Subgroups — C₆₇×#60346 #30739597

Order 17152.

1628 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3531	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2986	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2985	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2968	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2962	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2961	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
20	#564×C₆₇	C₄	1	1	yes	characteristic
21	#563×C₆₇	C₄	1	2	yes	—
22	#563×C₆₇	C₄	1	2	yes	—
23	#563×C₆₇	C₄	1	2	yes	—
24	#563×C₆₇	C₄	1	1	yes	characteristic
25	#563×C₆₇	C₄	1	2	yes	—
26	#563×C₆₇	C₄	1	1	yes	characteristic
27	#562×C₆₇	C₄	1	2	yes	—
28	#562×C₆₇	C₄	1	2	yes	—
29	#562×C₆₇	C₄	1	1	yes	characteristic
30	#533×C₆₇	C₂²	1	1	yes	characteristic
31	#533×C₆₇	C₂²	1	2	yes	—
32	#533×C₆₇	C₂²	1	2	yes	—
33	#529×C₆₇	C₂²	1	1	yes	characteristic
34	#529×C₆₇	C₂²	1	1	yes	characteristic
35	#529×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#529×C₆₇	C₂²	1	2	yes	—
39	#446×C₆₇	C₂²	1	2	yes	—
40	#446×C₆₇	C₂²	1	2	yes	—
41	#446×C₆₇	C₂²	1	1	yes	characteristic
42	#446×C₆₇	C₂²	1	2	yes	—
43	#446×C₆₇	C₂²	1	2	yes	—
44	#446×C₆₇	C₂²	1	2	yes	—
45	#446×C₆₇	C₂²	1	2	yes	—
46	#446×C₆₇	C₂²	1	2	yes	—
47	#446×C₆₇	C₂²	1	2	yes	—
48	#446×C₆₇	C₂²	1	2	yes	—
49	#446×C₆₇	C₂²	1	2	yes	—
50	#446×C₆₇	C₂²	1	2	yes	—
51	#446×C₆₇	C₂²	1	1	yes	characteristic
52	#446×C₆₇	C₂²	1	2	yes	—
53	#446×C₆₇	C₂²	1	2	yes	—
54	#446×C₆₇	C₂²	1	2	yes	—
55	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
56	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
57	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
59	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
61	#436×C₆₇	C₂²	1	1	yes	characteristic
62	#436×C₆₇	C₂²	1	1	yes	characteristic
63	#436×C₆₇	C₂²	1	2	yes	—
64	#436×C₆₇	C₂²	1	2	yes	—
65	#436×C₆₇	C₂²	1	2	yes	—
66	#436×C₆₇	C₂²	1	2	yes	—
67	#435×C₆₇	C₂²	1	2	yes	—
68	#435×C₆₇	C₂²	1	2	yes	—
69	#435×C₆₇	C₂²	1	2	yes	—
70	#435×C₆₇	C₂²	1	2	yes	—
71	#435×C₆₇	C₂²	1	2	yes	—
72	#435×C₆₇	C₂²	1	2	yes	—
73	#435×C₆₇	C₂²	1	2	yes	—
74	#435×C₆₇	C₂²	1	2	yes	—
75	#435×C₆₇	C₂²	1	2	yes	—
76	#435×C₆₇	C₂²	1	2	yes	—
77	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₆₇	C₂²	1	2	yes	—
82	C₈×D₄×C₆₇	C₂²	1	2	yes	—
83	#433×C₆₇	C₂²	1	2	yes	—
84	#433×C₆₇	C₂²	1	2	yes	—
85	#433×C₆₇	C₂²	1	2	yes	—
86	#433×C₆₇	C₂²	1	2	yes	—
87	#433×C₆₇	C₂²	1	2	yes	—
88	#433×C₆₇	C₂²	1	2	yes	—
89	#433×C₆₇	C₂²	1	2	yes	—
90	#433×C₆₇	C₂²	1	2	yes	—
91	#433×C₆₇	C₂²	1	2	yes	—
92	#433×C₆₇	C₂²	1	2	yes	—
93	#432×C₆₇	C₂²	1	1	yes	characteristic
94	#432×C₆₇	C₂²	1	1	yes	characteristic
95	#432×C₆₇	C₂²	1	2	yes	—
96	#431×C₆₇	C₂²	1	2	yes	—
97	#431×C₆₇	C₂²	1	2	yes	—
98	#431×C₆₇	C₂²	1	2	yes	—
99	#424×C₆₇	C₂²	1	1	yes	characteristic
100	#424×C₆₇	C₂²	1	1	yes	characteristic
101	#424×C₆₇	C₂²	1	2	yes	—
102	#424×C₆₇	C₂²	1	2	yes	—
103	#424×C₆₇	C₂²	1	2	yes	—
104	#424×C₆₇	C₂²	1	2	yes	—
105	#423×C₆₇	C₂²	1	1	yes	characteristic
106	#423×C₆₇	C₂²	1	2	yes	—
107	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
108	#405×C₆₇	C₂²	1	1	yes	characteristic
109	#405×C₆₇	C₂²	1	1	yes	characteristic
110	#405×C₆₇	C₂²	1	2	yes	—
111	#405×C₆₇	C₂²	1	2	yes	—
112	#405×C₆₇	C₂²	1	2	yes	—
113	#405×C₆₇	C₂²	1	2	yes	—
114	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
115	C₂×#97×C₆₇	C₂²	1	2	yes	—
116	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
118	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
119	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
125	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
127	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
128	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
130	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
131	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
132	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
133	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
134	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
135	#126×C₆₇	C₂×C₄	1	2	yes	—
136	#126×C₆₇	C₂×C₄	1	2	yes	—
137	#126×C₆₇	C₂×C₄	1	2	yes	—
138	#126×C₆₇	C₂×C₄	1	2	yes	—
139	#126×C₆₇	C₂×C₄	1	2	yes	—
140	#126×C₆₇	C₂×C₄	1	2	yes	—
141	#126×C₆₇	C₂×C₄	1	2	yes	—
142	#126×C₆₇	C₂×C₄	1	2	yes	—
143	#126×C₆₇	C₂×C₄	1	2	yes	—
144	#126×C₆₇	C₂×C₄	1	2	yes	—
145	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
146	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
147	#125×C₆₇	C₂×C₄	1	2	yes	—
148	#125×C₆₇	C₂×C₄	1	2	yes	—
149	#125×C₆₇	C₂×C₄	1	2	yes	—
150	#125×C₆₇	C₂×C₄	1	2	yes	—
151	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
152	#125×C₆₇	C₂×C₄	1	2	yes	—
153	#125×C₆₇	C₂×C₄	1	2	yes	—
154	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
155	#125×C₆₇	C₂×C₄	1	2	yes	—
156	#125×C₆₇	C₂×C₄	1	2	yes	—
157	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
158	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
159	#124×C₆₇	C₂×C₄	1	2	yes	—
160	#124×C₆₇	C₂×C₄	1	2	yes	—
161	#124×C₆₇	C₂×C₄	1	2	yes	—
162	#124×C₆₇	C₂×C₄	1	2	yes	—
163	#123×C₆₇	C₂×C₄	1	2	yes	—
164	#123×C₆₇	C₂×C₄	1	2	yes	—
165	#123×C₆₇	C₂×C₄	1	2	yes	—
166	#123×C₆₇	C₂×C₄	1	2	yes	—
167	#123×C₆₇	C₂×C₄	1	2	yes	—
168	#123×C₆₇	C₂×C₄	1	2	yes	—
169	#123×C₆₇	C₂×C₄	1	2	yes	—
170	#123×C₆₇	C₂×C₄	1	2	yes	—
171	#123×C₆₇	C₂×C₄	1	2	yes	—
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
174	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
175	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
177	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
183	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
186	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
187	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
189	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
190	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
191	#121×C₆₇	C₂×C₄	1	2	yes	—
192	#121×C₆₇	C₂×C₄	1	2	yes	—
193	#121×C₆₇	C₂×C₄	1	2	yes	—
194	#121×C₆₇	C₂×C₄	1	2	yes	—
195	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
196	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
197	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
198	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
199	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
200	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₄×D₄×C₆₇	C₂³	1	2	yes	—
204	C₄×D₄×C₆₇	C₂³	1	2	yes	—
205	C₄×D₄×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	C₂³	1	2	yes	—
207	#117×C₆₇	C₂³	1	2	yes	—
208	#117×C₆₇	C₂³	1	2	yes	—
209	#117×C₆₇	C₂³	1	2	yes	—
210	#117×C₆₇	C₂³	1	1	yes	characteristic
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
218	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
220	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
221	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
222	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
223	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
224	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
225	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
226	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
227	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
228	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	C₄⋊C₈×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	1	yes	characteristic
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
240	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
241	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
242	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
243	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
244	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
248	#97×C₆₇	C₂³	1	2	yes	—
249	#97×C₆₇	C₂³	1	2	yes	—
250	#97×C₆₇	C₂³	1	2	yes	—
251	#97×C₆₇	C₂³	1	2	yes	—
252	#97×C₆₇	C₂³	1	2	yes	—
253	#97×C₆₇	C₂³	1	2	yes	—
254	#97×C₆₇	C₂³	1	2	yes	—
255	#97×C₆₇	C₂³	1	2	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	2	yes	—
258	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₇	C₂³	1	2	yes	—
263	C₄×C₈×C₆₇	C₂³	1	2	yes	—
264	C₄×C₈×C₆₇	C₂³	1	2	yes	—
265	C₄×C₈×C₆₇	C₂³	1	2	yes	—
266	C₄×C₈×C₆₇	C₂³	1	2	yes	—
267	C₄×C₈×C₆₇	C₂³	1	2	yes	—
268	C₄×C₈×C₆₇	C₂³	1	2	yes	—
269	C₄×C₈×C₆₇	C₂³	1	2	yes	—
270	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
271	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
272	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
273	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
274	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
275	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
276	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
278	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
279	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
280	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
281	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	M₁₆×C₆₇	—	2	4	no	—
292	M₁₆×C₆₇	—	4	1	no	—
293	M₁₆×C₆₇	—	4	2	no	—
294	M₁₆×C₆₇	—	4	2	no	—
295	M₁₆×C₆₇	—	4	2	no	—
296	M₁₆×C₆₇	—	4	1	no	—
297	C₂×C₈×C₆₇	—	2	2	no	—
298	C₂×C₈×C₆₇	—	2	4	no	—
299	C₂×C₈×C₆₇	—	4	2	no	—
300	C₂×C₈×C₆₇	—	4	1	no	—
301	C₂×C₈×C₆₇	—	4	2	no	—
302	C₂×C₈×C₆₇	—	4	2	no	—
303	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
305	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
306	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
307	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
311	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
312	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
315	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
318	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
320	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
321	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
322	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
324	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
328	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
329	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
330	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
333	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
334	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
335	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
336	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
341	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
344	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
345	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
347	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
348	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
349	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
351	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
358	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
364	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
365	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
366	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
368	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
369	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
370	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
371	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
372	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
373	C₄²×C₆₇	C₂⁴	1	2	yes	—
374	C₄²×C₆₇	C₂⁴	1	2	yes	—
375	C₄²×C₆₇	C₂⁴	1	2	yes	—
376	C₄²×C₆₇	C₂⁴	1	2	yes	—
377	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
380	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
381	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
382	Q₈×C₆₇	—	4	1	no	—
383	Q₈×C₆₇	—	4	1	no	—
384	Q₈×C₆₇	—	4	2	no	—
385	Q₈×C₆₇	—	4	2	no	—
386	Q₈×C₆₇	—	4	2	no	—
387	Q₈×C₆₇	—	4	2	no	—
388	D₄×C₆₇	—	4	1	no	—
389	D₄×C₆₇	—	4	1	no	—
390	D₄×C₆₇	—	4	2	no	—
391	D₄×C₆₇	—	4	2	no	—
392	D₄×C₆₇	—	4	2	no	—
393	D₄×C₆₇	—	4	2	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	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	4	1	no	—
401	C₂×C₄×C₆₇	—	4	1	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	4	2	no	—
404	C₂×C₄×C₆₇	—	4	2	no	—
405	C₂×C₄×C₆₇	—	4	2	no	—
406	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
407	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
414	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
416	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
422	C₈×C₆₇	—	2	1	no	—
423	C₈×C₆₇	—	2	2	no	—
424	C₈×C₆₇	—	2	2	no	—
425	C₈×C₆₇	—	2	1	no	—
426	C₈×C₆₇	—	2	2	no	—
427	C₈×C₆₇	—	2	2	no	—
428	C₈×C₆₇	—	2	1	no	—
429	C₈×C₆₇	—	2	2	no	—
430	C₈×C₆₇	—	2	2	no	—
431	C₈×C₆₇	2₋¹⁺⁴	1	2	yes	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	1	no	—
436	C₂²×C₆₇	—	2	1	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	2	no	—
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	2	1	no	—
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	1	no	—
452	C₄×C₆₇	—	2	1	no	—
453	C₄×C₆₇	—	2	2	no	—
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	2	no	—
456	C₄×C₆₇	—	2	2	no	—
457	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
458	C₄×C₆₇	#585	1	1	yes	characteristic
459	#60346	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂×C₆₇	—	4	1	no	—
461	C₂×C₆₇	—	4	2	no	—
462	C₂×C₆₇	—	4	2	no	—
463	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₆₇	#3573	1	1	yes	characteristic
465	C₂×C₆₇	#3573	1	1	yes	characteristic
466	#3531	C₂×C₆₇	1	1	yes	characteristic
467	#2995	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#2995	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#2994	C₂×C₆₇	1	2	yes	complemented
470	#2993	C₂×C₆₇	1	2	yes	complemented
471	#2993	C₂×C₆₇	1	2	yes	complemented
472	#2992	C₂×C₆₇	1	2	yes	complemented
473	#2987	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#2986	C₂×C₆₇	1	2	yes	complemented
475	#2985	C₂×C₆₇	1	2	yes	complemented
476	#2969	C₂×C₆₇	1	2	yes	complemented
477	#2968	C₂×C₆₇	1	2	yes	complemented
478	#2968	C₂×C₆₇	1	2	yes	complemented
479	#2967	C₂×C₆₇	1	2	yes	complemented
480	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#2962	C₂×C₆₇	1	2	yes	complemented
483	#2961	C₂×C₆₇	1	2	yes	complemented
484	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
485	C₆₇	#60346	1	1	yes	characteristic, direct product factor, Sylow
486	#564	C₄×C₆₇	1	1	yes	characteristic
487	#563	C₄×C₆₇	1	2	yes	—
488	#563	C₄×C₆₇	1	2	yes	—
489	#563	C₄×C₆₇	1	2	yes	—
490	#563	C₄×C₆₇	1	1	yes	characteristic
491	#563	C₄×C₆₇	1	2	yes	—
492	#563	C₄×C₆₇	1	1	yes	characteristic
493	#562	C₄×C₆₇	1	2	yes	—
494	#562	C₄×C₆₇	1	2	yes	—
495	#562	C₄×C₆₇	1	1	yes	characteristic
496	#533	C₂²×C₆₇	1	1	yes	characteristic
497	#533	C₂²×C₆₇	1	2	yes	—
498	#533	C₂²×C₆₇	1	2	yes	—
499	#529	C₂²×C₆₇	1	1	yes	characteristic
500	#529	C₂²×C₆₇	1	1	yes	characteristic
501	#529	C₂²×C₆₇	1	2	yes	—
502	#529	C₂²×C₆₇	1	2	yes	—
503	#529	C₂²×C₆₇	1	2	yes	—
504	#529	C₂²×C₆₇	1	2	yes	—
505	#446	C₂²×C₆₇	1	2	yes	—
506	#446	C₂²×C₆₇	1	2	yes	—
507	#446	C₂²×C₆₇	1	1	yes	characteristic
508	#446	C₂²×C₆₇	1	2	yes	—
509	#446	C₂²×C₆₇	1	2	yes	—
510	#446	C₂²×C₆₇	1	2	yes	—
511	#446	C₂²×C₆₇	1	2	yes	—
512	#446	C₂²×C₆₇	1	2	yes	—
513	#446	C₂²×C₆₇	1	2	yes	—
514	#446	C₂²×C₆₇	1	2	yes	—
515	#446	C₂²×C₆₇	1	2	yes	—
516	#446	C₂²×C₆₇	1	2	yes	—
517	#446	C₂²×C₆₇	1	1	yes	characteristic
518	#446	C₂²×C₆₇	1	2	yes	—
519	#446	C₂²×C₆₇	1	2	yes	—
520	#446	C₂²×C₆₇	1	2	yes	—
521	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
522	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
523	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
524	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
525	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
526	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
527	#436	C₂²×C₆₇	1	1	yes	characteristic
528	#436	C₂²×C₆₇	1	1	yes	characteristic
529	#436	C₂²×C₆₇	1	2	yes	—
530	#436	C₂²×C₆₇	1	2	yes	—
531	#436	C₂²×C₆₇	1	2	yes	—
532	#436	C₂²×C₆₇	1	2	yes	—
533	#435	C₂²×C₆₇	1	2	yes	—
534	#435	C₂²×C₆₇	1	2	yes	—
535	#435	C₂²×C₆₇	1	2	yes	—
536	#435	C₂²×C₆₇	1	2	yes	—
537	#435	C₂²×C₆₇	1	2	yes	—
538	#435	C₂²×C₆₇	1	2	yes	—
539	#435	C₂²×C₆₇	1	2	yes	—
540	#435	C₂²×C₆₇	1	2	yes	—
541	#435	C₂²×C₆₇	1	2	yes	—
542	#435	C₂²×C₆₇	1	2	yes	—
543	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₈×D₄	C₂²×C₆₇	1	2	yes	—
545	C₈×D₄	C₂²×C₆₇	1	2	yes	—
546	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
547	C₈×D₄	C₂²×C₆₇	1	2	yes	—
548	C₈×D₄	C₂²×C₆₇	1	2	yes	—
549	#433	C₂²×C₆₇	1	2	yes	—
550	#433	C₂²×C₆₇	1	2	yes	—
551	#433	C₂²×C₆₇	1	2	yes	—
552	#433	C₂²×C₆₇	1	2	yes	—
553	#433	C₂²×C₆₇	1	2	yes	—
554	#433	C₂²×C₆₇	1	2	yes	—
555	#433	C₂²×C₆₇	1	2	yes	—
556	#433	C₂²×C₆₇	1	2	yes	—
557	#433	C₂²×C₆₇	1	2	yes	—
558	#433	C₂²×C₆₇	1	2	yes	—
559	#432	C₂²×C₆₇	1	1	yes	characteristic
560	#432	C₂²×C₆₇	1	1	yes	characteristic
561	#432	C₂²×C₆₇	1	2	yes	—
562	#431	C₂²×C₆₇	1	2	yes	—
563	#431	C₂²×C₆₇	1	2	yes	—
564	#431	C₂²×C₆₇	1	2	yes	—
565	#424	C₂²×C₆₇	1	1	yes	characteristic
566	#424	C₂²×C₆₇	1	1	yes	characteristic
567	#424	C₂²×C₆₇	1	2	yes	—
568	#424	C₂²×C₆₇	1	2	yes	—
569	#424	C₂²×C₆₇	1	2	yes	—
570	#424	C₂²×C₆₇	1	2	yes	—
571	#423	C₂²×C₆₇	1	1	yes	characteristic
572	#423	C₂²×C₆₇	1	2	yes	—
573	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
574	#405	C₂²×C₆₇	1	1	yes	characteristic
575	#405	C₂²×C₆₇	1	1	yes	characteristic
576	#405	C₂²×C₆₇	1	2	yes	—
577	#405	C₂²×C₆₇	1	2	yes	—
578	#405	C₂²×C₆₇	1	2	yes	—
579	#405	C₂²×C₆₇	1	2	yes	—
580	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
581	C₂×#97	C₂²×C₆₇	1	2	yes	—
582	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
584	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
585	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
587	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
588	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
591	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
592	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
593	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
594	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
595	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
596	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
597	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
598	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
599	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
600	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
601	#126	C₂×C₄×C₆₇	1	2	yes	—
602	#126	C₂×C₄×C₆₇	1	2	yes	—
603	#126	C₂×C₄×C₆₇	1	2	yes	—
604	#126	C₂×C₄×C₆₇	1	2	yes	—
605	#126	C₂×C₄×C₆₇	1	2	yes	—
606	#126	C₂×C₄×C₆₇	1	2	yes	—
607	#126	C₂×C₄×C₆₇	1	2	yes	—
608	#126	C₂×C₄×C₆₇	1	2	yes	—
609	#126	C₂×C₄×C₆₇	1	2	yes	—
610	#126	C₂×C₄×C₆₇	1	2	yes	—
611	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
612	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
613	#125	C₂×C₄×C₆₇	1	2	yes	—
614	#125	C₂×C₄×C₆₇	1	2	yes	—
615	#125	C₂×C₄×C₆₇	1	2	yes	—
616	#125	C₂×C₄×C₆₇	1	2	yes	—
617	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
618	#125	C₂×C₄×C₆₇	1	2	yes	—
619	#125	C₂×C₄×C₆₇	1	2	yes	—
620	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
621	#125	C₂×C₄×C₆₇	1	2	yes	—
622	#125	C₂×C₄×C₆₇	1	2	yes	—
623	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
624	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
625	#124	C₂×C₄×C₆₇	1	2	yes	—
626	#124	C₂×C₄×C₆₇	1	2	yes	—
627	#124	C₂×C₄×C₆₇	1	2	yes	—
628	#124	C₂×C₄×C₆₇	1	2	yes	—
629	#123	C₂×C₄×C₆₇	1	2	yes	—
630	#123	C₂×C₄×C₆₇	1	2	yes	—
631	#123	C₂×C₄×C₆₇	1	2	yes	—
632	#123	C₂×C₄×C₆₇	1	2	yes	—
633	#123	C₂×C₄×C₆₇	1	2	yes	—
634	#123	C₂×C₄×C₆₇	1	2	yes	—
635	#123	C₂×C₄×C₆₇	1	2	yes	—
636	#123	C₂×C₄×C₆₇	1	2	yes	—
637	#123	C₂×C₄×C₆₇	1	2	yes	—
638	#123	C₂×C₄×C₆₇	1	2	yes	—
639	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
640	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
641	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
642	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
643	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
644	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
645	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
646	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
647	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
648	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
649	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
650	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
651	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
652	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
653	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
654	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
655	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
656	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
657	#121	C₂×C₄×C₆₇	1	2	yes	—
658	#121	C₂×C₄×C₆₇	1	2	yes	—
659	#121	C₂×C₄×C₆₇	1	2	yes	—
660	#121	C₂×C₄×C₆₇	1	2	yes	—
661	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
662	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
663	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
664	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
665	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
666	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
667	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₄×D₄	C₂³×C₆₇	1	2	yes	—
670	C₄×D₄	C₂³×C₆₇	1	2	yes	—
671	C₄×D₄	C₂³×C₆₇	1	2	yes	—
672	C₄×D₄	C₂³×C₆₇	1	2	yes	—
673	#117	C₂³×C₆₇	1	2	yes	—
674	#117	C₂³×C₆₇	1	2	yes	—
675	#117	C₂³×C₆₇	1	2	yes	—
676	#117	C₂³×C₆₇	1	1	yes	characteristic
677	#117	C₂³×C₆₇	1	2	yes	—
678	#117	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
682	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
683	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
685	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
686	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
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	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
692	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
693	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
694	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
695	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
696	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
697	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
698	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
699	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
700	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
701	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
702	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
703	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
706	C₂²⋊C₈	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	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
714	#97	C₂³×C₆₇	1	2	yes	—
715	#97	C₂³×C₆₇	1	2	yes	—
716	#97	C₂³×C₆₇	1	2	yes	—
717	#97	C₂³×C₆₇	1	2	yes	—
718	#97	C₂³×C₆₇	1	2	yes	—
719	#97	C₂³×C₆₇	1	2	yes	—
720	#97	C₂³×C₆₇	1	2	yes	—
721	#97	C₂³×C₆₇	1	2	yes	—
722	#97	C₂³×C₆₇	1	2	yes	—
723	#97	C₂³×C₆₇	1	2	yes	—
724	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₆₇	1	2	yes	—
729	C₄×C₈	C₂³×C₆₇	1	2	yes	—
730	C₄×C₈	C₂³×C₆₇	1	2	yes	—
731	C₄×C₈	C₂³×C₆₇	1	2	yes	—
732	C₄×C₈	C₂³×C₆₇	1	2	yes	—
733	C₄×C₈	C₂³×C₆₇	1	2	yes	—
734	C₄×C₈	C₂³×C₆₇	1	2	yes	—
735	C₄×C₈	C₂³×C₆₇	1	2	yes	—
736	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
737	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
739	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
740	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
741	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
742	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
743	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
744	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
745	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
746	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
747	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
748	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
751	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
752	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
753	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
757	M₁₆	—	2	4	no	—
758	M₁₆	—	4	1	no	—
759	M₁₆	—	4	2	no	—
760	M₁₆	—	4	2	no	—
761	M₁₆	—	4	2	no	—
762	M₁₆	—	4	1	no	—
763	C₂×C₈	—	2	2	no	—
764	C₂×C₈	—	2	4	no	—
765	C₂×C₈	—	4	2	no	—
766	C₂×C₈	—	4	1	no	—
767	C₂×C₈	—	4	2	no	—
768	C₂×C₈	—	4	2	no	—
769	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
770	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
771	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
772	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
773	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
774	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
776	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
777	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
778	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
780	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
781	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
782	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
784	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
786	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
787	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
788	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
806	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
811	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
812	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
817	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
818	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
833	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
834	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
835	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
836	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
837	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
838	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
839	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
841	C₄²	C₂⁴×C₆₇	1	2	yes	—
842	C₄²	C₂⁴×C₆₇	1	2	yes	—
843	C₄²	C₂⁴×C₆₇	1	2	yes	—
844	C₄²	C₂⁴×C₆₇	1	2	yes	—
845	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
846	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
847	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
848	Q₈	—	4	1	no	—
849	Q₈	—	4	1	no	—
850	Q₈	—	4	2	no	—
851	Q₈	—	4	2	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	4	2	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
873	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
874	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
875	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
876	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
877	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
879	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
882	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
883	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
887	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
888	C₈	—	2	1	no	—
889	C₈	—	2	2	no	—
890	C₈	—	2	2	no	—
891	C₈	—	2	1	no	—
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	2	no	—
896	C₈	—	2	2	no	—
897	C₈	2₋¹⁺⁴×C₆₇	1	2	yes	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
924	C₄	#585×C₆₇	1	1	yes	characteristic
925	C₂	—	4	1	no	—
926	C₂	—	4	2	no	—
927	C₂	—	4	2	no	—
928	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
929	C₂	C₆₇×#3573	1	1	yes	characteristic
930	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3531	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2995	C₂	semidirect
4. C₆₇×#2994	C₂	semidirect
5. C₆₇×#2993	C₂	semidirect
6. C₆₇×#2993	C₂	semidirect
7. C₆₇×#2992	C₂	semidirect
8. C₆₇×#2987	C₂	semidirect
9. C₆₇×#2986	C₂	semidirect
10. C₆₇×#2985	C₂	semidirect
11. C₆₇×#2969	C₂	semidirect
12. C₆₇×#2968	C₂	semidirect
13. C₆₇×#2968	C₂	semidirect
14. C₆₇×#2967	C₂	semidirect
15. C₆₇×#2966	C₂	semidirect
16. C₆₇×#2966	C₂	semidirect
17. C₆₇×#2962	C₂	semidirect
18. C₆₇×#2961	C₂	semidirect
19. C₆₇×#2960	C₂	semidirect
459. #60346	C₆₇	direct (N × H)
467. #2995	C₂×C₆₇	semidirect
468. #2995	C₂×C₆₇	semidirect
469. #2994	C₂×C₆₇	semidirect
470. #2993	C₂×C₆₇	semidirect
471. #2993	C₂×C₆₇	semidirect
472. #2992	C₂×C₆₇	semidirect
473. #2987	C₂×C₆₇	semidirect
474. #2986	C₂×C₆₇	semidirect
475. #2985	C₂×C₆₇	semidirect
476. #2969	C₂×C₆₇	semidirect
477. #2968	C₂×C₆₇	semidirect
478. #2968	C₂×C₆₇	semidirect
479. #2967	C₂×C₆₇	semidirect
480. #2966	C₂×C₆₇	semidirect
481. #2966	C₂×C₆₇	semidirect
482. #2962	C₂×C₆₇	semidirect
483. #2961	C₂×C₆₇	semidirect
484. #2960	C₂×C₆₇	semidirect
485. C₆₇	#60346	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×#3531	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2987	2
C₆₇×#2986	2
C₆₇×#2985	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2962	2
C₆₇×#2961	2
C₆₇×#2960	2
#60346	67

Subgroups — C67×#60346 #30739597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60346 #30739597