Subgroups — C₆₇×#60594 #30739845

Order 17152.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 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	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3127	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3120	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3107	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3097	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#462×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3011	C₂	1	2	yes	maximal
15	C₆₇×#2950	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	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
21	#557×C₆₇	—	2	1	no	—
22	#557×C₆₇	—	2	1	no	—
23	#556×C₆₇	—	2	1	no	—
24	#556×C₆₇	—	2	1	no	—
25	#552×C₆₇	—	2	2	no	—
26	#552×C₆₇	—	2	2	no	—
27	#541×C₆₇	C₂²	1	4	yes	—
28	#536×C₆₇	C₂²	1	2	yes	—
29	#533×C₆₇	C₂²	1	2	yes	—
30	#533×C₆₇	C₂²	1	2	yes	—
31	#533×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	#520×C₆₇	—	2	2	no	—
34	#520×C₆₇	—	2	1	no	—
35	#520×C₆₇	C₂²	1	2	yes	—
36	#520×C₆₇	C₂²	1	1	yes	characteristic
37	#520×C₆₇	C₂²	1	1	yes	characteristic
38	#519×C₆₇	—	2	1	no	—
39	#519×C₆₇	C₂²	1	2	yes	—
40	#519×C₆₇	C₂²	1	1	yes	characteristic
41	#519×C₆₇	C₂²	1	2	yes	—
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	#485×C₆₇	C₂²	1	4	yes	—
52	#484×C₆₇	C₂²	1	4	yes	—
53	#483×C₆₇	C₂²	1	4	yes	—
54	#479×C₆₇	C₂²	1	2	yes	—
55	#479×C₆₇	C₂²	1	4	yes	—
56	#478×C₆₇	C₂²	1	2	yes	—
57	#477×C₆₇	C₂²	1	1	yes	characteristic
58	#477×C₆₇	C₂²	1	2	yes	—
59	#476×C₆₇	C₂²	1	1	yes	characteristic
60	#475×C₆₇	C₂²	1	1	yes	characteristic
61	#475×C₆₇	C₂²	1	2	yes	—
62	#474×C₆₇	C₂²	1	1	yes	characteristic
63	#462×C₆₇	C₂²	1	2	yes	—
64	#462×C₆₇	C₂²	1	2	yes	—
65	#462×C₆₇	C₂²	1	4	yes	—
66	#462×C₆₇	C₂²	1	2	yes	—
67	#462×C₆₇	C₂²	1	2	yes	—
68	#461×C₆₇	C₂²	1	2	yes	—
69	#461×C₆₇	C₂²	1	2	yes	—
70	#452×C₆₇	C₂²	1	4	yes	—
71	#452×C₆₇	C₂²	1	4	yes	—
72	#451×C₆₇	C₂²	1	4	yes	—
73	#451×C₆₇	C₂²	1	4	yes	—
74	#441×C₆₇	C₂²	1	4	yes	—
75	#441×C₆₇	C₂²	1	4	yes	—
76	#441×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×Q₁₆×C₆₇	C₂²	1	4	yes	—
81	C₄×SD₁₆×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	#427×C₆₇	C₂²	1	2	yes	—
87	#423×C₆₇	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
89	#419×C₆₇	C₂²	1	2	yes	—
90	#419×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	2	no	—
98	C₂×#41×C₆₇	—	2	1	no	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
101	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₆₇	—	2	1	no	—
103	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
104	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
106	#137×C₆₇	—	2	8	no	—
107	C₂×Q₁₆×C₆₇	—	2	8	no	—
108	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
109	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
112	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	—	2	2	no	—
115	C₄⋊Q₈×C₆₇	—	2	1	no	—
116	C₄⋊Q₈×C₆₇	—	2	1	no	—
117	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
121	#126×C₆₇	—	2	4	no	—
122	#126×C₆₇	—	2	4	no	—
123	#125×C₆₇	—	2	4	no	—
124	#125×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	2	no	—
126	#125×C₆₇	—	2	2	no	—
127	#125×C₆₇	C₂³	1	2	yes	—
128	#124×C₆₇	—	2	2	no	—
129	#123×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	1	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	C₄×Q₈×C₆₇	—	2	1	no	—
137	C₄×Q₈×C₆₇	—	2	1	no	—
138	C₄×Q₈×C₆₇	—	2	2	no	—
139	C₄×Q₈×C₆₇	—	2	1	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	—	2	2	no	—
142	C₄×Q₈×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	—	2	1	no	—
145	C₄×Q₈×C₆₇	—	2	2	no	—
146	C₄×Q₈×C₆₇	—	2	1	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₆₇	D₄	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	1	yes	characteristic
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	D₄	1	2	yes	—
172	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	#117×C₆₇	—	2	2	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	1	no	—
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	—	2	2	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	2	no	—
185	#117×C₆₇	—	2	4	no	—
186	#117×C₆₇	—	2	2	no	—
187	#117×C₆₇	—	2	1	no	—
188	#117×C₆₇	C₂³	1	2	yes	—
189	#117×C₆₇	C₂³	1	1	yes	characteristic
190	#117×C₆₇	C₂³	1	2	yes	—
191	#117×C₆₇	C₂³	1	1	yes	characteristic
192	#117×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	1	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	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	—	2	1	no	—
202	C₂×C₄²×C₆₇	—	2	2	no	—
203	C₂×C₄²×C₆₇	—	2	2	no	—
204	C₂×C₄²×C₆₇	—	2	1	no	—
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
207	#107×C₆₇	C₂³	1	2	yes	—
208	#107×C₆₇	C₂³	1	2	yes	—
209	#107×C₆₇	C₂³	1	4	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	#106×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#103×C₆₇	C₂³	1	2	yes	—
220	#103×C₆₇	C₂³	1	4	yes	—
221	#103×C₆₇	C₂³	1	4	yes	—
222	#103×C₆₇	C₂³	1	4	yes	—
223	#103×C₆₇	C₂³	1	4	yes	—
224	#103×C₆₇	C₂³	1	4	yes	—
225	#103×C₆₇	C₂³	1	4	yes	—
226	#102×C₆₇	C₂³	1	2	yes	—
227	#102×C₆₇	C₂³	1	2	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	#41	1	4	yes	—
240	C₂×Q₈×C₆₇	—	2	8	no	—
241	C₂×Q₈×C₆₇	—	2	4	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	—	2	1	no	—
245	C₂×Q₈×C₆₇	—	2	1	no	—
246	C₂×Q₈×C₆₇	—	2	1	no	—
247	C₂×Q₈×C₆₇	—	2	2	no	—
248	C₂×Q₈×C₆₇	—	2	2	no	—
249	C₂×Q₈×C₆₇	—	2	4	no	—
250	C₂×Q₈×C₆₇	—	2	4	no	—
251	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂×Q₈×C₆₇	#41	1	4	yes	—
253	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₆₇	—	2	8	no	—
278	Q₁₆×C₆₇	—	2	8	no	—
279	Q₁₆×C₆₇	—	2	8	no	—
280	SD₁₆×C₆₇	—	2	8	no	—
281	M₁₆×C₆₇	—	2	4	no	—
282	C₂×C₈×C₆₇	—	2	4	no	—
283	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
284	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
285	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	1	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	1	no	—
300	C₄⋊C₄×C₆₇	—	2	1	no	—
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	4	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	4	no	—
307	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	1	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	1	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	1	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	1	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	—	2	2	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	2	no	—
335	C₄²×C₆₇	—	2	1	no	—
336	C₄²×C₆₇	—	2	4	no	—
337	C₄²×C₆₇	—	2	4	no	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	C₂×D₄	1	2	yes	—
340	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₆₇	C₂×D₄	1	2	yes	—
342	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₄²×C₆₇	C₂⁴	1	2	yes	—
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
348	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₆₇	—	2	8	no	—
350	Q₈×C₆₇	—	2	2	no	—
351	Q₈×C₆₇	—	2	4	no	—
352	Q₈×C₆₇	—	2	1	no	—
353	Q₈×C₆₇	—	2	2	no	—
354	Q₈×C₆₇	—	2	4	no	—
355	Q₈×C₆₇	—	2	4	no	—
356	Q₈×C₆₇	—	4	2	no	—
357	Q₈×C₆₇	—	4	4	no	—
358	Q₈×C₆₇	—	4	2	no	—
359	Q₈×C₆₇	C₂×#41	1	2	yes	—
360	Q₈×C₆₇	C₂×#41	1	4	yes	—
361	D₄×C₆₇	—	2	8	no	—
362	D₄×C₆₇	—	2	4	no	—
363	D₄×C₆₇	—	2	4	no	—
364	D₄×C₆₇	—	2	2	no	—
365	D₄×C₆₇	—	2	1	no	—
366	D₄×C₆₇	C₂×#41	1	2	yes	—
367	C₂×C₄×C₆₇	—	2	8	no	—
368	C₂×C₄×C₆₇	—	2	8	no	—
369	C₂×C₄×C₆₇	—	2	4	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	1	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	4	1	no	—
384	C₂×C₄×C₆₇	—	4	2	no	—
385	C₂×C₄×C₆₇	—	4	4	no	—
386	C₂×C₄×C₆₇	—	4	2	no	—
387	C₂×C₄×C₆₇	—	8	2	no	—
388	C₂×C₄×C₆₇	—	8	1	no	—
389	C₂×C₄×C₆₇	—	8	1	no	—
390	C₂×C₄×C₆₇	—	8	2	no	—
391	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
400	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
402	C₈×C₆₇	—	2	2	no	—
403	C₈×C₆₇	—	2	2	no	—
404	C₈×C₆₇	—	2	4	no	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	1	no	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	4	1	no	—
413	C₂²×C₆₇	#525	1	2	yes	—
414	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₆₇	—	2	1	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	1	no	—
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	2	2	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	1	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	1	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	4	no	—
427	C₄×C₆₇	—	4	1	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	#525	1	2	yes	—
430	C₄×C₆₇	#578	1	2	yes	—
431	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
432	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
433	#60594	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₆₇	—	2	2	no	—
435	C₂×C₆₇	—	4	2	no	—
436	C₂×C₆₇	—	4	2	no	—
437	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
438	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
439	C₂×C₆₇	#3586	1	1	yes	characteristic
440	#3509	C₂×C₆₇	1	1	yes	characteristic, complemented
441	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic
442	#3127	C₂×C₆₇	1	4	yes	complemented
443	#3120	C₂×C₆₇	1	4	yes	complemented
444	#3116	C₂×C₆₇	1	2	yes	complemented
445	#3113	C₂×C₆₇	1	2	yes	complemented
446	#3107	C₂×C₆₇	1	2	yes	complemented
447	#3104	C₂×C₆₇	1	2	yes	complemented
448	#3097	C₂×C₆₇	1	2	yes	complemented
449	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
452	C₂×#462	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#3011	C₂×C₆₇	1	2	yes	—
454	#2950	C₂×C₆₇	1	2	yes	complemented
455	#2947	C₂×C₆₇	1	2	yes	complemented
456	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
457	C₆₇	#60594	1	1	yes	characteristic, direct product factor, Sylow
458	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#137	C₂²×C₆₇	1	2	yes	—
460	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
461	#557	—	2	1	no	—
462	#557	—	2	1	no	—
463	#556	—	2	1	no	—
464	#556	—	2	1	no	—
465	#552	—	2	2	no	—
466	#552	—	2	2	no	—
467	#541	C₂²×C₆₇	1	4	yes	—
468	#536	C₂²×C₆₇	1	2	yes	—
469	#533	C₂²×C₆₇	1	2	yes	—
470	#533	C₂²×C₆₇	1	2	yes	—
471	#533	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
473	#520	—	2	2	no	—
474	#520	—	2	1	no	—
475	#520	C₂²×C₆₇	1	2	yes	—
476	#520	C₂²×C₆₇	1	1	yes	characteristic
477	#520	C₂²×C₆₇	1	1	yes	characteristic
478	#519	—	2	1	no	—
479	#519	C₂²×C₆₇	1	2	yes	—
480	#519	C₂²×C₆₇	1	1	yes	characteristic
481	#519	C₂²×C₆₇	1	2	yes	—
482	C₄×#41	—	2	2	no	—
483	C₄×#41	—	2	1	no	—
484	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
485	C₄×#41	C₂²×C₆₇	1	2	yes	—
486	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×C₄×Q₈	—	2	1	no	—
488	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
490	#485	C₂²×C₆₇	1	4	yes	—
491	#485	C₂²×C₆₇	1	4	yes	—
492	#484	C₂²×C₆₇	1	4	yes	—
493	#483	C₂²×C₆₇	1	4	yes	—
494	#479	C₂²×C₆₇	1	2	yes	—
495	#479	C₂²×C₆₇	1	4	yes	—
496	#478	C₂²×C₆₇	1	2	yes	—
497	#477	C₂²×C₆₇	1	1	yes	characteristic
498	#477	C₂²×C₆₇	1	2	yes	—
499	#476	C₂²×C₆₇	1	1	yes	characteristic
500	#475	C₂²×C₆₇	1	1	yes	characteristic
501	#475	C₂²×C₆₇	1	2	yes	—
502	#474	C₂²×C₆₇	1	1	yes	characteristic
503	#462	C₂²×C₆₇	1	2	yes	—
504	#462	C₂²×C₆₇	1	2	yes	—
505	#462	C₂²×C₆₇	1	2	yes	—
506	#462	C₂²×C₆₇	1	4	yes	—
507	#462	C₂²×C₆₇	1	2	yes	—
508	#461	C₂²×C₆₇	1	2	yes	—
509	#461	C₂²×C₆₇	1	2	yes	—
510	#452	C₂²×C₆₇	1	4	yes	—
511	#452	C₂²×C₆₇	1	4	yes	—
512	#451	C₂²×C₆₇	1	4	yes	—
513	#451	C₂²×C₆₇	1	4	yes	—
514	#441	C₂²×C₆₇	1	4	yes	—
515	#441	C₂²×C₆₇	1	4	yes	—
516	#441	C₂²×C₆₇	1	4	yes	—
517	#440	C₂²×C₆₇	1	4	yes	—
518	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
519	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
520	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
521	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
522	#433	C₂²×C₆₇	1	4	yes	—
523	#432	C₂²×C₆₇	1	2	yes	—
524	#431	C₂²×C₆₇	1	2	yes	—
525	#428	C₂²×C₆₇	1	2	yes	—
526	#427	C₂²×C₆₇	1	2	yes	—
527	#423	C₂²×C₆₇	1	1	yes	characteristic
528	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
529	#419	C₂²×C₆₇	1	2	yes	—
530	#419	C₂²×C₆₇	1	2	yes	—
531	#416	C₂²×C₆₇	1	2	yes	—
532	C₂×#103	C₂²×C₆₇	1	2	yes	—
533	#408	C₂²×C₆₇	1	2	yes	—
534	#405	C₂²×C₆₇	1	2	yes	—
535	2₋¹⁺⁴	—	2	4	no	—
536	2₋¹⁺⁴	—	2	4	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	1	no	—
539	C₂×#41	C₂³×C₆₇	1	2	yes	—
540	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
544	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
545	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
546	#137	—	2	8	no	—
547	C₂×Q₁₆	—	2	8	no	—
548	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
549	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
550	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
552	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
553	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
554	C₄⋊Q₈	—	2	2	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
561	#126	—	2	4	no	—
562	#126	—	2	4	no	—
563	#125	—	2	4	no	—
564	#125	—	2	4	no	—
565	#125	—	2	2	no	—
566	#125	—	2	2	no	—
567	#125	C₂³×C₆₇	1	2	yes	—
568	#124	—	2	2	no	—
569	#123	—	2	4	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
575	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
592	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
594	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
596	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
597	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
598	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
599	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
601	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	D₄×C₆₇	1	2	yes	—
612	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
613	C₄×D₄	D₄×C₆₇	1	2	yes	—
614	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₆₇	1	2	yes	—
617	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	—	2	4	no	—
626	#117	—	2	2	no	—
627	#117	—	2	1	no	—
628	#117	C₂³×C₆₇	1	1	yes	characteristic
629	#117	C₂³×C₆₇	1	2	yes	—
630	#117	C₂³×C₆₇	1	2	yes	—
631	#117	C₂³×C₆₇	1	1	yes	characteristic
632	#117	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	2	no	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	—	2	2	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
647	#107	C₂³×C₆₇	1	2	yes	—
648	#107	C₂³×C₆₇	1	2	yes	—
649	#107	C₂³×C₆₇	1	4	yes	—
650	#106	C₂³×C₆₇	1	2	yes	—
651	#106	C₂³×C₆₇	1	2	yes	—
652	#106	C₂³×C₆₇	1	4	yes	—
653	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
654	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
655	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
656	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
657	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
658	#103	C₂³×C₆₇	1	4	yes	—
659	#103	C₂³×C₆₇	1	4	yes	—
660	#103	C₂³×C₆₇	1	2	yes	—
661	#103	C₂³×C₆₇	1	2	yes	—
662	#103	C₂³×C₆₇	1	4	yes	—
663	#103	C₂³×C₆₇	1	4	yes	—
664	#103	C₂³×C₆₇	1	4	yes	—
665	#103	C₂³×C₆₇	1	4	yes	—
666	#102	C₂³×C₆₇	1	2	yes	—
667	#102	C₂³×C₆₇	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
670	#97	C₂³×C₆₇	1	4	yes	—
671	C₄×C₈	C₂³×C₆₇	1	4	yes	—
672	#41	—	2	16	no	—
673	#41	—	2	8	no	—
674	#41	—	2	4	no	—
675	#41	—	2	4	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	#41×C₆₇	1	4	yes	—
680	C₂×Q₈	—	2	8	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
692	C₂×Q₈	#41×C₆₇	1	4	yes	—
693	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
694	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	Q₁₆	—	2	8	no	—
718	Q₁₆	—	2	8	no	—
719	Q₁₆	—	2	8	no	—
720	SD₁₆	—	2	8	no	—
721	M₁₆	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
724	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
725	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₆₇	1	2	yes	—
780	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₆₇	1	2	yes	—
782	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
783	C₄²	C₂⁴×C₆₇	1	2	yes	—
784	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
788	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
789	Q₈	—	2	8	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	4	no	—
792	Q₈	—	2	1	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	4	2	no	—
799	Q₈	C₂×#41×C₆₇	1	2	yes	—
800	Q₈	C₂×#41×C₆₇	1	4	yes	—
801	D₄	—	2	8	no	—
802	D₄	—	2	4	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	C₂×#41×C₆₇	1	2	yes	—
807	C₂×C₄	—	2	8	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	1	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
839	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
840	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
841	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₈	—	2	4	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	#525×C₆₇	1	2	yes	—
854	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	4	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	4	no	—
869	C₄	#525×C₆₇	1	2	yes	—
870	C₄	#578×C₆₇	1	2	yes	—
871	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
872	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	2	no	—
876	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
877	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
878	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	C₂×2₋¹⁺⁴×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×#3127	C₂	semidirect
4. C₆₇×#3120	C₂	semidirect
5. C₆₇×#3116	C₂	semidirect
6. C₆₇×#3113	C₂	semidirect
7. C₆₇×#3107	C₂	semidirect
8. C₆₇×#3104	C₂	semidirect
9. C₆₇×#3097	C₂	semidirect
10. C₆₇×#3078	C₂	semidirect
11. C₆₇×#3076	C₂	semidirect
12. C₆₇×#3039	C₂	semidirect
13. C₂×#462×C₆₇	C₂	semidirect
15. C₆₇×#2950	C₂	semidirect
16. C₆₇×#2947	C₂	semidirect
17. C₆₇×#2925	C₂	semidirect
433. #60594	C₆₇	direct (N × H)
440. #3509	C₂×C₆₇	semidirect
442. #3127	C₂×C₆₇	semidirect
443. #3120	C₂×C₆₇	semidirect
444. #3116	C₂×C₆₇	semidirect
445. #3113	C₂×C₆₇	semidirect
446. #3107	C₂×C₆₇	semidirect
447. #3104	C₂×C₆₇	semidirect
448. #3097	C₂×C₆₇	semidirect
449. #3078	C₂×C₆₇	semidirect
450. #3076	C₂×C₆₇	semidirect
451. #3039	C₂×C₆₇	semidirect
452. C₂×#462	C₂×C₆₇	semidirect
454. #2950	C₂×C₆₇	semidirect
455. #2947	C₂×C₆₇	semidirect
456. #2925	C₂×C₆₇	semidirect
457. C₆₇	#60594	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
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3127	2
C₆₇×#3120	2
C₆₇×#3116	2
C₆₇×#3113	2
C₆₇×#3107	2
C₆₇×#3104	2
C₆₇×#3097	2
C₆₇×#3078	2
C₆₇×#3076	2
C₆₇×#3039	2
C₂×#462×C₆₇	2
C₆₇×#3011	2
C₆₇×#2950	2
C₆₇×#2947	2
C₆₇×#2925	2
#60594	67

Subgroups — C67×#60594 #30739845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60594 #30739845