Subgroups — C₆₇×#60600 #30739851

Order 17152.

2046 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3124	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3121	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3112	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#477×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2951	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#137×C₆₇	C₂²	1	2	yes	—
20	C₂×#135×C₆₇	C₂²	1	2	yes	—
21	#556×C₆₇	—	2	1	no	—
22	#555×C₆₇	—	2	1	no	—
23	#554×C₆₇	—	2	1	no	—
24	#553×C₆₇	—	2	2	no	—
25	#548×C₆₇	—	2	2	no	—
26	#547×C₆₇	—	2	1	no	—
27	#542×C₆₇	C₂²	1	4	yes	—
28	#537×C₆₇	C₂²	1	2	yes	—
29	#533×C₆₇	C₂²	1	2	yes	—
30	#532×C₆₇	C₂²	1	1	yes	characteristic
31	#532×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	#520×C₆₇	—	2	1	no	—
34	#520×C₆₇	—	2	2	no	—
35	#520×C₆₇	C₂²	1	2	yes	—
36	#520×C₆₇	C₂²	1	1	yes	characteristic
37	#520×C₆₇	C₂²	1	2	yes	—
38	#520×C₆₇	C₂²	1	1	yes	characteristic
39	#519×C₆₇	—	2	1	no	—
40	#519×C₆₇	C₂²	1	2	yes	—
41	#519×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×#41×C₆₇	—	2	2	no	—
43	C₄×#41×C₆₇	—	2	1	no	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×#41×C₆₇	C₂²	1	2	yes	—
46	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
48	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
50	#485×C₆₇	C₂²	1	4	yes	—
51	#484×C₆₇	C₂²	1	4	yes	—
52	#482×C₆₇	C₂²	1	4	yes	—
53	#480×C₆₇	C₂²	1	4	yes	—
54	#477×C₆₇	C₂²	1	2	yes	—
55	#477×C₆₇	C₂²	1	2	yes	—
56	#477×C₆₇	C₂²	1	4	yes	—
57	#477×C₆₇	C₂²	1	2	yes	—
58	#476×C₆₇	C₂²	1	2	yes	—
59	#475×C₆₇	C₂²	1	2	yes	—
60	#474×C₆₇	C₂²	1	2	yes	—
61	#464×C₆₇	C₂²	1	2	yes	—
62	#464×C₆₇	C₂²	1	4	yes	—
63	#463×C₆₇	C₂²	1	2	yes	—
64	#462×C₆₇	C₂²	1	1	yes	characteristic
65	#462×C₆₇	C₂²	1	2	yes	—
66	#461×C₆₇	C₂²	1	1	yes	characteristic
67	#460×C₆₇	C₂²	1	1	yes	characteristic
68	#460×C₆₇	C₂²	1	2	yes	—
69	#459×C₆₇	C₂²	1	1	yes	characteristic
70	#452×C₆₇	C₂²	1	4	yes	—
71	#451×C₆₇	C₂²	1	4	yes	—
72	#449×C₆₇	C₂²	1	4	yes	—
73	#448×C₆₇	C₂²	1	4	yes	—
74	#441×C₆₇	C₂²	1	4	yes	—
75	#440×C₆₇	C₂²	1	4	yes	—
76	#440×C₆₇	C₂²	1	4	yes	—
77	#440×C₆₇	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
81	C₄×D₈×C₆₇	C₂²	1	4	yes	—
82	#433×C₆₇	C₂²	1	4	yes	—
83	#432×C₆₇	C₂²	1	2	yes	—
84	#431×C₆₇	C₂²	1	2	yes	—
85	#428×C₆₇	C₂²	1	2	yes	—
86	C₂×#107×C₆₇	C₂²	1	2	yes	—
87	#423×C₆₇	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
89	#417×C₆₇	C₂²	1	2	yes	—
90	#417×C₆₇	C₂²	1	2	yes	—
91	#416×C₆₇	C₂²	1	2	yes	—
92	C₂×#103×C₆₇	C₂²	1	2	yes	—
93	#408×C₆₇	C₂²	1	2	yes	—
94	#405×C₆₇	C₂²	1	2	yes	—
95	2₋¹⁺⁴×C₆₇	—	2	4	no	—
96	2₋¹⁺⁴×C₆₇	—	2	4	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	2	no	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₆₇	—	2	1	no	—
105	C₂²×Q₈×C₆₇	—	2	1	no	—
106	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	#137×C₆₇	—	2	8	no	—
109	#135×C₆₇	—	2	8	no	—
110	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
111	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
115	C₂×D₈×C₆₇	C₂³	1	2	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₆₇	—	2	1	no	—
119	C₄⋊Q₈×C₆₇	—	2	1	no	—
120	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
123	#127×C₆₇	C₂³	1	1	yes	characteristic
124	#126×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	2	no	—
126	#124×C₆₇	—	2	4	no	—
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	C₂³	1	2	yes	—
129	#123×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	4	no	—
136	#121×C₆₇	—	2	1	no	—
137	#121×C₆₇	—	2	1	no	—
138	#121×C₆₇	—	2	2	no	—
139	#121×C₆₇	C₂³	1	4	yes	—
140	C₄×Q₈×C₆₇	—	2	1	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	1	no	—
144	C₄×Q₈×C₆₇	—	2	2	no	—
145	C₄×Q₈×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	—	2	1	no	—
147	C₄×Q₈×C₆₇	—	2	1	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
151	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	4	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
175	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
176	C₄×D₄×C₆₇	D₄	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	4	yes	—
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	—	2	1	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	2	no	—
185	#117×C₆₇	—	2	2	no	—
186	#117×C₆₇	—	2	2	no	—
187	#117×C₆₇	—	2	2	no	—
188	#117×C₆₇	—	2	1	no	—
189	#117×C₆₇	—	2	2	no	—
190	#117×C₆₇	C₂³	1	2	yes	—
191	#117×C₆₇	C₂³	1	1	yes	characteristic
192	#117×C₆₇	C₂³	1	1	yes	characteristic
193	#117×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
198	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	—	2	1	no	—
204	C₂×C₄²×C₆₇	—	2	2	no	—
205	C₂×C₄²×C₆₇	—	2	2	no	—
206	C₂×C₄²×C₆₇	—	2	1	no	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	#107×C₆₇	C₂³	1	4	yes	—
210	#107×C₆₇	C₂³	1	4	yes	—
211	#107×C₆₇	C₂³	1	4	yes	—
212	#106×C₆₇	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	4	yes	—
219	#103×C₆₇	C₂³	1	4	yes	—
220	#103×C₆₇	C₂³	1	4	yes	—
221	#103×C₆₇	C₂³	1	2	yes	—
222	#103×C₆₇	C₂³	1	2	yes	—
223	#103×C₆₇	C₂³	1	4	yes	—
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	2	yes	—
226	#102×C₆₇	C₂³	1	2	yes	—
227	#102×C₆₇	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	#97×C₆₇	C₂³	1	4	yes	—
231	C₄×C₈×C₆₇	C₂³	1	4	yes	—
232	#41×C₆₇	—	2	16	no	—
233	#41×C₆₇	—	2	8	no	—
234	#41×C₆₇	—	2	4	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	2	no	—
237	#41×C₆₇	—	2	2	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	—	2	4	no	—
240	#41×C₆₇	—	2	4	no	—
241	#41×C₆₇	—	8	4	no	—
242	#41×C₆₇	#41	1	4	yes	complemented
243	C₂×Q₈×C₆₇	—	2	8	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	—	2	4	no	—
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	2	1	no	—
248	C₂×Q₈×C₆₇	—	2	2	no	—
249	C₂×Q₈×C₆₇	—	2	2	no	—
250	C₂×Q₈×C₆₇	—	2	2	no	—
251	C₂×Q₈×C₆₇	—	8	2	no	—
252	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
254	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	1	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	1	no	—
262	C₂×D₄×C₆₇	—	2	1	no	—
263	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	1	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	1	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	1	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	1	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₆₇	—	2	4	no	—
286	Q₁₆×C₆₇	—	2	8	no	—
287	SD₁₆×C₆₇	—	2	4	no	—
288	SD₁₆×C₆₇	—	2	8	no	—
289	SD₁₆×C₆₇	—	2	4	no	—
290	D₈×C₆₇	—	2	4	no	—
291	M₁₆×C₆₇	—	2	4	no	—
292	C₂×C₈×C₆₇	—	2	4	no	—
293	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
294	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
295	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	1	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	1	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₄⋊C₄×C₆₇	—	2	1	no	—
311	C₄⋊C₄×C₆₇	—	2	4	no	—
312	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	1	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	1	no	—
335	C₄²×C₆₇	—	2	1	no	—
336	C₄²×C₆₇	—	2	2	no	—
337	C₄²×C₆₇	—	2	2	no	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	—	2	2	no	—
341	C₄²×C₆₇	—	2	1	no	—
342	C₄²×C₆₇	—	2	4	no	—
343	C₄²×C₆₇	C₂×D₄	1	2	yes	—
344	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₆₇	C₂×D₄	1	2	yes	—
347	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₄²×C₆₇	C₂⁴	1	2	yes	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
353	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₆₇	—	2	8	no	—
355	Q₈×C₆₇	—	2	2	no	—
356	Q₈×C₆₇	—	2	4	no	—
357	Q₈×C₆₇	—	2	1	no	—
358	Q₈×C₆₇	—	2	2	no	—
359	Q₈×C₆₇	—	2	2	no	—
360	Q₈×C₆₇	—	2	2	no	—
361	Q₈×C₆₇	—	4	4	no	—
362	Q₈×C₆₇	—	8	2	no	—
363	Q₈×C₆₇	C₂×#41	1	2	yes	—
364	Q₈×C₆₇	C₂×#41	1	4	yes	—
365	D₄×C₆₇	—	2	8	no	—
366	D₄×C₆₇	—	2	4	no	—
367	D₄×C₆₇	—	2	4	no	—
368	D₄×C₆₇	—	2	2	no	—
369	D₄×C₆₇	—	2	1	no	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	2	2	no	—
372	D₄×C₆₇	—	4	2	no	—
373	D₄×C₆₇	—	4	4	no	—
374	D₄×C₆₇	—	4	2	no	—
375	D₄×C₆₇	—	8	4	no	—
376	D₄×C₆₇	C₂×#41	1	2	yes	—
377	C₂×C₄×C₆₇	—	2	8	no	—
378	C₂×C₄×C₆₇	—	2	8	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	4	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	4	no	—
392	C₂×C₄×C₆₇	—	4	1	no	—
393	C₂×C₄×C₆₇	—	4	2	no	—
394	C₂×C₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	4	2	no	—
396	C₂×C₄×C₆₇	—	8	2	no	—
397	C₂×C₄×C₆₇	—	8	1	no	—
398	C₂×C₄×C₆₇	—	8	4	no	—
399	C₂×C₄×C₆₇	—	8	1	no	—
400	C₂×C₄×C₆₇	—	8	2	no	—
401	C₂×C₄×C₆₇	—	8	2	no	—
402	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
412	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
413	C₈×C₆₇	—	2	2	no	—
414	C₈×C₆₇	—	2	2	no	—
415	C₈×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	1	no	—
417	C₂²×C₆₇	—	2	1	no	—
418	C₂²×C₆₇	—	2	2	no	—
419	C₂²×C₆₇	—	2	2	no	—
420	C₂²×C₆₇	—	2	2	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	#525	1	2	yes	—
428	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
429	C₄×C₆₇	—	2	1	no	—
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	1	no	—
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	2	no	—
434	C₄×C₆₇	—	2	2	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	1	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	4	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	1	no	—
442	C₄×C₆₇	#525	1	2	yes	—
443	C₄×C₆₇	#578	1	2	yes	—
444	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
445	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
446	#60600	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂×C₆₇	—	2	2	no	—
448	C₂×C₆₇	—	4	2	no	—
449	C₂×C₆₇	—	4	2	no	—
450	C₂×C₆₇	—	8	2	no	—
451	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
452	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
453	C₂×C₆₇	#3585	1	1	yes	characteristic
454	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
455	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3124	C₂×C₆₇	1	4	yes	complemented
457	#3121	C₂×C₆₇	1	4	yes	complemented
458	#3116	C₂×C₆₇	1	2	yes	complemented
459	#3112	C₂×C₆₇	1	2	yes	complemented
460	#3106	C₂×C₆₇	1	2	yes	complemented
461	#3104	C₂×C₆₇	1	2	yes	complemented
462	#3098	C₂×C₆₇	1	2	yes	complemented
463	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#477	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3013	C₂×C₆₇	1	2	yes	complemented
468	#2951	C₂×C₆₇	1	2	yes	complemented
469	#2947	C₂×C₆₇	1	2	yes	complemented
470	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
471	C₆₇	#60600	1	1	yes	characteristic, direct product factor, Sylow
472	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#137	C₂²×C₆₇	1	2	yes	—
474	C₂×#135	C₂²×C₆₇	1	2	yes	—
475	#556	—	2	1	no	—
476	#555	—	2	1	no	—
477	#554	—	2	1	no	—
478	#553	—	2	2	no	—
479	#548	—	2	2	no	—
480	#547	—	2	1	no	—
481	#542	C₂²×C₆₇	1	4	yes	—
482	#537	C₂²×C₆₇	1	2	yes	—
483	#533	C₂²×C₆₇	1	2	yes	—
484	#532	C₂²×C₆₇	1	1	yes	characteristic
485	#532	C₂²×C₆₇	1	2	yes	—
486	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
487	#520	—	2	1	no	—
488	#520	—	2	2	no	—
489	#520	C₂²×C₆₇	1	2	yes	—
490	#520	C₂²×C₆₇	1	1	yes	characteristic
491	#520	C₂²×C₆₇	1	2	yes	—
492	#520	C₂²×C₆₇	1	1	yes	characteristic
493	#519	—	2	1	no	—
494	#519	C₂²×C₆₇	1	2	yes	—
495	#519	C₂²×C₆₇	1	1	yes	characteristic
496	C₄×#41	—	2	2	no	—
497	C₄×#41	—	2	1	no	—
498	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
499	C₄×#41	C₂²×C₆₇	1	2	yes	—
500	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
501	C₂×C₄×Q₈	—	2	1	no	—
502	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
504	#485	C₂²×C₆₇	1	4	yes	—
505	#484	C₂²×C₆₇	1	4	yes	—
506	#482	C₂²×C₆₇	1	4	yes	—
507	#480	C₂²×C₆₇	1	4	yes	—
508	#477	C₂²×C₆₇	1	2	yes	—
509	#477	C₂²×C₆₇	1	2	yes	—
510	#477	C₂²×C₆₇	1	4	yes	—
511	#477	C₂²×C₆₇	1	2	yes	—
512	#476	C₂²×C₆₇	1	2	yes	—
513	#475	C₂²×C₆₇	1	2	yes	—
514	#474	C₂²×C₆₇	1	2	yes	—
515	#464	C₂²×C₆₇	1	2	yes	—
516	#464	C₂²×C₆₇	1	4	yes	—
517	#463	C₂²×C₆₇	1	2	yes	—
518	#462	C₂²×C₆₇	1	1	yes	characteristic
519	#462	C₂²×C₆₇	1	2	yes	—
520	#461	C₂²×C₆₇	1	1	yes	characteristic
521	#460	C₂²×C₆₇	1	2	yes	—
522	#460	C₂²×C₆₇	1	1	yes	characteristic
523	#459	C₂²×C₆₇	1	1	yes	characteristic
524	#452	C₂²×C₆₇	1	4	yes	—
525	#451	C₂²×C₆₇	1	4	yes	—
526	#449	C₂²×C₆₇	1	4	yes	—
527	#448	C₂²×C₆₇	1	4	yes	—
528	#441	C₂²×C₆₇	1	4	yes	—
529	#440	C₂²×C₆₇	1	4	yes	—
530	#440	C₂²×C₆₇	1	4	yes	—
531	#440	C₂²×C₆₇	1	4	yes	—
532	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
533	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
534	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
535	C₄×D₈	C₂²×C₆₇	1	4	yes	—
536	#433	C₂²×C₆₇	1	4	yes	—
537	#432	C₂²×C₆₇	1	2	yes	—
538	#431	C₂²×C₆₇	1	2	yes	—
539	#428	C₂²×C₆₇	1	2	yes	—
540	C₂×#107	C₂²×C₆₇	1	2	yes	—
541	#423	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
543	#417	C₂²×C₆₇	1	2	yes	—
544	#417	C₂²×C₆₇	1	2	yes	—
545	#416	C₂²×C₆₇	1	2	yes	—
546	C₂×#103	C₂²×C₆₇	1	2	yes	—
547	#408	C₂²×C₆₇	1	2	yes	—
548	#405	C₂²×C₆₇	1	2	yes	—
549	2₋¹⁺⁴	—	2	4	no	—
550	2₋¹⁺⁴	—	2	4	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	C₂³×C₆₇	1	2	yes	—
555	C₂×#41	C₂³×C₆₇	1	2	yes	—
556	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
558	C₂²×Q₈	—	2	1	no	—
559	C₂²×Q₈	—	2	1	no	—
560	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
561	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
562	#137	—	2	8	no	—
563	#135	—	2	8	no	—
564	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
565	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
567	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
568	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
569	C₂×D₈	C₂³×C₆₇	1	2	yes	—
570	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
571	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	—	2	1	no	—
574	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
577	#127	C₂³×C₆₇	1	1	yes	characteristic
578	#126	—	2	4	no	—
579	#125	—	2	2	no	—
580	#124	—	2	4	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₆₇	1	2	yes	—
583	#123	—	2	4	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₆₇	1	4	yes	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
605	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
607	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
609	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
610	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
611	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
612	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	D₄×C₆₇	1	2	yes	—
628	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
629	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
630	C₄×D₄	D₄×C₆₇	1	2	yes	—
631	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₆₇	1	2	yes	—
633	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₆₇	1	4	yes	—
635	#117	—	2	2	no	—
636	#117	—	2	1	no	—
637	#117	—	2	2	no	—
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	2	no	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	C₂³×C₆₇	1	1	yes	characteristic
645	#117	C₂³×C₆₇	1	2	yes	—
646	#117	C₂³×C₆₇	1	1	yes	characteristic
647	#117	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	2	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	2	no	—
659	C₂×C₄²	—	2	2	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
663	#107	C₂³×C₆₇	1	4	yes	—
664	#107	C₂³×C₆₇	1	4	yes	—
665	#107	C₂³×C₆₇	1	4	yes	—
666	#106	C₂³×C₆₇	1	4	yes	—
667	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
669	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
670	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
671	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
672	#103	C₂³×C₆₇	1	4	yes	—
673	#103	C₂³×C₆₇	1	4	yes	—
674	#103	C₂³×C₆₇	1	2	yes	—
675	#103	C₂³×C₆₇	1	2	yes	—
676	#103	C₂³×C₆₇	1	4	yes	—
677	#103	C₂³×C₆₇	1	4	yes	—
678	#102	C₂³×C₆₇	1	2	yes	—
679	#102	C₂³×C₆₇	1	2	yes	—
680	#102	C₂³×C₆₇	1	4	yes	—
681	#102	C₂³×C₆₇	1	4	yes	—
682	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
683	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
684	#97	C₂³×C₆₇	1	4	yes	—
685	C₄×C₈	C₂³×C₆₇	1	4	yes	—
686	#41	—	2	16	no	—
687	#41	—	2	8	no	—
688	#41	—	2	4	no	—
689	#41	—	2	4	no	—
690	#41	—	2	2	no	—
691	#41	—	2	2	no	—
692	#41	—	2	2	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	8	4	no	—
696	#41	#41×C₆₇	1	4	yes	complemented
697	C₂×Q₈	—	2	8	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	8	2	no	—
706	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
707	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
708	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	Q₁₆	—	2	4	no	—
740	Q₁₆	—	2	8	no	—
741	SD₁₆	—	2	4	no	—
742	SD₁₆	—	2	8	no	—
743	SD₁₆	—	2	4	no	—
744	D₈	—	2	4	no	—
745	M₁₆	—	2	4	no	—
746	C₂×C₈	—	2	4	no	—
747	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
748	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
749	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	1	no	—
796	C₄²	—	2	4	no	—
797	C₄²	C₂×D₄×C₆₇	1	2	yes	—
798	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
800	C₄²	C₂×D₄×C₆₇	1	2	yes	—
801	C₄²	C₂⁴×C₆₇	1	2	yes	—
802	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₂³	—	2	1	no	—
805	C₂³	—	2	2	no	—
806	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
807	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
808	Q₈	—	2	8	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	4	no	—
811	Q₈	—	2	1	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	4	no	—
816	Q₈	—	8	2	no	—
817	Q₈	C₂×#41×C₆₇	1	2	yes	—
818	Q₈	C₂×#41×C₆₇	1	4	yes	—
819	D₄	—	2	8	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	1	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	8	4	no	—
830	D₄	C₂×#41×C₆₇	1	2	yes	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	8	4	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	1	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	1	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
864	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
865	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
866	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
867	C₈	—	2	2	no	—
868	C₈	—	2	2	no	—
869	C₈	—	2	4	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	#525×C₆₇	1	2	yes	—
882	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
883	C₄	—	2	2	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	4	no	—
895	C₄	—	4	2	no	—
896	C₄	#525×C₆₇	1	2	yes	—
897	C₄	#578×C₆₇	1	2	yes	—
898	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
899	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
900	C₂	—	2	2	no	—
901	C₂	—	4	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
905	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
906	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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×#3511	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₆₇×#3124	C₂	semidirect
4. C₆₇×#3121	C₂	semidirect
5. C₆₇×#3116	C₂	semidirect
6. C₆₇×#3112	C₂	semidirect
7. C₆₇×#3106	C₂	semidirect
8. C₆₇×#3104	C₂	semidirect
9. C₆₇×#3098	C₂	semidirect
10. C₆₇×#3079	C₂	semidirect
11. C₂×#477×C₆₇	C₂	semidirect
12. C₆₇×#3037	C₂	semidirect
13. C₆₇×#3035	C₂	semidirect
14. C₆₇×#3013	C₂	semidirect
15. C₆₇×#2951	C₂	semidirect
16. C₆₇×#2947	C₂	semidirect
17. C₆₇×#2925	C₂	semidirect
242. #41×C₆₇	#41	semidirect
253. C₂×Q₈×C₆₇	#41	semidirect
446. #60600	C₆₇	direct (N × H)
454. #3511	C₂×C₆₇	semidirect
455. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
456. #3124	C₂×C₆₇	semidirect
457. #3121	C₂×C₆₇	semidirect
458. #3116	C₂×C₆₇	semidirect
459. #3112	C₂×C₆₇	semidirect
460. #3106	C₂×C₆₇	semidirect
461. #3104	C₂×C₆₇	semidirect
462. #3098	C₂×C₆₇	semidirect
463. #3079	C₂×C₆₇	semidirect
464. C₂×#477	C₂×C₆₇	semidirect
465. #3037	C₂×C₆₇	semidirect
466. #3035	C₂×C₆₇	semidirect
467. #3013	C₂×C₆₇	semidirect
468. #2951	C₂×C₆₇	semidirect
469. #2947	C₂×C₆₇	semidirect
470. #2925	C₂×C₆₇	semidirect
471. C₆₇	#60600	direct (N × H)
696. #41	#41×C₆₇	semidirect
707. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3116	2
C₆₇×#3112	2
C₆₇×#3106	2
C₆₇×#3104	2
C₆₇×#3098	2
C₆₇×#3079	2
C₂×#477×C₆₇	2
C₆₇×#3037	2
C₆₇×#3035	2
C₆₇×#3013	2
C₆₇×#2951	2
C₆₇×#2947	2
C₆₇×#2925	2
#60600	67

Subgroups — C67×#60600 #30739851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60600 #30739851