Subgroups — C₂×C₆₇×#3118 #30739798

Order 17152.

2274 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	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3118	C₂	1	16	yes	maximal, direct product factor
4	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#482×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#476×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#450×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×SD₁₆×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	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×D₈×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, complemented
25	C₂×#126×C₆₇	—	2	1	no	—
26	C₂×#124×C₆₇	—	2	1	no	—
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	#518×C₆₇	—	2	4	no	—
33	#518×C₆₇	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	—	2	1	no	—
36	C₂×C₄×D₄×C₆₇	—	2	1	no	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
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, complemented
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
45	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
46	#485×C₆₇	C₂²	1	8	yes	complemented
47	#482×C₆₇	C₂²	1	8	yes	complemented
48	#476×C₆₇	C₂²	1	8	yes	complemented
49	#474×C₆₇	C₂²	1	8	yes	complemented
50	#463×C₆₇	C₂²	1	8	yes	complemented
51	#463×C₆₇	C₂²	1	8	yes	complemented
52	#450×C₆₇	C₂²	1	8	yes	complemented
53	#447×C₆₇	C₂²	1	8	yes	—
54	#442×C₆₇	C₂²	1	8	yes	complemented
55	#440×C₆₇	C₂²	1	8	yes	complemented
56	C₄×SD₁₆×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, complemented
60	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#102×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, complemented
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
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, complemented
76	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₆₇	—	2	1	no	—
78	C₂²×Q₈×C₆₇	—	2	1	no	—
79	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₇	—	2	4	no	—
81	C₂²×D₄×C₆₇	—	2	4	no	—
82	C₂²×D₄×C₆₇	—	2	1	no	—
83	C₂²×D₄×C₆₇	—	2	1	no	—
84	C₂²×D₄×C₆₇	—	2	2	no	—
85	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×SD₁₆×C₆₇	—	2	4	no	—
96	C₂×SD₁₆×C₆₇	—	2	4	no	—
97	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
99	C₂×D₈×C₆₇	—	2	4	no	—
100	C₂×D₈×C₆₇	—	2	4	no	—
101	C₂×D₈×C₆₇	C₂³	1	4	yes	—
102	C₂×D₈×C₆₇	C₂³	1	4	yes	—
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	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
109	#126×C₆₇	—	2	8	no	—
110	#124×C₆₇	—	2	8	no	—
111	#124×C₆₇	—	2	2	no	—
112	#124×C₆₇	C₂³	1	4	yes	complemented
113	#123×C₆₇	—	2	8	no	—
114	C₂²⋊Q₈×C₆₇	—	2	2	no	—
115	C₂²⋊Q₈×C₆₇	—	2	8	no	—
116	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
117	#121×C₆₇	—	2	2	no	—
118	#121×C₆₇	C₂³	1	4	yes	—
119	C₄×Q₈×C₆₇	—	2	2	no	—
120	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
121	C₄×D₄×C₆₇	—	2	8	no	—
122	C₄×D₄×C₆₇	—	2	8	no	—
123	C₄×D₄×C₆₇	—	2	2	no	—
124	C₄×D₄×C₆₇	—	2	2	no	—
125	C₄×D₄×C₆₇	—	2	2	no	—
126	C₄×D₄×C₆₇	—	2	2	no	—
127	C₄×D₄×C₆₇	—	2	2	no	—
128	C₄×D₄×C₆₇	C₂³	1	4	yes	—
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	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
133	#117×C₆₇	—	2	2	no	—
134	#117×C₆₇	D₄	1	4	yes	—
135	#117×C₆₇	C₂³	1	4	yes	—
136	#117×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
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	8	no	—
157	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
158	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
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	complemented
165	#107×C₆₇	C₂³	1	4	yes	complemented
166	#106×C₆₇	C₂³	1	4	yes	complemented
167	#106×C₆₇	C₂³	1	4	yes	complemented
168	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
169	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
170	#103×C₆₇	C₂³	1	4	yes	complemented
171	#103×C₆₇	C₂³	1	4	yes	complemented
172	#102×C₆₇	C₂³	1	4	yes	—
173	#102×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	complemented
177	#102×C₆₇	C₂³	1	4	yes	complemented
178	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
180	#97×C₆₇	C₂³	1	4	yes	complemented
181	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
182	C₂⁴×C₆₇	—	2	8	no	—
183	C₂⁴×C₆₇	—	2	1	no	—
184	C₂⁴×C₆₇	—	2	1	no	—
185	C₂⁴×C₆₇	—	2	4	no	—
186	C₂⁴×C₆₇	—	2	1	no	—
187	C₂⁴×C₆₇	—	8	2	no	—
188	C₂⁴×C₆₇	—	8	2	no	—
189	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₆₇	—	2	1	no	—
191	C₂×Q₈×C₆₇	—	2	4	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	C₂⁴	1	2	yes	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	16	no	—
198	C₂×D₄×C₆₇	—	2	8	no	—
199	C₂×D₄×C₆₇	—	2	8	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	1	no	—
203	C₂×D₄×C₆₇	—	2	1	no	—
204	C₂×D₄×C₆₇	—	2	1	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	8	2	no	—
210	C₂×D₄×C₆₇	#41	1	4	yes	—
211	C₂×D₄×C₆₇	#41	1	4	yes	—
212	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	2	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	1	no	—
221	C₂²×C₄×C₆₇	—	2	1	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	8	2	no	—
228	C₂²×C₄×C₆₇	—	8	2	no	—
229	C₂²×C₄×C₆₇	—	8	2	no	—
230	C₂²×C₄×C₆₇	—	8	2	no	—
231	C₂²×C₄×C₆₇	—	8	2	no	—
232	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₆₇	—	2	8	no	—
241	SD₁₆×C₆₇	—	2	8	no	—
242	D₈×C₆₇	—	2	8	no	—
243	D₈×C₆₇	—	2	8	no	—
244	C₂×C₈×C₆₇	—	2	2	no	—
245	C₂×C₈×C₆₇	—	2	2	no	—
246	C₂×C₈×C₆₇	—	2	2	no	—
247	C₂×C₈×C₆₇	—	2	2	no	—
248	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
249	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	1	no	—
256	C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₆₇	C₂×D₄	1	4	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	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	C₂×D₄	1	2	yes	—
280	C₄²×C₆₇	C₂×D₄	1	2	yes	—
281	C₄²×C₆₇	C₂⁴	1	2	yes	—
282	C₄²×C₆₇	C₂⁴	1	2	yes	—
283	C₂³×C₆₇	—	2	16	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	4	no	—
286	C₂³×C₆₇	—	2	4	no	—
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	—	4	2	no	—
293	C₂³×C₆₇	—	4	2	no	—
294	C₂³×C₆₇	—	4	2	no	—
295	C₂³×C₆₇	—	4	2	no	—
296	C₂³×C₆₇	—	4	2	no	—
297	C₂³×C₆₇	—	4	2	no	—
298	C₂³×C₆₇	—	4	2	no	—
299	C₂³×C₆₇	—	8	4	no	—
300	C₂³×C₆₇	—	8	4	no	—
301	C₂³×C₆₇	—	8	16	no	—
302	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₆₇	—	2	2	no	—
305	Q₈×C₆₇	—	2	2	no	—
306	Q₈×C₆₇	—	4	2	no	—
307	Q₈×C₆₇	—	8	4	no	—
308	D₄×C₆₇	—	2	16	no	—
309	D₄×C₆₇	—	2	4	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	2	no	—
312	D₄×C₆₇	—	2	2	no	—
313	D₄×C₆₇	—	2	2	no	—
314	D₄×C₆₇	—	2	2	no	—
315	D₄×C₆₇	—	4	2	no	—
316	D₄×C₆₇	—	8	4	no	—
317	D₄×C₆₇	C₂×#41	1	4	yes	—
318	D₄×C₆₇	C₂×#41	1	4	yes	—
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	4	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	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	2	no	—
334	C₂×C₄×C₆₇	—	4	2	no	—
335	C₂×C₄×C₆₇	—	4	2	no	—
336	C₂×C₄×C₆₇	—	4	2	no	—
337	C₂×C₄×C₆₇	—	8	4	no	—
338	C₂×C₄×C₆₇	—	8	4	no	—
339	C₂×C₄×C₆₇	—	8	4	no	—
340	C₂×C₄×C₆₇	—	8	4	no	—
341	C₂×C₄×C₆₇	—	8	4	no	—
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	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	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
349	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
351	C₈×C₆₇	—	2	2	no	—
352	C₈×C₆₇	—	2	2	no	—
353	C₈×C₆₇	—	2	2	no	—
354	C₈×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	2	2	no	—
356	C₂²×C₆₇	—	2	4	no	—
357	C₂²×C₆₇	—	2	4	no	—
358	C₂²×C₆₇	—	2	2	no	—
359	C₂²×C₆₇	—	2	2	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	8	no	—
362	C₂²×C₆₇	—	4	8	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	2	no	—
370	C₂²×C₆₇	—	8	16	no	—
371	C₂²×C₆₇	—	8	4	no	—
372	C₂²×C₆₇	#525	1	2	yes	—
373	C₂²×C₆₇	#576	1	2	yes	—
374	C₂²×C₆₇	#577	1	2	yes	—
375	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	2	no	—
379	C₄×C₆₇	—	2	2	no	—
380	C₄×C₆₇	—	2	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	—	4	2	no	—
385	C₄×C₆₇	—	4	2	no	—
386	C₄×C₆₇	#525	1	2	yes	—
387	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
388	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
389	C₂×#3118	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂×C₆₇	—	4	2	no	—
391	C₂×C₆₇	—	4	4	no	—
392	C₂×C₆₇	—	4	4	no	—
393	C₂×C₆₇	—	8	2	no	—
394	C₂×C₆₇	#3118	1	4	yes	direct product factor
395	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
396	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
397	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
398	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
400	#3118	C₂×C₆₇	1	16	yes	direct product factor
401	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₂×#482	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₂×#476	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
406	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₂×#450	C₂×C₆₇	1	1	yes	characteristic, complemented
408	C₂×#447	C₂×C₆₇	1	1	yes	characteristic
409	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
410	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
411	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
412	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
413	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
414	C₆₇	C₂×#3118	1	1	yes	characteristic, direct product factor, Sylow
415	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
417	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
418	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
419	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
420	#542	—	2	4	no	—
421	#542	C₂²×C₆₇	1	8	yes	complemented
422	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
423	C₂×#126	—	2	1	no	—
424	C₂×#124	—	2	1	no	—
425	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
426	C₂×#123	—	2	1	no	—
427	C₂×C₂²⋊Q₈	—	2	1	no	—
428	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
430	#518	—	2	4	no	—
431	#518	C₂²×C₆₇	1	8	yes	complemented
432	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
433	C₂×C₄×D₄	—	2	1	no	—
434	C₂×C₄×D₄	—	2	1	no	—
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
441	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	—	2	1	no	—
443	C₂²×C₂²⋊C₄	—	2	1	no	—
444	#485	C₂²×C₆₇	1	8	yes	complemented
445	#482	C₂²×C₆₇	1	8	yes	complemented
446	#476	C₂²×C₆₇	1	8	yes	complemented
447	#474	C₂²×C₆₇	1	8	yes	complemented
448	#463	C₂²×C₆₇	1	8	yes	complemented
449	#463	C₂²×C₆₇	1	8	yes	complemented
450	#450	C₂²×C₆₇	1	8	yes	complemented
451	#447	C₂²×C₆₇	1	8	yes	—
452	#442	C₂²×C₆₇	1	8	yes	complemented
453	#440	C₂²×C₆₇	1	8	yes	complemented
454	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
455	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
456	#433	C₂²×C₆₇	1	8	yes	complemented
457	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
460	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
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×#102	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
474	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	C₂⁵	—	2	1	no	—
476	C₂²×Q₈	—	2	1	no	—
477	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₂²×D₄	—	2	4	no	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
485	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×SD₁₆	—	2	4	no	—
494	C₂×SD₁₆	—	2	4	no	—
495	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
497	C₂×D₈	—	2	4	no	—
498	C₂×D₈	—	2	4	no	—
499	C₂×D₈	C₂³×C₆₇	1	4	yes	—
500	C₂×D₈	C₂³×C₆₇	1	4	yes	—
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	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
507	#126	—	2	8	no	—
508	#124	—	2	8	no	—
509	#124	—	2	2	no	—
510	#124	C₂³×C₆₇	1	4	yes	complemented
511	#123	—	2	8	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	8	no	—
514	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
515	#121	—	2	2	no	—
516	#121	C₂³×C₆₇	1	4	yes	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	C₂³×C₆₇	1	4	yes	—
527	C₄×D₄	C₂³×C₆₇	1	4	yes	—
528	C₄×D₄	C₂³×C₆₇	1	4	yes	—
529	C₄×D₄	C₂³×C₆₇	1	4	yes	—
530	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
531	#117	—	2	2	no	—
532	#117	D₄×C₆₇	1	4	yes	—
533	#117	C₂³×C₆₇	1	4	yes	—
534	#117	C₂³×C₆₇	1	4	yes	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
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	8	no	—
555	C₂×C₂²⋊C₄	—	2	8	no	—
556	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
562	#107	C₂³×C₆₇	1	4	yes	complemented
563	#107	C₂³×C₆₇	1	4	yes	complemented
564	#106	C₂³×C₆₇	1	4	yes	complemented
565	#106	C₂³×C₆₇	1	4	yes	complemented
566	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
567	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
568	#103	C₂³×C₆₇	1	4	yes	complemented
569	#103	C₂³×C₆₇	1	4	yes	complemented
570	#102	C₂³×C₆₇	1	4	yes	—
571	#102	C₂³×C₆₇	1	4	yes	—
572	#102	C₂³×C₆₇	1	4	yes	—
573	#102	C₂³×C₆₇	1	4	yes	—
574	#102	C₂³×C₆₇	1	4	yes	complemented
575	#102	C₂³×C₆₇	1	4	yes	complemented
576	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
578	#97	C₂³×C₆₇	1	4	yes	complemented
579	C₄×C₈	C₂³×C₆₇	1	4	yes	complemented
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	—	2	1	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	8	2	no	—
586	C₂⁴	—	8	2	no	—
587	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	8	2	no	—
593	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	16	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	8	2	no	—
608	C₂×D₄	#41×C₆₇	1	4	yes	—
609	C₂×D₄	#41×C₆₇	1	4	yes	—
610	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	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	4	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	—	8	2	no	—
626	C₂²×C₄	—	8	2	no	—
627	C₂²×C₄	—	8	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	—	8	2	no	—
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	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	SD₁₆	—	2	8	no	—
639	SD₁₆	—	2	8	no	—
640	D₈	—	2	8	no	—
641	D₈	—	2	8	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	C₂⁴×C₆₇	1	2	yes	—
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	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
658	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
674	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	C₂×D₄×C₆₇	1	2	yes	—
678	C₄²	C₂×D₄×C₆₇	1	2	yes	—
679	C₄²	C₂⁴×C₆₇	1	2	yes	—
680	C₄²	C₂⁴×C₆₇	1	2	yes	—
681	C₂³	—	2	16	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	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	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	16	no	—
700	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
701	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	4	2	no	—
705	Q₈	—	8	4	no	—
706	D₄	—	2	16	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	8	4	no	—
715	D₄	C₂×#41×C₆₇	1	4	yes	—
716	D₄	C₂×#41×C₆₇	1	4	yes	—
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	4	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	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	4	2	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	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
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	2	yes	—
743	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
747	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
748	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	2	no	—
752	C₈	—	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	—	2	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	8	no	—
764	C₂²	—	4	8	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	16	no	—
769	C₂²	—	8	4	no	—
770	C₂²	#525×C₆₇	1	2	yes	—
771	C₂²	#576×C₆₇	1	2	yes	—
772	C₂²	#577×C₆₇	1	2	yes	—
773	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	#525×C₆₇	1	2	yes	—
785	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
786	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
787	C₂	—	4	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	4	4	no	—
790	C₂	—	8	2	no	—
791	C₂	C₆₇×#3118	1	4	yes	direct product factor
792	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
793	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
794	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#447×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×#518×C₆₇	C₂	semidirect
3. C₆₇×#3118	C₂	direct (N × H)
4. C₂×#485×C₆₇	C₂	semidirect
5. C₂×#482×C₆₇	C₂	semidirect
6. C₂×#476×C₆₇	C₂	semidirect
7. C₂×#474×C₆₇	C₂	semidirect
8. C₂×#463×C₆₇	C₂	semidirect
9. C₂×#463×C₆₇	C₂	semidirect
10. C₂×#450×C₆₇	C₂	semidirect
12. C₂×#442×C₆₇	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
15. C₂×C₄×D₈×C₆₇	C₂	semidirect
16. C₂×#433×C₆₇	C₂	semidirect
23. #542×C₆₇	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
27. C₂×#124×C₆₇	C₂²	semidirect
33. #518×C₆₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
41. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. #485×C₆₇	C₂²	semidirect
47. #482×C₆₇	C₂²	semidirect
48. #476×C₆₇	C₂²	semidirect
49. #474×C₆₇	C₂²	semidirect
50. #463×C₆₇	C₂²	semidirect
51. #463×C₆₇	C₂²	semidirect
52. #450×C₆₇	C₂²	semidirect
54. #442×C₆₇	C₂²	semidirect
55. #440×C₆₇	C₂²	semidirect
56. C₄×SD₁₆×C₆₇	C₂²	semidirect
57. C₄×D₈×C₆₇	C₂²	semidirect
58. #433×C₆₇	C₂²	semidirect
59. C₂×#107×C₆₇	C₂²	semidirect
60. C₂×#107×C₆₇	C₂²	semidirect
61. C₂×#106×C₆₇	C₂²	semidirect
62. C₂×#106×C₆₇	C₂²	semidirect
63. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
64. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
65. C₂×#103×C₆₇	C₂²	semidirect
66. C₂×#103×C₆₇	C₂²	semidirect
71. C₂×#102×C₆₇	C₂²	semidirect
72. C₂×#102×C₆₇	C₂²	semidirect
75. C₂×#97×C₆₇	C₂²	semidirect
76. C₂×C₄×C₈×C₆₇	C₂²	semidirect
108. C₄⋊Q₈×C₆₇	C₂³	semidirect
112. #124×C₆₇	C₂³	semidirect
120. C₄×Q₈×C₆₇	C₂³	semidirect
132. C₄×D₄×C₆₇	C₂³	semidirect
164. #107×C₆₇	C₂³	semidirect
165. #107×C₆₇	C₂³	semidirect
166. #106×C₆₇	C₂³	semidirect
167. #106×C₆₇	C₂³	semidirect
168. C₄⋊C₈×C₆₇	C₂³	semidirect
169. C₄⋊C₈×C₆₇	C₂³	semidirect
170. #103×C₆₇	C₂³	semidirect
171. #103×C₆₇	C₂³	semidirect
176. #102×C₆₇	C₂³	semidirect
177. #102×C₆₇	C₂³	semidirect
180. #97×C₆₇	C₂³	semidirect
181. C₄×C₈×C₆₇	C₂³	semidirect
389. C₂×#3118	C₆₇	direct (N × H)
394. C₂×C₆₇	#3118	direct (N × H)
398. C₂×#542	C₂×C₆₇	semidirect
399. C₂×#518	C₂×C₆₇	semidirect
400. #3118	C₂×C₆₇	direct (N × H)
401. C₂×#485	C₂×C₆₇	semidirect
402. C₂×#482	C₂×C₆₇	semidirect
403. C₂×#476	C₂×C₆₇	semidirect
404. C₂×#474	C₂×C₆₇	semidirect
405. C₂×#463	C₂×C₆₇	semidirect
406. C₂×#463	C₂×C₆₇	semidirect
407. C₂×#450	C₂×C₆₇	semidirect
409. C₂×#442	C₂×C₆₇	semidirect
410. C₂×#440	C₂×C₆₇	semidirect
411. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
412. C₂×C₄×D₈	C₂×C₆₇	semidirect
413. C₂×#433	C₂×C₆₇	semidirect
414. C₆₇	C₂×#3118	direct (N × H)
421. #542	C₂²×C₆₇	semidirect
422. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
425. C₂×#124	C₂²×C₆₇	semidirect
431. #518	C₂²×C₆₇	semidirect
432. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
439. C₂×C₄×D₄	C₂²×C₆₇	semidirect
444. #485	C₂²×C₆₇	semidirect
445. #482	C₂²×C₆₇	semidirect
446. #476	C₂²×C₆₇	semidirect
447. #474	C₂²×C₆₇	semidirect
448. #463	C₂²×C₆₇	semidirect
449. #463	C₂²×C₆₇	semidirect
450. #450	C₂²×C₆₇	semidirect
452. #442	C₂²×C₆₇	semidirect
453. #440	C₂²×C₆₇	semidirect
454. C₄×SD₁₆	C₂²×C₆₇	semidirect
455. C₄×D₈	C₂²×C₆₇	semidirect
456. #433	C₂²×C₆₇	semidirect
457. C₂×#107	C₂²×C₆₇	semidirect
458. C₂×#107	C₂²×C₆₇	semidirect
459. C₂×#106	C₂²×C₆₇	semidirect
460. C₂×#106	C₂²×C₆₇	semidirect
461. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
462. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
463. C₂×#103	C₂²×C₆₇	semidirect
464. C₂×#103	C₂²×C₆₇	semidirect
469. C₂×#102	C₂²×C₆₇	semidirect
470. C₂×#102	C₂²×C₆₇	semidirect
473. C₂×#97	C₂²×C₆₇	semidirect
474. C₂×C₄×C₈	C₂²×C₆₇	semidirect
506. C₄⋊Q₈	C₂³×C₆₇	semidirect
510. #124	C₂³×C₆₇	semidirect
518. C₄×Q₈	C₂³×C₆₇	semidirect
530. C₄×D₄	C₂³×C₆₇	semidirect
562. #107	C₂³×C₆₇	semidirect
563. #107	C₂³×C₆₇	semidirect
564. #106	C₂³×C₆₇	semidirect
565. #106	C₂³×C₆₇	semidirect
566. C₄⋊C₈	C₂³×C₆₇	semidirect
567. C₄⋊C₈	C₂³×C₆₇	semidirect
568. #103	C₂³×C₆₇	semidirect
569. #103	C₂³×C₆₇	semidirect
574. #102	C₂³×C₆₇	semidirect
575. #102	C₂³×C₆₇	semidirect
578. #97	C₂³×C₆₇	semidirect
579. C₄×C₈	C₂³×C₆₇	semidirect
791. C₂	C₆₇×#3118	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×#518×C₆₇	2
C₆₇×#3118	2
C₂×#485×C₆₇	2
C₂×#482×C₆₇	2
C₂×#476×C₆₇	2
C₂×#474×C₆₇	2
C₂×#463×C₆₇	2
C₂×#450×C₆₇	2
C₂×#447×C₆₇	2
C₂×#442×C₆₇	2
C₂×#440×C₆₇	2
C₂×C₄×SD₁₆×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#433×C₆₇	2
C₂×#3118	67

Subgroups — C2×C67×#3118 #30739798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3118 #30739798