Subgroups — C₂×C₆₇×#3312 #30740382

Order 17152.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3312	C₂	1	16	yes	maximal, direct product factor
4	C₂×#491×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#470×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#467×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#462×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic
15	C₂×#419×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
24	#552×C₆₇	—	2	4	no	—
25	#552×C₆₇	C₂²	1	8	yes	—
26	D₄×Q₈×C₆₇	—	2	4	no	—
27	D₄×Q₈×C₆₇	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#126×C₆₇	—	2	1	no	—
31	C₂×#125×C₆₇	—	2	1	no	—
32	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#123×C₆₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	—	2	1	no	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₇	—	2	1	no	—
45	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
47	#491×C₆₇	C₂²	1	8	yes	complemented
48	#485×C₆₇	C₂²	1	8	yes	complemented
49	#483×C₆₇	C₂²	1	8	yes	complemented
50	#479×C₆₇	C₂²	1	8	yes	complemented
51	#470×C₆₇	C₂²	1	8	yes	complemented
52	#467×C₆₇	C₂²	1	8	yes	complemented
53	#462×C₆₇	C₂²	1	8	yes	complemented
54	#451×C₆₇	C₂²	1	8	yes	complemented
55	#451×C₆₇	C₂²	1	8	yes	complemented
56	#441×C₆₇	C₂²	1	8	yes	complemented
57	#435×C₆₇	C₂²	1	8	yes	—
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
62	#419×C₆₇	C₂²	1	8	yes	complemented
63	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#103×C₆₇	C₂²	1	8	yes	complemented
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₆₇	—	2	1	no	—
78	C₂²×Q₈×C₆₇	—	2	1	no	—
79	C₂²×Q₈×C₆₇	—	2	2	no	—
80	C₂²×Q₈×C₆₇	—	2	2	no	—
81	C₂²×Q₈×C₆₇	—	2	4	no	—
82	C₂²×Q₈×C₆₇	—	2	4	no	—
83	C₂²×Q₈×C₆₇	—	4	2	no	—
84	C₂²×Q₈×C₆₇	—	4	2	no	—
85	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
89	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	—	2	1	no	—
93	C₂³×C₄×C₆₇	—	2	1	no	—
94	C₂³×C₄×C₆₇	—	2	1	no	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂×Q₁₆×C₆₇	—	2	4	no	—
98	C₂×Q₁₆×C₆₇	—	4	2	no	—
99	C₂×Q₁₆×C₆₇	—	4	2	no	—
100	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	—	4	2	no	—
104	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₇	—	4	2	no	—
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₆₇	—	2	8	no	—
112	C₄⋊Q₈×C₆₇	—	2	2	no	—
113	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
114	#126×C₆₇	—	2	8	no	—
115	#125×C₆₇	—	2	8	no	—
116	#125×C₆₇	—	2	2	no	—
117	#125×C₆₇	C₂³	1	4	yes	—
118	#123×C₆₇	—	2	8	no	—
119	C₂²⋊Q₈×C₆₇	—	2	2	no	—
120	C₂²⋊Q₈×C₆₇	—	2	2	no	—
121	C₂²⋊Q₈×C₆₇	—	2	2	no	—
122	C₂²⋊Q₈×C₆₇	—	2	2	no	—
123	C₂²⋊Q₈×C₆₇	—	2	8	no	—
124	C₂²⋊Q₈×C₆₇	—	2	8	no	—
125	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
126	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
127	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
129	C₄×Q₈×C₆₇	—	2	2	no	—
130	C₄×Q₈×C₆₇	—	2	2	no	—
131	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
132	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
133	C₄×D₄×C₆₇	—	2	8	no	—
134	C₄×D₄×C₆₇	D₄	1	4	yes	—
135	C₄×D₄×C₆₇	C₂³	1	4	yes	—
136	#117×C₆₇	—	2	2	no	—
137	#117×C₆₇	—	2	8	no	—
138	#117×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
141	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
144	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
145	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
147	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
149	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
150	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
151	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₆₇	—	2	1	no	—
165	C₂×C₄²×C₆₇	—	2	1	no	—
166	C₂×C₄²×C₆₇	—	2	1	no	—
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	#107×C₆₇	C₂³	1	4	yes	—
169	#106×C₆₇	C₂³	1	4	yes	—
170	#106×C₆₇	C₂³	1	4	yes	—
171	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
172	#103×C₆₇	C₂³	1	4	yes	—
173	#103×C₆₇	C₂³	1	4	yes	—
174	#103×C₆₇	C₂³	1	4	yes	—
175	#103×C₆₇	C₂³	1	4	yes	—
176	#103×C₆₇	C₂³	1	4	yes	—
177	#103×C₆₇	C₂³	1	4	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	4	yes	—
180	#103×C₆₇	C₂³	1	4	yes	—
181	#103×C₆₇	C₂³	1	4	yes	—
182	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
184	#97×C₆₇	C₂³	1	4	yes	—
185	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₆₇	—	2	1	no	—
188	C₂×Q₈×C₆₇	—	2	1	no	—
189	C₂×Q₈×C₆₇	—	2	4	no	—
190	C₂×Q₈×C₆₇	—	2	4	no	—
191	C₂×Q₈×C₆₇	—	2	1	no	—
192	C₂×Q₈×C₆₇	—	2	1	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	—	2	8	no	—
195	C₂×Q₈×C₆₇	—	2	8	no	—
196	C₂×Q₈×C₆₇	—	2	2	no	—
197	C₂×Q₈×C₆₇	—	2	2	no	—
198	C₂×Q₈×C₆₇	—	2	2	no	—
199	C₂×Q₈×C₆₇	—	2	2	no	—
200	C₂×Q₈×C₆₇	—	2	2	no	—
201	C₂×Q₈×C₆₇	—	2	2	no	—
202	C₂×Q₈×C₆₇	—	4	4	no	—
203	C₂×Q₈×C₆₇	—	4	4	no	—
204	C₂×Q₈×C₆₇	—	4	4	no	—
205	C₂×Q₈×C₆₇	—	4	4	no	—
206	C₂×Q₈×C₆₇	—	4	8	no	—
207	C₂×Q₈×C₆₇	—	4	8	no	—
208	C₂×Q₈×C₆₇	#41	1	4	yes	—
209	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₇	—	2	4	no	—
214	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₆₇	—	2	1	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	4	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	1	no	—
226	C₂²×C₄×C₆₇	—	2	1	no	—
227	C₂²×C₄×C₆₇	—	2	1	no	—
228	C₂²×C₄×C₆₇	—	2	1	no	—
229	C₂²×C₄×C₆₇	—	2	1	no	—
230	C₂²×C₄×C₆₇	—	4	4	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	—	4	4	no	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₇	—	2	8	no	—
243	Q₁₆×C₆₇	—	4	4	no	—
244	Q₁₆×C₆₇	—	4	4	no	—
245	M₁₆×C₆₇	—	4	4	no	—
246	C₂×C₈×C₆₇	—	2	2	no	—
247	C₂×C₈×C₆₇	—	2	2	no	—
248	C₂×C₈×C₆₇	—	2	2	no	—
249	C₂×C₈×C₆₇	—	2	2	no	—
250	C₂×C₈×C₆₇	—	4	4	no	—
251	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
252	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	4	no	—
263	C₄⋊C₄×C₆₇	—	2	4	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
271	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	4	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
281	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
282	C₄²×C₆₇	—	2	4	no	—
283	C₄²×C₆₇	—	2	4	no	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	C₂×D₄	1	2	yes	—
286	C₄²×C₆₇	C₂⁴	1	2	yes	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	#137	1	4	yes	—
293	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
294	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
295	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₆₇	—	2	4	no	—
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	2	2	no	—
299	Q₈×C₆₇	—	2	2	no	—
300	Q₈×C₆₇	—	2	2	no	—
301	Q₈×C₆₇	—	2	2	no	—
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	2	2	no	—
304	Q₈×C₆₇	—	4	8	no	—
305	Q₈×C₆₇	—	4	8	no	—
306	Q₈×C₆₇	—	4	2	no	—
307	Q₈×C₆₇	—	4	2	no	—
308	Q₈×C₆₇	—	4	2	no	—
309	Q₈×C₆₇	C₂×#41	1	4	yes	—
310	D₄×C₆₇	—	2	8	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	4	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	4	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	4	8	no	—
331	C₂×C₄×C₆₇	—	4	8	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	2	no	—
334	C₂×C₄×C₆₇	—	4	2	no	—
335	C₂×C₄×C₆₇	—	4	8	no	—
336	C₂×C₄×C₆₇	—	4	2	no	—
337	C₂×C₄×C₆₇	—	4	2	no	—
338	C₂×C₄×C₆₇	—	4	2	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
348	C₈×C₆₇	—	2	2	no	—
349	C₈×C₆₇	—	2	2	no	—
350	C₈×C₆₇	—	2	2	no	—
351	C₈×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	—	2	2	no	—
353	C₂²×C₆₇	—	2	8	no	—
354	C₂²×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	2	2	no	—
356	C₂²×C₆₇	—	2	2	no	—
357	C₂²×C₆₇	—	2	2	no	—
358	C₂²×C₆₇	—	4	4	no	—
359	C₂²×C₆₇	#546	1	2	yes	—
360	C₂²×C₆₇	C₂×#137	1	4	yes	—
361	C₂²×C₆₇	C₂×#137	1	2	yes	—
362	C₂²×C₆₇	#578	1	2	yes	—
363	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₆₇	—	2	2	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	2	2	no	—
369	C₄×C₆₇	—	4	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	#546	1	2	yes	—
377	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
378	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×#3312	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₆₇	—	2	4	no	—
381	C₂×C₆₇	—	4	2	no	—
382	C₂×C₆₇	#3312	1	4	yes	direct product factor
383	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
384	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
385	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
386	C₂×#552	C₂×C₆₇	1	1	yes	characteristic
387	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic
388	#3312	C₂×C₆₇	1	16	yes	direct product factor
389	C₂×#491	C₂×C₆₇	1	1	yes	characteristic, complemented
390	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#470	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₂×#467	C₂×C₆₇	1	1	yes	characteristic, complemented
395	C₂×#462	C₂×C₆₇	1	1	yes	characteristic, complemented
396	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
397	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
398	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#435	C₂×C₆₇	1	1	yes	characteristic
400	C₂×#419	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₆₇	C₂×#3312	1	1	yes	characteristic, direct product factor, Sylow
403	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
404	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
407	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
409	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
410	#552	—	2	4	no	—
411	#552	C₂²×C₆₇	1	8	yes	—
412	D₄×Q₈	—	2	4	no	—
413	D₄×Q₈	C₂²×C₆₇	1	8	yes	—
414	C₂×C₄⋊Q₈	—	2	1	no	—
415	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#126	—	2	1	no	—
417	C₂×#125	—	2	1	no	—
418	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#123	—	2	1	no	—
420	C₂×C₂²⋊Q₈	—	2	1	no	—
421	C₂×C₂²⋊Q₈	—	2	1	no	—
422	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×C₄×D₄	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#117	—	2	1	no	—
431	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
433	#491	C₂²×C₆₇	1	8	yes	complemented
434	#485	C₂²×C₆₇	1	8	yes	complemented
435	#483	C₂²×C₆₇	1	8	yes	complemented
436	#479	C₂²×C₆₇	1	8	yes	complemented
437	#470	C₂²×C₆₇	1	8	yes	complemented
438	#467	C₂²×C₆₇	1	8	yes	complemented
439	#462	C₂²×C₆₇	1	8	yes	complemented
440	#451	C₂²×C₆₇	1	8	yes	complemented
441	#451	C₂²×C₆₇	1	8	yes	complemented
442	#441	C₂²×C₆₇	1	8	yes	complemented
443	#435	C₂²×C₆₇	1	8	yes	—
444	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
448	#419	C₂²×C₆₇	1	8	yes	complemented
449	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#103	C₂²×C₆₇	1	8	yes	complemented
460	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	4	no	—
468	C₂²×Q₈	—	2	4	no	—
469	C₂²×Q₈	—	4	2	no	—
470	C₂²×Q₈	—	4	2	no	—
471	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
475	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
476	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
477	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×Q₁₆	—	2	4	no	—
484	C₂×Q₁₆	—	4	2	no	—
485	C₂×Q₁₆	—	4	2	no	—
486	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
487	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
488	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
489	C₂×M₁₆	—	4	2	no	—
490	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
491	C₂²×C₈	—	4	2	no	—
492	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
497	C₄⋊Q₈	—	2	8	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
500	#126	—	2	8	no	—
501	#125	—	2	8	no	—
502	#125	—	2	2	no	—
503	#125	C₂³×C₆₇	1	4	yes	—
504	#123	—	2	8	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	8	no	—
510	C₂²⋊Q₈	—	2	8	no	—
511	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
512	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
513	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
514	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
518	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	D₄×C₆₇	1	4	yes	—
521	C₄×D₄	C₂³×C₆₇	1	4	yes	—
522	#117	—	2	2	no	—
523	#117	—	2	8	no	—
524	#117	C₂³×C₆₇	1	4	yes	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	—	2	1	no	—
553	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
554	#107	C₂³×C₆₇	1	4	yes	—
555	#106	C₂³×C₆₇	1	4	yes	—
556	#106	C₂³×C₆₇	1	4	yes	—
557	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
558	#103	C₂³×C₆₇	1	4	yes	—
559	#103	C₂³×C₆₇	1	4	yes	—
560	#103	C₂³×C₆₇	1	4	yes	—
561	#103	C₂³×C₆₇	1	4	yes	—
562	#103	C₂³×C₆₇	1	4	yes	—
563	#103	C₂³×C₆₇	1	4	yes	—
564	#103	C₂³×C₆₇	1	4	yes	—
565	#103	C₂³×C₆₇	1	4	yes	—
566	#103	C₂³×C₆₇	1	4	yes	—
567	#103	C₂³×C₆₇	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
570	#97	C₂³×C₆₇	1	4	yes	—
571	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
572	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	8	no	—
581	C₂×Q₈	—	2	8	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×Q₈	—	4	4	no	—
592	C₂×Q₈	—	4	8	no	—
593	C₂×Q₈	—	4	8	no	—
594	C₂×Q₈	#41×C₆₇	1	4	yes	—
595	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
596	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
597	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
598	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	Q₁₆	—	2	8	no	—
629	Q₁₆	—	4	4	no	—
630	Q₁₆	—	4	4	no	—
631	M₁₆	—	4	4	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	4	4	no	—
637	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
638	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
639	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
640	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
667	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	C₂×D₄×C₆₇	1	2	yes	—
672	C₄²	C₂⁴×C₆₇	1	2	yes	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	#137×C₆₇	1	4	yes	—
679	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
680	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
681	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	8	no	—
691	Q₈	—	4	8	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	—	4	2	no	—
695	Q₈	C₂×#41×C₆₇	1	4	yes	—
696	D₄	—	2	8	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
732	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
733	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	—	2	2	no	—
738	C₂²	—	2	8	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	#546×C₆₇	1	2	yes	—
746	C₂²	C₂×#137×C₆₇	1	4	yes	—
747	C₂²	C₂×#137×C₆₇	1	2	yes	—
748	C₂²	#578×C₆₇	1	2	yes	—
749	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	#546×C₆₇	1	2	yes	—
763	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
764	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
765	C₂	—	2	4	no	—
766	C₂	—	4	2	no	—
767	C₂	C₆₇×#3312	1	4	yes	direct product factor
768	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
769	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
770	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₇×#3312	C₂	direct (N × H)
4. C₂×#491×C₆₇	C₂	semidirect
5. C₂×#485×C₆₇	C₂	semidirect
6. C₂×#483×C₆₇	C₂	semidirect
7. C₂×#479×C₆₇	C₂	semidirect
8. C₂×#470×C₆₇	C₂	semidirect
9. C₂×#467×C₆₇	C₂	semidirect
10. C₂×#462×C₆₇	C₂	semidirect
11. C₂×#451×C₆₇	C₂	semidirect
12. C₂×#451×C₆₇	C₂	semidirect
13. C₂×#441×C₆₇	C₂	semidirect
15. C₂×#419×C₆₇	C₂	semidirect
16. C₂²×#103×C₆₇	C₂	semidirect
47. #491×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
50. #479×C₆₇	C₂²	semidirect
51. #470×C₆₇	C₂²	semidirect
52. #467×C₆₇	C₂²	semidirect
53. #462×C₆₇	C₂²	semidirect
54. #451×C₆₇	C₂²	semidirect
55. #451×C₆₇	C₂²	semidirect
56. #441×C₆₇	C₂²	semidirect
62. #419×C₆₇	C₂²	semidirect
73. C₂×#103×C₆₇	C₂²	semidirect
379. C₂×#3312	C₆₇	direct (N × H)
382. C₂×C₆₇	#3312	direct (N × H)
388. #3312	C₂×C₆₇	direct (N × H)
389. C₂×#491	C₂×C₆₇	semidirect
390. C₂×#485	C₂×C₆₇	semidirect
391. C₂×#483	C₂×C₆₇	semidirect
392. C₂×#479	C₂×C₆₇	semidirect
393. C₂×#470	C₂×C₆₇	semidirect
394. C₂×#467	C₂×C₆₇	semidirect
395. C₂×#462	C₂×C₆₇	semidirect
396. C₂×#451	C₂×C₆₇	semidirect
397. C₂×#451	C₂×C₆₇	semidirect
398. C₂×#441	C₂×C₆₇	semidirect
400. C₂×#419	C₂×C₆₇	semidirect
401. C₂²×#103	C₂×C₆₇	semidirect
402. C₆₇	C₂×#3312	direct (N × H)
433. #491	C₂²×C₆₇	semidirect
434. #485	C₂²×C₆₇	semidirect
435. #483	C₂²×C₆₇	semidirect
436. #479	C₂²×C₆₇	semidirect
437. #470	C₂²×C₆₇	semidirect
438. #467	C₂²×C₆₇	semidirect
439. #462	C₂²×C₆₇	semidirect
440. #451	C₂²×C₆₇	semidirect
441. #451	C₂²×C₆₇	semidirect
442. #441	C₂²×C₆₇	semidirect
448. #419	C₂²×C₆₇	semidirect
459. C₂×#103	C₂²×C₆₇	semidirect
767. C₂	C₆₇×#3312	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#552×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₆₇×#3312	2
C₂×#491×C₆₇	2
C₂×#485×C₆₇	2
C₂×#483×C₆₇	2
C₂×#479×C₆₇	2
C₂×#470×C₆₇	2
C₂×#467×C₆₇	2
C₂×#462×C₆₇	2
C₂×#451×C₆₇	2
C₂×#441×C₆₇	2
C₂×#435×C₆₇	2
C₂×#419×C₆₇	2
C₂²×#103×C₆₇	2
C₂×#3312	67

Subgroups — C2×C67×#3312 #30740382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3312 #30740382