Subgroups — C₆₇×#60975 #30740226

Order 17152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3461	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3263	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3261	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3258	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3204	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#3202	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3181	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₆₇	C₂²	1	2	yes	—
21	#542×C₆₇	—	2	2	no	—
22	#542×C₆₇	C₂²	1	2	yes	—
23	#542×C₆₇	C₂²	1	2	yes	—
24	#541×C₆₇	—	2	2	no	—
25	#541×C₆₇	C₂²	1	2	yes	—
26	#541×C₆₇	C₂²	1	2	yes	—
27	#539×C₆₇	—	2	2	no	—
28	#539×C₆₇	—	2	2	no	—
29	#537×C₆₇	C₂²	1	2	yes	—
30	#536×C₆₇	C₂²	1	2	yes	—
31	#536×C₆₇	C₂²	1	2	yes	—
32	#533×C₆₇	—	2	2	no	—
33	#533×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	C₂²	1	2	yes	—
35	#529×C₆₇	—	2	2	no	—
36	#529×C₆₇	—	2	2	no	—
37	#529×C₆₇	—	2	2	no	—
38	#529×C₆₇	C₂²	1	2	yes	—
39	#529×C₆₇	C₂²	1	2	yes	—
40	C₄×#41×C₆₇	C₂²	1	2	yes	—
41	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
43	#501×C₆₇	C₂²	1	2	yes	—
44	#499×C₆₇	C₂²	1	1	yes	characteristic
45	#498×C₆₇	C₂²	1	1	yes	characteristic
46	#497×C₆₇	C₂²	1	2	yes	—
47	#495×C₆₇	C₂²	1	1	yes	characteristic
48	#494×C₆₇	C₂²	1	1	yes	characteristic
49	#491×C₆₇	C₂²	1	2	yes	—
50	#489×C₆₇	C₂²	1	2	yes	—
51	#488×C₆₇	C₂²	1	2	yes	—
52	#487×C₆₇	C₂²	1	2	yes	—
53	#485×C₆₇	C₂²	1	2	yes	—
54	#485×C₆₇	C₂²	1	2	yes	—
55	#485×C₆₇	C₂²	1	2	yes	—
56	#484×C₆₇	C₂²	1	2	yes	—
57	#483×C₆₇	C₂²	1	2	yes	—
58	#483×C₆₇	C₂²	1	2	yes	—
59	#482×C₆₇	C₂²	1	2	yes	—
60	#481×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	2	yes	—
62	#479×C₆₇	C₂²	1	2	yes	—
63	#479×C₆₇	C₂²	1	2	yes	—
64	#478×C₆₇	C₂²	1	2	yes	—
65	#477×C₆₇	C₂²	1	2	yes	—
66	#476×C₆₇	C₂²	1	2	yes	—
67	#475×C₆₇	C₂²	1	2	yes	—
68	#475×C₆₇	C₂²	1	2	yes	—
69	#470×C₆₇	C₂²	1	1	yes	characteristic
70	#470×C₆₇	C₂²	1	2	yes	—
71	#470×C₆₇	C₂²	1	1	yes	characteristic
72	#470×C₆₇	C₂²	1	1	yes	characteristic
73	#469×C₆₇	C₂²	1	1	yes	characteristic
74	#468×C₆₇	C₂²	1	2	yes	—
75	#467×C₆₇	C₂²	1	2	yes	—
76	#467×C₆₇	C₂²	1	2	yes	—
77	#465×C₆₇	C₂²	1	2	yes	—
78	#465×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	—
80	#464×C₆₇	C₂²	1	2	yes	—
81	#464×C₆₇	C₂²	1	2	yes	—
82	#463×C₆₇	C₂²	1	2	yes	—
83	#462×C₆₇	C₂²	1	2	yes	—
84	#462×C₆₇	C₂²	1	2	yes	—
85	#462×C₆₇	C₂²	1	2	yes	—
86	#461×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	2	yes	—
91	#451×C₆₇	C₂²	1	2	yes	—
92	#451×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#448×C₆₇	C₂²	1	2	yes	—
95	#442×C₆₇	C₂²	1	1	yes	characteristic
96	#441×C₆₇	C₂²	1	2	yes	—
97	#441×C₆₇	C₂²	1	1	yes	characteristic
98	#441×C₆₇	C₂²	1	2	yes	—
99	#441×C₆₇	C₂²	1	2	yes	—
100	#441×C₆₇	C₂²	1	1	yes	characteristic
101	#441×C₆₇	C₂²	1	1	yes	characteristic
102	#440×C₆₇	C₂²	1	2	yes	—
103	#440×C₆₇	C₂²	1	2	yes	—
104	#440×C₆₇	C₂²	1	2	yes	—
105	#433×C₆₇	C₂²	1	2	yes	—
106	#433×C₆₇	C₂²	1	2	yes	—
107	#432×C₆₇	C₂²	1	2	yes	—
108	#432×C₆₇	C₂²	1	2	yes	—
109	#424×C₆₇	C₂²	1	1	yes	characteristic
110	#424×C₆₇	C₂²	1	1	yes	characteristic
111	#408×C₆₇	C₂²	1	1	yes	characteristic
112	#408×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₇	C₂³	1	2	yes	—
116	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
118	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₆₇	—	2	2	no	—
133	C₄⋊Q₈×C₆₇	—	2	2	no	—
134	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#126×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	2	no	—
147	#125×C₆₇	—	2	2	no	—
148	#125×C₆₇	—	2	2	no	—
149	#125×C₆₇	—	2	2	no	—
150	#125×C₆₇	—	2	2	no	—
151	#125×C₆₇	—	2	2	no	—
152	#125×C₆₇	—	2	2	no	—
153	#125×C₆₇	C₂³	1	2	yes	—
154	#125×C₆₇	C₂³	1	2	yes	—
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	—	2	2	no	—
157	#124×C₆₇	—	2	2	no	—
158	#124×C₆₇	C₂³	1	2	yes	—
159	#124×C₆₇	C₂³	1	2	yes	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	#123×C₆₇	—	2	2	no	—
166	#123×C₆₇	—	2	2	no	—
167	#123×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	—	2	2	no	—
172	C₂²⋊Q₈×C₆₇	—	2	2	no	—
173	C₂²⋊Q₈×C₆₇	—	2	2	no	—
174	C₂²⋊Q₈×C₆₇	—	2	2	no	—
175	C₂²⋊Q₈×C₆₇	—	2	2	no	—
176	C₂²⋊Q₈×C₆₇	—	2	2	no	—
177	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	—	2	2	no	—
184	#121×C₆₇	—	2	2	no	—
185	#121×C₆₇	—	2	2	no	—
186	#121×C₆₇	C₂³	1	2	yes	—
187	#121×C₆₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₇	—	2	2	no	—
189	C₄×Q₈×C₆₇	—	2	2	no	—
190	C₄×Q₈×C₆₇	—	2	2	no	—
191	C₄×Q₈×C₆₇	—	2	2	no	—
192	C₄×Q₈×C₆₇	D₄	1	2	yes	—
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
195	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
196	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
197	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
198	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	—	2	2	no	—
201	C₄×D₄×C₆₇	—	2	2	no	—
202	C₄×D₄×C₆₇	—	2	2	no	—
203	C₄×D₄×C₆₇	D₄	1	2	yes	—
204	C₄×D₄×C₆₇	D₄	1	2	yes	—
205	C₄×D₄×C₆₇	D₄	1	2	yes	—
206	C₄×D₄×C₆₇	C₂³	1	2	yes	—
207	C₄×D₄×C₆₇	C₂³	1	2	yes	—
208	#117×C₆₇	—	2	2	no	—
209	#117×C₆₇	—	2	2	no	—
210	#117×C₆₇	—	2	2	no	—
211	#117×C₆₇	—	2	2	no	—
212	#117×C₆₇	—	2	2	no	—
213	#117×C₆₇	C₂³	1	2	yes	—
214	#117×C₆₇	C₂³	1	2	yes	—
215	#117×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₇	—	2	2	no	—
219	C₂×C₄²×C₆₇	—	2	2	no	—
220	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	#107×C₆₇	C₂³	1	2	yes	—
223	#107×C₆₇	C₂³	1	2	yes	—
224	#107×C₆₇	C₂³	1	2	yes	—
225	#106×C₆₇	C₂³	1	2	yes	—
226	#106×C₆₇	C₂³	1	2	yes	—
227	#106×C₆₇	C₂³	1	1	yes	characteristic
228	#106×C₆₇	C₂³	1	2	yes	—
229	#106×C₆₇	C₂³	1	1	yes	characteristic
230	#106×C₆₇	C₂³	1	1	yes	characteristic
231	#106×C₆₇	C₂³	1	1	yes	characteristic
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	#103×C₆₇	C₂³	1	2	yes	—
237	#103×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#103×C₆₇	C₂³	1	2	yes	—
243	#103×C₆₇	C₂³	1	2	yes	—
244	#103×C₆₇	C₂³	1	2	yes	—
245	#103×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	2	yes	—
258	#97×C₆₇	C₂³	1	1	yes	characteristic
259	#97×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	#41×C₆₇	—	4	1	no	—
263	#41×C₆₇	—	4	1	no	—
264	#41×C₆₇	—	4	2	no	—
265	#41×C₆₇	—	4	2	no	—
266	C₂×Q₈×C₆₇	—	2	2	no	—
267	C₂×Q₈×C₆₇	—	2	2	no	—
268	C₂×Q₈×C₆₇	—	2	2	no	—
269	C₂×Q₈×C₆₇	—	4	2	no	—
270	C₂×Q₈×C₆₇	—	4	2	no	—
271	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
272	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	2	no	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	Q₁₆×C₆₇	—	4	2	no	—
292	Q₁₆×C₆₇	—	4	2	no	—
293	Q₁₆×C₆₇	—	4	1	no	—
294	Q₁₆×C₆₇	—	4	1	no	—
295	Q₁₆×C₆₇	—	4	2	no	—
296	Q₁₆×C₆₇	—	4	1	no	—
297	SD₁₆×C₆₇	—	4	2	no	—
298	SD₁₆×C₆₇	—	4	2	no	—
299	SD₁₆×C₆₇	—	4	2	no	—
300	D₈×C₆₇	—	4	1	no	—
301	M₁₆×C₆₇	—	4	1	no	—
302	M₁₆×C₆₇	—	4	1	no	—
303	C₂×C₈×C₆₇	—	4	1	no	—
304	C₂×C₈×C₆₇	—	4	1	no	—
305	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	2	2	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	2	2	no	—
362	C₄²×C₆₇	—	2	2	no	—
363	C₄²×C₆₇	—	2	2	no	—
364	C₄²×C₆₇	—	2	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	C₂×D₄	1	2	yes	—
368	C₄²×C₆₇	C₂×D₄	1	2	yes	—
369	C₄²×C₆₇	C₂×D₄	1	2	yes	—
370	C₄²×C₆₇	C₂⁴	1	2	yes	—
371	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
376	Q₈×C₆₇	—	2	2	no	—
377	Q₈×C₆₇	—	2	2	no	—
378	Q₈×C₆₇	—	2	2	no	—
379	Q₈×C₆₇	—	2	2	no	—
380	Q₈×C₆₇	—	2	2	no	—
381	Q₈×C₆₇	—	2	2	no	—
382	Q₈×C₆₇	—	4	1	no	—
383	Q₈×C₆₇	—	4	4	no	—
384	Q₈×C₆₇	—	8	2	no	—
385	Q₈×C₆₇	—	8	2	no	—
386	D₄×C₆₇	—	2	2	no	—
387	D₄×C₆₇	—	2	2	no	—
388	D₄×C₆₇	—	4	2	no	—
389	D₄×C₆₇	—	4	1	no	—
390	D₄×C₆₇	—	4	4	no	—
391	D₄×C₆₇	—	8	2	no	—
392	D₄×C₆₇	—	8	2	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	4	2	no	—
405	C₂×C₄×C₆₇	—	4	2	no	—
406	C₂×C₄×C₆₇	—	4	2	no	—
407	C₂×C₄×C₆₇	—	4	4	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	4	no	—
410	C₂×C₄×C₆₇	—	8	2	no	—
411	C₂×C₄×C₆₇	—	8	2	no	—
412	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	2	no	—
420	C₈×C₆₇	—	2	2	no	—
421	C₈×C₆₇	—	2	1	no	—
422	C₈×C₆₇	—	2	1	no	—
423	C₈×C₆₇	—	2	1	no	—
424	C₈×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	2	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₆₇	—	2	2	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	1	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	#585	1	1	yes	characteristic
448	C₄×C₆₇	#585	1	1	yes	characteristic
449	#60975	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
450	C₂×C₆₇	—	4	2	no	—
451	C₂×C₆₇	—	4	1	no	—
452	C₂×C₆₇	—	8	2	no	—
453	C₂×C₆₇	#3449	1	1	yes	characteristic
454	C₂×C₆₇	#3586	1	2	yes	—
455	#3461	C₂×C₆₇	1	2	yes	complemented
456	#3263	C₂×C₆₇	1	1	yes	characteristic, complemented
457	#3261	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#3258	C₂×C₆₇	1	2	yes	complemented
459	#3244	C₂×C₆₇	1	2	yes	complemented
460	#3242	C₂×C₆₇	1	2	yes	complemented
461	#3225	C₂×C₆₇	1	2	yes	complemented
462	#3223	C₂×C₆₇	1	2	yes	complemented
463	#3204	C₂×C₆₇	1	1	yes	characteristic
464	#3202	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#3201	C₂×C₆₇	1	2	yes	complemented
466	#3185	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3183	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3181	C₂×C₆₇	1	2	yes	complemented
469	#3117	C₂×C₆₇	1	2	yes	complemented
470	#3116	C₂×C₆₇	1	2	yes	complemented
471	#3113	C₂×C₆₇	1	2	yes	complemented
472	#3111	C₂×C₆₇	1	2	yes	complemented
473	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
474	C₆₇	#60975	1	1	yes	characteristic, direct product factor, Sylow
475	#544	C₂²×C₆₇	1	2	yes	—
476	#542	—	2	2	no	—
477	#542	C₂²×C₆₇	1	2	yes	—
478	#542	C₂²×C₆₇	1	2	yes	—
479	#541	—	2	2	no	—
480	#541	C₂²×C₆₇	1	2	yes	—
481	#541	C₂²×C₆₇	1	2	yes	—
482	#539	—	2	2	no	—
483	#539	—	2	2	no	—
484	#537	C₂²×C₆₇	1	2	yes	—
485	#536	C₂²×C₆₇	1	2	yes	—
486	#536	C₂²×C₆₇	1	2	yes	—
487	#533	—	2	2	no	—
488	#533	C₂²×C₆₇	1	2	yes	—
489	#533	C₂²×C₆₇	1	2	yes	—
490	#529	—	2	2	no	—
491	#529	—	2	2	no	—
492	#529	—	2	2	no	—
493	#529	C₂²×C₆₇	1	2	yes	—
494	#529	C₂²×C₆₇	1	2	yes	—
495	C₄×#41	C₂²×C₆₇	1	2	yes	—
496	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
498	#501	C₂²×C₆₇	1	2	yes	—
499	#499	C₂²×C₆₇	1	1	yes	characteristic
500	#498	C₂²×C₆₇	1	1	yes	characteristic
501	#497	C₂²×C₆₇	1	2	yes	—
502	#495	C₂²×C₆₇	1	1	yes	characteristic
503	#494	C₂²×C₆₇	1	1	yes	characteristic
504	#491	C₂²×C₆₇	1	2	yes	—
505	#489	C₂²×C₆₇	1	2	yes	—
506	#488	C₂²×C₆₇	1	2	yes	—
507	#487	C₂²×C₆₇	1	2	yes	—
508	#485	C₂²×C₆₇	1	2	yes	—
509	#485	C₂²×C₆₇	1	2	yes	—
510	#485	C₂²×C₆₇	1	2	yes	—
511	#484	C₂²×C₆₇	1	2	yes	—
512	#483	C₂²×C₆₇	1	2	yes	—
513	#483	C₂²×C₆₇	1	2	yes	—
514	#482	C₂²×C₆₇	1	2	yes	—
515	#481	C₂²×C₆₇	1	2	yes	—
516	#479	C₂²×C₆₇	1	2	yes	—
517	#479	C₂²×C₆₇	1	2	yes	—
518	#479	C₂²×C₆₇	1	2	yes	—
519	#478	C₂²×C₆₇	1	2	yes	—
520	#477	C₂²×C₆₇	1	2	yes	—
521	#476	C₂²×C₆₇	1	2	yes	—
522	#475	C₂²×C₆₇	1	2	yes	—
523	#475	C₂²×C₆₇	1	2	yes	—
524	#470	C₂²×C₆₇	1	1	yes	characteristic
525	#470	C₂²×C₆₇	1	2	yes	—
526	#470	C₂²×C₆₇	1	1	yes	characteristic
527	#470	C₂²×C₆₇	1	1	yes	characteristic
528	#469	C₂²×C₆₇	1	1	yes	characteristic
529	#468	C₂²×C₆₇	1	2	yes	—
530	#467	C₂²×C₆₇	1	2	yes	—
531	#467	C₂²×C₆₇	1	2	yes	—
532	#465	C₂²×C₆₇	1	2	yes	—
533	#465	C₂²×C₆₇	1	2	yes	—
534	#464	C₂²×C₆₇	1	2	yes	—
535	#464	C₂²×C₆₇	1	2	yes	—
536	#464	C₂²×C₆₇	1	2	yes	—
537	#463	C₂²×C₆₇	1	2	yes	—
538	#462	C₂²×C₆₇	1	2	yes	—
539	#462	C₂²×C₆₇	1	2	yes	—
540	#462	C₂²×C₆₇	1	2	yes	—
541	#461	C₂²×C₆₇	1	2	yes	—
542	#452	C₂²×C₆₇	1	2	yes	—
543	#452	C₂²×C₆₇	1	2	yes	—
544	#452	C₂²×C₆₇	1	2	yes	—
545	#451	C₂²×C₆₇	1	2	yes	—
546	#451	C₂²×C₆₇	1	2	yes	—
547	#451	C₂²×C₆₇	1	2	yes	—
548	#449	C₂²×C₆₇	1	2	yes	—
549	#448	C₂²×C₆₇	1	2	yes	—
550	#442	C₂²×C₆₇	1	1	yes	characteristic
551	#441	C₂²×C₆₇	1	2	yes	—
552	#441	C₂²×C₆₇	1	1	yes	characteristic
553	#441	C₂²×C₆₇	1	2	yes	—
554	#441	C₂²×C₆₇	1	2	yes	—
555	#441	C₂²×C₆₇	1	1	yes	characteristic
556	#441	C₂²×C₆₇	1	1	yes	characteristic
557	#440	C₂²×C₆₇	1	2	yes	—
558	#440	C₂²×C₆₇	1	2	yes	—
559	#440	C₂²×C₆₇	1	2	yes	—
560	#433	C₂²×C₆₇	1	2	yes	—
561	#433	C₂²×C₆₇	1	2	yes	—
562	#432	C₂²×C₆₇	1	2	yes	—
563	#432	C₂²×C₆₇	1	2	yes	—
564	#424	C₂²×C₆₇	1	1	yes	characteristic
565	#424	C₂²×C₆₇	1	1	yes	characteristic
566	#408	C₂²×C₆₇	1	1	yes	characteristic
567	#408	C₂²×C₆₇	1	1	yes	characteristic
568	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×#41	C₂³×C₆₇	1	2	yes	—
571	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
577	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
578	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
579	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
583	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
587	C₄⋊Q₈	—	2	2	no	—
588	C₄⋊Q₈	—	2	2	no	—
589	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₆₇	1	2	yes	—
609	#125	C₂³×C₆₇	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	—	2	2	no	—
612	#124	—	2	2	no	—
613	#124	C₂³×C₆₇	1	2	yes	—
614	#124	C₂³×C₆₇	1	2	yes	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
633	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	C₂³×C₆₇	1	2	yes	—
642	#121	C₂³×C₆₇	1	2	yes	—
643	C₄×Q₈	—	2	2	no	—
644	C₄×Q₈	—	2	2	no	—
645	C₄×Q₈	—	2	2	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	D₄×C₆₇	1	2	yes	—
648	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
649	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
650	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
651	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
652	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
653	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	D₄×C₆₇	1	2	yes	—
659	C₄×D₄	D₄×C₆₇	1	2	yes	—
660	C₄×D₄	D₄×C₆₇	1	2	yes	—
661	C₄×D₄	C₂³×C₆₇	1	2	yes	—
662	C₄×D₄	C₂³×C₆₇	1	2	yes	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	—	2	2	no	—
667	#117	—	2	2	no	—
668	#117	C₂³×C₆₇	1	2	yes	—
669	#117	C₂³×C₆₇	1	2	yes	—
670	#117	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₄⋊C₄	—	2	2	no	—
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄²	—	2	2	no	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	#107	C₂³×C₆₇	1	2	yes	—
678	#107	C₂³×C₆₇	1	2	yes	—
679	#107	C₂³×C₆₇	1	2	yes	—
680	#106	C₂³×C₆₇	1	2	yes	—
681	#106	C₂³×C₆₇	1	2	yes	—
682	#106	C₂³×C₆₇	1	1	yes	characteristic
683	#106	C₂³×C₆₇	1	2	yes	—
684	#106	C₂³×C₆₇	1	1	yes	characteristic
685	#106	C₂³×C₆₇	1	1	yes	characteristic
686	#106	C₂³×C₆₇	1	1	yes	characteristic
687	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
688	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
689	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
690	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
691	#103	C₂³×C₆₇	1	2	yes	—
692	#103	C₂³×C₆₇	1	2	yes	—
693	#103	C₂³×C₆₇	1	2	yes	—
694	#103	C₂³×C₆₇	1	2	yes	—
695	#103	C₂³×C₆₇	1	2	yes	—
696	#103	C₂³×C₆₇	1	2	yes	—
697	#103	C₂³×C₆₇	1	2	yes	—
698	#103	C₂³×C₆₇	1	2	yes	—
699	#103	C₂³×C₆₇	1	2	yes	—
700	#103	C₂³×C₆₇	1	2	yes	—
701	#103	C₂³×C₆₇	1	2	yes	—
702	#103	C₂³×C₆₇	1	2	yes	—
703	#102	C₂³×C₆₇	1	2	yes	—
704	#102	C₂³×C₆₇	1	2	yes	—
705	#102	C₂³×C₆₇	1	2	yes	—
706	#102	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	2	yes	—
710	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
711	#97	C₂³×C₆₇	1	2	yes	—
712	#97	C₂³×C₆₇	1	2	yes	—
713	#97	C₂³×C₆₇	1	1	yes	characteristic
714	#97	C₂³×C₆₇	1	1	yes	characteristic
715	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
716	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
717	#41	—	4	1	no	—
718	#41	—	4	1	no	—
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
727	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
728	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
735	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	Q₁₆	—	4	2	no	—
747	Q₁₆	—	4	2	no	—
748	Q₁₆	—	4	1	no	—
749	Q₁₆	—	4	1	no	—
750	Q₁₆	—	4	2	no	—
751	Q₁₆	—	4	1	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	D₈	—	4	1	no	—
756	M₁₆	—	4	1	no	—
757	M₁₆	—	4	1	no	—
758	C₂×C₈	—	4	1	no	—
759	C₂×C₈	—	4	1	no	—
760	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
761	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
762	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
763	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
765	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
812	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
814	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	C₂×D₄×C₆₇	1	2	yes	—
823	C₄²	C₂×D₄×C₆₇	1	2	yes	—
824	C₄²	C₂×D₄×C₆₇	1	2	yes	—
825	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
826	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
827	C₄²	C₂⁴×C₆₇	1	2	yes	—
828	C₂³	—	2	2	no	—
829	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
831	Q₈	—	2	2	no	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	4	1	no	—
838	Q₈	—	4	4	no	—
839	Q₈	—	8	2	no	—
840	Q₈	—	8	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	2	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	4	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
873	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
874	C₈	—	2	2	no	—
875	C₈	—	2	2	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	1	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	1	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	#585×C₆₇	1	1	yes	characteristic
903	C₄	#585×C₆₇	1	1	yes	characteristic
904	C₂	—	4	2	no	—
905	C₂	—	4	1	no	—
906	C₂	—	8	2	no	—
907	C₂	C₆₇×#3449	1	1	yes	characteristic
908	C₂	C₆₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3204	C₂
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×#3461	C₂	semidirect
2. C₆₇×#3263	C₂	semidirect
3. C₆₇×#3261	C₂	semidirect
4. C₆₇×#3258	C₂	semidirect
5. C₆₇×#3244	C₂	semidirect
6. C₆₇×#3242	C₂	semidirect
7. C₆₇×#3225	C₂	semidirect
8. C₆₇×#3223	C₂	semidirect
10. C₆₇×#3202	C₂	semidirect
11. C₆₇×#3201	C₂	semidirect
12. C₆₇×#3185	C₂	semidirect
13. C₆₇×#3183	C₂	semidirect
14. C₆₇×#3181	C₂	semidirect
15. C₆₇×#3117	C₂	semidirect
16. C₆₇×#3116	C₂	semidirect
17. C₆₇×#3113	C₂	semidirect
18. C₆₇×#3111	C₂	semidirect
19. C₆₇×#2923	C₂	semidirect
449. #60975	C₆₇	direct (N × H)
455. #3461	C₂×C₆₇	semidirect
456. #3263	C₂×C₆₇	semidirect
457. #3261	C₂×C₆₇	semidirect
458. #3258	C₂×C₆₇	semidirect
459. #3244	C₂×C₆₇	semidirect
460. #3242	C₂×C₆₇	semidirect
461. #3225	C₂×C₆₇	semidirect
462. #3223	C₂×C₆₇	semidirect
464. #3202	C₂×C₆₇	semidirect
465. #3201	C₂×C₆₇	semidirect
466. #3185	C₂×C₆₇	semidirect
467. #3183	C₂×C₆₇	semidirect
468. #3181	C₂×C₆₇	semidirect
469. #3117	C₂×C₆₇	semidirect
470. #3116	C₂×C₆₇	semidirect
471. #3113	C₂×C₆₇	semidirect
472. #3111	C₂×C₆₇	semidirect
473. #2923	C₂×C₆₇	semidirect
474. C₆₇	#60975	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3461	2
C₆₇×#3263	2
C₆₇×#3261	2
C₆₇×#3258	2
C₆₇×#3244	2
C₆₇×#3242	2
C₆₇×#3225	2
C₆₇×#3223	2
C₆₇×#3204	2
C₆₇×#3202	2
C₆₇×#3201	2
C₆₇×#3185	2
C₆₇×#3183	2
C₆₇×#3181	2
C₆₇×#3117	2
C₆₇×#3116	2
C₆₇×#3113	2
C₆₇×#3111	2
C₆₇×#2923	2
#60975	67

Subgroups — C67×#60975 #30740226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60975 #30740226