Subgroups — C₆₇×#61057 #30740308

Order 17152.

2696 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3489	C₂	1	2	yes	maximal, complemented
4	D₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3283	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#467×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3046	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	#578×C₆₇	—	2	8	no	—
21	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#135×C₆₇	—	2	8	no	—
25	C₂×#135×C₆₇	C₂²	1	2	yes	—
26	C₂×#135×C₆₇	C₂²	1	2	yes	—
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
32	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
36	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₇	C₂²	1	4	yes	—
40	#548×C₆₇	C₂²	1	4	yes	complemented
41	#547×C₆₇	—	2	4	no	—
42	#547×C₆₇	C₂²	1	4	yes	complemented
43	#546×C₆₇	—	2	4	no	—
44	#546×C₆₇	C₂²	1	4	yes	—
45	#537×C₆₇	—	2	2	no	—
46	#537×C₆₇	C₂²	1	2	yes	complemented
47	#536×C₆₇	—	2	2	no	—
48	#536×C₆₇	C₂²	1	2	yes	complemented
49	#525×C₆₇	—	2	2	no	—
50	#525×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
52	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
53	#520×C₆₇	C₂²	1	2	yes	complemented
54	#497×C₆₇	C₂²	1	4	yes	complemented
55	#495×C₆₇	C₂²	1	2	yes	complemented
56	#494×C₆₇	C₂²	1	2	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#467×C₆₇	C₂²	1	2	yes	—
59	#467×C₆₇	C₂²	1	2	yes	—
60	#467×C₆₇	C₂²	1	2	yes	complemented
61	#467×C₆₇	C₂²	1	2	yes	complemented
62	#467×C₆₇	C₂²	1	2	yes	complemented
63	#466×C₆₇	C₂²	1	2	yes	complemented
64	#464×C₆₇	C₂²	1	4	yes	complemented
65	#463×C₆₇	C₂²	1	4	yes	complemented
66	#462×C₆₇	C₂²	1	4	yes	complemented
67	#461×C₆₇	C₂²	1	4	yes	complemented
68	#452×C₆₇	C₂²	1	4	yes	complemented
69	#452×C₆₇	C₂²	1	4	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#451×C₆₇	C₂²	1	4	yes	—
72	#451×C₆₇	C₂²	1	4	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	—
74	#449×C₆₇	C₂²	1	4	yes	complemented
75	#448×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
78	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
79	#435×C₆₇	C₂²	1	2	yes	—
80	#435×C₆₇	C₂²	1	2	yes	complemented
81	C₈×D₄×C₆₇	C₂²	1	2	yes	—
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#417×C₆₇	C₂²	1	2	yes	complemented
86	#417×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
88	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#407×C₆₇	C₂²	1	1	yes	characteristic
90	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	2₋¹⁺⁴×C₆₇	—	2	8	no	—
92	2₋¹⁺⁴×C₆₇	—	4	4	no	—
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	4	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	8	no	—
98	C₂×#41×C₆₇	—	4	4	no	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	2	yes	—
103	C₂×#41×C₆₇	C₂³	1	2	yes	—
104	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₆₇	—	2	2	no	—
106	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
107	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	—	2	2	no	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	—	2	2	no	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	#137×C₆₇	—	2	8	no	—
114	#137×C₆₇	—	2	16	no	—
115	#137×C₆₇	—	4	4	no	—
116	#135×C₆₇	—	2	8	no	—
117	#135×C₆₇	—	2	4	no	—
118	#135×C₆₇	—	2	8	no	—
119	#135×C₆₇	—	2	4	no	—
120	#135×C₆₇	—	2	8	no	—
121	#135×C₆₇	—	2	4	no	—
122	#135×C₆₇	D₄	1	8	yes	complemented
123	C₂×Q₁₆×C₆₇	—	2	4	no	—
124	C₂×Q₁₆×C₆₇	—	2	8	no	—
125	C₂×Q₁₆×C₆₇	—	2	4	no	—
126	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
127	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
132	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×SD₁₆×C₆₇	—	2	8	no	—
134	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
139	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×D₈×C₆₇	—	2	4	no	—
141	C₂×D₈×C₆₇	C₂³	1	2	yes	—
142	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
144	#131×C₆₇	—	2	4	no	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	—	2	4	no	—
149	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₇	—	2	4	no	—
157	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
158	#124×C₆₇	—	2	4	no	—
159	#124×C₆₇	C₂³	1	4	yes	—
160	#123×C₆₇	—	2	4	no	—
161	#123×C₆₇	—	2	4	no	—
162	#123×C₆₇	—	2	4	no	—
163	#123×C₆₇	—	2	4	no	—
164	#123×C₆₇	D₄	1	2	yes	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	4	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	—	2	4	no	—
172	C₂²⋊Q₈×C₆₇	—	2	4	no	—
173	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
174	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
175	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
176	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
177	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
178	#121×C₆₇	—	2	2	no	—
179	#121×C₆₇	—	2	4	no	—
180	#121×C₆₇	—	2	4	no	—
181	#121×C₆₇	—	2	4	no	—
182	#121×C₆₇	—	2	4	no	—
183	#121×C₆₇	D₄	1	1	yes	characteristic
184	#121×C₆₇	D₄	1	1	yes	characteristic
185	#121×C₆₇	C₂³	1	4	yes	—
186	#120×C₆₇	—	2	4	no	—
187	#120×C₆₇	D₄	1	2	yes	—
188	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
189	C₄×D₄×C₆₇	—	2	4	no	—
190	C₄×D₄×C₆₇	—	2	4	no	—
191	C₄×D₄×C₆₇	—	2	4	no	—
192	C₄×D₄×C₆₇	C₂³	1	4	yes	—
193	C₄×D₄×C₆₇	C₂³	1	2	yes	—
194	C₄×D₄×C₆₇	C₂³	1	2	yes	—
195	#117×C₆₇	—	2	2	no	—
196	#117×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
203	#107×C₆₇	C₂³	1	2	yes	—
204	#107×C₆₇	C₂³	1	2	yes	—
205	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
206	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
207	#103×C₆₇	C₂³	1	4	yes	—
208	#103×C₆₇	C₂³	1	4	yes	—
209	#103×C₆₇	C₂³	1	4	yes	—
210	#103×C₆₇	C₂³	1	4	yes	—
211	#102×C₆₇	C₂³	1	4	yes	—
212	#102×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
217	#97×C₆₇	C₂³	1	2	yes	—
218	C₄×C₈×C₆₇	C₂³	1	2	yes	—
219	C₂⁴×C₆₇	—	2	2	no	—
220	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
221	#41×C₆₇	—	2	2	no	—
222	#41×C₆₇	—	2	4	no	—
223	#41×C₆₇	—	2	2	no	—
224	#41×C₆₇	—	2	4	no	—
225	#41×C₆₇	—	2	4	no	—
226	#41×C₆₇	—	2	8	no	—
227	#41×C₆₇	—	2	4	no	—
228	#41×C₆₇	—	2	4	no	—
229	#41×C₆₇	—	4	8	no	—
230	#41×C₆₇	—	4	2	no	—
231	#41×C₆₇	—	4	2	no	—
232	#41×C₆₇	—	4	4	no	—
233	#41×C₆₇	—	4	8	no	—
234	#41×C₆₇	—	4	8	no	—
235	#41×C₆₇	—	4	16	no	—
236	#41×C₆₇	C₂×D₄	1	8	yes	—
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	2	4	no	—
239	C₂×Q₈×C₆₇	—	2	2	no	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	2	8	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	4	no	—
244	C₂×Q₈×C₆₇	—	4	2	no	—
245	C₂×Q₈×C₆₇	—	4	4	no	—
246	C₂×Q₈×C₆₇	—	4	8	no	—
247	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
249	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
250	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	8	no	—
261	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	4	8	no	—
280	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	Q₁₆×C₆₇	—	2	4	no	—
288	Q₁₆×C₆₇	—	2	8	no	—
289	Q₁₆×C₆₇	—	2	4	no	—
290	Q₁₆×C₆₇	—	2	2	no	—
291	Q₁₆×C₆₇	—	2	4	no	—
292	Q₁₆×C₆₇	—	4	4	no	—
293	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
294	SD₁₆×C₆₇	—	2	4	no	—
295	SD₁₆×C₆₇	—	2	4	no	—
296	SD₁₆×C₆₇	—	2	8	no	—
297	SD₁₆×C₆₇	—	2	4	no	—
298	SD₁₆×C₆₇	—	4	4	no	—
299	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
300	D₈×C₆₇	—	2	4	no	—
301	D₈×C₆₇	—	2	2	no	—
302	D₈×C₆₇	C₂×D₄	1	4	yes	—
303	M₁₆×C₆₇	—	2	2	no	—
304	M₁₆×C₆₇	—	2	2	no	—
305	M₁₆×C₆₇	—	2	4	no	—
306	C₂×C₈×C₆₇	—	2	2	no	—
307	C₂×C₈×C₆₇	—	2	2	no	—
308	C₂×C₈×C₆₇	—	2	2	no	—
309	C₂×C₈×C₆₇	—	2	2	no	—
310	C₂×C₈×C₆₇	—	2	2	no	—
311	C₂×C₈×C₆₇	—	2	4	no	—
312	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
313	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
314	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
315	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	—	2	4	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	4	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	4	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₄²×C₆₇	—	2	4	no	—
344	C₄²×C₆₇	C₂⁴	1	2	yes	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	4	1	no	—
350	C₂³×C₆₇	—	4	4	no	—
351	C₂³×C₆₇	—	4	4	no	—
352	C₂³×C₆₇	—	8	2	no	—
353	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
355	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₆₇	—	2	2	no	—
358	Q₈×C₆₇	—	2	2	no	—
359	Q₈×C₆₇	—	2	2	no	—
360	Q₈×C₆₇	—	2	4	no	—
361	Q₈×C₆₇	—	2	4	no	—
362	Q₈×C₆₇	—	2	2	no	—
363	Q₈×C₆₇	—	4	8	no	—
364	Q₈×C₆₇	—	4	4	no	—
365	Q₈×C₆₇	—	4	4	no	—
366	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
367	D₄×C₆₇	—	2	8	no	—
368	D₄×C₆₇	—	2	4	no	—
369	D₄×C₆₇	—	2	4	no	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	2	2	no	—
372	D₄×C₆₇	—	2	2	no	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	4	2	no	—
375	D₄×C₆₇	—	4	4	no	—
376	D₄×C₆₇	—	4	4	no	—
377	D₄×C₆₇	—	4	4	no	—
378	D₄×C₆₇	—	4	8	no	—
379	D₄×C₆₇	—	4	4	no	—
380	D₄×C₆₇	—	8	4	no	—
381	D₄×C₆₇	C₂²×D₄	1	4	yes	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	8	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	4	no	—
394	C₂×C₄×C₆₇	—	2	4	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	4	4	no	—
397	C₂×C₄×C₆₇	—	4	4	no	—
398	C₂×C₄×C₆₇	—	4	4	no	—
399	C₂×C₄×C₆₇	—	4	8	no	—
400	C₂×C₄×C₆₇	—	4	8	no	—
401	C₂×C₄×C₆₇	—	4	4	no	—
402	C₂×C₄×C₆₇	—	4	4	no	—
403	C₂×C₄×C₆₇	—	8	4	no	—
404	C₂×C₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
413	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
414	C₈×C₆₇	—	2	1	no	—
415	C₈×C₆₇	—	2	1	no	—
416	C₈×C₆₇	—	2	2	no	—
417	C₈×C₆₇	—	2	2	no	—
418	C₈×C₆₇	C₂²×D₄	1	2	yes	—
419	C₈×C₆₇	C₂²×D₄	1	2	yes	—
420	C₂²×C₆₇	—	2	1	no	—
421	C₂²×C₆₇	—	2	1	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	1	no	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	2	no	—
430	C₂²×C₆₇	—	2	1	no	—
431	C₂²×C₆₇	—	4	4	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	2	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	—	8	8	no	—
438	C₂²×C₆₇	D₄²	1	2	yes	—
439	C₂²×C₆₇	#578	1	2	yes	complemented
440	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	2	no	—
447	C₄×C₆₇	—	4	4	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	4	no	—
450	C₄×C₆₇	D₄²	1	2	yes	—
451	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	#61057	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂×C₆₇	—	2	2	no	—
455	C₂×C₆₇	—	2	2	no	—
456	C₂×C₆₇	—	4	2	no	—
457	C₂×C₆₇	—	4	1	no	—
458	C₂×C₆₇	—	4	4	no	—
459	C₂×C₆₇	—	8	2	no	—
460	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
461	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
462	C₂×C₆₇	#3584	1	1	yes	characteristic
463	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#3489	C₂×C₆₇	1	2	yes	complemented
466	D₄×Q₁₆	C₂×C₆₇	1	2	yes	complemented
467	#3285	C₂×C₆₇	1	2	yes	complemented
468	#3283	C₂×C₆₇	1	2	yes	complemented
469	#3280	C₂×C₆₇	1	2	yes	complemented
470	#3269	C₂×C₆₇	1	4	yes	complemented
471	#3266	C₂×C₆₇	1	4	yes	complemented
472	#3156	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3061	C₂×C₆₇	1	1	yes	characteristic, complemented
474	C₂×#467	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#3046	C₂×C₆₇	1	2	yes	complemented
476	#3013	C₂×C₆₇	1	2	yes	complemented
477	#3007	C₂×C₆₇	1	2	yes	complemented
478	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
480	C₆₇	#61057	1	1	yes	characteristic, direct product factor, Sylow
481	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
482	C₂²×#41	C₂²×C₆₇	1	2	yes	—
483	#578	—	2	8	no	—
484	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
485	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
486	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
487	C₂×#135	—	2	8	no	—
488	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#135	C₂²×C₆₇	1	2	yes	—
490	C₂×#135	C₂²×C₆₇	1	2	yes	—
491	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
494	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
495	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
496	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
498	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
499	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
501	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
502	D₄×Q₈	C₂²×C₆₇	1	4	yes	—
503	#548	C₂²×C₆₇	1	4	yes	complemented
504	#547	—	2	4	no	—
505	#547	C₂²×C₆₇	1	4	yes	complemented
506	#546	—	2	4	no	—
507	#546	C₂²×C₆₇	1	4	yes	—
508	#537	—	2	2	no	—
509	#537	C₂²×C₆₇	1	2	yes	complemented
510	#536	—	2	2	no	—
511	#536	C₂²×C₆₇	1	2	yes	complemented
512	#525	—	2	2	no	—
513	#525	C₂²×C₆₇	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	—	2	2	no	—
515	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
516	#520	C₂²×C₆₇	1	2	yes	complemented
517	#497	C₂²×C₆₇	1	4	yes	complemented
518	#495	C₂²×C₆₇	1	2	yes	complemented
519	#494	C₂²×C₆₇	1	2	yes	complemented
520	#468	C₂²×C₆₇	1	4	yes	complemented
521	#467	C₂²×C₆₇	1	2	yes	—
522	#467	C₂²×C₆₇	1	2	yes	—
523	#467	C₂²×C₆₇	1	2	yes	complemented
524	#467	C₂²×C₆₇	1	2	yes	complemented
525	#467	C₂²×C₆₇	1	2	yes	complemented
526	#466	C₂²×C₆₇	1	2	yes	complemented
527	#464	C₂²×C₆₇	1	4	yes	complemented
528	#463	C₂²×C₆₇	1	4	yes	complemented
529	#462	C₂²×C₆₇	1	4	yes	complemented
530	#461	C₂²×C₆₇	1	4	yes	complemented
531	#452	C₂²×C₆₇	1	4	yes	complemented
532	#452	C₂²×C₆₇	1	4	yes	complemented
533	#452	C₂²×C₆₇	1	4	yes	complemented
534	#451	C₂²×C₆₇	1	4	yes	—
535	#451	C₂²×C₆₇	1	4	yes	complemented
536	#450	C₂²×C₆₇	1	4	yes	—
537	#449	C₂²×C₆₇	1	4	yes	complemented
538	#448	C₂²×C₆₇	1	4	yes	complemented
539	#440	C₂²×C₆₇	1	4	yes	complemented
540	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
541	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
542	#435	C₂²×C₆₇	1	2	yes	—
543	#435	C₂²×C₆₇	1	2	yes	complemented
544	C₈×D₄	C₂²×C₆₇	1	2	yes	—
545	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
546	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
547	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
548	#417	C₂²×C₆₇	1	2	yes	complemented
549	#417	C₂²×C₆₇	1	2	yes	complemented
550	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
551	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	#407	C₂²×C₆₇	1	1	yes	characteristic
553	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	2₋¹⁺⁴	—	2	8	no	—
555	2₋¹⁺⁴	—	4	4	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	2	4	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	2	8	no	—
561	C₂×#41	—	4	4	no	—
562	C₂×#41	C₂³×C₆₇	1	2	yes	—
563	C₂×#41	C₂³×C₆₇	1	4	yes	—
564	C₂×#41	C₂³×C₆₇	1	2	yes	—
565	C₂×#41	C₂³×C₆₇	1	2	yes	—
566	C₂×#41	C₂³×C₆₇	1	2	yes	—
567	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
568	C₂²×Q₈	—	2	2	no	—
569	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
570	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
571	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	—	2	2	no	—
575	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
576	#137	—	2	8	no	—
577	#137	—	2	16	no	—
578	#137	—	4	4	no	—
579	#135	—	2	8	no	—
580	#135	—	2	4	no	—
581	#135	—	2	8	no	—
582	#135	—	2	4	no	—
583	#135	—	2	8	no	—
584	#135	—	2	4	no	—
585	#135	D₄×C₆₇	1	8	yes	complemented
586	C₂×Q₁₆	—	2	4	no	—
587	C₂×Q₁₆	—	2	8	no	—
588	C₂×Q₁₆	—	2	4	no	—
589	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
590	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
592	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
593	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
595	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×SD₁₆	—	2	8	no	—
597	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
603	C₂×D₈	—	2	4	no	—
604	C₂×D₈	C₂³×C₆₇	1	2	yes	—
605	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
607	#131	—	2	4	no	—
608	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
610	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
611	C₂²×C₈	—	2	4	no	—
612	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
616	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
618	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₄⋊Q₈	—	2	4	no	—
620	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
621	#124	—	2	4	no	—
622	#124	C₂³×C₆₇	1	4	yes	—
623	#123	—	2	4	no	—
624	#123	—	2	4	no	—
625	#123	—	2	4	no	—
626	#123	—	2	4	no	—
627	#123	D₄×C₆₇	1	2	yes	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
637	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
638	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
639	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
640	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
641	#121	—	2	2	no	—
642	#121	—	2	4	no	—
643	#121	—	2	4	no	—
644	#121	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	D₄×C₆₇	1	1	yes	characteristic
647	#121	D₄×C₆₇	1	1	yes	characteristic
648	#121	C₂³×C₆₇	1	4	yes	—
649	#120	—	2	4	no	—
650	#120	D₄×C₆₇	1	2	yes	—
651	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	4	no	—
655	C₄×D₄	C₂³×C₆₇	1	4	yes	—
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	C₄×D₄	C₂³×C₆₇	1	2	yes	—
658	#117	—	2	2	no	—
659	#117	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₄⋊C₄	—	2	2	no	—
661	C₂×C₄⋊C₄	—	2	2	no	—
662	C₂×C₄⋊C₄	—	2	4	no	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	—	2	4	no	—
666	#107	C₂³×C₆₇	1	2	yes	—
667	#107	C₂³×C₆₇	1	2	yes	—
668	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
669	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
670	#103	C₂³×C₆₇	1	4	yes	—
671	#103	C₂³×C₆₇	1	4	yes	—
672	#103	C₂³×C₆₇	1	4	yes	—
673	#103	C₂³×C₆₇	1	4	yes	—
674	#102	C₂³×C₆₇	1	4	yes	—
675	#102	C₂³×C₆₇	1	4	yes	—
676	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
680	#97	C₂³×C₆₇	1	2	yes	—
681	C₄×C₈	C₂³×C₆₇	1	2	yes	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
684	#41	—	2	2	no	—
685	#41	—	2	4	no	—
686	#41	—	2	2	no	—
687	#41	—	2	4	no	—
688	#41	—	2	4	no	—
689	#41	—	2	8	no	—
690	#41	—	2	4	no	—
691	#41	—	2	4	no	—
692	#41	—	4	8	no	—
693	#41	—	4	2	no	—
694	#41	—	4	2	no	—
695	#41	—	4	4	no	—
696	#41	—	4	8	no	—
697	#41	—	4	8	no	—
698	#41	—	4	16	no	—
699	#41	C₂×D₄×C₆₇	1	8	yes	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	8	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	4	2	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
711	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
713	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	8	no	—
724	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
725	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
726	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
727	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
728	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	4	8	no	—
743	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	Q₁₆	—	2	4	no	—
751	Q₁₆	—	2	8	no	—
752	Q₁₆	—	2	4	no	—
753	Q₁₆	—	2	2	no	—
754	Q₁₆	—	2	4	no	—
755	Q₁₆	—	4	4	no	—
756	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
757	SD₁₆	—	2	4	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	2	8	no	—
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
763	D₈	—	2	4	no	—
764	D₈	—	2	2	no	—
765	D₈	C₂×D₄×C₆₇	1	4	yes	—
766	M₁₆	—	2	2	no	—
767	M₁₆	—	2	2	no	—
768	M₁₆	—	2	4	no	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	—	2	2	no	—
774	C₂×C₈	—	2	4	no	—
775	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
776	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
777	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
778	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
805	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	C₂⁴×C₆₇	1	2	yes	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
818	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	4	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	4	8	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	4	no	—
829	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
830	D₄	—	2	8	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	4	2	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	4	no	—
844	D₄	C₂²×D₄×C₆₇	1	4	yes	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
875	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
876	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
877	C₈	—	2	1	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	2	no	—
881	C₈	C₂²×D₄×C₆₇	1	2	yes	—
882	C₈	C₂²×D₄×C₆₇	1	2	yes	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	8	8	no	—
901	C₂²	D₄²×C₆₇	1	2	yes	—
902	C₂²	#578×C₆₇	1	2	yes	complemented
903	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	4	no	—
913	C₄	D₄²×C₆₇	1	2	yes	—
914	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
915	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	4	1	no	—
919	C₂	—	4	2	no	—
920	C₂	—	4	4	no	—
921	C₂	—	8	2	no	—
922	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
923	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
924	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂²×#135×C₆₇	C₂	semidirect
3. C₆₇×#3489	C₂	semidirect
4. D₄×Q₁₆×C₆₇	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. C₆₇×#3283	C₂	semidirect
7. C₆₇×#3280	C₂	semidirect
8. C₆₇×#3269	C₂	semidirect
9. C₆₇×#3266	C₂	semidirect
10. C₆₇×#3156	C₂	semidirect
11. C₆₇×#3061	C₂	semidirect
12. C₂×#467×C₆₇	C₂	semidirect
13. C₆₇×#3046	C₂	semidirect
14. C₆₇×#3013	C₂	semidirect
15. C₆₇×#3007	C₂	semidirect
16. C₆₇×#2951	C₂	semidirect
17. C₆₇×#2929	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
21. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#135×C₆₇	C₂²	semidirect
33. C₂²×Q₁₆×C₆₇	C₂²	semidirect
34. C₂²×Q₁₆×C₆₇	C₂²	semidirect
37. C₂×#131×C₆₇	C₂²	semidirect
40. #548×C₆₇	C₂²	semidirect
42. #547×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
48. #536×C₆₇	C₂²	semidirect
53. #520×C₆₇	C₂²	semidirect
54. #497×C₆₇	C₂²	semidirect
55. #495×C₆₇	C₂²	semidirect
56. #494×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
60. #467×C₆₇	C₂²	semidirect
61. #467×C₆₇	C₂²	semidirect
62. #467×C₆₇	C₂²	semidirect
63. #466×C₆₇	C₂²	semidirect
64. #464×C₆₇	C₂²	semidirect
65. #463×C₆₇	C₂²	semidirect
66. #462×C₆₇	C₂²	semidirect
67. #461×C₆₇	C₂²	semidirect
68. #452×C₆₇	C₂²	semidirect
69. #452×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
72. #451×C₆₇	C₂²	semidirect
74. #449×C₆₇	C₂²	semidirect
75. #448×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. C₄×Q₁₆×C₆₇	C₂²	semidirect
78. C₄×D₈×C₆₇	C₂²	semidirect
80. #435×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₂×#107×C₆₇	C₂²	semidirect
84. #424×C₆₇	C₂²	semidirect
85. #417×C₆₇	C₂²	semidirect
86. #417×C₆₇	C₂²	semidirect
87. C₂×#103×C₆₇	C₂²	semidirect
88. #408×C₆₇	C₂²	semidirect
90. #405×C₆₇	C₂²	semidirect
122. #135×C₆₇	D₄	semidirect
439. C₂²×C₆₇	#578	semidirect
453. #61057	C₆₇	direct (N × H)
463. C₂×#578	C₂×C₆₇	semidirect
464. C₂²×#135	C₂×C₆₇	semidirect
465. #3489	C₂×C₆₇	semidirect
466. D₄×Q₁₆	C₂×C₆₇	semidirect
467. #3285	C₂×C₆₇	semidirect
468. #3283	C₂×C₆₇	semidirect
469. #3280	C₂×C₆₇	semidirect
470. #3269	C₂×C₆₇	semidirect
471. #3266	C₂×C₆₇	semidirect
472. #3156	C₂×C₆₇	semidirect
473. #3061	C₂×C₆₇	semidirect
474. C₂×#467	C₂×C₆₇	semidirect
475. #3046	C₂×C₆₇	semidirect
476. #3013	C₂×C₆₇	semidirect
477. #3007	C₂×C₆₇	semidirect
478. #2951	C₂×C₆₇	semidirect
479. #2929	C₂×C₆₇	semidirect
480. C₆₇	#61057	direct (N × H)
481. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
484. C₂×#137	C₂²×C₆₇	semidirect
485. C₂×#137	C₂²×C₆₇	semidirect
486. C₂×#137	C₂²×C₆₇	semidirect
494. C₂×#135	C₂²×C₆₇	semidirect
496. C₂²×Q₁₆	C₂²×C₆₇	semidirect
497. C₂²×Q₁₆	C₂²×C₆₇	semidirect
500. C₂×#131	C₂²×C₆₇	semidirect
503. #548	C₂²×C₆₇	semidirect
505. #547	C₂²×C₆₇	semidirect
509. #537	C₂²×C₆₇	semidirect
511. #536	C₂²×C₆₇	semidirect
516. #520	C₂²×C₆₇	semidirect
517. #497	C₂²×C₆₇	semidirect
518. #495	C₂²×C₆₇	semidirect
519. #494	C₂²×C₆₇	semidirect
520. #468	C₂²×C₆₇	semidirect
523. #467	C₂²×C₆₇	semidirect
524. #467	C₂²×C₆₇	semidirect
525. #467	C₂²×C₆₇	semidirect
526. #466	C₂²×C₆₇	semidirect
527. #464	C₂²×C₆₇	semidirect
528. #463	C₂²×C₆₇	semidirect
529. #462	C₂²×C₆₇	semidirect
530. #461	C₂²×C₆₇	semidirect
531. #452	C₂²×C₆₇	semidirect
532. #452	C₂²×C₆₇	semidirect
533. #452	C₂²×C₆₇	semidirect
535. #451	C₂²×C₆₇	semidirect
537. #449	C₂²×C₆₇	semidirect
538. #448	C₂²×C₆₇	semidirect
539. #440	C₂²×C₆₇	semidirect
540. C₄×Q₁₆	C₂²×C₆₇	semidirect
541. C₄×D₈	C₂²×C₆₇	semidirect
543. #435	C₂²×C₆₇	semidirect
545. C₈×D₄	C₂²×C₆₇	semidirect
546. C₂×#107	C₂²×C₆₇	semidirect
547. #424	C₂²×C₆₇	semidirect
548. #417	C₂²×C₆₇	semidirect
549. #417	C₂²×C₆₇	semidirect
550. C₂×#103	C₂²×C₆₇	semidirect
551. #408	C₂²×C₆₇	semidirect
553. #405	C₂²×C₆₇	semidirect
585. #135	D₄×C₆₇	semidirect
902. C₂²	#578×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₆₇	2
C₂²×#135×C₆₇	2
C₆₇×#3489	2
D₄×Q₁₆×C₆₇	2
C₆₇×#3285	2
C₆₇×#3283	2
C₆₇×#3280	2
C₆₇×#3269	2
C₆₇×#3266	2
C₆₇×#3156	2
C₆₇×#3061	2
C₂×#467×C₆₇	2
C₆₇×#3046	2
C₆₇×#3013	2
C₆₇×#3007	2
C₆₇×#2951	2
C₆₇×#2929	2
#61057	67

Subgroups — C67×#61057 #30740308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61057 #30740308