Subgroups — C₆₇×#60290 #30739541

Order 17152.

1816 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2974	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2969	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2966	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2924	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#529×C₆₇	C₄	1	2	yes	—
15	#529×C₆₇	C₄	1	2	yes	—
16	#529×C₆₇	C₄	1	2	yes	—
17	#529×C₆₇	C₄	1	2	yes	—
18	#529×C₆₇	C₂²	1	2	yes	—
19	#529×C₆₇	C₂²	1	2	yes	—
20	#529×C₆₇	C₂²	1	2	yes	—
21	#529×C₆₇	C₂²	1	2	yes	—
22	C₂×#126×C₆₇	C₄	1	2	yes	—
23	C₂×#125×C₆₇	C₄	1	1	yes	characteristic
24	C₂×#124×C₆₇	C₄	1	1	yes	characteristic
25	C₂×#123×C₆₇	C₄	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
27	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#446×C₆₇	C₂²	1	4	yes	complemented
34	#446×C₆₇	C₂²	1	4	yes	complemented
35	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₆₇	C₂²	1	4	yes	complemented
37	#436×C₆₇	C₂²	1	4	yes	complemented
38	#436×C₆₇	C₂²	1	8	yes	complemented
39	#436×C₆₇	C₂²	1	4	yes	complemented
40	#435×C₆₇	C₂²	1	8	yes	complemented
41	#435×C₆₇	C₂²	1	8	yes	complemented
42	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
43	C₈×D₄×C₆₇	C₂²	1	8	yes	complemented
44	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
45	#433×C₆₇	C₂²	1	8	yes	complemented
46	#433×C₆₇	C₂²	1	8	yes	complemented
47	#432×C₆₇	C₂²	1	2	yes	—
48	#432×C₆₇	C₂²	1	4	yes	—
49	#432×C₆₇	C₂²	1	2	yes	complemented
50	#431×C₆₇	C₂²	1	2	yes	—
51	#431×C₆₇	C₂²	1	1	yes	characteristic
52	#431×C₆₇	C₂²	1	1	yes	characteristic
53	#431×C₆₇	C₂²	1	1	yes	characteristic
54	#431×C₆₇	C₂²	1	1	yes	characteristic
55	#431×C₆₇	C₂²	1	4	yes	—
56	#431×C₆₇	C₂²	1	2	yes	complemented
57	#431×C₆₇	C₂²	1	2	yes	complemented
58	#431×C₆₇	C₂²	1	2	yes	complemented
59	#424×C₆₇	C₂²	1	8	yes	complemented
60	#423×C₆₇	C₂²	1	2	yes	complemented
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
62	#407×C₆₇	C₂²	1	2	yes	—
63	#407×C₆₇	C₂²	1	4	yes	—
64	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
65	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
66	#405×C₆₇	C₂²	1	8	yes	complemented
67	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
68	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
69	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
72	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
76	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
77	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
78	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
79	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
80	#126×C₆₇	C₂×C₄	1	4	yes	—
81	#126×C₆₇	C₂×C₄	1	4	yes	—
82	#126×C₆₇	C₂×C₄	1	4	yes	—
83	#126×C₆₇	C₂×C₄	1	4	yes	—
84	#125×C₆₇	C₂×C₄	1	2	yes	—
85	#125×C₆₇	C₂×C₄	1	2	yes	—
86	#125×C₆₇	C₂×C₄	1	2	yes	—
87	#125×C₆₇	C₂×C₄	1	2	yes	—
88	#124×C₆₇	C₂×C₄	1	2	yes	—
89	#124×C₆₇	C₂×C₄	1	2	yes	—
90	#124×C₆₇	C₂×C₄	1	2	yes	—
91	#124×C₆₇	C₂×C₄	1	2	yes	—
92	#123×C₆₇	C₂×C₄	1	4	yes	—
93	#123×C₆₇	C₂×C₄	1	4	yes	—
94	#123×C₆₇	C₂×C₄	1	4	yes	—
95	#123×C₆₇	C₂×C₄	1	4	yes	—
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
98	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
99	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
100	#121×C₆₇	C₂×C₄	1	2	yes	—
101	#121×C₆₇	C₂×C₄	1	2	yes	—
102	#121×C₆₇	C₂×C₄	1	2	yes	—
103	#121×C₆₇	C₂×C₄	1	2	yes	—
104	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
105	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
106	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
107	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
108	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
111	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
112	C₄×D₄×C₆₇	C₂³	1	4	yes	—
113	C₄×D₄×C₆₇	C₂³	1	2	yes	—
114	C₄×D₄×C₆₇	C₂³	1	2	yes	—
115	C₄×D₄×C₆₇	C₂³	1	4	yes	—
116	#117×C₆₇	C₂×C₄	1	4	yes	—
117	#117×C₆₇	C₂×C₄	1	4	yes	—
118	#117×C₆₇	C₂³	1	4	yes	—
119	#117×C₆₇	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
131	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
145	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
146	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
147	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
149	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
150	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
151	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
152	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
153	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
155	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
156	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
157	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
158	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
160	#97×C₆₇	C₂³	1	4	yes	—
161	#97×C₆₇	C₂³	1	8	yes	—
162	C₄×C₈×C₆₇	C₂³	1	4	yes	—
163	C₄×C₈×C₆₇	C₂³	1	2	yes	—
164	C₄×C₈×C₆₇	C₂³	1	2	yes	—
165	C₄×C₈×C₆₇	C₂³	1	2	yes	—
166	C₄×C₈×C₆₇	C₂³	1	2	yes	—
167	C₄×C₈×C₆₇	C₂³	1	8	yes	—
168	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
170	C₂×Q₈×C₆₇	—	2	4	no	—
171	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
172	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	4	4	no	—
175	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
176	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	4	2	no	—
181	C₂²×C₄×C₆₇	—	4	4	no	—
182	C₂²×C₄×C₆₇	—	4	2	no	—
183	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
206	M₁₆×C₆₇	—	4	4	no	—
207	M₁₆×C₆₇	—	4	8	no	—
208	C₂×C₈×C₆₇	—	4	8	no	—
209	C₂×C₈×C₆₇	—	4	4	no	—
210	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
211	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
212	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
213	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
224	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
229	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
236	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
238	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
249	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₄²×C₆₇	C₂⁴	1	4	yes	—
253	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	4	no	—
257	C₂³×C₆₇	—	4	1	no	—
258	C₂³×C₆₇	—	4	2	no	—
259	C₂³×C₆₇	—	4	2	no	—
260	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
261	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
262	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
263	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
264	Q₈×C₆₇	—	2	4	no	—
265	Q₈×C₆₇	—	2	4	no	—
266	D₄×C₆₇	—	2	8	no	—
267	D₄×C₆₇	—	2	4	no	—
268	D₄×C₆₇	—	2	4	no	—
269	D₄×C₆₇	—	4	4	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	4	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	8	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	4	1	no	—
283	C₂×C₄×C₆₇	—	4	1	no	—
284	C₂×C₄×C₆₇	—	4	4	no	—
285	C₂×C₄×C₆₇	—	4	1	no	—
286	C₂×C₄×C₆₇	—	4	2	no	—
287	C₂×C₄×C₆₇	—	4	1	no	—
288	C₂×C₄×C₆₇	—	4	1	no	—
289	C₂×C₄×C₆₇	—	4	1	no	—
290	C₂×C₄×C₆₇	—	4	1	no	—
291	C₂×C₄×C₆₇	—	4	2	no	—
292	C₂×C₄×C₆₇	#131	1	4	yes	—
293	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
308	C₈×C₆₇	—	2	4	no	—
309	C₈×C₆₇	—	2	4	no	—
310	C₈×C₆₇	—	2	4	no	—
311	C₈×C₆₇	—	2	4	no	—
312	C₂²×C₆₇	—	2	1	no	—
313	C₂²×C₆₇	—	2	1	no	—
314	C₂²×C₆₇	—	2	1	no	—
315	C₂²×C₆₇	—	2	1	no	—
316	C₂²×C₆₇	—	2	1	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	2	1	no	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	1	no	—
321	C₂²×C₆₇	—	2	4	no	—
322	C₂²×C₆₇	—	4	4	no	—
323	C₂²×C₆₇	—	8	4	no	—
324	C₂²×C₆₇	C₂×#131	1	2	yes	—
325	C₂²×C₆₇	#568	1	2	yes	—
326	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
327	C₄×C₆₇	—	2	1	no	—
328	C₄×C₆₇	—	2	1	no	—
329	C₄×C₆₇	—	2	4	no	—
330	C₄×C₆₇	—	2	1	no	—
331	C₄×C₆₇	—	2	1	no	—
332	C₄×C₆₇	—	2	1	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	1	no	—
335	C₄×C₆₇	—	2	1	no	—
336	C₄×C₆₇	—	2	1	no	—
337	C₄×C₆₇	—	2	1	no	—
338	C₄×C₆₇	—	2	4	no	—
339	C₄×C₆₇	C₂×#131	1	2	yes	—
340	C₄×C₆₇	C₂×#131	1	2	yes	—
341	C₄×C₆₇	#585	1	2	yes	—
342	#60290	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂×C₆₇	—	2	2	no	—
344	C₂×C₆₇	—	2	2	no	—
345	C₂×C₆₇	—	4	1	no	—
346	C₂×C₆₇	—	4	4	no	—
347	C₂×C₆₇	#3428	1	1	yes	characteristic
348	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
349	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
350	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
351	#2994	C₂×C₆₇	1	4	yes	complemented
352	#2993	C₂×C₆₇	1	4	yes	complemented
353	#2983	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2982	C₂×C₆₇	1	1	yes	characteristic, complemented
355	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
356	#2974	C₂×C₆₇	1	4	yes	complemented
357	#2972	C₂×C₆₇	1	1	yes	characteristic, complemented
358	#2969	C₂×C₆₇	1	4	yes	complemented
359	#2966	C₂×C₆₇	1	4	yes	complemented
360	#2924	C₂×C₆₇	1	4	yes	complemented
361	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
362	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
363	C₆₇	#60290	1	1	yes	characteristic, direct product factor, Sylow
364	#529	C₄×C₆₇	1	2	yes	—
365	#529	C₄×C₆₇	1	2	yes	—
366	#529	C₄×C₆₇	1	2	yes	—
367	#529	C₄×C₆₇	1	2	yes	—
368	#529	C₂²×C₆₇	1	2	yes	—
369	#529	C₂²×C₆₇	1	2	yes	—
370	#529	C₂²×C₆₇	1	2	yes	—
371	#529	C₂²×C₆₇	1	2	yes	—
372	C₂×#126	C₄×C₆₇	1	2	yes	—
373	C₂×#125	C₄×C₆₇	1	1	yes	characteristic
374	C₂×#124	C₄×C₆₇	1	1	yes	characteristic
375	C₂×#123	C₄×C₆₇	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
377	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
381	C₂×#117	C₂²×C₆₇	1	2	yes	—
382	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
383	#446	C₂²×C₆₇	1	4	yes	complemented
384	#446	C₂²×C₆₇	1	4	yes	complemented
385	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
386	C₈×Q₈	C₂²×C₆₇	1	4	yes	complemented
387	#436	C₂²×C₆₇	1	4	yes	complemented
388	#436	C₂²×C₆₇	1	8	yes	complemented
389	#436	C₂²×C₆₇	1	4	yes	complemented
390	#435	C₂²×C₆₇	1	8	yes	complemented
391	#435	C₂²×C₆₇	1	8	yes	complemented
392	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
393	C₈×D₄	C₂²×C₆₇	1	8	yes	complemented
394	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
395	#433	C₂²×C₆₇	1	8	yes	complemented
396	#433	C₂²×C₆₇	1	8	yes	complemented
397	#432	C₂²×C₆₇	1	2	yes	—
398	#432	C₂²×C₆₇	1	4	yes	—
399	#432	C₂²×C₆₇	1	2	yes	complemented
400	#431	C₂²×C₆₇	1	2	yes	—
401	#431	C₂²×C₆₇	1	1	yes	characteristic
402	#431	C₂²×C₆₇	1	1	yes	characteristic
403	#431	C₂²×C₆₇	1	1	yes	characteristic
404	#431	C₂²×C₆₇	1	1	yes	characteristic
405	#431	C₂²×C₆₇	1	4	yes	—
406	#431	C₂²×C₆₇	1	2	yes	complemented
407	#431	C₂²×C₆₇	1	2	yes	complemented
408	#431	C₂²×C₆₇	1	2	yes	complemented
409	#424	C₂²×C₆₇	1	8	yes	complemented
410	#423	C₂²×C₆₇	1	2	yes	complemented
411	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
412	#407	C₂²×C₆₇	1	2	yes	—
413	#407	C₂²×C₆₇	1	4	yes	—
414	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
415	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
416	#405	C₂²×C₆₇	1	8	yes	complemented
417	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
418	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
419	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
420	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
421	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
422	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
425	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
426	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
427	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
428	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
429	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
430	#126	C₂×C₄×C₆₇	1	4	yes	—
431	#126	C₂×C₄×C₆₇	1	4	yes	—
432	#126	C₂×C₄×C₆₇	1	4	yes	—
433	#126	C₂×C₄×C₆₇	1	4	yes	—
434	#125	C₂×C₄×C₆₇	1	2	yes	—
435	#125	C₂×C₄×C₆₇	1	2	yes	—
436	#125	C₂×C₄×C₆₇	1	2	yes	—
437	#125	C₂×C₄×C₆₇	1	2	yes	—
438	#124	C₂×C₄×C₆₇	1	2	yes	—
439	#124	C₂×C₄×C₆₇	1	2	yes	—
440	#124	C₂×C₄×C₆₇	1	2	yes	—
441	#124	C₂×C₄×C₆₇	1	2	yes	—
442	#123	C₂×C₄×C₆₇	1	4	yes	—
443	#123	C₂×C₄×C₆₇	1	4	yes	—
444	#123	C₂×C₄×C₆₇	1	4	yes	—
445	#123	C₂×C₄×C₆₇	1	4	yes	—
446	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
447	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
448	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
449	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
450	#121	C₂×C₄×C₆₇	1	2	yes	—
451	#121	C₂×C₄×C₆₇	1	2	yes	—
452	#121	C₂×C₄×C₆₇	1	2	yes	—
453	#121	C₂×C₄×C₆₇	1	2	yes	—
454	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
455	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
456	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
457	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
458	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
459	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
460	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
461	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
462	C₄×D₄	C₂³×C₆₇	1	4	yes	—
463	C₄×D₄	C₂³×C₆₇	1	2	yes	—
464	C₄×D₄	C₂³×C₆₇	1	2	yes	—
465	C₄×D₄	C₂³×C₆₇	1	4	yes	—
466	#117	C₂×C₄×C₆₇	1	4	yes	—
467	#117	C₂×C₄×C₆₇	1	4	yes	—
468	#117	C₂³×C₆₇	1	4	yes	—
469	#117	C₂³×C₆₇	1	4	yes	—
470	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
472	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
474	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
481	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
482	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
483	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
484	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
485	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
486	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
494	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
495	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
496	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
497	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
498	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
499	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
500	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
501	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
502	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
503	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
504	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
505	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
506	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
507	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
508	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
509	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
510	#97	C₂³×C₆₇	1	4	yes	—
511	#97	C₂³×C₆₇	1	8	yes	—
512	C₄×C₈	C₂³×C₆₇	1	4	yes	—
513	C₄×C₈	C₂³×C₆₇	1	2	yes	—
514	C₄×C₈	C₂³×C₆₇	1	2	yes	—
515	C₄×C₈	C₂³×C₆₇	1	2	yes	—
516	C₄×C₈	C₂³×C₆₇	1	2	yes	—
517	C₄×C₈	C₂³×C₆₇	1	8	yes	—
518	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
519	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
522	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
526	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
527	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
541	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
549	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
550	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
556	M₁₆	—	4	4	no	—
557	M₁₆	—	4	8	no	—
558	C₂×C₈	—	4	8	no	—
559	C₂×C₈	—	4	4	no	—
560	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
561	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
562	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
563	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
566	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
567	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
569	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
573	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
586	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
587	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
588	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
589	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
590	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
593	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
599	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
600	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
601	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
602	C₄²	C₂⁴×C₆₇	1	4	yes	—
603	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
611	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
612	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
613	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
614	Q₈	—	2	4	no	—
615	Q₈	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	#131×C₆₇	1	4	yes	—
643	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
652	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
657	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
658	C₈	—	2	4	no	—
659	C₈	—	2	4	no	—
660	C₈	—	2	4	no	—
661	C₈	—	2	4	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	8	4	no	—
674	C₂²	C₂×#131×C₆₇	1	2	yes	—
675	C₂²	#568×C₆₇	1	2	yes	—
676	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	1	no	—
689	C₄	C₂×#131×C₆₇	1	2	yes	—
690	C₄	C₂×#131×C₆₇	1	2	yes	—
691	C₄	#585×C₆₇	1	2	yes	—
692	C₂	—	2	2	no	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	4	no	—
696	C₂	C₆₇×#3428	1	1	yes	characteristic
697	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
698	C₂	C₂×#568×C₆₇	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	C₂×#121×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×#2994	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2983	C₂	semidirect
5. C₆₇×#2982	C₂	semidirect
6. C₆₇×#2975	C₂	semidirect
7. C₆₇×#2974	C₂	semidirect
8. C₆₇×#2972	C₂	semidirect
9. C₆₇×#2969	C₂	semidirect
10. C₆₇×#2966	C₂	semidirect
11. C₆₇×#2924	C₂	semidirect
12. C₆₇×#2920	C₂	semidirect
13. C₂×#431×C₆₇	C₂	semidirect
33. #446×C₆₇	C₂²	semidirect
34. #446×C₆₇	C₂²	semidirect
35. C₈×Q₈×C₆₇	C₂²	semidirect
36. C₈×Q₈×C₆₇	C₂²	semidirect
37. #436×C₆₇	C₂²	semidirect
38. #436×C₆₇	C₂²	semidirect
39. #436×C₆₇	C₂²	semidirect
40. #435×C₆₇	C₂²	semidirect
41. #435×C₆₇	C₂²	semidirect
42. C₈×D₄×C₆₇	C₂²	semidirect
43. C₈×D₄×C₆₇	C₂²	semidirect
44. C₈×D₄×C₆₇	C₂²	semidirect
45. #433×C₆₇	C₂²	semidirect
46. #433×C₆₇	C₂²	semidirect
49. #432×C₆₇	C₂²	semidirect
56. #431×C₆₇	C₂²	semidirect
57. #431×C₆₇	C₂²	semidirect
58. #431×C₆₇	C₂²	semidirect
59. #424×C₆₇	C₂²	semidirect
60. #423×C₆₇	C₂²	semidirect
61. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
66. #405×C₆₇	C₂²	semidirect
67. C₄×M₁₆×C₆₇	C₂²	semidirect
68. C₂×C₄×C₈×C₆₇	C₂²	semidirect
342. #60290	C₆₇	direct (N × H)
351. #2994	C₂×C₆₇	semidirect
352. #2993	C₂×C₆₇	semidirect
353. #2983	C₂×C₆₇	semidirect
354. #2982	C₂×C₆₇	semidirect
355. #2975	C₂×C₆₇	semidirect
356. #2974	C₂×C₆₇	semidirect
357. #2972	C₂×C₆₇	semidirect
358. #2969	C₂×C₆₇	semidirect
359. #2966	C₂×C₆₇	semidirect
360. #2924	C₂×C₆₇	semidirect
361. #2920	C₂×C₆₇	semidirect
362. C₂×#431	C₂×C₆₇	semidirect
363. C₆₇	#60290	direct (N × H)
383. #446	C₂²×C₆₇	semidirect
384. #446	C₂²×C₆₇	semidirect
385. C₈×Q₈	C₂²×C₆₇	semidirect
386. C₈×Q₈	C₂²×C₆₇	semidirect
387. #436	C₂²×C₆₇	semidirect
388. #436	C₂²×C₆₇	semidirect
389. #436	C₂²×C₆₇	semidirect
390. #435	C₂²×C₆₇	semidirect
391. #435	C₂²×C₆₇	semidirect
392. C₈×D₄	C₂²×C₆₇	semidirect
393. C₈×D₄	C₂²×C₆₇	semidirect
394. C₈×D₄	C₂²×C₆₇	semidirect
395. #433	C₂²×C₆₇	semidirect
396. #433	C₂²×C₆₇	semidirect
399. #432	C₂²×C₆₇	semidirect
406. #431	C₂²×C₆₇	semidirect
407. #431	C₂²×C₆₇	semidirect
408. #431	C₂²×C₆₇	semidirect
409. #424	C₂²×C₆₇	semidirect
410. #423	C₂²×C₆₇	semidirect
411. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
416. #405	C₂²×C₆₇	semidirect
417. C₄×M₁₆	C₂²×C₆₇	semidirect
418. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2983	2
C₆₇×#2982	2
C₆₇×#2975	2
C₆₇×#2974	2
C₆₇×#2972	2
C₆₇×#2969	2
C₆₇×#2966	2
C₆₇×#2924	2
C₆₇×#2920	2
C₂×#431×C₆₇	2
#60290	67

Subgroups — C67×#60290 #30739541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60290 #30739541