Subgroups — C₆₇×#34937 #30714188

Order 17152.

3314 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2545	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2544	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2543	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2416	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
13	C₄×#121×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2297	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	2	yes	—
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	#532×C₆₇	—	2	16	no	—
19	#532×C₆₇	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#127×C₆₇	C₂²	1	2	yes	—
23	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#124×C₆₇	C₂²	1	2	yes	—
25	C₂×#124×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	4	yes	—
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	8	yes	—
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₄×#41×C₆₇	—	2	8	no	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
41	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
45	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
46	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
47	#398×C₆₇	C₂²	1	4	yes	—
48	#397×C₆₇	C₂²	1	4	yes	—
49	#396×C₆₇	C₂²	1	8	yes	—
50	#394×C₆₇	C₂²	1	4	yes	—
51	#394×C₆₇	C₂²	1	8	yes	—
52	#392×C₆₇	C₂²	1	4	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	4	yes	—
58	#389×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	8	yes	—
60	#386×C₆₇	C₂²	1	8	yes	—
61	#386×C₆₇	C₂²	1	8	yes	—
62	#380×C₆₇	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
69	C₂×#95×C₆₇	C₂²	1	2	yes	—
70	C₂×#41×C₆₇	—	2	4	no	—
71	C₂×#41×C₆₇	—	2	8	no	—
72	C₂×#41×C₆₇	—	2	8	no	—
73	C₂×#41×C₆₇	—	2	4	no	—
74	C₂×#41×C₆₇	—	2	8	no	—
75	C₂×#41×C₆₇	D₄	1	8	yes	complemented
76	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
77	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
79	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
87	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₄⋊Q₈×C₆₇	—	2	8	no	—
94	C₄⋊Q₈×C₆₇	—	2	4	no	—
95	#127×C₆₇	—	2	8	no	—
96	#127×C₆₇	—	2	4	no	—
97	#124×C₆₇	—	2	8	no	—
98	#124×C₆₇	—	2	8	no	—
99	#124×C₆₇	—	2	8	no	—
100	#121×C₆₇	—	2	32	no	—
101	#121×C₆₇	—	2	8	no	—
102	#121×C₆₇	—	2	8	no	—
103	#121×C₆₇	—	2	16	no	—
104	C₄×Q₈×C₆₇	—	2	4	no	—
105	C₄×Q₈×C₆₇	—	2	4	no	—
106	C₄×D₄×C₆₇	—	2	8	no	—
107	C₄×D₄×C₆₇	—	2	8	no	—
108	C₄×D₄×C₆₇	—	2	32	no	—
109	C₄×D₄×C₆₇	—	2	4	no	—
110	C₄×D₄×C₆₇	—	2	4	no	—
111	C₄×D₄×C₆₇	—	2	8	no	—
112	C₄×D₄×C₆₇	—	2	8	no	—
113	#117×C₆₇	—	2	4	no	—
114	#117×C₆₇	—	2	8	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
135	C₂×C₄²×C₆₇	—	2	8	no	—
136	C₂×C₄²×C₆₇	—	2	8	no	—
137	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
138	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
148	#95×C₆₇	C₂³	1	4	yes	—
149	#95×C₆₇	C₂³	1	2	yes	—
150	#95×C₆₇	C₂³	1	2	yes	—
151	#95×C₆₇	C₂³	1	8	yes	—
152	#95×C₆₇	C₂³	1	8	yes	—
153	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
154	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
155	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
156	#41×C₆₇	—	2	32	no	—
157	#41×C₆₇	—	4	32	no	—
158	C₂×Q₈×C₆₇	—	2	2	no	—
159	C₂×Q₈×C₆₇	—	2	4	no	—
160	C₂×Q₈×C₆₇	—	2	4	no	—
161	C₂×Q₈×C₆₇	—	2	2	no	—
162	C₂×Q₈×C₆₇	—	2	4	no	—
163	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₆₇	—	2	4	no	—
165	C₂×D₄×C₆₇	—	2	4	no	—
166	C₂×D₄×C₆₇	—	2	16	no	—
167	C₂×D₄×C₆₇	—	2	8	no	—
168	C₂×D₄×C₆₇	—	2	8	no	—
169	C₂×D₄×C₆₇	—	2	8	no	—
170	C₂×D₄×C₆₇	—	2	2	no	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	2	no	—
176	C₂×D₄×C₆₇	—	2	16	no	—
177	C₂×D₄×C₆₇	—	2	8	no	—
178	C₂×D₄×C₆₇	—	2	4	no	—
179	C₂×D₄×C₆₇	—	4	8	no	—
180	C₂×D₄×C₆₇	—	4	4	no	—
181	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
182	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	4	no	—
186	C₂²×C₄×C₆₇	—	2	8	no	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	—	2	4	no	—
189	C₂²×C₄×C₆₇	—	2	8	no	—
190	C₂²×C₄×C₆₇	—	2	8	no	—
191	C₂²×C₄×C₆₇	—	2	8	no	—
192	C₂²×C₄×C₆₇	—	2	8	no	—
193	C₂²×C₄×C₆₇	—	2	8	no	—
194	C₂²×C₄×C₆₇	—	4	2	no	—
195	C₂²×C₄×C₆₇	—	4	4	no	—
196	C₂²×C₄×C₆₇	—	4	4	no	—
197	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
199	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₆₇	#41	1	4	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	—	2	16	no	—
220	C₄⋊C₄×C₆₇	—	2	4	no	—
221	C₄⋊C₄×C₆₇	—	2	4	no	—
222	C₄⋊C₄×C₆₇	—	2	8	no	—
223	C₄⋊C₄×C₆₇	—	2	4	no	—
224	C₄⋊C₄×C₆₇	#41	1	8	yes	complemented
225	C₂²⋊C₄×C₆₇	—	2	4	no	—
226	C₂²⋊C₄×C₆₇	—	2	16	no	—
227	C₂²⋊C₄×C₆₇	—	2	4	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	16	no	—
230	C₂²⋊C₄×C₆₇	—	2	8	no	—
231	C₂²⋊C₄×C₆₇	—	2	8	no	—
232	C₂²⋊C₄×C₆₇	—	2	16	no	—
233	C₂²⋊C₄×C₆₇	—	4	8	no	—
234	C₄²×C₆₇	—	2	4	no	—
235	C₄²×C₆₇	—	2	8	no	—
236	C₄²×C₆₇	—	2	4	no	—
237	C₄²×C₆₇	—	2	4	no	—
238	C₄²×C₆₇	—	2	4	no	—
239	C₄²×C₆₇	—	2	4	no	—
240	C₄²×C₆₇	C₂×D₄	1	4	yes	—
241	C₄²×C₆₇	C₂×D₄	1	4	yes	—
242	C₄²×C₆₇	C₂×D₄	1	4	yes	—
243	C₄²×C₆₇	C₂×D₄	1	4	yes	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	2	4	no	—
250	C₂³×C₆₇	—	2	4	no	—
251	C₂³×C₆₇	—	2	4	no	—
252	C₂³×C₆₇	—	2	8	no	—
253	C₂³×C₆₇	—	2	4	no	—
254	C₂³×C₆₇	—	2	8	no	—
255	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
256	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
257	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
258	C₂³×C₆₇	C₂×#41	1	2	yes	—
259	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
260	Q₈×C₆₇	—	2	8	no	—
261	Q₈×C₆₇	—	4	8	no	—
262	D₄×C₆₇	—	2	16	no	—
263	D₄×C₆₇	—	2	8	no	—
264	D₄×C₆₇	—	4	32	no	—
265	D₄×C₆₇	—	4	8	no	—
266	D₄×C₆₇	—	4	16	no	—
267	D₄×C₆₇	—	4	8	no	—
268	D₄×C₆₇	—	4	8	no	—
269	C₂×C₄×C₆₇	—	2	4	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	16	no	—
277	C₂×C₄×C₆₇	—	2	8	no	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	4	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	4	4	no	—
289	C₂×C₄×C₆₇	—	4	16	no	—
290	C₂×C₄×C₆₇	—	4	8	no	—
291	C₂×C₄×C₆₇	—	4	16	no	—
292	C₂×C₄×C₆₇	—	4	8	no	—
293	C₂×C₄×C₆₇	#121	1	16	yes	complemented
294	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
305	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
306	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	2	no	—
309	C₂²×C₆₇	—	2	4	no	—
310	C₂²×C₆₇	—	2	4	no	—
311	C₂²×C₆₇	—	2	4	no	—
312	C₂²×C₆₇	—	2	8	no	—
313	C₂²×C₆₇	—	4	2	no	—
314	C₂²×C₆₇	—	4	2	no	—
315	C₂²×C₆₇	—	4	4	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	—	4	4	no	—
318	C₂²×C₆₇	—	4	4	no	—
319	C₂²×C₆₇	—	4	8	no	—
320	C₂²×C₆₇	—	4	8	no	—
321	C₂²×C₆₇	C₂×#121	1	4	yes	—
322	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
323	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
324	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₆₇	C₂²×#41	1	2	yes	—
326	C₂²×C₆₇	#585	1	2	yes	—
327	C₄×C₆₇	—	2	4	no	—
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	2	8	no	—
332	C₄×C₆₇	—	4	4	no	—
333	C₄×C₆₇	—	4	2	no	—
334	C₄×C₆₇	—	4	2	no	—
335	C₄×C₆₇	—	4	4	no	—
336	C₄×C₆₇	C₂×#121	1	4	yes	—
337	C₄×C₆₇	C₂×#121	1	4	yes	—
338	C₄×C₆₇	#532	1	4	yes	complemented
339	#34937	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂×C₆₇	—	2	4	no	—
341	C₂×C₆₇	—	4	4	no	—
342	C₂×C₆₇	—	8	4	no	—
343	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
344	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
345	C₂×C₆₇	#3449	1	1	yes	characteristic
346	C₂×C₆₇	D₄×#41	1	2	yes	—
347	C₂×C₆₇	#3480	1	2	yes	—
348	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
349	C₂×#532	C₂×C₆₇	1	2	yes	complemented
350	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
351	#2548	C₂×C₆₇	1	1	yes	characteristic, complemented
352	#2547	C₂×C₆₇	1	1	yes	characteristic, complemented
353	#2546	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2545	C₂×C₆₇	1	2	yes	complemented
355	#2544	C₂×C₆₇	1	2	yes	complemented
356	#2543	C₂×C₆₇	1	4	yes	complemented
357	#2541	C₂×C₆₇	1	1	yes	characteristic, complemented
358	#2416	C₂×C₆₇	1	4	yes	complemented
359	#2392	C₂×C₆₇	1	4	yes	complemented
360	C₄×#121	C₂×C₆₇	1	4	yes	complemented
361	#2297	C₂×C₆₇	1	2	yes	complemented
362	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
363	C₆₇	#34937	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²×#41	C₂²×C₆₇	1	2	yes	—
365	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
366	#532	—	2	16	no	—
367	#532	—	2	8	no	—
368	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
369	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
370	C₂×#127	C₂²×C₆₇	1	2	yes	—
371	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
372	C₂×#124	C₂²×C₆₇	1	2	yes	—
373	C₂×#124	C₂²×C₆₇	1	2	yes	—
374	C₂×#124	C₂²×C₆₇	1	2	yes	—
375	C₂×#121	C₂²×C₆₇	1	2	yes	—
376	C₂×#121	C₂²×C₆₇	1	8	yes	—
377	C₂×#121	C₂²×C₆₇	1	4	yes	—
378	C₂×#121	C₂²×C₆₇	1	2	yes	—
379	C₄×#41	—	2	8	no	—
380	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
384	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
389	C₂×#117	C₂²×C₆₇	1	2	yes	—
390	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
392	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
393	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
394	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
395	#398	C₂²×C₆₇	1	4	yes	—
396	#397	C₂²×C₆₇	1	4	yes	—
397	#396	C₂²×C₆₇	1	8	yes	—
398	#394	C₂²×C₆₇	1	8	yes	—
399	#394	C₂²×C₆₇	1	4	yes	—
400	#392	C₂²×C₆₇	1	4	yes	—
401	#391	C₂²×C₆₇	1	2	yes	—
402	#391	C₂²×C₆₇	1	2	yes	—
403	#390	C₂²×C₆₇	1	4	yes	—
404	#390	C₂²×C₆₇	1	2	yes	—
405	#390	C₂²×C₆₇	1	2	yes	—
406	#389	C₂²×C₆₇	1	4	yes	—
407	#388	C₂²×C₆₇	1	8	yes	—
408	#386	C₂²×C₆₇	1	8	yes	—
409	#386	C₂²×C₆₇	1	8	yes	—
410	#380	C₂²×C₆₇	1	4	yes	—
411	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
416	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
417	C₂×#95	C₂²×C₆₇	1	2	yes	—
418	C₂×#41	—	2	4	no	—
419	C₂×#41	—	2	8	no	—
420	C₂×#41	—	2	8	no	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	8	no	—
423	C₂×#41	D₄×C₆₇	1	8	yes	complemented
424	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
425	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
427	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
428	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
429	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
430	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
431	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
433	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
434	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
435	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
436	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
439	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
441	C₄⋊Q₈	—	2	8	no	—
442	C₄⋊Q₈	—	2	4	no	—
443	#127	—	2	8	no	—
444	#127	—	2	4	no	—
445	#124	—	2	8	no	—
446	#124	—	2	8	no	—
447	#124	—	2	8	no	—
448	#121	—	2	32	no	—
449	#121	—	2	8	no	—
450	#121	—	2	8	no	—
451	#121	—	2	16	no	—
452	C₄×Q₈	—	2	4	no	—
453	C₄×Q₈	—	2	4	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	—	2	32	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	2	4	no	—
459	C₄×D₄	—	2	8	no	—
460	C₄×D₄	—	2	8	no	—
461	#117	—	2	4	no	—
462	#117	—	2	8	no	—
463	C₂×C₄⋊C₄	—	2	8	no	—
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
483	C₂×C₄²	—	2	8	no	—
484	C₂×C₄²	—	2	8	no	—
485	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
486	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
487	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
488	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	#95	C₂³×C₆₇	1	4	yes	—
497	#95	C₂³×C₆₇	1	2	yes	—
498	#95	C₂³×C₆₇	1	2	yes	—
499	#95	C₂³×C₆₇	1	8	yes	—
500	#95	C₂³×C₆₇	1	8	yes	—
501	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
502	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
503	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
504	#41	—	2	32	no	—
505	#41	—	4	32	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	4	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	16	no	—
515	C₂×D₄	—	2	8	no	—
516	C₂×D₄	—	2	8	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	16	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	4	8	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
530	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	8	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
546	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
547	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
548	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
550	C₂²×C₄	#41×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	16	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	8	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	#41×C₆₇	1	8	yes	complemented
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	16	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	16	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	16	no	—
581	C₂²⋊C₄	—	4	8	no	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	8	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	C₂×D₄×C₆₇	1	4	yes	—
589	C₄²	C₂×D₄×C₆₇	1	4	yes	—
590	C₄²	C₂×D₄×C₆₇	1	4	yes	—
591	C₄²	C₂×D₄×C₆₇	1	4	yes	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	8	no	—
603	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
604	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
605	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
606	C₂³	C₂×#41×C₆₇	1	2	yes	—
607	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
608	Q₈	—	2	8	no	—
609	Q₈	—	4	8	no	—
610	D₄	—	2	16	no	—
611	D₄	—	2	8	no	—
612	D₄	—	4	32	no	—
613	D₄	—	4	8	no	—
614	D₄	—	4	16	no	—
615	D₄	—	4	8	no	—
616	D₄	—	4	8	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	16	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	16	no	—
638	C₂×C₄	—	4	8	no	—
639	C₂×C₄	—	4	16	no	—
640	C₂×C₄	—	4	8	no	—
641	C₂×C₄	#121×C₆₇	1	16	yes	complemented
642	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
644	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
645	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
646	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
651	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
652	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
653	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
654	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	8	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	8	no	—
668	C₂²	—	4	8	no	—
669	C₂²	C₂×#121×C₆₇	1	4	yes	—
670	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
671	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
672	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₆₇	1	2	yes	—
674	C₂²	#585×C₆₇	1	2	yes	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	8	no	—
680	C₄	—	4	4	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	4	no	—
684	C₄	C₂×#121×C₆₇	1	4	yes	—
685	C₄	C₂×#121×C₆₇	1	4	yes	—
686	C₄	#532×C₆₇	1	4	yes	complemented
687	C₂	—	2	4	no	—
688	C₂	—	4	4	no	—
689	C₂	—	8	4	no	—
690	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
691	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
692	C₂	C₆₇×#3449	1	1	yes	characteristic
693	C₂	D₄×#41×C₆₇	1	2	yes	—
694	C₂	C₆₇×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#532×C₆₇	C₂	semidirect
2. C₂×#532×C₆₇	C₂	semidirect
3. C₂×C₄×#41×C₆₇	C₂	semidirect
4. C₆₇×#2548	C₂	semidirect
5. C₆₇×#2547	C₂	semidirect
6. C₆₇×#2546	C₂	semidirect
7. C₆₇×#2545	C₂	semidirect
8. C₆₇×#2544	C₂	semidirect
9. C₆₇×#2543	C₂	semidirect
10. C₆₇×#2541	C₂	semidirect
11. C₆₇×#2416	C₂	semidirect
12. C₆₇×#2392	C₂	semidirect
13. C₄×#121×C₆₇	C₂	semidirect
14. C₆₇×#2297	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
75. C₂×#41×C₆₇	D₄	semidirect
137. C₂×C₄²×C₆₇	D₄	semidirect
224. C₄⋊C₄×C₆₇	#41	semidirect
293. C₂×C₄×C₆₇	#121	semidirect
338. C₄×C₆₇	#532	semidirect
339. #34937	C₆₇	direct (N × H)
348. C₂×#532	C₂×C₆₇	semidirect
349. C₂×#532	C₂×C₆₇	semidirect
350. C₂×C₄×#41	C₂×C₆₇	semidirect
351. #2548	C₂×C₆₇	semidirect
352. #2547	C₂×C₆₇	semidirect
353. #2546	C₂×C₆₇	semidirect
354. #2545	C₂×C₆₇	semidirect
355. #2544	C₂×C₆₇	semidirect
356. #2543	C₂×C₆₇	semidirect
357. #2541	C₂×C₆₇	semidirect
358. #2416	C₂×C₆₇	semidirect
359. #2392	C₂×C₆₇	semidirect
360. C₄×#121	C₂×C₆₇	semidirect
361. #2297	C₂×C₆₇	semidirect
362. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
363. C₆₇	#34937	direct (N × H)
423. C₂×#41	D₄×C₆₇	semidirect
485. C₂×C₄²	D₄×C₆₇	semidirect
572. C₄⋊C₄	#41×C₆₇	semidirect
641. C₂×C₄	#121×C₆₇	semidirect
686. C₄	#532×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2548	2
C₆₇×#2547	2
C₆₇×#2546	2
C₆₇×#2545	2
C₆₇×#2544	2
C₆₇×#2543	2
C₆₇×#2541	2
C₆₇×#2416	2
C₆₇×#2392	2
C₄×#121×C₆₇	2
C₆₇×#2297	2
C₂×C₄×C₄⋊C₄×C₆₇	2
#34937	67

Subgroups — C67×#34937 #30714188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34937 #30714188