Subgroups — C₆₇×#60168 #30739419

Order 17152.

2882 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2949	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2948	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2946	C₂	1	8	yes	maximal, complemented
7	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	8	yes	maximal, complemented
8	C₆₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#418×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₆₇	C₄	1	16	yes	complemented
15	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	—
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	—
17	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
18	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	#520×C₆₇	—	2	2	no	—
22	#520×C₆₇	C₂²	1	4	yes	complemented
23	#519×C₆₇	C₂²	1	2	yes	complemented
24	#518×C₆₇	—	2	2	no	—
25	#518×C₆₇	—	2	2	no	—
26	#518×C₆₇	—	2	2	no	—
27	#518×C₆₇	C₂²	1	4	yes	—
28	#518×C₆₇	C₂²	1	4	yes	complemented
29	#518×C₆₇	C₂²	1	2	yes	complemented
30	C₄×#41×C₆₇	—	2	2	no	—
31	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
32	C₂×C₄×D₄×C₆₇	—	2	2	no	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
34	C₂×#117×C₆₇	—	2	2	no	—
35	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
39	#442×C₆₇	C₂²	1	16	yes	complemented
40	#440×C₆₇	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₆₇	C₂²	1	16	yes	complemented
42	C₄×D₈×C₆₇	C₂²	1	16	yes	complemented
43	#428×C₆₇	C₂²	1	4	yes	complemented
44	#428×C₆₇	C₂²	1	4	yes	complemented
45	#427×C₆₇	C₂²	1	4	yes	complemented
46	#419×C₆₇	C₂²	1	2	yes	complemented
47	#418×C₆₇	C₂²	1	4	yes	—
48	#418×C₆₇	C₂²	1	4	yes	complemented
49	#418×C₆₇	C₂²	1	2	yes	complemented
50	#417×C₆₇	C₂²	1	4	yes	complemented
51	#416×C₆₇	C₂²	1	4	yes	complemented
52	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
53	#405×C₆₇	C₂²	1	4	yes	complemented
54	#405×C₆₇	C₂²	1	4	yes	complemented
55	C₄×M₁₆×C₆₇	C₂²	1	4	yes	complemented
56	C₂⁵×C₆₇	—	2	1	no	—
57	C₂×#41×C₆₇	—	2	1	no	—
58	C₂×#41×C₆₇	—	2	1	no	—
59	C₂×#41×C₆₇	—	2	4	no	—
60	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
61	C₂×#41×C₆₇	C₂³	1	2	yes	—
62	C₂×#41×C₆₇	C₂³	1	2	yes	—
63	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₇	—	2	1	no	—
65	C₂²×D₄×C₆₇	—	2	1	no	—
66	C₂²×D₄×C₆₇	—	2	1	no	—
67	C₂²×D₄×C₆₇	—	2	1	no	—
68	C₂²×D₄×C₆₇	—	2	4	no	—
69	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
70	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
71	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
72	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	—	2	4	no	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	AGL(1,ℤ/8)×C₆₇	C₂×C₄	1	32	yes	complemented
78	AGL(1,ℤ/8)×C₆₇	C₂×C₄	1	32	yes	complemented
79	C₂×SD₁₆×C₆₇	C₂×C₄	1	16	yes	complemented
80	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
81	C₂×D₈×C₆₇	C₂×C₄	1	16	yes	complemented
82	C₂×D₈×C₆₇	C₂³	1	8	yes	—
83	C₂×M₁₆×C₆₇	—	2	4	no	—
84	C₂×M₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
91	C₄×Q₈×C₆₇	—	2	4	no	—
92	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
93	C₄×D₄×C₆₇	—	2	8	no	—
94	C₄×D₄×C₆₇	—	2	8	no	—
95	C₄×D₄×C₆₇	—	2	8	no	—
96	C₄×D₄×C₆₇	—	2	4	no	—
97	C₄×D₄×C₆₇	—	2	8	no	—
98	C₄×D₄×C₆₇	—	2	8	no	—
99	C₄×D₄×C₆₇	C₂³	1	16	yes	—
100	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
101	#117×C₆₇	—	2	1	no	—
102	#117×C₆₇	—	2	1	no	—
103	#117×C₆₇	—	2	1	no	—
104	#117×C₆₇	—	2	1	no	—
105	#117×C₆₇	—	2	4	no	—
106	#117×C₆₇	—	2	4	no	—
107	#117×C₆₇	—	2	4	no	—
108	#117×C₆₇	D₄	1	2	yes	—
109	#117×C₆₇	D₄	1	2	yes	—
110	#117×C₆₇	C₂³	1	2	yes	—
111	#117×C₆₇	C₂³	1	2	yes	—
112	#117×C₆₇	C₂³	1	2	yes	—
113	#117×C₆₇	C₂³	1	2	yes	—
114	#117×C₆₇	C₂³	1	2	yes	—
115	#117×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
127	C₂×C₄²×C₆₇	—	2	1	no	—
128	C₂×C₄²×C₆₇	—	2	1	no	—
129	C₂×C₄²×C₆₇	—	2	4	no	—
130	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
131	#107×C₆₇	C₂³	1	8	yes	complemented
132	#106×C₆₇	C₂³	1	8	yes	complemented
133	#103×C₆₇	C₂³	1	8	yes	complemented
134	#102×C₆₇	C₂³	1	16	yes	—
135	#102×C₆₇	C₂³	1	8	yes	complemented
136	#97×C₆₇	C₂³	1	8	yes	complemented
137	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
138	C₂⁴×C₆₇	—	2	2	no	—
139	C₂⁴×C₆₇	—	2	8	no	—
140	C₂⁴×C₆₇	—	2	1	no	—
141	C₂⁴×C₆₇	—	2	2	no	—
142	C₂⁴×C₆₇	—	2	2	no	—
143	C₂⁴×C₆₇	—	8	4	no	—
144	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
145	#41×C₆₇	—	2	8	no	—
146	#41×C₆₇	—	2	8	no	—
147	#41×C₆₇	—	2	4	no	—
148	#41×C₆₇	—	2	4	no	—
149	#41×C₆₇	C₂²×C₄	1	8	yes	—
150	#41×C₆₇	C₂²×C₄	1	8	yes	complemented
151	C₂×Q₈×C₆₇	—	2	1	no	—
152	C₂×Q₈×C₆₇	—	2	2	no	—
153	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	complemented
154	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
155	C₂×D₄×C₆₇	—	2	8	no	—
156	C₂×D₄×C₆₇	—	2	2	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	2	8	no	—
159	C₂×D₄×C₆₇	—	2	8	no	—
160	C₂×D₄×C₆₇	—	2	8	no	—
161	C₂×D₄×C₆₇	—	2	2	no	—
162	C₂×D₄×C₆₇	—	2	2	no	—
163	C₂×D₄×C₆₇	—	2	2	no	—
164	C₂×D₄×C₆₇	—	2	1	no	—
165	C₂×D₄×C₆₇	—	2	4	no	—
166	C₂×D₄×C₆₇	—	2	4	no	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	2	2	no	—
169	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	complemented
173	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
174	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	8	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	8	no	—
182	C₂²×C₄×C₆₇	—	2	16	no	—
183	C₂²×C₄×C₆₇	—	8	8	no	—
184	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	#41	1	4	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
193	SD₁₆×C₆₇	C₂²×C₄	1	32	yes	complemented
194	D₈×C₆₇	C₂²×C₄	1	32	yes	complemented
195	M₁₆×C₆₇	—	2	4	no	—
196	M₁₆×C₆₇	—	2	4	no	—
197	M₁₆×C₆₇	C₂²×C₄	1	8	yes	—
198	M₁₆×C₆₇	C₂²×C₄	1	8	yes	complemented
199	C₂×C₈×C₆₇	—	2	4	no	—
200	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	complemented
201	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
202	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
203	C₄⋊C₄×C₆₇	—	2	2	no	—
204	C₄⋊C₄×C₆₇	—	2	8	no	—
205	C₄⋊C₄×C₆₇	—	2	2	no	—
206	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
207	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
208	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
209	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
210	C₂²⋊C₄×C₆₇	—	2	2	no	—
211	C₂²⋊C₄×C₆₇	—	2	2	no	—
212	C₂²⋊C₄×C₆₇	—	2	2	no	—
213	C₂²⋊C₄×C₆₇	—	2	2	no	—
214	C₂²⋊C₄×C₆₇	—	2	16	no	—
215	C₂²⋊C₄×C₆₇	—	2	8	no	—
216	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
217	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
218	C₄²×C₆₇	—	2	2	no	—
219	C₄²×C₆₇	—	2	8	no	—
220	C₄²×C₆₇	—	2	2	no	—
221	C₄²×C₆₇	—	2	2	no	—
222	C₄²×C₆₇	—	2	2	no	—
223	C₄²×C₆₇	C₂×D₄	1	4	yes	—
224	C₄²×C₆₇	C₂⁴	1	4	yes	—
225	C₂³×C₆₇	—	2	8	no	—
226	C₂³×C₆₇	—	2	2	no	—
227	C₂³×C₆₇	—	2	4	no	—
228	C₂³×C₆₇	—	2	4	no	—
229	C₂³×C₆₇	—	2	8	no	—
230	C₂³×C₆₇	—	2	8	no	—
231	C₂³×C₆₇	—	4	2	no	—
232	C₂³×C₆₇	—	4	8	no	—
233	C₂³×C₆₇	—	8	2	no	—
234	C₂³×C₆₇	—	8	4	no	—
235	C₂³×C₆₇	—	8	4	no	—
236	C₂³×C₆₇	—	8	16	no	—
237	C₂³×C₆₇	C₄×D₄	1	4	yes	—
238	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
239	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
240	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₆₇	—	2	4	no	—
242	Q₈×C₆₇	—	2	2	no	—
243	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
244	D₄×C₆₇	—	2	8	no	—
245	D₄×C₆₇	—	2	8	no	—
246	D₄×C₆₇	—	2	8	no	—
247	D₄×C₆₇	—	2	8	no	—
248	D₄×C₆₇	—	2	8	no	—
249	D₄×C₆₇	—	2	4	no	—
250	D₄×C₆₇	—	2	4	no	—
251	D₄×C₆₇	—	2	2	no	—
252	D₄×C₆₇	C₂³×C₄	1	4	yes	—
253	D₄×C₆₇	C₂³×C₄	1	8	yes	—
254	C₂×C₄×C₆₇	—	2	4	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	2	8	no	—
257	C₂×C₄×C₆₇	—	2	8	no	—
258	C₂×C₄×C₆₇	—	2	4	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	4	4	no	—
261	C₂×C₄×C₆₇	—	4	4	no	—
262	C₂×C₄×C₆₇	—	8	8	no	—
263	C₂×C₄×C₆₇	—	8	16	no	—
264	C₂×C₄×C₆₇	—	8	2	no	—
265	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
266	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
267	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
268	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
272	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
276	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
277	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
278	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
279	C₈×C₆₇	—	2	4	no	—
280	C₈×C₆₇	C₂³×C₄	1	8	yes	—
281	C₂²×C₆₇	—	2	2	no	—
282	C₂²×C₆₇	—	2	2	no	—
283	C₂²×C₆₇	—	2	2	no	—
284	C₂²×C₆₇	—	2	4	no	—
285	C₂²×C₆₇	—	2	8	no	—
286	C₂²×C₆₇	—	4	4	no	—
287	C₂²×C₆₇	—	4	16	no	—
288	C₂²×C₆₇	—	4	8	no	—
289	C₂²×C₆₇	—	4	4	no	—
290	C₂²×C₆₇	—	8	4	no	—
291	C₂²×C₆₇	—	8	8	no	—
292	C₂²×C₆₇	—	8	8	no	—
293	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
294	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
295	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
296	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
297	C₄×C₆₇	—	2	8	no	—
298	C₄×C₆₇	—	2	4	no	—
299	C₄×C₆₇	—	4	4	no	—
300	C₄×C₆₇	—	4	4	no	—
301	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
302	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
303	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
304	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
305	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
306	#60168	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂×C₆₇	—	2	2	no	—
308	C₂×C₆₇	—	2	2	no	—
309	C₂×C₆₇	—	2	2	no	—
310	C₂×C₆₇	—	4	8	no	—
311	C₂×C₆₇	—	4	4	no	—
312	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
313	C₂×C₆₇	#3585	1	2	yes	—
314	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic
315	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
316	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
317	#2949	C₂×C₆₇	1	4	yes	complemented
318	#2948	C₂×C₆₇	1	4	yes	complemented
319	#2946	C₂×C₆₇	1	8	yes	complemented
320	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	8	yes	complemented
321	#2911	C₂×C₆₇	1	1	yes	characteristic, complemented
322	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
323	C₂×#418	C₂×C₆₇	1	1	yes	characteristic, complemented
324	#2873	C₂×C₆₇	1	1	yes	characteristic, complemented
325	C₆₇	#60168	1	1	yes	characteristic, direct product factor, Sylow
326	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
327	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
328	C₂×AGL(1,ℤ/8)	C₄×C₆₇	1	16	yes	complemented
329	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	—
330	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	—
331	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
332	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
333	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
334	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
335	#520	—	2	2	no	—
336	#520	C₂²×C₆₇	1	4	yes	complemented
337	#519	C₂²×C₆₇	1	2	yes	complemented
338	#518	—	2	2	no	—
339	#518	—	2	2	no	—
340	#518	—	2	2	no	—
341	#518	C₂²×C₆₇	1	4	yes	—
342	#518	C₂²×C₆₇	1	4	yes	complemented
343	#518	C₂²×C₆₇	1	2	yes	complemented
344	C₄×#41	—	2	2	no	—
345	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
346	C₂×C₄×D₄	—	2	2	no	—
347	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
348	C₂×#117	—	2	2	no	—
349	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
350	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
351	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	—	2	2	no	—
353	#442	C₂²×C₆₇	1	16	yes	complemented
354	#440	C₂²×C₆₇	1	16	yes	complemented
355	C₄×SD₁₆	C₂²×C₆₇	1	16	yes	complemented
356	C₄×D₈	C₂²×C₆₇	1	16	yes	complemented
357	#428	C₂²×C₆₇	1	4	yes	complemented
358	#428	C₂²×C₆₇	1	4	yes	complemented
359	#427	C₂²×C₆₇	1	4	yes	complemented
360	#419	C₂²×C₆₇	1	2	yes	complemented
361	#418	C₂²×C₆₇	1	4	yes	—
362	#418	C₂²×C₆₇	1	4	yes	complemented
363	#418	C₂²×C₆₇	1	2	yes	complemented
364	#417	C₂²×C₆₇	1	4	yes	complemented
365	#416	C₂²×C₆₇	1	4	yes	complemented
366	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
367	#405	C₂²×C₆₇	1	4	yes	complemented
368	#405	C₂²×C₆₇	1	4	yes	complemented
369	C₄×M₁₆	C₂²×C₆₇	1	4	yes	complemented
370	C₂⁵	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	4	no	—
374	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
375	C₂×#41	C₂³×C₆₇	1	2	yes	—
376	C₂×#41	C₂³×C₆₇	1	2	yes	—
377	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂²×D₄	—	2	4	no	—
383	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
384	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
385	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
386	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
387	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	4	no	—
390	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
391	AGL(1,ℤ/8)	C₂×C₄×C₆₇	1	32	yes	complemented
392	AGL(1,ℤ/8)	C₂×C₄×C₆₇	1	32	yes	complemented
393	C₂×SD₁₆	C₂×C₄×C₆₇	1	16	yes	complemented
394	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
395	C₂×D₈	C₂×C₄×C₆₇	1	16	yes	complemented
396	C₂×D₈	C₂³×C₆₇	1	8	yes	—
397	C₂×M₁₆	—	2	4	no	—
398	C₂×M₁₆	C₂×C₄×C₆₇	1	8	yes	complemented
399	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
400	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
401	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
402	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
403	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
404	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
405	C₄×Q₈	—	2	4	no	—
406	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
407	C₄×D₄	—	2	8	no	—
408	C₄×D₄	—	2	8	no	—
409	C₄×D₄	—	2	8	no	—
410	C₄×D₄	—	2	4	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	C₂³×C₆₇	1	16	yes	—
414	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	4	no	—
420	#117	—	2	4	no	—
421	#117	—	2	4	no	—
422	#117	D₄×C₆₇	1	2	yes	—
423	#117	D₄×C₆₇	1	2	yes	—
424	#117	C₂³×C₆₇	1	2	yes	—
425	#117	C₂³×C₆₇	1	2	yes	—
426	#117	C₂³×C₆₇	1	2	yes	—
427	#117	C₂³×C₆₇	1	2	yes	—
428	#117	C₂³×C₆₇	1	2	yes	—
429	#117	C₂³×C₆₇	1	2	yes	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	4	no	—
437	C₂×C₂²⋊C₄	—	2	8	no	—
438	C₂×C₂²⋊C₄	—	2	8	no	—
439	C₂×C₂²⋊C₄	—	2	4	no	—
440	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	4	no	—
444	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
445	#107	C₂³×C₆₇	1	8	yes	complemented
446	#106	C₂³×C₆₇	1	8	yes	complemented
447	#103	C₂³×C₆₇	1	8	yes	complemented
448	#102	C₂³×C₆₇	1	16	yes	—
449	#102	C₂³×C₆₇	1	8	yes	complemented
450	#97	C₂³×C₆₇	1	8	yes	complemented
451	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	8	no	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	2	2	no	—
457	C₂⁴	—	8	4	no	—
458	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
459	#41	—	2	8	no	—
460	#41	—	2	8	no	—
461	#41	—	2	4	no	—
462	#41	—	2	4	no	—
463	#41	C₂²×C₄×C₆₇	1	8	yes	—
464	#41	C₂²×C₄×C₆₇	1	8	yes	complemented
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	complemented
468	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
484	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
485	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
486	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	complemented
487	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
488	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	8	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	16	no	—
497	C₂²×C₄	—	8	8	no	—
498	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
499	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
500	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
503	C₂²×C₄	#41×C₆₇	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
507	SD₁₆	C₂²×C₄×C₆₇	1	32	yes	complemented
508	D₈	C₂²×C₄×C₆₇	1	32	yes	complemented
509	M₁₆	—	2	4	no	—
510	M₁₆	—	2	4	no	—
511	M₁₆	C₂²×C₄×C₆₇	1	8	yes	—
512	M₁₆	C₂²×C₄×C₆₇	1	8	yes	complemented
513	C₂×C₈	—	2	4	no	—
514	C₂×C₈	C₂²×C₄×C₆₇	1	8	yes	complemented
515	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
516	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
521	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
522	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
523	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	16	no	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
531	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	8	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	C₂×D₄×C₆₇	1	4	yes	—
538	C₄²	C₂⁴×C₆₇	1	4	yes	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	8	no	—
544	C₂³	—	2	8	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	8	4	no	—
548	C₂³	—	8	4	no	—
549	C₂³	—	8	2	no	—
550	C₂³	—	8	16	no	—
551	C₂³	C₄×D₄×C₆₇	1	4	yes	—
552	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
553	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
554	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
555	Q₈	—	2	4	no	—
556	Q₈	—	2	2	no	—
557	Q₈	C₂³×C₄×C₆₇	1	4	yes	—
558	D₄	—	2	8	no	—
559	D₄	—	2	8	no	—
560	D₄	—	2	8	no	—
561	D₄	—	2	8	no	—
562	D₄	—	2	8	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂³×C₄×C₆₇	1	4	yes	—
567	D₄	C₂³×C₄×C₆₇	1	8	yes	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	8	16	no	—
577	C₂×C₄	—	8	8	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
580	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
581	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
582	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
583	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
584	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
585	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
586	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
590	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
591	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
592	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
593	C₈	—	2	4	no	—
594	C₈	C₂³×C₄×C₆₇	1	8	yes	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	16	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	8	8	no	—
605	C₂²	—	8	8	no	—
606	C₂²	—	8	4	no	—
607	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
608	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
609	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
610	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
611	C₄	—	2	8	no	—
612	C₄	—	2	4	no	—
613	C₄	—	4	4	no	—
614	C₄	—	4	4	no	—
615	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
616	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
617	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
618	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
619	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
620	C₂	—	2	2	no	—
621	C₂	—	2	2	no	—
622	C₂	—	2	2	no	—
623	C₂	—	4	8	no	—
624	C₂	—	4	4	no	—
625	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
626	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×AGL(1,ℤ/8)×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3428	C₂	semidirect
3. C₂×#518×C₆₇	C₂	semidirect
4. C₆₇×#2949	C₂	semidirect
5. C₆₇×#2948	C₂	semidirect
6. C₆₇×#2946	C₂	semidirect
7. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
8. C₆₇×#2911	C₂	semidirect
9. C₆₇×#2896	C₂	semidirect
10. C₂×#418×C₆₇	C₂	semidirect
11. C₆₇×#2873	C₂	semidirect
14. C₂×AGL(1,ℤ/8)×C₆₇	C₄	semidirect
22. #520×C₆₇	C₂²	semidirect
23. #519×C₆₇	C₂²	semidirect
28. #518×C₆₇	C₂²	semidirect
29. #518×C₆₇	C₂²	semidirect
31. C₄×#41×C₆₇	C₂²	semidirect
33. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. #442×C₆₇	C₂²	semidirect
40. #440×C₆₇	C₂²	semidirect
41. C₄×SD₁₆×C₆₇	C₂²	semidirect
42. C₄×D₈×C₆₇	C₂²	semidirect
43. #428×C₆₇	C₂²	semidirect
44. #428×C₆₇	C₂²	semidirect
45. #427×C₆₇	C₂²	semidirect
46. #419×C₆₇	C₂²	semidirect
48. #418×C₆₇	C₂²	semidirect
49. #418×C₆₇	C₂²	semidirect
50. #417×C₆₇	C₂²	semidirect
51. #416×C₆₇	C₂²	semidirect
52. C₂×#102×C₆₇	C₂²	semidirect
53. #405×C₆₇	C₂²	semidirect
54. #405×C₆₇	C₂²	semidirect
55. C₄×M₁₆×C₆₇	C₂²	semidirect
60. C₂×#41×C₆₇	C₂×C₄	semidirect
69. C₂²×D₄×C₆₇	C₂×C₄	semidirect
77. AGL(1,ℤ/8)×C₆₇	C₂×C₄	semidirect
78. AGL(1,ℤ/8)×C₆₇	C₂×C₄	semidirect
79. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
81. C₂×D₈×C₆₇	C₂×C₄	semidirect
84. C₂×M₁₆×C₆₇	C₂×C₄	semidirect
92. C₄×Q₈×C₆₇	C₂³	semidirect
100. C₄×D₄×C₆₇	C₂³	semidirect
131. #107×C₆₇	C₂³	semidirect
132. #106×C₆₇	C₂³	semidirect
133. #103×C₆₇	C₂³	semidirect
135. #102×C₆₇	C₂³	semidirect
136. #97×C₆₇	C₂³	semidirect
137. C₄×C₈×C₆₇	C₂³	semidirect
150. #41×C₆₇	C₂²×C₄	semidirect
153. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
172. C₂×D₄×C₆₇	C₂²×C₄	semidirect
193. SD₁₆×C₆₇	C₂²×C₄	semidirect
194. D₈×C₆₇	C₂²×C₄	semidirect
198. M₁₆×C₆₇	C₂²×C₄	semidirect
200. C₂×C₈×C₆₇	C₂²×C₄	semidirect
306. #60168	C₆₇	direct (N × H)
315. #3428	C₂×C₆₇	semidirect
316. C₂×#518	C₂×C₆₇	semidirect
317. #2949	C₂×C₆₇	semidirect
318. #2948	C₂×C₆₇	semidirect
319. #2946	C₂×C₆₇	semidirect
320. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
321. #2911	C₂×C₆₇	semidirect
322. #2896	C₂×C₆₇	semidirect
323. C₂×#418	C₂×C₆₇	semidirect
324. #2873	C₂×C₆₇	semidirect
325. C₆₇	#60168	direct (N × H)
328. C₂×AGL(1,ℤ/8)	C₄×C₆₇	semidirect
336. #520	C₂²×C₆₇	semidirect
337. #519	C₂²×C₆₇	semidirect
342. #518	C₂²×C₆₇	semidirect
343. #518	C₂²×C₆₇	semidirect
345. C₄×#41	C₂²×C₆₇	semidirect
347. C₂×C₄×D₄	C₂²×C₆₇	semidirect
353. #442	C₂²×C₆₇	semidirect
354. #440	C₂²×C₆₇	semidirect
355. C₄×SD₁₆	C₂²×C₆₇	semidirect
356. C₄×D₈	C₂²×C₆₇	semidirect
357. #428	C₂²×C₆₇	semidirect
358. #428	C₂²×C₆₇	semidirect
359. #427	C₂²×C₆₇	semidirect
360. #419	C₂²×C₆₇	semidirect
362. #418	C₂²×C₆₇	semidirect
363. #418	C₂²×C₆₇	semidirect
364. #417	C₂²×C₆₇	semidirect
365. #416	C₂²×C₆₇	semidirect
366. C₂×#102	C₂²×C₆₇	semidirect
367. #405	C₂²×C₆₇	semidirect
368. #405	C₂²×C₆₇	semidirect
369. C₄×M₁₆	C₂²×C₆₇	semidirect
374. C₂×#41	C₂×C₄×C₆₇	semidirect
383. C₂²×D₄	C₂×C₄×C₆₇	semidirect
391. AGL(1,ℤ/8)	C₂×C₄×C₆₇	semidirect
392. AGL(1,ℤ/8)	C₂×C₄×C₆₇	semidirect
393. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
395. C₂×D₈	C₂×C₄×C₆₇	semidirect
398. C₂×M₁₆	C₂×C₄×C₆₇	semidirect
406. C₄×Q₈	C₂³×C₆₇	semidirect
414. C₄×D₄	C₂³×C₆₇	semidirect
445. #107	C₂³×C₆₇	semidirect
446. #106	C₂³×C₆₇	semidirect
447. #103	C₂³×C₆₇	semidirect
449. #102	C₂³×C₆₇	semidirect
450. #97	C₂³×C₆₇	semidirect
451. C₄×C₈	C₂³×C₆₇	semidirect
464. #41	C₂²×C₄×C₆₇	semidirect
467. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
486. C₂×D₄	C₂²×C₄×C₆₇	semidirect
507. SD₁₆	C₂²×C₄×C₆₇	semidirect
508. D₈	C₂²×C₄×C₆₇	semidirect
512. M₁₆	C₂²×C₄×C₆₇	semidirect
514. C₂×C₈	C₂²×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#3428	2
C₂×#518×C₆₇	2
C₆₇×#2949	2
C₆₇×#2948	2
C₆₇×#2946	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2911	2
C₆₇×#2896	2
C₂×#418×C₆₇	2
C₆₇×#2873	2
#60168	67

Subgroups — C67×#60168 #30739419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60168 #30739419