Subgroups — C₂×C₆₇×#3315 #30740385

Order 17152.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 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, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3315	C₂	1	16	yes	maximal, direct product factor
4	C₂×#491×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#484×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#478×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×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×#41×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×SD₁₆×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	complemented
26	#547×C₆₇	—	2	4	no	—
27	#547×C₆₇	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#126×C₆₇	—	2	1	no	—
30	C₂×#125×C₆₇	—	2	1	no	—
31	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#123×C₆₇	—	2	1	no	—
33	C₂×#123×C₆₇	—	2	1	no	—
34	C₂×#123×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
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×#121×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	—	2	1	no	—
44	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
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	#484×C₆₇	C₂²	1	8	yes	complemented
50	#478×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	#452×C₆₇	C₂²	1	8	yes	complemented
55	#452×C₆₇	C₂²	1	8	yes	complemented
56	#440×C₆₇	C₂²	1	8	yes	complemented
57	#435×C₆₇	C₂²	1	8	yes	complemented
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#107×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	#417×C₆₇	C₂²	1	8	yes	complemented
63	#416×C₆₇	C₂²	1	8	yes	complemented
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×#102×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
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	C₂×#41×C₆₇	—	2	2	no	—
78	C₂×#41×C₆₇	—	2	2	no	—
79	C₂×#41×C₆₇	—	2	4	no	—
80	C₂×#41×C₆₇	—	2	4	no	—
81	C₂×#41×C₆₇	—	4	2	no	—
82	C₂×#41×C₆₇	—	4	2	no	—
83	C₂×#41×C₆₇	C₂³	1	4	yes	—
84	C₂×#41×C₆₇	C₂³	1	4	yes	—
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×D₄×C₆₇	—	2	1	no	—
89	C₂²×D₄×C₆₇	—	2	1	no	—
90	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	C₂³	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	—	2	1	no	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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×SD₁₆×C₆₇	—	2	4	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×M₁₆×C₆₇	—	4	2	no	—
105	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₇	—	4	2	no	—
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	1	yes	characteristic
111	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
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	#123×C₆₇	—	2	8	no	—
120	#123×C₆₇	—	2	8	no	—
121	C₂²⋊Q₈×C₆₇	—	2	2	no	—
122	C₂²⋊Q₈×C₆₇	—	2	2	no	—
123	C₂²⋊Q₈×C₆₇	—	2	2	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	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	#121×C₆₇	—	2	8	no	—
130	C₄×Q₈×C₆₇	—	2	2	no	—
131	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
132	C₄×D₄×C₆₇	—	2	2	no	—
133	C₄×D₄×C₆₇	D₄	1	4	yes	—
134	C₄×D₄×C₆₇	C₂³	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	1	no	—
141	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	2	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	8	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	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
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	#107×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	#102×C₆₇	C₂³	1	4	yes	—
180	#102×C₆₇	C₂³	1	4	yes	—
181	#102×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	—	2	1	no	—
186	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
188	#41×C₆₇	—	2	8	no	—
189	#41×C₆₇	—	2	8	no	—
190	#41×C₆₇	—	4	4	no	—
191	#41×C₆₇	—	4	4	no	—
192	#41×C₆₇	—	4	8	no	—
193	#41×C₆₇	—	4	8	no	—
194	C₂×Q₈×C₆₇	—	2	1	no	—
195	C₂×Q₈×C₆₇	—	2	1	no	—
196	C₂×Q₈×C₆₇	—	2	1	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	—	2	2	no	—
203	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
204	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
206	C₂×D₄×C₆₇	—	2	4	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	2	1	no	—
209	C₂×D₄×C₆₇	—	2	2	no	—
210	C₂×D₄×C₆₇	—	4	2	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	4	4	no	—
213	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₆₇	#41	1	4	yes	—
215	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
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	1	no	—
222	C₂²×C₄×C₆₇	—	2	1	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	4	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	—	4	4	no	—
233	C₂²×C₄×C₆₇	—	4	4	no	—
234	C₂²×C₄×C₆₇	—	4	4	no	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	Q₁₆×C₆₇	—	4	4	no	—
245	Q₁₆×C₆₇	—	4	4	no	—
246	SD₁₆×C₆₇	—	2	8	no	—
247	M₁₆×C₆₇	—	4	4	no	—
248	C₂×C₈×C₆₇	—	2	2	no	—
249	C₂×C₈×C₆₇	—	2	2	no	—
250	C₂×C₈×C₆₇	—	2	2	no	—
251	C₂×C₈×C₆₇	—	2	2	no	—
252	C₂×C₈×C₆₇	—	4	4	no	—
253	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
255	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
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	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	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	4	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	C₂×D₄	1	4	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	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	4	no	—
282	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
283	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	4	no	—
286	C₄²×C₆₇	C₂×D₄	1	2	yes	—
287	C₄²×C₆₇	C₂⁴	1	2	yes	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	4	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	2	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	4	2	no	—
297	C₂³×C₆₇	—	4	2	no	—
298	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
300	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₆₇	—	2	2	no	—
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	2	2	no	—
304	Q₈×C₆₇	—	2	2	no	—
305	Q₈×C₆₇	—	2	2	no	—
306	Q₈×C₆₇	—	2	2	no	—
307	Q₈×C₆₇	—	4	2	no	—
308	Q₈×C₆₇	—	4	2	no	—
309	Q₈×C₆₇	—	4	2	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	2	no	—
312	D₄×C₆₇	—	4	4	no	—
313	D₄×C₆₇	—	4	8	no	—
314	D₄×C₆₇	—	4	8	no	—
315	D₄×C₆₇	C₂×#41	1	4	yes	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	4	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	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	—	4	8	no	—
335	C₂×C₄×C₆₇	—	4	8	no	—
336	C₂×C₄×C₆₇	—	4	8	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	—	4	2	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	4	2	no	—
343	C₂×C₄×C₆₇	—	4	2	no	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
351	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
352	C₈×C₆₇	—	2	2	no	—
353	C₈×C₆₇	—	2	2	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₈×C₆₇	—	2	2	no	—
356	C₂²×C₆₇	—	2	2	no	—
357	C₂²×C₆₇	—	2	2	no	—
358	C₂²×C₆₇	—	2	4	no	—
359	C₂²×C₆₇	—	2	2	no	—
360	C₂²×C₆₇	—	2	2	no	—
361	C₂²×C₆₇	—	2	2	no	—
362	C₂²×C₆₇	—	2	2	no	—
363	C₂²×C₆₇	—	4	4	no	—
364	C₂²×C₆₇	—	4	4	no	—
365	C₂²×C₆₇	—	4	8	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	#546	1	2	yes	—
369	C₂²×C₆₇	#575	1	2	yes	—
370	C₂²×C₆₇	#578	1	2	yes	—
371	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₆₇	—	2	2	no	—
373	C₄×C₆₇	—	2	2	no	—
374	C₄×C₆₇	—	2	2	no	—
375	C₄×C₆₇	—	2	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	#546	1	2	yes	—
384	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
385	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂×#3315	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂×C₆₇	—	4	2	no	—
388	C₂×C₆₇	—	4	2	no	—
389	C₂×C₆₇	—	4	4	no	—
390	C₂×C₆₇	#3315	1	4	yes	direct product factor
391	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
392	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
393	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
394	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
395	C₂×#547	C₂×C₆₇	1	1	yes	characteristic
396	#3315	C₂×C₆₇	1	16	yes	direct product factor
397	C₂×#491	C₂×C₆₇	1	1	yes	characteristic, complemented
398	C₂×#484	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₂×#470	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₂×#467	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₂×#462	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
406	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
408	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
409	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
410	C₆₇	C₂×#3315	1	1	yes	characteristic, direct product factor, Sylow
411	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
412	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
413	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
414	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
416	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
417	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
418	#552	—	2	4	no	—
419	#552	C₂²×C₆₇	1	8	yes	complemented
420	#547	—	2	4	no	—
421	#547	C₂²×C₆₇	1	8	yes	—
422	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#126	—	2	1	no	—
424	C₂×#125	—	2	1	no	—
425	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#123	—	2	1	no	—
427	C₂×#123	—	2	1	no	—
428	C₂×#123	—	2	1	no	—
429	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#121	—	2	1	no	—
434	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×#117	—	2	1	no	—
438	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	—	2	1	no	—
440	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
441	#491	C₂²×C₆₇	1	8	yes	complemented
442	#485	C₂²×C₆₇	1	8	yes	complemented
443	#484	C₂²×C₆₇	1	8	yes	complemented
444	#478	C₂²×C₆₇	1	8	yes	complemented
445	#470	C₂²×C₆₇	1	8	yes	complemented
446	#467	C₂²×C₆₇	1	8	yes	complemented
447	#462	C₂²×C₆₇	1	8	yes	complemented
448	#452	C₂²×C₆₇	1	8	yes	complemented
449	#452	C₂²×C₆₇	1	8	yes	complemented
450	#440	C₂²×C₆₇	1	8	yes	complemented
451	#435	C₂²×C₆₇	1	8	yes	complemented
452	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
456	#417	C₂²×C₆₇	1	8	yes	complemented
457	#416	C₂²×C₆₇	1	8	yes	complemented
458	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
463	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	4	no	—
474	C₂×#41	—	2	4	no	—
475	C₂×#41	—	4	2	no	—
476	C₂×#41	—	4	2	no	—
477	C₂×#41	C₂³×C₆₇	1	4	yes	—
478	C₂×#41	C₂³×C₆₇	1	4	yes	—
479	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×Q₁₆	—	4	2	no	—
493	C₂×Q₁₆	—	4	2	no	—
494	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
495	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
496	C₂×SD₁₆	—	2	4	no	—
497	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
498	C₂×M₁₆	—	4	2	no	—
499	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂²×C₈	—	4	2	no	—
501	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
508	#126	—	2	8	no	—
509	#125	—	2	8	no	—
510	#125	—	2	2	no	—
511	#125	C₂³×C₆₇	1	4	yes	—
512	#123	—	2	8	no	—
513	#123	—	2	8	no	—
514	#123	—	2	8	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
520	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
521	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
522	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
523	#121	—	2	8	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	D₄×C₆₇	1	4	yes	—
528	C₄×D₄	C₂³×C₆₇	1	4	yes	—
529	C₄×D₄	C₂³×C₆₇	1	4	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	8	no	—
532	#117	C₂³×C₆₇	1	4	yes	—
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	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	8	no	—
545	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
562	#107	C₂³×C₆₇	1	4	yes	—
563	#107	C₂³×C₆₇	1	4	yes	—
564	#106	C₂³×C₆₇	1	4	yes	—
565	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
566	#103	C₂³×C₆₇	1	4	yes	—
567	#103	C₂³×C₆₇	1	4	yes	—
568	#103	C₂³×C₆₇	1	4	yes	—
569	#103	C₂³×C₆₇	1	4	yes	—
570	#103	C₂³×C₆₇	1	4	yes	—
571	#103	C₂³×C₆₇	1	4	yes	—
572	#103	C₂³×C₆₇	1	4	yes	—
573	#102	C₂³×C₆₇	1	4	yes	—
574	#102	C₂³×C₆₇	1	4	yes	—
575	#102	C₂³×C₆₇	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
578	#97	C₂³×C₆₇	1	4	yes	—
579	C₂⁴	—	2	1	no	—
580	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
582	#41	—	2	8	no	—
583	#41	—	2	8	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	#41	—	4	8	no	—
587	#41	—	4	8	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
598	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
599	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
608	C₂×D₄	#41×C₆₇	1	4	yes	—
609	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	Q₁₆	—	4	4	no	—
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	2	8	no	—
641	M₁₆	—	4	4	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
649	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
650	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
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	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
677	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	4	no	—
680	C₄²	C₂×D₄×C₆₇	1	2	yes	—
681	C₄²	C₂⁴×C₆₇	1	2	yes	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
693	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
694	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
695	Q₈	—	2	2	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	D₄	—	2	4	no	—
705	D₄	—	2	2	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	C₂×#41×C₆₇	1	4	yes	—
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	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
744	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
745	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	4	4	no	—
759	C₂²	—	4	8	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	#546×C₆₇	1	2	yes	—
763	C₂²	#575×C₆₇	1	2	yes	—
764	C₂²	#578×C₆₇	1	2	yes	—
765	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	#546×C₆₇	1	2	yes	—
778	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
779	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
780	C₂	—	4	2	no	—
781	C₂	—	4	2	no	—
782	C₂	—	4	4	no	—
783	C₂	C₆₇×#3315	1	4	yes	direct product factor
784	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
785	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
786	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	C₂×#547×C₆₇	C₂
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
1. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#3315	C₂	direct (N × H)
4. C₂×#491×C₆₇	C₂	semidirect
5. C₂×#484×C₆₇	C₂	semidirect
6. C₂×#485×C₆₇	C₂	semidirect
7. C₂×#478×C₆₇	C₂	semidirect
8. C₂×#470×C₆₇	C₂	semidirect
9. C₂×#467×C₆₇	C₂	semidirect
10. C₂×#462×C₆₇	C₂	semidirect
11. C₂×#452×C₆₇	C₂	semidirect
12. C₂×#452×C₆₇	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₂×#435×C₆₇	C₂	semidirect
15. C₂×#417×C₆₇	C₂	semidirect
16. C₂×#416×C₆₇	C₂	semidirect
25. #552×C₆₇	C₂²	semidirect
47. #491×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #478×C₆₇	C₂²	semidirect
51. #470×C₆₇	C₂²	semidirect
52. #467×C₆₇	C₂²	semidirect
53. #462×C₆₇	C₂²	semidirect
54. #452×C₆₇	C₂²	semidirect
55. #452×C₆₇	C₂²	semidirect
56. #440×C₆₇	C₂²	semidirect
57. #435×C₆₇	C₂²	semidirect
62. #417×C₆₇	C₂²	semidirect
63. #416×C₆₇	C₂²	semidirect
386. C₂×#3315	C₆₇	direct (N × H)
390. C₂×C₆₇	#3315	direct (N × H)
394. C₂×#552	C₂×C₆₇	semidirect
396. #3315	C₂×C₆₇	direct (N × H)
397. C₂×#491	C₂×C₆₇	semidirect
398. C₂×#484	C₂×C₆₇	semidirect
399. C₂×#485	C₂×C₆₇	semidirect
400. C₂×#478	C₂×C₆₇	semidirect
401. C₂×#470	C₂×C₆₇	semidirect
402. C₂×#467	C₂×C₆₇	semidirect
403. C₂×#462	C₂×C₆₇	semidirect
404. C₂×#452	C₂×C₆₇	semidirect
405. C₂×#452	C₂×C₆₇	semidirect
406. C₂×#440	C₂×C₆₇	semidirect
407. C₂×#435	C₂×C₆₇	semidirect
408. C₂×#417	C₂×C₆₇	semidirect
409. C₂×#416	C₂×C₆₇	semidirect
410. C₆₇	C₂×#3315	direct (N × H)
419. #552	C₂²×C₆₇	semidirect
441. #491	C₂²×C₆₇	semidirect
442. #485	C₂²×C₆₇	semidirect
443. #484	C₂²×C₆₇	semidirect
444. #478	C₂²×C₆₇	semidirect
445. #470	C₂²×C₆₇	semidirect
446. #467	C₂²×C₆₇	semidirect
447. #462	C₂²×C₆₇	semidirect
448. #452	C₂²×C₆₇	semidirect
449. #452	C₂²×C₆₇	semidirect
450. #440	C₂²×C₆₇	semidirect
451. #435	C₂²×C₆₇	semidirect
456. #417	C₂²×C₆₇	semidirect
457. #416	C₂²×C₆₇	semidirect
783. C₂	C₆₇×#3315	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×#547×C₆₇	2
C₆₇×#3315	2
C₂×#491×C₆₇	2
C₂×#484×C₆₇	2
C₂×#485×C₆₇	2
C₂×#478×C₆₇	2
C₂×#470×C₆₇	2
C₂×#467×C₆₇	2
C₂×#462×C₆₇	2
C₂×#452×C₆₇	2
C₂×#440×C₆₇	2
C₂×#435×C₆₇	2
C₂×#417×C₆₇	2
C₂×#416×C₆₇	2
C₂×#3315	67

Subgroups — C2×C67×#3315 #30740385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3315 #30740385