Subgroups — C₂×C₆₇×#3124 #30739804

Order 17152.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3124	C₂	1	16	yes	maximal, direct product factor
4	C₂×#484×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#480×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#477×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	#542×C₆₇	—	2	4	no	—
23	#542×C₆₇	C₂²	1	8	yes	complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	—	2	1	no	—
26	C₂×#124×C₆₇	—	2	1	no	—
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₇	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	#520×C₆₇	—	2	4	no	—
33	#520×C₆₇	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	—	2	1	no	—
38	C₂×C₄×D₄×C₆₇	—	2	1	no	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	—	2	1	no	—
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	#484×C₆₇	C₂²	1	8	yes	complemented
47	#480×C₆₇	C₂²	1	8	yes	complemented
48	#477×C₆₇	C₂²	1	8	yes	complemented
49	#474×C₆₇	C₂²	1	8	yes	complemented
50	#464×C₆₇	C₂²	1	8	yes	complemented
51	#463×C₆₇	C₂²	1	8	yes	complemented
52	#452×C₆₇	C₂²	1	8	yes	complemented
53	#449×C₆₇	C₂²	1	8	yes	—
54	#440×C₆₇	C₂²	1	8	yes	complemented
55	#440×C₆₇	C₂²	1	8	yes	complemented
56	C₄×Q₁₆×C₆₇	C₂²	1	8	yes	complemented
57	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
58	#433×C₆₇	C₂²	1	8	yes	complemented
59	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×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×#102×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#102×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×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×#41×C₆₇	—	2	4	no	—
78	C₂×#41×C₆₇	—	2	4	no	—
79	C₂×#41×C₆₇	—	2	2	no	—
80	C₂×#41×C₆₇	C₂³	1	4	yes	—
81	C₂²×Q₈×C₆₇	—	2	1	no	—
82	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	—	2	1	no	—
85	C₂²×D₄×C₆₇	—	2	1	no	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	—	2	1	no	—
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	—	2	1	no	—
92	C₂³×C₄×C₆₇	—	2	1	no	—
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×Q₁₆×C₆₇	—	2	4	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₆₇	—	2	4	no	—
97	C₂×SD₁₆×C₆₇	—	2	4	no	—
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×D₈×C₆₇	—	2	4	no	—
101	C₂×D₈×C₆₇	C₂³	1	4	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₇	—	2	2	no	—
107	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
108	#126×C₆₇	—	2	8	no	—
109	#124×C₆₇	—	2	8	no	—
110	#124×C₆₇	—	2	2	no	—
111	#124×C₆₇	C₂³	1	4	yes	—
112	#123×C₆₇	—	2	8	no	—
113	C₂²⋊Q₈×C₆₇	—	2	2	no	—
114	C₂²⋊Q₈×C₆₇	—	2	8	no	—
115	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
116	#121×C₆₇	—	2	2	no	—
117	#121×C₆₇	C₂³	1	4	yes	—
118	C₄×Q₈×C₆₇	—	2	2	no	—
119	C₄×Q₈×C₆₇	—	2	2	no	—
120	C₄×Q₈×C₆₇	—	2	2	no	—
121	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
122	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
123	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
124	C₄×D₄×C₆₇	—	2	8	no	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	2	no	—
127	C₄×D₄×C₆₇	—	2	2	no	—
128	C₄×D₄×C₆₇	—	2	2	no	—
129	C₄×D₄×C₆₇	C₂³	1	4	yes	—
130	C₄×D₄×C₆₇	C₂³	1	4	yes	—
131	C₄×D₄×C₆₇	C₂³	1	4	yes	—
132	#117×C₆₇	—	2	8	no	—
133	#117×C₆₇	D₄	1	4	yes	—
134	#117×C₆₇	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
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	8	no	—
143	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	—	2	1	no	—
160	C₂×C₄²×C₆₇	—	2	1	no	—
161	C₂×C₄²×C₆₇	—	2	1	no	—
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	#107×C₆₇	C₂³	1	4	yes	—
165	#107×C₆₇	C₂³	1	4	yes	—
166	#107×C₆₇	C₂³	1	4	yes	—
167	#107×C₆₇	C₂³	1	4	yes	—
168	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
169	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
170	#103×C₆₇	C₂³	1	4	yes	—
171	#103×C₆₇	C₂³	1	4	yes	—
172	#103×C₆₇	C₂³	1	4	yes	—
173	#103×C₆₇	C₂³	1	4	yes	—
174	#102×C₆₇	C₂³	1	4	yes	—
175	#102×C₆₇	C₂³	1	4	yes	—
176	#102×C₆₇	C₂³	1	4	yes	—
177	#102×C₆₇	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
180	#97×C₆₇	C₂³	1	4	yes	—
181	C₄×C₈×C₆₇	C₂³	1	4	yes	—
182	C₂⁴×C₆₇	—	2	1	no	—
183	C₂⁴×C₆₇	—	2	1	no	—
184	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
185	#41×C₆₇	—	2	16	no	—
186	#41×C₆₇	—	2	8	no	—
187	#41×C₆₇	—	2	8	no	—
188	C₂×Q₈×C₆₇	—	2	1	no	—
189	C₂×Q₈×C₆₇	—	2	1	no	—
190	C₂×Q₈×C₆₇	—	2	4	no	—
191	C₂×Q₈×C₆₇	—	2	2	no	—
192	C₂×Q₈×C₆₇	—	2	2	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	—	8	2	no	—
195	C₂×Q₈×C₆₇	#41	1	4	yes	—
196	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
198	C₂×D₄×C₆₇	—	2	8	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	1	no	—
202	C₂×D₄×C₆₇	—	2	1	no	—
203	C₂×D₄×C₆₇	—	2	2	no	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	8	2	no	—
207	C₂×D₄×C₆₇	#41	1	4	yes	—
208	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	—	2	8	no	—
211	C₂²×C₄×C₆₇	—	2	1	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	2	2	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	1	no	—
216	C₂²×C₄×C₆₇	—	2	1	no	—
217	C₂²×C₄×C₆₇	—	2	1	no	—
218	C₂²×C₄×C₆₇	—	2	1	no	—
219	C₂²×C₄×C₆₇	—	2	1	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	4	no	—
224	C₂²×C₄×C₆₇	—	8	2	no	—
225	C₂²×C₄×C₆₇	—	8	2	no	—
226	C₂²×C₄×C₆₇	—	8	2	no	—
227	C₂²×C₄×C₆₇	—	8	2	no	—
228	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₆₇	—	2	8	no	—
237	SD₁₆×C₆₇	—	2	8	no	—
238	SD₁₆×C₆₇	—	2	8	no	—
239	D₈×C₆₇	—	2	8	no	—
240	C₂×C₈×C₆₇	—	2	2	no	—
241	C₂×C₈×C₆₇	—	2	2	no	—
242	C₂×C₈×C₆₇	—	2	2	no	—
243	C₂×C₈×C₆₇	—	2	2	no	—
244	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	1	no	—
252	C₄⋊C₄×C₆₇	—	2	1	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
273	C₄²×C₆₇	—	2	4	no	—
274	C₄²×C₆₇	—	2	4	no	—
275	C₄²×C₆₇	—	2	4	no	—
276	C₄²×C₆₇	C₂×D₄	1	2	yes	—
277	C₄²×C₆₇	C₂×D₄	1	2	yes	—
278	C₄²×C₆₇	C₂⁴	1	2	yes	—
279	C₄²×C₆₇	C₂⁴	1	2	yes	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	4	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	4	2	no	—
287	C₂³×C₆₇	—	4	2	no	—
288	C₂³×C₆₇	—	4	2	no	—
289	C₂³×C₆₇	—	4	2	no	—
290	C₂³×C₆₇	—	4	2	no	—
291	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
292	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₆₇	—	2	4	no	—
294	Q₈×C₆₇	—	2	2	no	—
295	Q₈×C₆₇	—	2	2	no	—
296	Q₈×C₆₇	—	2	2	no	—
297	Q₈×C₆₇	—	4	2	no	—
298	Q₈×C₆₇	—	8	4	no	—
299	Q₈×C₆₇	C₂×#41	1	4	yes	—
300	D₄×C₆₇	—	2	16	no	—
301	D₄×C₆₇	—	2	4	no	—
302	D₄×C₆₇	—	2	2	no	—
303	D₄×C₆₇	—	2	2	no	—
304	D₄×C₆₇	—	2	2	no	—
305	D₄×C₆₇	—	4	2	no	—
306	D₄×C₆₇	—	8	4	no	—
307	D₄×C₆₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₆₇	—	2	16	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	4	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	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	—	4	2	no	—
325	C₂×C₄×C₆₇	—	4	2	no	—
326	C₂×C₄×C₆₇	—	4	2	no	—
327	C₂×C₄×C₆₇	—	4	2	no	—
328	C₂×C₄×C₆₇	—	4	2	no	—
329	C₂×C₄×C₆₇	—	8	4	no	—
330	C₂×C₄×C₆₇	—	8	4	no	—
331	C₂×C₄×C₆₇	—	8	4	no	—
332	C₂×C₄×C₆₇	—	8	4	no	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
340	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
341	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
342	C₈×C₆₇	—	2	2	no	—
343	C₈×C₆₇	—	2	2	no	—
344	C₈×C₆₇	—	2	2	no	—
345	C₈×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	2	no	—
347	C₂²×C₆₇	—	2	4	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	4	4	no	—
351	C₂²×C₆₇	—	4	8	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	2	no	—
356	C₂²×C₆₇	—	4	2	no	—
357	C₂²×C₆₇	—	8	4	no	—
358	C₂²×C₆₇	#525	1	2	yes	—
359	C₂²×C₆₇	#576	1	2	yes	—
360	C₂²×C₆₇	#578	1	2	yes	—
361	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	2	4	no	—
364	C₄×C₆₇	—	2	2	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	2	no	—
367	C₄×C₆₇	—	2	2	no	—
368	C₄×C₆₇	—	4	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	#525	1	2	yes	—
374	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
375	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
376	C₂×#3124	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂×C₆₇	—	4	2	no	—
378	C₂×C₆₇	—	4	4	no	—
379	C₂×C₆₇	—	8	2	no	—
380	C₂×C₆₇	#3124	1	4	yes	direct product factor
381	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
382	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
383	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
384	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
386	#3124	C₂×C₆₇	1	16	yes	direct product factor
387	C₂×#484	C₂×C₆₇	1	1	yes	characteristic, complemented
388	C₂×#480	C₂×C₆₇	1	1	yes	characteristic, complemented
389	C₂×#477	C₂×C₆₇	1	1	yes	characteristic, complemented
390	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₂×#449	C₂×C₆₇	1	1	yes	characteristic
395	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
396	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
397	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
398	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₆₇	C₂×#3124	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
402	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
403	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
404	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
406	#542	—	2	4	no	—
407	#542	C₂²×C₆₇	1	8	yes	complemented
408	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×#126	—	2	1	no	—
410	C₂×#124	—	2	1	no	—
411	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#123	—	2	1	no	—
413	C₂×C₂²⋊Q₈	—	2	1	no	—
414	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
416	#520	—	2	4	no	—
417	#520	C₂²×C₆₇	1	8	yes	complemented
418	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×C₄×D₄	—	2	1	no	—
422	C₂×C₄×D₄	—	2	1	no	—
423	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#117	—	2	1	no	—
427	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	—	2	1	no	—
429	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
430	#484	C₂²×C₆₇	1	8	yes	complemented
431	#480	C₂²×C₆₇	1	8	yes	complemented
432	#477	C₂²×C₆₇	1	8	yes	complemented
433	#474	C₂²×C₆₇	1	8	yes	complemented
434	#464	C₂²×C₆₇	1	8	yes	complemented
435	#463	C₂²×C₆₇	1	8	yes	complemented
436	#452	C₂²×C₆₇	1	8	yes	complemented
437	#449	C₂²×C₆₇	1	8	yes	—
438	#440	C₂²×C₆₇	1	8	yes	complemented
439	#440	C₂²×C₆₇	1	8	yes	complemented
440	C₄×Q₁₆	C₂²×C₆₇	1	8	yes	complemented
441	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
442	#433	C₂²×C₆₇	1	8	yes	complemented
443	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
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×#102	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	4	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	C₂³×C₆₇	1	4	yes	—
465	C₂²×Q₈	—	2	1	no	—
466	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
467	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
478	C₂×Q₁₆	—	2	4	no	—
479	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
480	C₂×SD₁₆	—	2	4	no	—
481	C₂×SD₁₆	—	2	4	no	—
482	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
484	C₂×D₈	—	2	4	no	—
485	C₂×D₈	C₂³×C₆₇	1	4	yes	—
486	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
490	C₄⋊Q₈	—	2	2	no	—
491	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
492	#126	—	2	8	no	—
493	#124	—	2	8	no	—
494	#124	—	2	2	no	—
495	#124	C₂³×C₆₇	1	4	yes	—
496	#123	—	2	8	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	8	no	—
499	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
500	#121	—	2	2	no	—
501	#121	C₂³×C₆₇	1	4	yes	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
506	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
507	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	C₂³×C₆₇	1	4	yes	—
514	C₄×D₄	C₂³×C₆₇	1	4	yes	—
515	C₄×D₄	C₂³×C₆₇	1	4	yes	—
516	#117	—	2	8	no	—
517	#117	D₄×C₆₇	1	4	yes	—
518	#117	C₂³×C₆₇	1	4	yes	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	2	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	8	no	—
527	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
528	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	#107	C₂³×C₆₇	1	4	yes	—
549	#107	C₂³×C₆₇	1	4	yes	—
550	#107	C₂³×C₆₇	1	4	yes	—
551	#107	C₂³×C₆₇	1	4	yes	—
552	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
554	#103	C₂³×C₆₇	1	4	yes	—
555	#103	C₂³×C₆₇	1	4	yes	—
556	#103	C₂³×C₆₇	1	4	yes	—
557	#103	C₂³×C₆₇	1	4	yes	—
558	#102	C₂³×C₆₇	1	4	yes	—
559	#102	C₂³×C₆₇	1	4	yes	—
560	#102	C₂³×C₆₇	1	4	yes	—
561	#102	C₂³×C₆₇	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
564	#97	C₂³×C₆₇	1	4	yes	—
565	C₄×C₈	C₂³×C₆₇	1	4	yes	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
569	#41	—	2	16	no	—
570	#41	—	2	8	no	—
571	#41	—	2	8	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	8	2	no	—
579	C₂×Q₈	#41×C₆₇	1	4	yes	—
580	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
581	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	8	2	no	—
591	C₂×D₄	#41×C₆₇	1	4	yes	—
592	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
593	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	8	2	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	—	8	2	no	—
612	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
620	Q₁₆	—	2	8	no	—
621	SD₁₆	—	2	8	no	—
622	SD₁₆	—	2	8	no	—
623	D₈	—	2	8	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
629	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
630	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
631	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
643	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₆₇	1	2	yes	—
661	C₄²	C₂×D₄×C₆₇	1	2	yes	—
662	C₄²	C₂⁴×C₆₇	1	2	yes	—
663	C₄²	C₂⁴×C₆₇	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
676	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
677	Q₈	—	2	4	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	2	no	—
682	Q₈	—	8	4	no	—
683	Q₈	C₂×#41×C₆₇	1	4	yes	—
684	D₄	—	2	16	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	8	4	no	—
691	D₄	C₂×#41×C₆₇	1	4	yes	—
692	C₂×C₄	—	2	16	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
724	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
725	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	4	no	—
742	C₂²	#525×C₆₇	1	2	yes	—
743	C₂²	#576×C₆₇	1	2	yes	—
744	C₂²	#578×C₆₇	1	2	yes	—
745	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	#525×C₆₇	1	2	yes	—
758	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
759	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₆₇×#3124	1	4	yes	direct product factor
764	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
765	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
766	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×#449×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#542×C₆₇	C₂	semidirect
2. C₂×#520×C₆₇	C₂	semidirect
3. C₆₇×#3124	C₂	direct (N × H)
4. C₂×#484×C₆₇	C₂	semidirect
5. C₂×#480×C₆₇	C₂	semidirect
6. C₂×#477×C₆₇	C₂	semidirect
7. C₂×#474×C₆₇	C₂	semidirect
8. C₂×#464×C₆₇	C₂	semidirect
9. C₂×#463×C₆₇	C₂	semidirect
10. C₂×#452×C₆₇	C₂	semidirect
12. C₂×#440×C₆₇	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
15. C₂×C₄×D₈×C₆₇	C₂	semidirect
16. C₂×#433×C₆₇	C₂	semidirect
23. #542×C₆₇	C₂²	semidirect
33. #520×C₆₇	C₂²	semidirect
46. #484×C₆₇	C₂²	semidirect
47. #480×C₆₇	C₂²	semidirect
48. #477×C₆₇	C₂²	semidirect
49. #474×C₆₇	C₂²	semidirect
50. #464×C₆₇	C₂²	semidirect
51. #463×C₆₇	C₂²	semidirect
52. #452×C₆₇	C₂²	semidirect
54. #440×C₆₇	C₂²	semidirect
55. #440×C₆₇	C₂²	semidirect
56. C₄×Q₁₆×C₆₇	C₂²	semidirect
57. C₄×D₈×C₆₇	C₂²	semidirect
58. #433×C₆₇	C₂²	semidirect
376. C₂×#3124	C₆₇	direct (N × H)
380. C₂×C₆₇	#3124	direct (N × H)
384. C₂×#542	C₂×C₆₇	semidirect
385. C₂×#520	C₂×C₆₇	semidirect
386. #3124	C₂×C₆₇	direct (N × H)
387. C₂×#484	C₂×C₆₇	semidirect
388. C₂×#480	C₂×C₆₇	semidirect
389. C₂×#477	C₂×C₆₇	semidirect
390. C₂×#474	C₂×C₆₇	semidirect
391. C₂×#464	C₂×C₆₇	semidirect
392. C₂×#463	C₂×C₆₇	semidirect
393. C₂×#452	C₂×C₆₇	semidirect
395. C₂×#440	C₂×C₆₇	semidirect
396. C₂×#440	C₂×C₆₇	semidirect
397. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
398. C₂×C₄×D₈	C₂×C₆₇	semidirect
399. C₂×#433	C₂×C₆₇	semidirect
400. C₆₇	C₂×#3124	direct (N × H)
407. #542	C₂²×C₆₇	semidirect
417. #520	C₂²×C₆₇	semidirect
430. #484	C₂²×C₆₇	semidirect
431. #480	C₂²×C₆₇	semidirect
432. #477	C₂²×C₆₇	semidirect
433. #474	C₂²×C₆₇	semidirect
434. #464	C₂²×C₆₇	semidirect
435. #463	C₂²×C₆₇	semidirect
436. #452	C₂²×C₆₇	semidirect
438. #440	C₂²×C₆₇	semidirect
439. #440	C₂²×C₆₇	semidirect
440. C₄×Q₁₆	C₂²×C₆₇	semidirect
441. C₄×D₈	C₂²×C₆₇	semidirect
442. #433	C₂²×C₆₇	semidirect
763. C₂	C₆₇×#3124	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×#542×C₆₇	2
C₂×#520×C₆₇	2
C₆₇×#3124	2
C₂×#484×C₆₇	2
C₂×#480×C₆₇	2
C₂×#477×C₆₇	2
C₂×#474×C₆₇	2
C₂×#464×C₆₇	2
C₂×#463×C₆₇	2
C₂×#452×C₆₇	2
C₂×#449×C₆₇	2
C₂×#440×C₆₇	2
C₂×C₄×Q₁₆×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#433×C₆₇	2
C₂×#3124	67

Subgroups — C2×C67×#3124 #30739804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3124 #30739804