Subgroups — C₆₇×#60340 #30739591

Order 17152.

1666 conjugacy classes of subgroups.

The subgroup lattice has 944 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	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2990	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2987	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2985	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2970	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	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₆₇	C₄	1	1	yes	characteristic
21	#542×C₆₇	C₄	1	2	yes	—
22	#542×C₆₇	C₄	1	2	yes	—
23	#541×C₆₇	C₄	1	2	yes	—
24	#541×C₆₇	C₄	1	2	yes	—
25	#539×C₆₇	C₄	1	1	yes	characteristic
26	#539×C₆₇	C₄	1	1	yes	characteristic
27	#539×C₆₇	C₄	1	2	yes	—
28	#537×C₆₇	C₄	1	1	yes	characteristic
29	#536×C₆₇	C₄	1	2	yes	—
30	#533×C₆₇	C₂²	1	2	yes	—
31	#533×C₆₇	C₂²	1	2	yes	—
32	#529×C₆₇	C₂²	1	1	yes	characteristic
33	#529×C₆₇	C₂²	1	1	yes	characteristic
34	#529×C₆₇	C₂²	1	2	yes	—
35	#529×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	2	yes	—
37	C₄×#41×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	#446×C₆₇	C₂²	1	2	yes	—
40	#446×C₆₇	C₂²	1	2	yes	—
41	#446×C₆₇	C₂²	1	2	yes	—
42	#446×C₆₇	C₂²	1	2	yes	—
43	#446×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
52	#446×C₆₇	C₂²	1	2	yes	—
53	#446×C₆₇	C₂²	1	1	yes	characteristic
54	#446×C₆₇	C₂²	1	2	yes	—
55	#446×C₆₇	C₂²	1	2	yes	—
56	#446×C₆₇	C₂²	1	2	yes	—
57	#446×C₆₇	C₂²	1	2	yes	—
58	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
60	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
61	#436×C₆₇	C₂²	1	1	yes	characteristic
62	#436×C₆₇	C₂²	1	1	yes	characteristic
63	#436×C₆₇	C₂²	1	2	yes	—
64	#435×C₆₇	C₂²	1	2	yes	—
65	#435×C₆₇	C₂²	1	2	yes	—
66	#435×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	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₆₇	C₂²	1	2	yes	—
78	C₈×D₄×C₆₇	C₂²	1	2	yes	—
79	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₆₇	C₂²	1	2	yes	—
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	#432×C₆₇	C₂²	1	1	yes	characteristic
92	#432×C₆₇	C₂²	1	1	yes	characteristic
93	#432×C₆₇	C₂²	1	2	yes	—
94	#432×C₆₇	C₂²	1	2	yes	—
95	#432×C₆₇	C₂²	1	2	yes	—
96	#432×C₆₇	C₂²	1	2	yes	—
97	#431×C₆₇	C₂²	1	2	yes	—
98	#431×C₆₇	C₂²	1	2	yes	—
99	#424×C₆₇	C₂²	1	2	yes	—
100	#424×C₆₇	C₂²	1	2	yes	—
101	#424×C₆₇	C₂²	1	2	yes	—
102	#424×C₆₇	C₂²	1	2	yes	—
103	#423×C₆₇	C₂²	1	2	yes	—
104	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
106	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
107	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
108	#405×C₆₇	C₂²	1	2	yes	—
109	#405×C₆₇	C₂²	1	2	yes	—
110	#405×C₆₇	C₂²	1	2	yes	—
111	#405×C₆₇	C₂²	1	2	yes	—
112	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
113	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#97×C₆₇	C₂²	1	2	yes	—
116	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
118	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
127	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
129	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
130	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
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	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
144	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
145	#125×C₆₇	C₂×C₄	1	2	yes	—
146	#125×C₆₇	C₂×C₄	1	2	yes	—
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	2	yes	—
152	#124×C₆₇	C₂×C₄	1	2	yes	—
153	#124×C₆₇	C₂×C₄	1	2	yes	—
154	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
155	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
156	#124×C₆₇	C₂×C₄	1	2	yes	—
157	#123×C₆₇	C₂×C₄	1	2	yes	—
158	#123×C₆₇	C₂×C₄	1	2	yes	—
159	#123×C₆₇	C₂×C₄	1	2	yes	—
160	#123×C₆₇	C₂×C₄	1	2	yes	—
161	#123×C₆₇	C₂×C₄	1	2	yes	—
162	#123×C₆₇	C₂×C₄	1	2	yes	—
163	#123×C₆₇	C₂×C₄	1	2	yes	—
164	#123×C₆₇	C₂×C₄	1	2	yes	—
165	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
166	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
167	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
168	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
169	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
170	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
171	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
172	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
173	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
174	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
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	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
179	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
180	#121×C₆₇	C₂×C₄	1	2	yes	—
181	#121×C₆₇	C₂×C₄	1	2	yes	—
182	#121×C₆₇	C₂×C₄	1	2	yes	—
183	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
184	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
185	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
186	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
187	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
190	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
192	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
193	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
194	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
195	C₄×D₄×C₆₇	C₂³	1	2	yes	—
196	C₄×D₄×C₆₇	C₂³	1	2	yes	—
197	C₄×D₄×C₆₇	C₂³	1	2	yes	—
198	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	#117×C₆₇	C₂×C₄	1	2	yes	—
202	#117×C₆₇	C₂×C₄	1	2	yes	—
203	#117×C₆₇	C₂×C₄	1	2	yes	—
204	#117×C₆₇	C₂³	1	2	yes	—
205	#117×C₆₇	C₂³	1	2	yes	—
206	#117×C₆₇	C₂³	1	2	yes	—
207	#117×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×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	1	yes	characteristic
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
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	#97×C₆₇	C₂³	1	2	yes	—
259	#97×C₆₇	C₂³	1	2	yes	—
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
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	#41×C₆₇	—	4	4	no	—
271	C₂×Q₈×C₆₇	—	4	2	no	—
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	1	yes	characteristic
276	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
277	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
282	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
283	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	M₁₆×C₆₇	—	2	4	no	—
298	M₁₆×C₆₇	—	4	2	no	—
299	M₁₆×C₆₇	—	4	2	no	—
300	M₁₆×C₆₇	—	4	2	no	—
301	C₂×C₈×C₆₇	—	2	2	no	—
302	C₂×C₈×C₆₇	—	2	4	no	—
303	C₂×C₈×C₆₇	—	4	2	no	—
304	C₂×C₈×C₆₇	—	4	1	no	—
305	C₂×C₈×C₆₇	—	4	1	no	—
306	C₂×C₈×C₆₇	—	4	1	no	—
307	C₂×C₈×C₆₇	—	4	2	no	—
308	C₂×C₈×C₆₇	—	4	2	no	—
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	2	yes	—
313	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
315	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
316	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
318	C₂×C₈×C₆₇	C₂⁴	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	2	yes	—
323	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
324	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
325	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
326	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	2	yes	—
332	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
340	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
341	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
343	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
348	C₄⋊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	2	yes	—
368	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
369	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
370	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
371	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
372	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
374	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
375	C₄²×C₆₇	C₂⁴	1	2	yes	—
376	C₄²×C₆₇	C₂⁴	1	2	yes	—
377	C₄²×C₆₇	C₂⁴	1	2	yes	—
378	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₄²×C₆₇	C₂⁴	1	2	yes	—
381	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
382	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
383	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
384	Q₈×C₆₇	—	4	2	no	—
385	Q₈×C₆₇	—	4	2	no	—
386	Q₈×C₆₇	—	4	1	no	—
387	Q₈×C₆₇	—	4	1	no	—
388	Q₈×C₆₇	—	4	2	no	—
389	Q₈×C₆₇	—	4	2	no	—
390	D₄×C₆₇	—	2	4	no	—
391	D₄×C₆₇	—	2	4	no	—
392	D₄×C₆₇	—	4	1	no	—
393	D₄×C₆₇	—	4	1	no	—
394	D₄×C₆₇	—	4	2	no	—
395	D₄×C₆₇	—	4	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	1	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	4	1	no	—
406	C₂×C₄×C₆₇	—	4	2	no	—
407	C₂×C₄×C₆₇	—	4	2	no	—
408	C₂×C₄×C₆₇	—	4	1	no	—
409	C₂×C₄×C₆₇	—	4	1	no	—
410	C₂×C₄×C₆₇	—	4	2	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
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	2	yes	—
416	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
419	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
425	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
426	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
428	C₈×C₆₇	—	2	1	no	—
429	C₈×C₆₇	—	2	2	no	—
430	C₈×C₆₇	—	2	2	no	—
431	C₈×C₆₇	—	2	1	no	—
432	C₈×C₆₇	—	2	2	no	—
433	C₈×C₆₇	—	2	2	no	—
434	C₈×C₆₇	—	2	2	no	—
435	C₈×C₆₇	—	2	1	no	—
436	C₈×C₆₇	—	2	2	no	—
437	C₈×C₆₇	2₋¹⁺⁴	1	2	yes	—
438	C₂²×C₆₇	—	2	1	no	—
439	C₂²×C₆₇	—	2	1	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	#568	1	2	yes	—
447	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
448	C₄×C₆₇	—	2	1	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	2	no	—
452	C₄×C₆₇	—	2	1	no	—
453	C₄×C₆₇	—	2	1	no	—
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	2	no	—
456	C₄×C₆₇	—	2	2	no	—
457	C₄×C₆₇	—	2	2	no	—
458	C₄×C₆₇	—	2	1	no	—
459	C₄×C₆₇	—	2	1	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₄×C₆₇	#585	1	1	yes	characteristic
465	#60340	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂×C₆₇	—	2	2	no	—
467	C₂×C₆₇	—	4	2	no	—
468	C₂×C₆₇	—	4	2	no	—
469	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
470	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
471	C₂×C₆₇	#3573	1	1	yes	characteristic
472	#3461	C₂×C₆₇	1	1	yes	characteristic
473	#2995	C₂×C₆₇	1	2	yes	complemented
474	#2994	C₂×C₆₇	1	2	yes	complemented
475	#2992	C₂×C₆₇	1	1	yes	characteristic, complemented
476	#2992	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#2992	C₂×C₆₇	1	2	yes	complemented
478	#2990	C₂×C₆₇	1	2	yes	complemented
479	#2987	C₂×C₆₇	1	2	yes	complemented
480	#2985	C₂×C₆₇	1	2	yes	complemented
481	#2983	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#2970	C₂×C₆₇	1	2	yes	complemented
483	#2968	C₂×C₆₇	1	2	yes	complemented
484	#2968	C₂×C₆₇	1	2	yes	complemented
485	#2967	C₂×C₆₇	1	2	yes	complemented
486	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2962	C₂×C₆₇	1	2	yes	complemented
489	#2961	C₂×C₆₇	1	2	yes	complemented
490	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
491	C₆₇	#60340	1	1	yes	characteristic, direct product factor, Sylow
492	#544	C₄×C₆₇	1	1	yes	characteristic
493	#542	C₄×C₆₇	1	2	yes	—
494	#542	C₄×C₆₇	1	2	yes	—
495	#541	C₄×C₆₇	1	2	yes	—
496	#541	C₄×C₆₇	1	2	yes	—
497	#539	C₄×C₆₇	1	1	yes	characteristic
498	#539	C₄×C₆₇	1	1	yes	characteristic
499	#539	C₄×C₆₇	1	2	yes	—
500	#537	C₄×C₆₇	1	1	yes	characteristic
501	#536	C₄×C₆₇	1	2	yes	—
502	#533	C₂²×C₆₇	1	2	yes	—
503	#533	C₂²×C₆₇	1	2	yes	—
504	#529	C₂²×C₆₇	1	1	yes	characteristic
505	#529	C₂²×C₆₇	1	1	yes	characteristic
506	#529	C₂²×C₆₇	1	2	yes	—
507	#529	C₂²×C₆₇	1	2	yes	—
508	#529	C₂²×C₆₇	1	2	yes	—
509	C₄×#41	C₂²×C₆₇	1	2	yes	—
510	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
516	#446	C₂²×C₆₇	1	2	yes	—
517	#446	C₂²×C₆₇	1	2	yes	—
518	#446	C₂²×C₆₇	1	2	yes	—
519	#446	C₂²×C₆₇	1	2	yes	—
520	#446	C₂²×C₆₇	1	2	yes	—
521	#446	C₂²×C₆₇	1	2	yes	—
522	#446	C₂²×C₆₇	1	2	yes	—
523	#446	C₂²×C₆₇	1	2	yes	—
524	#446	C₂²×C₆₇	1	2	yes	—
525	#446	C₂²×C₆₇	1	1	yes	characteristic
526	#446	C₂²×C₆₇	1	2	yes	—
527	#446	C₂²×C₆₇	1	2	yes	—
528	#446	C₂²×C₆₇	1	2	yes	—
529	#446	C₂²×C₆₇	1	2	yes	—
530	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
531	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
532	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
533	#436	C₂²×C₆₇	1	1	yes	characteristic
534	#436	C₂²×C₆₇	1	1	yes	characteristic
535	#436	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	#435	C₂²×C₆₇	1	2	yes	—
544	#435	C₂²×C₆₇	1	2	yes	—
545	#435	C₂²×C₆₇	1	2	yes	—
546	#435	C₂²×C₆₇	1	2	yes	—
547	#435	C₂²×C₆₇	1	2	yes	—
548	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
549	C₈×D₄	C₂²×C₆₇	1	2	yes	—
550	C₈×D₄	C₂²×C₆₇	1	2	yes	—
551	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
552	C₈×D₄	C₂²×C₆₇	1	2	yes	—
553	C₈×D₄	C₂²×C₆₇	1	2	yes	—
554	C₈×D₄	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	#433	C₂²×C₆₇	1	2	yes	—
560	#433	C₂²×C₆₇	1	2	yes	—
561	#433	C₂²×C₆₇	1	2	yes	—
562	#433	C₂²×C₆₇	1	2	yes	—
563	#432	C₂²×C₆₇	1	1	yes	characteristic
564	#432	C₂²×C₆₇	1	1	yes	characteristic
565	#432	C₂²×C₆₇	1	2	yes	—
566	#432	C₂²×C₆₇	1	2	yes	—
567	#432	C₂²×C₆₇	1	2	yes	—
568	#432	C₂²×C₆₇	1	2	yes	—
569	#431	C₂²×C₆₇	1	2	yes	—
570	#431	C₂²×C₆₇	1	2	yes	—
571	#424	C₂²×C₆₇	1	2	yes	—
572	#424	C₂²×C₆₇	1	2	yes	—
573	#424	C₂²×C₆₇	1	2	yes	—
574	#424	C₂²×C₆₇	1	2	yes	—
575	#423	C₂²×C₆₇	1	2	yes	—
576	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
578	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
579	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
580	#405	C₂²×C₆₇	1	2	yes	—
581	#405	C₂²×C₆₇	1	2	yes	—
582	#405	C₂²×C₆₇	1	2	yes	—
583	#405	C₂²×C₆₇	1	2	yes	—
584	C₄×M₁₆	C₂²×C₆₇	1	2	yes	—
585	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
586	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
587	C₂×#97	C₂²×C₆₇	1	2	yes	—
588	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
590	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
591	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
592	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
593	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
595	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
596	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
597	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
600	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
601	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
602	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
603	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
604	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
605	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
606	C₄⋊Q₈	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	#126	C₂×C₄×C₆₇	1	2	yes	—
612	#126	C₂×C₄×C₆₇	1	2	yes	—
613	#126	C₂×C₄×C₆₇	1	2	yes	—
614	#126	C₂×C₄×C₆₇	1	2	yes	—
615	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
616	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
617	#125	C₂×C₄×C₆₇	1	2	yes	—
618	#125	C₂×C₄×C₆₇	1	2	yes	—
619	#125	C₂×C₄×C₆₇	1	2	yes	—
620	#125	C₂×C₄×C₆₇	1	2	yes	—
621	#125	C₂×C₄×C₆₇	1	2	yes	—
622	#125	C₂×C₄×C₆₇	1	2	yes	—
623	#125	C₂×C₄×C₆₇	1	2	yes	—
624	#124	C₂×C₄×C₆₇	1	2	yes	—
625	#124	C₂×C₄×C₆₇	1	2	yes	—
626	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
627	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
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	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
638	C₂²⋊Q₈	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	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
651	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
652	#121	C₂×C₄×C₆₇	1	2	yes	—
653	#121	C₂×C₄×C₆₇	1	2	yes	—
654	#121	C₂×C₄×C₆₇	1	2	yes	—
655	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
656	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
657	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
658	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
659	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
660	C₄×Q₈	C₂³×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×D₄	C₂×C₄×C₆₇	1	2	yes	—
665	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
666	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
667	C₄×D₄	C₂³×C₆₇	1	2	yes	—
668	C₄×D₄	C₂³×C₆₇	1	2	yes	—
669	C₄×D₄	C₂³×C₆₇	1	2	yes	—
670	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
672	C₄×D₄	C₂³×C₆₇	1	2	yes	—
673	#117	C₂×C₄×C₆₇	1	2	yes	—
674	#117	C₂×C₄×C₆₇	1	2	yes	—
675	#117	C₂×C₄×C₆₇	1	2	yes	—
676	#117	C₂³×C₆₇	1	2	yes	—
677	#117	C₂³×C₆₇	1	2	yes	—
678	#117	C₂³×C₆₇	1	2	yes	—
679	#117	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
687	C₂×C₄²	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	2	yes	—
696	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
697	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
698	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
699	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
700	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
701	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
702	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
703	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
705	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
706	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
707	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
708	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
709	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
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	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
719	C₂²⋊C₈	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	#97	C₂³×C₆₇	1	2	yes	—
725	#97	C₂³×C₆₇	1	2	yes	—
726	#97	C₂³×C₆₇	1	2	yes	—
727	#97	C₂³×C₆₇	1	2	yes	—
728	#97	C₂³×C₆₇	1	2	yes	—
729	#97	C₂³×C₆₇	1	2	yes	—
730	#97	C₂³×C₆₇	1	2	yes	—
731	#97	C₂³×C₆₇	1	2	yes	—
732	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₆₇	1	2	yes	—
737	C₄×C₈	C₂³×C₆₇	1	2	yes	—
738	C₄×C₈	C₂³×C₆₇	1	2	yes	—
739	C₄×C₈	C₂³×C₆₇	1	2	yes	—
740	C₄×C₈	C₂³×C₆₇	1	2	yes	—
741	C₄×C₈	C₂³×C₆₇	1	2	yes	—
742	#41	—	4	4	no	—
743	C₂×Q₈	—	4	2	no	—
744	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
745	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
746	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
747	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
748	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
749	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
750	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
751	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
752	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
753	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
754	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
755	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
758	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
760	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
762	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
763	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
764	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
769	M₁₆	—	2	4	no	—
770	M₁₆	—	4	2	no	—
771	M₁₆	—	4	2	no	—
772	M₁₆	—	4	2	no	—
773	C₂×C₈	—	2	2	no	—
774	C₂×C₈	—	2	4	no	—
775	C₂×C₈	—	4	2	no	—
776	C₂×C₈	—	4	1	no	—
777	C₂×C₈	—	4	1	no	—
778	C₂×C₈	—	4	1	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	—	4	2	no	—
781	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
782	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
783	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
785	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
787	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
788	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
789	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
790	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
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	2	yes	—
798	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
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	1	yes	characteristic
812	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
813	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
814	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
815	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
816	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
817	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
818	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
819	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
820	C₄⋊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	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
836	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
837	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
838	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
839	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
840	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
841	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
842	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
843	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
844	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
845	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
846	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
847	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
848	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
849	C₄²	C₂⁴×C₆₇	1	2	yes	—
850	C₄²	C₂⁴×C₆₇	1	2	yes	—
851	C₄²	C₂⁴×C₆₇	1	2	yes	—
852	C₄²	C₂⁴×C₆₇	1	2	yes	—
853	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
854	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
855	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
856	Q₈	—	4	2	no	—
857	Q₈	—	4	2	no	—
858	Q₈	—	4	2	no	—
859	Q₈	—	4	1	no	—
860	Q₈	—	4	1	no	—
861	Q₈	—	4	2	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	4	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
885	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
889	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
891	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
892	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
893	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
894	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
895	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
896	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
897	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
898	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
899	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
900	C₈	—	2	1	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	1	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	2	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	2	no	—
909	C₈	2₋¹⁺⁴×C₆₇	1	2	yes	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	#568×C₆₇	1	2	yes	—
919	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
936	C₄	#585×C₆₇	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	4	2	no	—
940	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
941	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
942	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	#537×C₆₇	C₄
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×#2994	C₂	semidirect
4. C₆₇×#2992	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2992	C₂	semidirect
7. C₆₇×#2990	C₂	semidirect
8. C₆₇×#2987	C₂	semidirect
9. C₆₇×#2985	C₂	semidirect
10. C₆₇×#2983	C₂	semidirect
11. C₆₇×#2970	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. C₂×#446×C₆₇	C₂	semidirect
465. #60340	C₆₇	direct (N × H)
473. #2995	C₂×C₆₇	semidirect
474. #2994	C₂×C₆₇	semidirect
475. #2992	C₂×C₆₇	semidirect
476. #2992	C₂×C₆₇	semidirect
477. #2992	C₂×C₆₇	semidirect
478. #2990	C₂×C₆₇	semidirect
479. #2987	C₂×C₆₇	semidirect
480. #2985	C₂×C₆₇	semidirect
481. #2983	C₂×C₆₇	semidirect
482. #2970	C₂×C₆₇	semidirect
483. #2968	C₂×C₆₇	semidirect
484. #2968	C₂×C₆₇	semidirect
485. #2967	C₂×C₆₇	semidirect
486. #2966	C₂×C₆₇	semidirect
487. #2966	C₂×C₆₇	semidirect
488. #2962	C₂×C₆₇	semidirect
489. #2961	C₂×C₆₇	semidirect
490. C₂×#446	C₂×C₆₇	semidirect
491. C₆₇	#60340	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×#2995	2
C₆₇×#2994	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2987	2
C₆₇×#2985	2
C₆₇×#2983	2
C₆₇×#2970	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2962	2
C₆₇×#2961	2
C₂×#446×C₆₇	2
#60340	67

Subgroups — C67×#60340 #30739591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60340 #30739591