Subgroups — C₂×C₆₇×#3319 #30740387

Order 17152.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3319	C₂	1	16	yes	maximal, direct product factor
4	C₂×#489×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#485×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#482×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#468×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#466×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#418×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	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	#555×C₆₇	—	2	4	no	—
25	#555×C₆₇	C₂²	1	8	yes	complemented
26	#546×C₆₇	—	2	4	no	—
27	#546×C₆₇	C₂²	1	8	yes	complemented
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#124×C₆₇	—	2	1	no	—
30	C₂×#124×C₆₇	—	2	1	no	—
31	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#123×C₆₇	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₇	—	2	1	no	—
35	C₂×#121×C₆₇	—	2	1	no	—
36	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#120×C₆₇	—	2	1	no	—
40	C₂×C₄×D₄×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, complemented
43	C₂×#117×C₆₇	—	2	1	no	—
44	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
47	#489×C₆₇	C₂²	1	8	yes	complemented
48	#485×C₆₇	C₂²	1	8	yes	complemented
49	#482×C₆₇	C₂²	1	8	yes	complemented
50	#474×C₆₇	C₂²	1	8	yes	complemented
51	#468×C₆₇	C₂²	1	8	yes	complemented
52	#466×C₆₇	C₂²	1	8	yes	complemented
53	#463×C₆₇	C₂²	1	8	yes	complemented
54	#449×C₆₇	C₂²	1	8	yes	complemented
55	#447×C₆₇	C₂²	1	8	yes	complemented
56	#442×C₆₇	C₂²	1	8	yes	complemented
57	#435×C₆₇	C₂²	1	8	yes	complemented
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#418×C₆₇	C₂²	1	8	yes	complemented
63	#416×C₆₇	C₂²	1	8	yes	complemented
64	C₂×#103×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
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₆₇	—	2	1	no	—
78	C₂×#41×C₆₇	—	2	2	no	—
79	C₂×#41×C₆₇	—	2	4	no	—
80	C₂×#41×C₆₇	—	4	2	no	—
81	C₂×#41×C₆₇	C₂³	1	4	yes	—
82	C₂²×Q₈×C₆₇	—	2	1	no	—
83	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	—	2	4	no	—
85	C₂²×D₄×C₆₇	—	2	1	no	—
86	C₂²×D₄×C₆₇	—	2	1	no	—
87	C₂²×D₄×C₆₇	—	2	1	no	—
88	C₂²×D₄×C₆₇	—	2	1	no	—
89	C₂²×D₄×C₆₇	—	2	1	no	—
90	C₂²×D₄×C₆₇	—	2	2	no	—
91	C₂²×D₄×C₆₇	—	4	2	no	—
92	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	—	2	1	no	—
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	C₂³×C₄×C₆₇	—	2	1	no	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₆₇	—	4	2	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
104	C₂×D₈×C₆₇	—	2	4	no	—
105	C₂×D₈×C₆₇	—	4	2	no	—
106	C₂×D₈×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	4	yes	—
108	C₂×M₁₆×C₆₇	—	4	2	no	—
109	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂²×C₈×C₆₇	—	4	2	no	—
111	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
116	C₄⋊Q₈×C₆₇	—	2	2	no	—
117	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
118	#124×C₆₇	—	2	8	no	—
119	#124×C₆₇	—	2	8	no	—
120	#124×C₆₇	—	2	2	no	—
121	#124×C₆₇	C₂³	1	4	yes	—
122	#123×C₆₇	—	2	8	no	—
123	C₂²⋊Q₈×C₆₇	—	2	2	no	—
124	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
125	#121×C₆₇	—	2	8	no	—
126	#121×C₆₇	—	2	2	no	—
127	#121×C₆₇	—	2	2	no	—
128	#121×C₆₇	—	2	2	no	—
129	#121×C₆₇	—	2	8	no	—
130	#121×C₆₇	C₂³	1	4	yes	—
131	#121×C₆₇	C₂³	1	4	yes	—
132	#121×C₆₇	C₂³	1	4	yes	complemented
133	#120×C₆₇	—	2	8	no	—
134	C₄×D₄×C₆₇	—	2	2	no	—
135	C₄×D₄×C₆₇	—	2	2	no	—
136	C₄×D₄×C₆₇	D₄	1	4	yes	—
137	C₄×D₄×C₆₇	C₂³	1	4	yes	—
138	C₄×D₄×C₆₇	C₂³	1	4	yes	—
139	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
140	#117×C₆₇	—	2	2	no	—
141	#117×C₆₇	—	2	2	no	—
142	#117×C₆₇	—	2	8	no	—
143	#117×C₆₇	C₂³	1	4	yes	—
144	#117×C₆₇	C₂³	1	4	yes	complemented
145	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
147	C₂×C₄⋊C₄×C₆₇	D₄	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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	—	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	8	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	complemented
169	#107×C₆₇	C₂³	1	4	yes	complemented
170	#106×C₆₇	C₂³	1	4	yes	complemented
171	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
172	#103×C₆₇	C₂³	1	4	yes	complemented
173	#103×C₆₇	C₂³	1	4	yes	complemented
174	#103×C₆₇	C₂³	1	4	yes	complemented
175	#102×C₆₇	C₂³	1	4	yes	—
176	#102×C₆₇	C₂³	1	4	yes	—
177	#102×C₆₇	C₂³	1	4	yes	—
178	#102×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	complemented
182	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
184	#97×C₆₇	C₂³	1	4	yes	complemented
185	C₂⁴×C₆₇	—	2	1	no	—
186	C₂⁴×C₆₇	—	2	1	no	—
187	C₂⁴×C₆₇	—	2	1	no	—
188	C₂⁴×C₆₇	—	2	4	no	—
189	C₂⁴×C₆₇	—	4	4	no	—
190	C₂⁴×C₆₇	—	4	4	no	—
191	C₂⁴×C₆₇	—	8	2	no	—
192	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
194	#41×C₆₇	—	2	8	no	—
195	#41×C₆₇	—	4	4	no	—
196	#41×C₆₇	—	4	8	no	—
197	C₂×Q₈×C₆₇	—	2	1	no	—
198	C₂×Q₈×C₆₇	—	2	4	no	—
199	C₂×Q₈×C₆₇	—	2	2	no	—
200	C₂×Q₈×C₆₇	—	2	2	no	—
201	C₂×Q₈×C₆₇	—	8	2	no	—
202	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
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	1	no	—
210	C₂×D₄×C₆₇	—	2	4	no	—
211	C₂×D₄×C₆₇	—	2	1	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	2	2	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	2	no	—
217	C₂×D₄×C₆₇	—	4	4	no	—
218	C₂×D₄×C₆₇	—	4	8	no	—
219	C₂×D₄×C₆₇	—	4	2	no	—
220	C₂×D₄×C₆₇	—	4	4	no	—
221	C₂×D₄×C₆₇	—	4	4	no	—
222	C₂×D₄×C₆₇	—	8	2	no	—
223	C₂×D₄×C₆₇	—	8	2	no	—
224	C₂×D₄×C₆₇	—	8	2	no	—
225	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
226	C₂×D₄×C₆₇	#41	1	4	yes	—
227	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	1	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	4	4	no	—
243	C₂²×C₄×C₆₇	—	4	4	no	—
244	C₂²×C₄×C₆₇	—	8	2	no	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₆₇	—	4	4	no	—
255	D₈×C₆₇	—	2	8	no	—
256	D₈×C₆₇	—	4	4	no	—
257	M₁₆×C₆₇	—	4	4	no	—
258	C₂×C₈×C₆₇	—	2	2	no	—
259	C₂×C₈×C₆₇	—	2	2	no	—
260	C₂×C₈×C₆₇	—	2	2	no	—
261	C₂×C₈×C₆₇	—	2	2	no	—
262	C₂×C₈×C₆₇	—	4	4	no	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
265	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
266	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
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	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
274	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
290	C₄²×C₆₇	—	2	4	no	—
291	C₄²×C₆₇	—	2	4	no	—
292	C₄²×C₆₇	C₂×D₄	1	2	yes	—
293	C₄²×C₆₇	C₂⁴	1	2	yes	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	4	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	2	2	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	4	8	no	—
305	C₂³×C₆₇	—	4	8	no	—
306	C₂³×C₆₇	—	4	2	no	—
307	C₂³×C₆₇	—	4	2	no	—
308	C₂³×C₆₇	—	4	2	no	—
309	C₂³×C₆₇	—	4	2	no	—
310	C₂³×C₆₇	—	4	2	no	—
311	C₂³×C₆₇	—	4	2	no	—
312	C₂³×C₆₇	—	4	2	no	—
313	C₂³×C₆₇	—	4	2	no	—
314	C₂³×C₆₇	—	8	4	no	—
315	C₂³×C₆₇	—	8	16	no	—
316	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₆₇	—	2	2	no	—
320	Q₈×C₆₇	—	2	2	no	—
321	Q₈×C₆₇	—	4	2	no	—
322	Q₈×C₆₇	—	8	4	no	—
323	D₄×C₆₇	—	2	4	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	2	2	no	—
326	D₄×C₆₇	—	2	2	no	—
327	D₄×C₆₇	—	2	2	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	4	4	no	—
330	D₄×C₆₇	—	4	8	no	—
331	D₄×C₆₇	—	4	8	no	—
332	D₄×C₆₇	—	4	2	no	—
333	D₄×C₆₇	—	4	2	no	—
334	D₄×C₆₇	—	8	4	no	—
335	D₄×C₆₇	—	8	4	no	—
336	D₄×C₆₇	—	8	4	no	—
337	D₄×C₆₇	C₂×#41	1	4	yes	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	4	no	—
343	C₂×C₄×C₆₇	—	2	4	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	4	8	no	—
354	C₂×C₄×C₆₇	—	4	8	no	—
355	C₂×C₄×C₆₇	—	4	2	no	—
356	C₂×C₄×C₆₇	—	4	2	no	—
357	C₂×C₄×C₆₇	—	4	2	no	—
358	C₂×C₄×C₆₇	—	4	2	no	—
359	C₂×C₄×C₆₇	—	4	2	no	—
360	C₂×C₄×C₆₇	—	8	4	no	—
361	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
367	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
369	C₈×C₆₇	—	2	2	no	—
370	C₈×C₆₇	—	2	2	no	—
371	C₈×C₆₇	—	2	2	no	—
372	C₈×C₆₇	—	2	2	no	—
373	C₂²×C₆₇	—	2	2	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	4	no	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	2	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	4	4	no	—
381	C₂²×C₆₇	—	4	4	no	—
382	C₂²×C₆₇	—	4	8	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	4	2	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	8	16	no	—
392	C₂²×C₆₇	—	8	4	no	—
393	C₂²×C₆₇	—	8	4	no	—
394	C₂²×C₆₇	#546	1	2	yes	—
395	C₂²×C₆₇	#575	1	2	yes	—
396	C₂²×C₆₇	#576	1	2	yes	—
397	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₆₇	—	2	2	no	—
399	C₄×C₆₇	—	2	2	no	—
400	C₄×C₆₇	—	2	2	no	—
401	C₄×C₆₇	—	2	2	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	—	4	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	#546	1	2	yes	—
408	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
409	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×#3319	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₆₇	—	4	2	no	—
412	C₂×C₆₇	—	4	2	no	—
413	C₂×C₆₇	—	4	4	no	—
414	C₂×C₆₇	—	8	2	no	—
415	C₂×C₆₇	—	8	2	no	—
416	C₂×C₆₇	#3319	1	4	yes	direct product factor
417	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
418	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
419	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
420	C₂×#555	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3319	C₂×C₆₇	1	16	yes	direct product factor
423	C₂×#489	C₂×C₆₇	1	1	yes	characteristic, complemented
424	C₂×#485	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#482	C₂×C₆₇	1	1	yes	characteristic, complemented
426	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
427	C₂×#468	C₂×C₆₇	1	1	yes	characteristic, complemented
428	C₂×#466	C₂×C₆₇	1	1	yes	characteristic, complemented
429	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
430	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
431	C₂×#447	C₂×C₆₇	1	1	yes	characteristic, complemented
432	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
434	C₂×#418	C₂×C₆₇	1	1	yes	characteristic, complemented
435	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
436	C₆₇	C₂×#3319	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
438	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
441	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
443	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
444	#555	—	2	4	no	—
445	#555	C₂²×C₆₇	1	8	yes	complemented
446	#546	—	2	4	no	—
447	#546	C₂²×C₆₇	1	8	yes	complemented
448	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
449	C₂×#124	—	2	1	no	—
450	C₂×#124	—	2	1	no	—
451	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×#123	—	2	1	no	—
453	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
454	C₂×#121	—	2	1	no	—
455	C₂×#121	—	2	1	no	—
456	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	C₂×#120	—	2	1	no	—
460	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#117	—	2	1	no	—
464	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	C₂²×C₂²⋊C₄	—	2	1	no	—
467	#489	C₂²×C₆₇	1	8	yes	complemented
468	#485	C₂²×C₆₇	1	8	yes	complemented
469	#482	C₂²×C₆₇	1	8	yes	complemented
470	#474	C₂²×C₆₇	1	8	yes	complemented
471	#468	C₂²×C₆₇	1	8	yes	complemented
472	#466	C₂²×C₆₇	1	8	yes	complemented
473	#463	C₂²×C₆₇	1	8	yes	complemented
474	#449	C₂²×C₆₇	1	8	yes	complemented
475	#447	C₂²×C₆₇	1	8	yes	complemented
476	#442	C₂²×C₆₇	1	8	yes	complemented
477	#435	C₂²×C₆₇	1	8	yes	complemented
478	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
481	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#418	C₂²×C₆₇	1	8	yes	complemented
483	#416	C₂²×C₆₇	1	8	yes	complemented
484	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
496	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	C₂⁵	—	2	1	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	4	2	no	—
501	C₂×#41	C₂³×C₆₇	1	4	yes	—
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	4	2	no	—
512	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
516	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂×SD₁₆	—	4	2	no	—
523	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
524	C₂×D₈	—	2	4	no	—
525	C₂×D₈	—	4	2	no	—
526	C₂×D₈	C₂³×C₆₇	1	4	yes	—
527	C₂×D₈	C₂³×C₆₇	1	4	yes	—
528	C₂×M₁₆	—	4	2	no	—
529	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
530	C₂²×C₈	—	4	2	no	—
531	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
538	#124	—	2	8	no	—
539	#124	—	2	8	no	—
540	#124	—	2	2	no	—
541	#124	C₂³×C₆₇	1	4	yes	—
542	#123	—	2	8	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
545	#121	—	2	8	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	8	no	—
550	#121	C₂³×C₆₇	1	4	yes	—
551	#121	C₂³×C₆₇	1	4	yes	—
552	#121	C₂³×C₆₇	1	4	yes	complemented
553	#120	—	2	8	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	D₄×C₆₇	1	4	yes	—
557	C₄×D₄	C₂³×C₆₇	1	4	yes	—
558	C₄×D₄	C₂³×C₆₇	1	4	yes	—
559	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
560	#117	—	2	2	no	—
561	#117	—	2	2	no	—
562	#117	—	2	8	no	—
563	#117	C₂³×C₆₇	1	4	yes	—
564	#117	C₂³×C₆₇	1	4	yes	complemented
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	8	no	—
583	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
588	#107	C₂³×C₆₇	1	4	yes	complemented
589	#107	C₂³×C₆₇	1	4	yes	complemented
590	#106	C₂³×C₆₇	1	4	yes	complemented
591	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
592	#103	C₂³×C₆₇	1	4	yes	complemented
593	#103	C₂³×C₆₇	1	4	yes	complemented
594	#103	C₂³×C₆₇	1	4	yes	complemented
595	#102	C₂³×C₆₇	1	4	yes	—
596	#102	C₂³×C₆₇	1	4	yes	—
597	#102	C₂³×C₆₇	1	4	yes	—
598	#102	C₂³×C₆₇	1	4	yes	—
599	#102	C₂³×C₆₇	1	4	yes	—
600	#102	C₂³×C₆₇	1	4	yes	—
601	#102	C₂³×C₆₇	1	4	yes	complemented
602	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
603	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
604	#97	C₂³×C₆₇	1	4	yes	complemented
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	—	2	4	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	8	2	no	—
612	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
614	#41	—	2	8	no	—
615	#41	—	4	4	no	—
616	#41	—	4	8	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	8	2	no	—
622	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	8	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	8	2	no	—
643	C₂×D₄	—	8	2	no	—
644	C₂×D₄	—	8	2	no	—
645	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
646	C₂×D₄	#41×C₆₇	1	4	yes	—
647	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
648	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
649	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
674	SD₁₆	—	4	4	no	—
675	D₈	—	2	8	no	—
676	D₈	—	4	4	no	—
677	M₁₆	—	4	4	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
684	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
685	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
686	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
694	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
709	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
710	C₄²	—	2	4	no	—
711	C₄²	—	2	4	no	—
712	C₄²	C₂×D₄×C₆₇	1	2	yes	—
713	C₄²	C₂⁴×C₆₇	1	2	yes	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	8	4	no	—
735	C₂³	—	8	16	no	—
736	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
737	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
738	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	Q₈	—	8	4	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	C₂×#41×C₆₇	1	4	yes	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
783	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
786	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
787	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
788	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	4	8	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	16	no	—
812	C₂²	—	8	4	no	—
813	C₂²	—	8	4	no	—
814	C₂²	#546×C₆₇	1	2	yes	—
815	C₂²	#575×C₆₇	1	2	yes	—
816	C₂²	#576×C₆₇	1	2	yes	—
817	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	#546×C₆₇	1	2	yes	—
828	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
829	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₆₇×#3319	1	4	yes	direct product factor
836	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
837	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
838	C₂	C₂×#576×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
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×#555×C₆₇	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3319	C₂	direct (N × H)
4. C₂×#489×C₆₇	C₂	semidirect
5. C₂×#485×C₆₇	C₂	semidirect
6. C₂×#482×C₆₇	C₂	semidirect
7. C₂×#474×C₆₇	C₂	semidirect
8. C₂×#468×C₆₇	C₂	semidirect
9. C₂×#466×C₆₇	C₂	semidirect
10. C₂×#463×C₆₇	C₂	semidirect
11. C₂×#449×C₆₇	C₂	semidirect
12. C₂×#447×C₆₇	C₂	semidirect
13. C₂×#442×C₆₇	C₂	semidirect
14. C₂×#435×C₆₇	C₂	semidirect
15. C₂×#418×C₆₇	C₂	semidirect
16. C₂×#416×C₆₇	C₂	semidirect
19. C₂²×SD₁₆×C₆₇	C₂²	semidirect
23. C₂³×C₈×C₆₇	C₂²	semidirect
25. #555×C₆₇	C₂²	semidirect
27. #546×C₆₇	C₂²	semidirect
28. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×#121×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. C₂×#117×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #482×C₆₇	C₂²	semidirect
50. #474×C₆₇	C₂²	semidirect
51. #468×C₆₇	C₂²	semidirect
52. #466×C₆₇	C₂²	semidirect
53. #463×C₆₇	C₂²	semidirect
54. #449×C₆₇	C₂²	semidirect
55. #447×C₆₇	C₂²	semidirect
56. #442×C₆₇	C₂²	semidirect
57. #435×C₆₇	C₂²	semidirect
58. C₂×#107×C₆₇	C₂²	semidirect
59. C₂×#107×C₆₇	C₂²	semidirect
60. C₂×#106×C₆₇	C₂²	semidirect
61. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
62. #418×C₆₇	C₂²	semidirect
63. #416×C₆₇	C₂²	semidirect
64. C₂×#103×C₆₇	C₂²	semidirect
65. C₂×#103×C₆₇	C₂²	semidirect
66. C₂×#103×C₆₇	C₂²	semidirect
73. C₂×#102×C₆₇	C₂²	semidirect
75. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
76. C₂×#97×C₆₇	C₂²	semidirect
103. C₂×SD₁₆×C₆₇	C₂³	semidirect
115. C₂²×C₈×C₆₇	C₂³	semidirect
117. C₄⋊Q₈×C₆₇	C₂³	semidirect
132. #121×C₆₇	C₂³	semidirect
139. C₄×D₄×C₆₇	C₂³	semidirect
144. #117×C₆₇	C₂³	semidirect
168. #107×C₆₇	C₂³	semidirect
169. #107×C₆₇	C₂³	semidirect
170. #106×C₆₇	C₂³	semidirect
171. C₄⋊C₈×C₆₇	C₂³	semidirect
172. #103×C₆₇	C₂³	semidirect
173. #103×C₆₇	C₂³	semidirect
174. #103×C₆₇	C₂³	semidirect
181. #102×C₆₇	C₂³	semidirect
183. C₂²⋊C₈×C₆₇	C₂³	semidirect
184. #97×C₆₇	C₂³	semidirect
410. C₂×#3319	C₆₇	direct (N × H)
416. C₂×C₆₇	#3319	direct (N × H)
420. C₂×#555	C₂×C₆₇	semidirect
421. C₂×#546	C₂×C₆₇	semidirect
422. #3319	C₂×C₆₇	direct (N × H)
423. C₂×#489	C₂×C₆₇	semidirect
424. C₂×#485	C₂×C₆₇	semidirect
425. C₂×#482	C₂×C₆₇	semidirect
426. C₂×#474	C₂×C₆₇	semidirect
427. C₂×#468	C₂×C₆₇	semidirect
428. C₂×#466	C₂×C₆₇	semidirect
429. C₂×#463	C₂×C₆₇	semidirect
430. C₂×#449	C₂×C₆₇	semidirect
431. C₂×#447	C₂×C₆₇	semidirect
432. C₂×#442	C₂×C₆₇	semidirect
433. C₂×#435	C₂×C₆₇	semidirect
434. C₂×#418	C₂×C₆₇	semidirect
435. C₂×#416	C₂×C₆₇	semidirect
436. C₆₇	C₂×#3319	direct (N × H)
439. C₂²×SD₁₆	C₂²×C₆₇	semidirect
443. C₂³×C₈	C₂²×C₆₇	semidirect
445. #555	C₂²×C₆₇	semidirect
447. #546	C₂²×C₆₇	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
458. C₂×#121	C₂²×C₆₇	semidirect
462. C₂×C₄×D₄	C₂²×C₆₇	semidirect
465. C₂×#117	C₂²×C₆₇	semidirect
467. #489	C₂²×C₆₇	semidirect
468. #485	C₂²×C₆₇	semidirect
469. #482	C₂²×C₆₇	semidirect
470. #474	C₂²×C₆₇	semidirect
471. #468	C₂²×C₆₇	semidirect
472. #466	C₂²×C₆₇	semidirect
473. #463	C₂²×C₆₇	semidirect
474. #449	C₂²×C₆₇	semidirect
475. #447	C₂²×C₆₇	semidirect
476. #442	C₂²×C₆₇	semidirect
477. #435	C₂²×C₆₇	semidirect
478. C₂×#107	C₂²×C₆₇	semidirect
479. C₂×#107	C₂²×C₆₇	semidirect
480. C₂×#106	C₂²×C₆₇	semidirect
481. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
482. #418	C₂²×C₆₇	semidirect
483. #416	C₂²×C₆₇	semidirect
484. C₂×#103	C₂²×C₆₇	semidirect
485. C₂×#103	C₂²×C₆₇	semidirect
486. C₂×#103	C₂²×C₆₇	semidirect
493. C₂×#102	C₂²×C₆₇	semidirect
495. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
496. C₂×#97	C₂²×C₆₇	semidirect
523. C₂×SD₁₆	C₂³×C₆₇	semidirect
535. C₂²×C₈	C₂³×C₆₇	semidirect
537. C₄⋊Q₈	C₂³×C₆₇	semidirect
552. #121	C₂³×C₆₇	semidirect
559. C₄×D₄	C₂³×C₆₇	semidirect
564. #117	C₂³×C₆₇	semidirect
588. #107	C₂³×C₆₇	semidirect
589. #107	C₂³×C₆₇	semidirect
590. #106	C₂³×C₆₇	semidirect
591. C₄⋊C₈	C₂³×C₆₇	semidirect
592. #103	C₂³×C₆₇	semidirect
593. #103	C₂³×C₆₇	semidirect
594. #103	C₂³×C₆₇	semidirect
601. #102	C₂³×C₆₇	semidirect
603. C₂²⋊C₈	C₂³×C₆₇	semidirect
604. #97	C₂³×C₆₇	semidirect
835. C₂	C₆₇×#3319	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×#555×C₆₇	2
C₂×#546×C₆₇	2
C₆₇×#3319	2
C₂×#489×C₆₇	2
C₂×#485×C₆₇	2
C₂×#482×C₆₇	2
C₂×#474×C₆₇	2
C₂×#468×C₆₇	2
C₂×#466×C₆₇	2
C₂×#463×C₆₇	2
C₂×#449×C₆₇	2
C₂×#447×C₆₇	2
C₂×#442×C₆₇	2
C₂×#435×C₆₇	2
C₂×#418×C₆₇	2
C₂×#416×C₆₇	2
C₂×#3319	67

Subgroups — C2×C67×#3319 #30740387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3319 #30740387