	C₂²×C₆₇	1	2	yes	—
687	#491	C₂²×C₆₇	1	2	yes	—
688	#491	C₂²×C₆₇	1	2	yes	—
689	#488	C₂²×C₆₇	1	2	yes	—
690	#487	C₂²×C₆₇	1	2	yes	—
691	#485	C₂²×C₆₇	1	2	yes	—
692	#485	C₂²×C₆₇	1	2	yes	—
693	#485	C₂²×C₆₇	1	2	yes	—
694	#485	C₂²×C₆₇	1	2	yes	—
695	#485	C₂²×C₆₇	1	2	yes	—
696	#484	C₂²×C₆₇	1	2	yes	—
697	#483	C₂²×C₆₇	1	2	yes	—
698	#482	C₂²×C₆₇	1	2	yes	—
699	#479	C₂²×C₆₇	1	2	yes	—
700	#479	C₂²×C₆₇	1	2	yes	—
701	#477	C₂²×C₆₇	1	1	yes	characteristic
702	#477	C₂²×C₆₇	1	1	yes	characteristic
703	#477	C₂²×C₆₇	1	1	yes	characteristic
704	#477	C₂²×C₆₇	1	2	yes	—
705	#476	C₂²×C₆₇	1	1	yes	characteristic
706	#475	C₂²×C₆₇	1	1	yes	characteristic
707	#475	C₂²×C₆₇	1	1	yes	characteristic
708	#475	C₂²×C₆₇	1	1	yes	characteristic
709	#475	C₂²×C₆₇	1	2	yes	—
710	#474	C₂²×C₆₇	1	1	yes	characteristic
711	#470	C₂²×C₆₇	1	2	yes	—
712	#470	C₂²×C₆₇	1	2	yes	—
713	#470	C₂²×C₆₇	1	2	yes	—
714	#468	C₂²×C₆₇	1	2	yes	—
715	#467	C₂²×C₆₇	1	2	yes	—
716	#467	C₂²×C₆₇	1	2	yes	—
717	#467	C₂²×C₆₇	1	2	yes	—
718	#465	C₂²×C₆₇	1	2	yes	—
719	#464	C₂²×C₆₇	1	2	yes	—
720	#464	C₂²×C₆₇	1	2	yes	—
721	#462	C₂²×C₆₇	1	1	yes	characteristic
722	#462	C₂²×C₆₇	1	1	yes	characteristic
723	#462	C₂²×C₆₇	1	1	yes	characteristic
724	#462	C₂²×C₆₇	1	1	yes	characteristic
725	#462	C₂²×C₆₇	1	1	yes	characteristic
726	#462	C₂²×C₆₇	1	1	yes	characteristic
727	#462	C₂²×C₆₇	1	2	yes	—
728	#462	C₂²×C₆₇	1	2	yes	—
729	#461	C₂²×C₆₇	1	1	yes	characteristic
730	#461	C₂²×C₆₇	1	1	yes	characteristic
731	#452	C₂²×C₆₇	1	2	yes	—
732	#452	C₂²×C₆₇	1	2	yes	—
733	#451	C₂²×C₆₇	1	2	yes	—
734	#451	C₂²×C₆₇	1	2	yes	—
735	#451	C₂²×C₆₇	1	2	yes	—
736	#451	C₂²×C₆₇	1	2	yes	—
737	#451	C₂²×C₆₇	1	2	yes	—
738	#448	C₂²×C₆₇	1	2	yes	—
739	#441	C₂²×C₆₇	1	2	yes	—
740	#441	C₂²×C₆₇	1	2	yes	—
741	#441	C₂²×C₆₇	1	2	yes	—
742	#440	C₂²×C₆₇	1	2	yes	—
743	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
744	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
745	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
746	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
747	#433	C₂²×C₆₇	1	2	yes	—
748	#433	C₂²×C₆₇	1	2	yes	—
749	#432	C₂²×C₆₇	1	1	yes	characteristic
750	#432	C₂²×C₆₇	1	1	yes	characteristic
751	#431	C₂²×C₆₇	1	1	yes	characteristic
752	#431	C₂²×C₆₇	1	1	yes	characteristic
753	#423	C₂²×C₆₇	1	1	yes	characteristic
754	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
755	#408	C₂²×C₆₇	1	2	yes	—
756	#405	C₂²×C₆₇	1	2	yes	—
757	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
759	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
760	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
764	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
765	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
766	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
768	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
769	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
770	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
771	C₄⋊Q₈	—	2	1	no	—
772	C₄⋊Q₈	—	2	2	no	—
773	C₄⋊Q₈	—	2	1	no	—
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	—	2	1	no	—
776	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
779	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
781	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
784	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
785	#126	—	2	1	no	—
786	#126	—	2	1	no	—
787	#126	—	2	1	no	—
788	#126	—	2	1	no	—
789	#126	—	2	1	no	—
790	#126	—	2	1	no	—
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#125	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	—	2	2	no	—
803	#125	—	2	2	no	—
804	#125	—	2	2	no	—
805	#125	—	2	2	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	C₂³×C₆₇	1	1	yes	characteristic
813	#125	C₂³×C₆₇	1	1	yes	characteristic
814	#125	C₂³×C₆₇	1	2	yes	—
815	#124	—	2	1	no	—
816	#124	—	2	2	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	C₂³×C₆₇	1	1	yes	characteristic
820	#124	C₂³×C₆₇	1	1	yes	characteristic
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
849	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
850	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
851	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
852	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	C₂³×C₆₇	1	1	yes	characteristic
860	#121	C₂³×C₆₇	1	1	yes	characteristic
861	C₄×Q₈	—	2	2	no	—
862	C₄×Q₈	—	2	2	no	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
874	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
880	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
881	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
882	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
883	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
884	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
890	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
891	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
892	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
893	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
894	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	—	2	1	no	—
902	#117	—	2	1	no	—
903	#117	—	2	2	no	—
904	#117	—	2	2	no	—
905	#117	—	2	1	no	—
906	#117	—	2	1	no	—
907	#117	—	2	1	no	—
908	#117	C₂³×C₆₇	1	1	yes	characteristic
909	#117	C₂³×C₆₇	1	2	yes	—
910	#117	C₂³×C₆₇	1	1	yes	characteristic
911	#117	C₂³×C₆₇	1	1	yes	characteristic
912	#117	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₄²	—	2	1	no	—
918	C₂×C₄²	—	2	1	no	—
919	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
921	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
922	#107	C₂³×C₆₇	1	2	yes	—
923	#107	C₂³×C₆₇	1	2	yes	—
924	#107	C₂³×C₆₇	1	2	yes	—
925	#107	C₂³×C₆₇	1	2	yes	—
926	#106	C₂³×C₆₇	1	2	yes	—
927	#106	C₂³×C₆₇	1	2	yes	—
928	#106	C₂³×C₆₇	1	2	yes	—
929	#106	C₂³×C₆₇	1	2	yes	—
930	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
931	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
932	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
933	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
935	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
936	#103	C₂³×C₆₇	1	2	yes	—
937	#103	C₂³×C₆₇	1	2	yes	—
938	#103	C₂³×C₆₇	1	2	yes	—
939	#103	C₂³×C₆₇	1	2	yes	—
940	#103	C₂³×C₆₇	1	2	yes	—
941	#103	C₂³×C₆₇	1	2	yes	—
942	#103	C₂³×C₆₇	1	2	yes	—
943	#103	C₂³×C₆₇	1	2	yes	—
944	#103	C₂³×C₆₇	1	2	yes	—
945	#103	C₂³×C₆₇	1	2	yes	—
946	#103	C₂³×C₆₇	1	2	yes	—
947	#103	C₂³×C₆₇	1	2	yes	—
948	#103	C₂³×C₆₇	1	2	yes	—
949	#103	C₂³×C₆₇	1	2	yes	—
950	#102	C₂³×C₆₇	1	2	yes	—
951	#102	C₂³×C₆₇	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
955	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
956	#97	C₂³×C₆₇	1	2	yes	—
957	#97	C₂³×C₆₇	1	2	yes	—
958	C₄×C₈	C₂³×C₆₇	1	2	yes	—
959	C₄×C₈	C₂³×C₆₇	1	2	yes	—
960	#41	—	4	1	no	—
961	#41	—	4	1	no	—
962	#41	—	4	1	no	—
963	#41	—	4	1	no	—
964	C₂×Q₈	—	2	1	no	—
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	1	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	1	no	—
969	C₂×Q₈	—	2	1	no	—
970	C₂×Q₈	—	4	2	no	—
971	C₂×Q₈	—	4	2	no	—
972	C₂×Q₈	—	4	1	no	—
973	C₂×Q₈	—	4	1	no	—
974	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
978	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
985	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
996	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1002	Q₁₆	—	4	2	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	Q₁₆	—	4	2	no	—
1006	Q₁₆	—	4	2	no	—
1007	Q₁₆	—	4	2	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	M₁₆	—	4	2	no	—
1011	C₂×C₈	—	4	2	no	—
1012	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1013	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1014	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1015	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1058	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1059	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1090	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1091	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1092	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1093	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1094	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	—	2	2	no	—
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	2	2	no	—
1106	C₄²	—	2	2	no	—
1107	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1108	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1109	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1110	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1111	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1112	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1113	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1114	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1115	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1116	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1117	C₂³	—	2	1	no	—
1118	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1119	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1120	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	2	1	no	—
1126	Q₈	—	2	1	no	—
1127	Q₈	—	2	2	no	—
1128	Q₈	—	2	2	no	—
1129	Q₈	—	2	1	no	—
1130	Q₈	—	2	1	no	—
1131	Q₈	—	4	1	no	—
1132	Q₈	—	4	2	no	—
1133	Q₈	—	4	4	no	—
1134	Q₈	—	4	2	no	—
1135	Q₈	—	4	2	no	—
1136	Q₈	—	8	1	no	—
1137	Q₈	—	8	1	no	—
1138	D₄	—	2	1	no	—
1139	D₄	—	2	1	no	—
1140	D₄	—	4	1	no	—
1141	D₄	—	4	1	no	—
1142	D₄	—	4	1	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	8	1	no	—
1145	D₄	—	8	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1179	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1183	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1184	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1185	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1186	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1187	C₈	—	2	2	no	—
1188	C₈	—	2	2	no	—
1189	C₈	—	2	2	no	—
1190	C₈	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	1	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	2	no	—
1224	C₄	—	4	2	no	—
1225	C₄	#578×C₆₇	1	2	yes	—
1226	C₄	#585×C₆₇	1	1	yes	characteristic
1227	C₄	#585×C₆₇	1	1	yes	characteristic
1228	C₂	—	4	1	no	—
1229	C₂	—	4	1	no	—
1230	C₂	—	4	1	no	—
1231	C₂	—	8	1	no	—
1232	C₂	C₆₇×#3449	1	1	yes	characteristic
1233	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1234	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	#537×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3509	C₂	semidirect
3. C₆₇×#3255	C₂	semidirect
4. C₆₇×#3252	C₂	semidirect
5. C₆₇×#3249	C₂	semidirect
6. C₆₇×#3248	C₂	semidirect
7. C₆₇×#3242	C₂	semidirect
8. C₆₇×#3237	C₂	semidirect
9. C₆₇×#3233	C₂	semidirect
10. C₆₇×#3223	C₂	semidirect
11. C₆₇×#3218	C₂	semidirect
12. C₆₇×#3209	C₂	semidirect
13. C₆₇×#3202	C₂	semidirect
15. C₆₇×#3178	C₂	semidirect
16. C₆₇×#3177	C₂	semidirect
17. C₆₇×#3127	C₂	semidirect
18. C₆₇×#3121	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3113	C₂	semidirect
21. C₆₇×#3107	C₂	semidirect
22. C₆₇×#3104	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
610. #60995	C₆₇	direct (N × H)
618. #3509	C₂×C₆₇	semidirect
620. #3255	C₂×C₆₇	semidirect
621. #3252	C₂×C₆₇	semidirect
622. #3249	C₂×C₆₇	semidirect
623. #3248	C₂×C₆₇	semidirect
624. #3242	C₂×C₆₇	semidirect
625. #3237	C₂×C₆₇	semidirect
626. #3233	C₂×C₆₇	semidirect
627. #3223	C₂×C₆₇	semidirect
628. #3218	C₂×C₆₇	semidirect
629. #3209	C₂×C₆₇	semidirect
630. #3202	C₂×C₆₇	semidirect
632. #3178	C₂×C₆₇	semidirect
633. #3177	C₂×C₆₇	semidirect
634. #3127	C₂×C₆₇	semidirect
635. #3121	C₂×C₆₇	semidirect
636. #3116	C₂×C₆₇	semidirect
637. #3113	C₂×C₆₇	semidirect
638. #3107	C₂×C₆₇	semidirect
639. #3104	C₂×C₆₇	semidirect
640. #2925	C₂×C₆₇	semidirect
641. C₆₇	#60995	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×#3509	2
C₆₇×#3461	2
C₆₇×#3255	2
C₆₇×#3252	2
C₆₇×#3249	2
C₆₇×#3248	2
C₆₇×#3242	2
C₆₇×#3237	2
C₆₇×#3233	2
C₆₇×#3223	2
C₆₇×#3218	2
C₆₇×#3209	2
C₆₇×#3202	2
C₆₇×#3201	2
C₆₇×#3178	2
C₆₇×#3177	2
C₆₇×#3127	2
C₆₇×#3121	2
C₆₇×#3116	2
C₆₇×#3113	2
C₆₇×#3107	2
C₆₇×#3104	2
C₆₇×#2925	2
#60995	67

Subgroups — C67×#60995 #30740246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60995 #30740246