Subgroups — C₆₇×#60323 #30739574

Order 17152.

1940 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3481	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2976	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2972	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2966	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2933	C₂	1	4	yes	maximal, complemented
16	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#436×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
19	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	complemented
20	#559×C₆₇	C₄	1	1	yes	characteristic
21	#554×C₆₇	C₄	1	1	yes	characteristic
22	#554×C₆₇	C₄	1	1	yes	characteristic
23	#553×C₆₇	C₄	1	2	yes	—
24	#553×C₆₇	C₄	1	2	yes	—
25	#551×C₆₇	C₄	1	4	yes	—
26	#546×C₆₇	C₄	1	2	yes	—
27	#546×C₆₇	C₄	1	2	yes	—
28	D₄²×C₆₇	C₄	1	1	yes	characteristic
29	#532×C₆₇	C₂²	1	1	yes	characteristic
30	#529×C₆₇	C₂²	1	2	yes	—
31	#529×C₆₇	C₂²	1	2	yes	—
32	#525×C₆₇	C₂²	1	4	yes	—
33	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
34	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#446×C₆₇	C₂²	1	2	yes	complemented
40	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
43	#436×C₆₇	C₂²	1	1	yes	characteristic
44	#436×C₆₇	C₂²	1	2	yes	—
45	#436×C₆₇	C₂²	1	1	yes	characteristic
46	#436×C₆₇	C₂²	1	2	yes	complemented
47	#436×C₆₇	C₂²	1	4	yes	complemented
48	#436×C₆₇	C₂²	1	4	yes	complemented
49	#436×C₆₇	C₂²	1	2	yes	complemented
50	#436×C₆₇	C₂²	1	2	yes	complemented
51	#436×C₆₇	C₂²	1	4	yes	complemented
52	#436×C₆₇	C₂²	1	2	yes	complemented
53	#435×C₆₇	C₂²	1	2	yes	complemented
54	#435×C₆₇	C₂²	1	4	yes	complemented
55	#435×C₆₇	C₂²	1	4	yes	complemented
56	#435×C₆₇	C₂²	1	4	yes	complemented
57	#435×C₆₇	C₂²	1	4	yes	complemented
58	#435×C₆₇	C₂²	1	2	yes	complemented
59	#435×C₆₇	C₂²	1	4	yes	complemented
60	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	C₈×D₄×C₆₇	C₂²	1	2	yes	—
62	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
63	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
64	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
65	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
66	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
67	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
68	C₈×D₄×C₆₇	C₂²	1	4	yes	complemented
69	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
70	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
71	#433×C₆₇	C₂²	1	4	yes	complemented
72	#433×C₆₇	C₂²	1	4	yes	complemented
73	#432×C₆₇	C₂²	1	2	yes	complemented
74	#431×C₆₇	C₂²	1	2	yes	complemented
75	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#431×C₆₇	C₂²	1	2	yes	complemented
77	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#431×C₆₇	C₂²	1	2	yes	complemented
79	#424×C₆₇	C₂²	1	4	yes	complemented
80	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#423×C₆₇	C₂²	1	2	yes	complemented
82	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
83	#408×C₆₇	C₂²	1	2	yes	complemented
84	#408×C₆₇	C₂²	1	4	yes	complemented
85	#407×C₆₇	C₂²	1	4	yes	complemented
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
88	#405×C₆₇	C₂²	1	4	yes	complemented
89	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
90	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
91	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
96	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
98	#131×C₆₇	—	4	4	no	—
99	C₂×M₁₆×C₆₇	—	4	8	no	—
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
110	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
114	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
115	#126×C₆₇	C₂×C₄	1	4	yes	—
116	#126×C₆₇	C₂×C₄	1	4	yes	—
117	#125×C₆₇	C₂×C₄	1	2	yes	—
118	#125×C₆₇	C₂×C₄	1	2	yes	—
119	#124×C₆₇	C₂×C₄	1	2	yes	—
120	#124×C₆₇	C₂×C₄	1	2	yes	—
121	#124×C₆₇	C₂×C₄	1	2	yes	—
122	#123×C₆₇	C₂×C₄	1	4	yes	—
123	#123×C₆₇	C₂×C₄	1	4	yes	—
124	#123×C₆₇	C₂×C₄	1	4	yes	—
125	#123×C₆₇	C₂×C₄	1	4	yes	—
126	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
127	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
128	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
130	#121×C₆₇	C₂×C₄	1	4	yes	—
131	#121×C₆₇	C₂×C₄	1	4	yes	—
132	#121×C₆₇	C₂×C₄	1	2	yes	—
133	#121×C₆₇	C₂×C₄	1	2	yes	—
134	#121×C₆₇	C₂×C₄	1	2	yes	—
135	#121×C₆₇	C₂×C₄	1	2	yes	—
136	#120×C₆₇	C₂×C₄	1	4	yes	—
137	#120×C₆₇	C₂×C₄	1	4	yes	—
138	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
141	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
143	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
144	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
145	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
146	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
147	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
151	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
152	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₆₇	C₂³	1	4	yes	—
155	C₄×D₄×C₆₇	C₂³	1	4	yes	—
156	C₄×D₄×C₆₇	C₂³	1	2	yes	—
157	C₄×D₄×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	#117×C₆₇	C₂×C₄	1	2	yes	—
161	#117×C₆₇	C₂×C₄	1	2	yes	—
162	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
163	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
164	#117×C₆₇	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
172	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
174	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
175	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
178	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
179	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
181	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
184	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
185	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
186	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
187	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
189	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
191	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
196	#97×C₆₇	C₂³	1	2	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	#97×C₆₇	C₂³	1	4	yes	—
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₆₇	C₂³	1	2	yes	—
202	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₆₇	C₂³	1	2	yes	—
205	C₄×C₈×C₆₇	C₂³	1	2	yes	—
206	C₄×C₈×C₆₇	C₂³	1	2	yes	—
207	C₄×C₈×C₆₇	C₂³	1	4	yes	—
208	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
209	#41×C₆₇	—	2	4	no	—
210	#41×C₆₇	—	4	2	no	—
211	#41×C₆₇	—	4	2	no	—
212	#41×C₆₇	—	4	2	no	—
213	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₆₇	—	2	8	no	—
217	C₂×D₄×C₆₇	—	4	4	no	—
218	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
219	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
220	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
223	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
224	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
225	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	—	4	4	no	—
229	C₂²×C₄×C₆₇	—	4	4	no	—
230	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
238	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
243	M₁₆×C₆₇	—	2	4	no	—
244	M₁₆×C₆₇	—	2	8	no	—
245	M₁₆×C₆₇	—	4	4	no	—
246	M₁₆×C₆₇	—	4	4	no	—
247	M₁₆×C₆₇	—	4	2	no	—
248	M₁₆×C₆₇	—	4	2	no	—
249	C₂×C₈×C₆₇	—	2	4	no	—
250	C₂×C₈×C₆₇	—	2	2	no	—
251	C₂×C₈×C₆₇	—	4	2	no	—
252	C₂×C₈×C₆₇	—	4	4	no	—
253	C₂×C₈×C₆₇	—	4	1	no	—
254	C₂×C₈×C₆₇	—	4	4	no	—
255	C₂×C₈×C₆₇	—	4	4	no	—
256	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
259	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
270	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
272	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
280	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
284	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
289	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
293	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
294	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
295	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
296	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
297	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
298	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄²×C₆₇	C₂⁴	1	2	yes	—
302	C₄²×C₆₇	C₂⁴	1	2	yes	—
303	C₂³×C₆₇	—	2	8	no	—
304	C₂³×C₆₇	—	4	4	no	—
305	C₂³×C₆₇	—	4	4	no	—
306	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
307	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
308	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
309	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
310	Q₈×C₆₇	—	2	2	no	—
311	Q₈×C₆₇	—	2	2	no	—
312	Q₈×C₆₇	—	4	2	no	—
313	D₄×C₆₇	—	2	8	no	—
314	D₄×C₆₇	—	2	4	no	—
315	D₄×C₆₇	—	2	4	no	—
316	D₄×C₆₇	—	2	2	no	—
317	D₄×C₆₇	—	2	4	no	—
318	D₄×C₆₇	—	4	4	no	—
319	D₄×C₆₇	—	4	4	no	—
320	D₄×C₆₇	—	4	2	no	—
321	D₄×C₆₇	—	4	2	no	—
322	D₄×C₆₇	#131	1	4	yes	complemented
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	1	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	4	4	no	—
337	C₂×C₄×C₆₇	—	4	4	no	—
338	C₂×C₄×C₆₇	—	4	4	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
349	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
350	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
353	C₈×C₆₇	—	2	1	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₈×C₆₇	—	2	2	no	—
356	C₈×C₆₇	—	2	4	no	—
357	C₈×C₆₇	—	2	1	no	—
358	C₈×C₆₇	—	2	2	no	—
359	C₈×C₆₇	—	2	2	no	—
360	C₈×C₆₇	—	2	1	no	—
361	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
362	C₂²×C₆₇	—	2	2	no	—
363	C₂²×C₆₇	—	2	2	no	—
364	C₂²×C₆₇	—	2	2	no	—
365	C₂²×C₆₇	—	2	4	no	—
366	C₂²×C₆₇	—	2	1	no	—
367	C₂²×C₆₇	—	2	1	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	2	4	no	—
370	C₂²×C₆₇	—	2	1	no	—
371	C₂²×C₆₇	—	2	2	no	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	8	8	no	—
374	C₂²×C₆₇	C₂×#131	1	4	yes	—
375	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	4	no	—
379	C₄×C₆₇	—	2	1	no	—
380	C₄×C₆₇	—	2	1	no	—
381	C₄×C₆₇	—	2	2	no	—
382	C₄×C₆₇	—	2	2	no	—
383	C₄×C₆₇	—	2	1	no	—
384	C₄×C₆₇	—	2	2	no	—
385	C₄×C₆₇	—	2	2	no	—
386	C₄×C₆₇	C₂×#131	1	2	yes	—
387	C₄×C₆₇	#568	1	2	yes	—
388	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₄×C₆₇	#585	1	1	yes	characteristic
390	#60323	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₆₇	—	2	4	no	—
392	C₂×C₆₇	—	4	1	no	—
393	C₂×C₆₇	—	4	4	no	—
394	C₂×C₆₇	—	4	2	no	—
395	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
397	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
398	#3481	C₂×C₆₇	1	1	yes	characteristic
399	#2994	C₂×C₆₇	1	2	yes	complemented
400	#2993	C₂×C₆₇	1	2	yes	complemented
401	#2991	C₂×C₆₇	1	1	yes	characteristic, complemented
402	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#2976	C₂×C₆₇	1	4	yes	complemented
405	#2974	C₂×C₆₇	1	2	yes	complemented
406	#2972	C₂×C₆₇	1	2	yes	complemented
407	#2969	C₂×C₆₇	1	2	yes	complemented
408	#2966	C₂×C₆₇	1	2	yes	complemented
409	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
410	C₈×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
411	D₄×M₁₆	C₂×C₆₇	1	2	yes	complemented
412	#2933	C₂×C₆₇	1	4	yes	complemented
413	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
414	C₂×#436	C₂×C₆₇	1	2	yes	complemented
415	C₆₇	#60323	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
417	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	complemented
418	#559	C₄×C₆₇	1	1	yes	characteristic
419	#554	C₄×C₆₇	1	1	yes	characteristic
420	#554	C₄×C₆₇	1	1	yes	characteristic
421	#553	C₄×C₆₇	1	2	yes	—
422	#553	C₄×C₆₇	1	2	yes	—
423	#551	C₄×C₆₇	1	4	yes	—
424	#546	C₄×C₆₇	1	2	yes	—
425	#546	C₄×C₆₇	1	2	yes	—
426	D₄²	C₄×C₆₇	1	1	yes	characteristic
427	#532	C₂²×C₆₇	1	1	yes	characteristic
428	#529	C₂²×C₆₇	1	2	yes	—
429	#529	C₂²×C₆₇	1	2	yes	—
430	#525	C₂²×C₆₇	1	4	yes	—
431	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
432	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
434	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
435	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
436	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
437	#446	C₂²×C₆₇	1	2	yes	complemented
438	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
439	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
441	#436	C₂²×C₆₇	1	1	yes	characteristic
442	#436	C₂²×C₆₇	1	2	yes	—
443	#436	C₂²×C₆₇	1	1	yes	characteristic
444	#436	C₂²×C₆₇	1	2	yes	complemented
445	#436	C₂²×C₆₇	1	4	yes	complemented
446	#436	C₂²×C₆₇	1	4	yes	complemented
447	#436	C₂²×C₆₇	1	2	yes	complemented
448	#436	C₂²×C₆₇	1	2	yes	complemented
449	#436	C₂²×C₆₇	1	4	yes	complemented
450	#436	C₂²×C₆₇	1	2	yes	complemented
451	#435	C₂²×C₆₇	1	2	yes	complemented
452	#435	C₂²×C₆₇	1	4	yes	complemented
453	#435	C₂²×C₆₇	1	4	yes	complemented
454	#435	C₂²×C₆₇	1	4	yes	complemented
455	#435	C₂²×C₆₇	1	4	yes	complemented
456	#435	C₂²×C₆₇	1	2	yes	complemented
457	#435	C₂²×C₆₇	1	4	yes	complemented
458	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
459	C₈×D₄	C₂²×C₆₇	1	2	yes	—
460	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
461	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
462	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
463	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
464	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
465	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
466	C₈×D₄	C₂²×C₆₇	1	4	yes	complemented
467	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
468	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
469	#433	C₂²×C₆₇	1	4	yes	complemented
470	#433	C₂²×C₆₇	1	4	yes	complemented
471	#432	C₂²×C₆₇	1	2	yes	complemented
472	#431	C₂²×C₆₇	1	2	yes	complemented
473	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
474	#431	C₂²×C₆₇	1	2	yes	complemented
475	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
476	#431	C₂²×C₆₇	1	2	yes	complemented
477	#424	C₂²×C₆₇	1	4	yes	complemented
478	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	#423	C₂²×C₆₇	1	2	yes	complemented
480	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
481	#408	C₂²×C₆₇	1	2	yes	complemented
482	#408	C₂²×C₆₇	1	4	yes	complemented
483	#407	C₂²×C₆₇	1	4	yes	complemented
484	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
485	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
486	#405	C₂²×C₆₇	1	4	yes	complemented
487	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
488	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
489	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
490	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
491	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
492	C₂×#41	C₂³×C₆₇	1	2	yes	—
493	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
494	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
495	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
496	#131	—	4	4	no	—
497	C₂×M₁₆	—	4	8	no	—
498	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
499	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
501	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
502	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
503	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
504	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
505	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
507	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
508	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
509	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
511	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
512	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
513	#126	C₂×C₄×C₆₇	1	4	yes	—
514	#126	C₂×C₄×C₆₇	1	4	yes	—
515	#125	C₂×C₄×C₆₇	1	2	yes	—
516	#125	C₂×C₄×C₆₇	1	2	yes	—
517	#124	C₂×C₄×C₆₇	1	2	yes	—
518	#124	C₂×C₄×C₆₇	1	2	yes	—
519	#124	C₂×C₄×C₆₇	1	2	yes	—
520	#123	C₂×C₄×C₆₇	1	4	yes	—
521	#123	C₂×C₄×C₆₇	1	4	yes	—
522	#123	C₂×C₄×C₆₇	1	4	yes	—
523	#123	C₂×C₄×C₆₇	1	4	yes	—
524	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
525	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
527	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
528	#121	C₂×C₄×C₆₇	1	4	yes	—
529	#121	C₂×C₄×C₆₇	1	4	yes	—
530	#121	C₂×C₄×C₆₇	1	2	yes	—
531	#121	C₂×C₄×C₆₇	1	2	yes	—
532	#121	C₂×C₄×C₆₇	1	2	yes	—
533	#121	C₂×C₄×C₆₇	1	2	yes	—
534	#120	C₂×C₄×C₆₇	1	4	yes	—
535	#120	C₂×C₄×C₆₇	1	4	yes	—
536	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
537	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
538	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
539	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
540	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
541	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
542	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
543	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
544	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
545	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
546	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
547	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
548	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
549	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
550	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₄×D₄	C₂³×C₆₇	1	4	yes	—
553	C₄×D₄	C₂³×C₆₇	1	4	yes	—
554	C₄×D₄	C₂³×C₆₇	1	2	yes	—
555	C₄×D₄	C₂³×C₆₇	1	2	yes	—
556	C₄×D₄	C₂³×C₆₇	1	2	yes	—
557	C₄×D₄	C₂³×C₆₇	1	2	yes	—
558	#117	C₂×C₄×C₆₇	1	2	yes	—
559	#117	C₂×C₄×C₆₇	1	2	yes	—
560	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
561	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
562	#117	C₂³×C₆₇	1	4	yes	—
563	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
567	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
569	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
572	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
573	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
574	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
576	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
577	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
578	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
581	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
586	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
592	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
593	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
594	#97	C₂³×C₆₇	1	2	yes	—
595	#97	C₂³×C₆₇	1	2	yes	—
596	#97	C₂³×C₆₇	1	4	yes	—
597	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₆₇	1	2	yes	—
600	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₄×C₈	C₂³×C₆₇	1	2	yes	—
603	C₄×C₈	C₂³×C₆₇	1	2	yes	—
604	C₄×C₈	C₂³×C₆₇	1	2	yes	—
605	C₄×C₈	C₂³×C₆₇	1	4	yes	—
606	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
607	#41	—	2	4	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
612	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
613	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
617	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
618	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
619	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
620	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
621	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
622	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
623	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
624	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
625	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
629	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
630	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
631	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
635	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
636	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
641	M₁₆	—	2	4	no	—
642	M₁₆	—	2	8	no	—
643	M₁₆	—	4	4	no	—
644	M₁₆	—	4	4	no	—
645	M₁₆	—	4	2	no	—
646	M₁₆	—	4	2	no	—
647	C₂×C₈	—	2	4	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	4	4	no	—
650	C₂×C₈	—	4	4	no	—
651	C₂×C₈	—	4	2	no	—
652	C₂×C₈	—	4	4	no	—
653	C₂×C₈	—	4	1	no	—
654	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
656	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
658	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
659	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
660	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
661	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
662	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
664	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
669	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
670	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
672	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
673	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
674	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
675	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
676	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
689	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
690	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
691	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
692	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
693	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
694	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
695	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
696	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
697	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₄²	C₂⁴×C₆₇	1	2	yes	—
700	C₄²	C₂⁴×C₆₇	1	2	yes	—
701	C₂³	—	2	8	no	—
702	C₂³	—	4	4	no	—
703	C₂³	—	4	4	no	—
704	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
705	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
706	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
707	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	2	no	—
711	D₄	—	2	8	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	2	no	—
720	D₄	#131×C₆₇	1	4	yes	complemented
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
740	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
741	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
742	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
744	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
745	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
746	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
747	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
748	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
749	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
750	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
751	C₈	—	2	1	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	4	no	—
755	C₈	—	2	1	no	—
756	C₈	—	2	2	no	—
757	C₈	—	2	2	no	—
758	C₈	—	2	1	no	—
759	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	8	8	no	—
772	C₂²	C₂×#131×C₆₇	1	4	yes	—
773	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	1	no	—
784	C₄	C₂×#131×C₆₇	1	2	yes	—
785	C₄	#568×C₆₇	1	2	yes	—
786	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
787	C₄	#585×C₆₇	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	4	1	no	—
792	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
793	C₂	C₂²×#131×C₆₇	1	1	yes	characteristic
794	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	C₆₇×#3481	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×#2994	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2991	C₂	semidirect
5. C₆₇×#2990	C₂	semidirect
6. C₆₇×#2979	C₂	semidirect
7. C₆₇×#2976	C₂	semidirect
8. C₆₇×#2974	C₂	semidirect
9. C₆₇×#2972	C₂	semidirect
10. C₆₇×#2969	C₂	semidirect
11. C₆₇×#2966	C₂	semidirect
12. C₆₇×#2965	C₂	semidirect
13. C₈×#41×C₆₇	C₂	semidirect
14. D₄×M₁₆×C₆₇	C₂	semidirect
15. C₆₇×#2933	C₂	semidirect
16. C₆₇×#2931	C₂	semidirect
17. C₂×#436×C₆₇	C₂	semidirect
18. C₂×#131×C₆₇	C₂²	semidirect
19. C₂²×M₁₆×C₆₇	C₂²	semidirect
37. #446×C₆₇	C₂²	semidirect
38. #446×C₆₇	C₂²	semidirect
39. #446×C₆₇	C₂²	semidirect
40. C₈×Q₈×C₆₇	C₂²	semidirect
41. C₈×Q₈×C₆₇	C₂²	semidirect
42. C₈×Q₈×C₆₇	C₂²	semidirect
46. #436×C₆₇	C₂²	semidirect
47. #436×C₆₇	C₂²	semidirect
48. #436×C₆₇	C₂²	semidirect
49. #436×C₆₇	C₂²	semidirect
50. #436×C₆₇	C₂²	semidirect
51. #436×C₆₇	C₂²	semidirect
52. #436×C₆₇	C₂²	semidirect
53. #435×C₆₇	C₂²	semidirect
54. #435×C₆₇	C₂²	semidirect
55. #435×C₆₇	C₂²	semidirect
56. #435×C₆₇	C₂²	semidirect
57. #435×C₆₇	C₂²	semidirect
58. #435×C₆₇	C₂²	semidirect
59. #435×C₆₇	C₂²	semidirect
63. C₈×D₄×C₆₇	C₂²	semidirect
64. C₈×D₄×C₆₇	C₂²	semidirect
65. C₈×D₄×C₆₇	C₂²	semidirect
66. C₈×D₄×C₆₇	C₂²	semidirect
67. C₈×D₄×C₆₇	C₂²	semidirect
68. C₈×D₄×C₆₇	C₂²	semidirect
69. C₈×D₄×C₆₇	C₂²	semidirect
70. C₈×D₄×C₆₇	C₂²	semidirect
71. #433×C₆₇	C₂²	semidirect
72. #433×C₆₇	C₂²	semidirect
73. #432×C₆₇	C₂²	semidirect
74. #431×C₆₇	C₂²	semidirect
75. #431×C₆₇	C₂²	semidirect
76. #431×C₆₇	C₂²	semidirect
77. #431×C₆₇	C₂²	semidirect
78. #431×C₆₇	C₂²	semidirect
79. #424×C₆₇	C₂²	semidirect
80. #423×C₆₇	C₂²	semidirect
81. #423×C₆₇	C₂²	semidirect
82. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
83. #408×C₆₇	C₂²	semidirect
84. #408×C₆₇	C₂²	semidirect
85. #407×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
87. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
88. #405×C₆₇	C₂²	semidirect
89. C₄×M₁₆×C₆₇	C₂²	semidirect
90. C₂×C₄×C₈×C₆₇	C₂²	semidirect
91. C₂×C₄×C₈×C₆₇	C₂²	semidirect
322. D₄×C₆₇	#131	semidirect
390. #60323	C₆₇	direct (N × H)
399. #2994	C₂×C₆₇	semidirect
400. #2993	C₂×C₆₇	semidirect
401. #2991	C₂×C₆₇	semidirect
402. #2990	C₂×C₆₇	semidirect
403. #2979	C₂×C₆₇	semidirect
404. #2976	C₂×C₆₇	semidirect
405. #2974	C₂×C₆₇	semidirect
406. #2972	C₂×C₆₇	semidirect
407. #2969	C₂×C₆₇	semidirect
408. #2966	C₂×C₆₇	semidirect
409. #2965	C₂×C₆₇	semidirect
410. C₈×#41	C₂×C₆₇	semidirect
411. D₄×M₁₆	C₂×C₆₇	semidirect
412. #2933	C₂×C₆₇	semidirect
413. #2931	C₂×C₆₇	semidirect
414. C₂×#436	C₂×C₆₇	semidirect
415. C₆₇	#60323	direct (N × H)
416. C₂×#131	C₂²×C₆₇	semidirect
417. C₂²×M₁₆	C₂²×C₆₇	semidirect
435. #446	C₂²×C₆₇	semidirect
436. #446	C₂²×C₆₇	semidirect
437. #446	C₂²×C₆₇	semidirect
438. C₈×Q₈	C₂²×C₆₇	semidirect
439. C₈×Q₈	C₂²×C₆₇	semidirect
440. C₈×Q₈	C₂²×C₆₇	semidirect
444. #436	C₂²×C₆₇	semidirect
445. #436	C₂²×C₆₇	semidirect
446. #436	C₂²×C₆₇	semidirect
447. #436	C₂²×C₆₇	semidirect
448. #436	C₂²×C₆₇	semidirect
449. #436	C₂²×C₆₇	semidirect
450. #436	C₂²×C₆₇	semidirect
451. #435	C₂²×C₆₇	semidirect
452. #435	C₂²×C₆₇	semidirect
453. #435	C₂²×C₆₇	semidirect
454. #435	C₂²×C₆₇	semidirect
455. #435	C₂²×C₆₇	semidirect
456. #435	C₂²×C₆₇	semidirect
457. #435	C₂²×C₆₇	semidirect
461. C₈×D₄	C₂²×C₆₇	semidirect
462. C₈×D₄	C₂²×C₆₇	semidirect
463. C₈×D₄	C₂²×C₆₇	semidirect
464. C₈×D₄	C₂²×C₆₇	semidirect
465. C₈×D₄	C₂²×C₆₇	semidirect
466. C₈×D₄	C₂²×C₆₇	semidirect
467. C₈×D₄	C₂²×C₆₇	semidirect
468. C₈×D₄	C₂²×C₆₇	semidirect
469. #433	C₂²×C₆₇	semidirect
470. #433	C₂²×C₆₇	semidirect
471. #432	C₂²×C₆₇	semidirect
472. #431	C₂²×C₆₇	semidirect
473. #431	C₂²×C₆₇	semidirect
474. #431	C₂²×C₆₇	semidirect
475. #431	C₂²×C₆₇	semidirect
476. #431	C₂²×C₆₇	semidirect
477. #424	C₂²×C₆₇	semidirect
478. #423	C₂²×C₆₇	semidirect
479. #423	C₂²×C₆₇	semidirect
480. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
481. #408	C₂²×C₆₇	semidirect
482. #408	C₂²×C₆₇	semidirect
483. #407	C₂²×C₆₇	semidirect
484. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
485. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
486. #405	C₂²×C₆₇	semidirect
487. C₄×M₁₆	C₂²×C₆₇	semidirect
488. C₂×C₄×C₈	C₂²×C₆₇	semidirect
489. C₂×C₄×C₈	C₂²×C₆₇	semidirect
720. D₄	#131×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3481	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2991	2
C₆₇×#2990	2
C₆₇×#2979	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2972	2
C₆₇×#2969	2
C₆₇×#2966	2
C₆₇×#2965	2
C₈×#41×C₆₇	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2931	2
C₂×#436×C₆₇	2
#60323	67

Subgroups — C67×#60323 #30739574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60323 #30739574