Subgroups — C₆₇×#59653 #30738904

Order 17152.

2072 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2725	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2545	C₂	1	2	yes	maximal
6	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2519	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2489	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2448	C₂	1	2	yes	maximal
10	C₆₇×#2446	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2441	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2429	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2362	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2351	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
18	#557×C₆₇	—	2	8	no	—
19	#556×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×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#126×C₆₇	C₂²	1	4	yes	—
24	C₂×#125×C₆₇	C₂²	1	4	yes	—
25	C₂×#125×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	#400×C₆₇	C₂²	1	4	yes	—
40	#399×C₆₇	C₂²	1	4	yes	—
41	#398×C₆₇	C₂²	1	4	yes	—
42	#398×C₆₇	C₂²	1	4	yes	—
43	#397×C₆₇	C₂²	1	4	yes	—
44	#396×C₆₇	C₂²	1	4	yes	—
45	#396×C₆₇	C₂²	1	4	yes	—
46	#396×C₆₇	C₂²	1	4	yes	—
47	#391×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	2	yes	—
53	#390×C₆₇	C₂²	1	2	yes	—
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	2	yes	—
56	#389×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	2	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	4	yes	—
63	#389×C₆₇	C₂²	1	4	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	4	yes	—
66	#388×C₆₇	C₂²	1	4	yes	—
67	#388×C₆₇	C₂²	1	4	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	4	yes	—
70	#387×C₆₇	C₂²	1	4	yes	—
71	#387×C₆₇	C₂²	1	4	yes	—
72	#384×C₆₇	C₂²	1	1	yes	characteristic
73	#384×C₆₇	C₂²	1	1	yes	characteristic
74	#382×C₆₇	C₂²	1	4	yes	—
75	#382×C₆₇	C₂²	1	1	yes	characteristic
76	#380×C₆₇	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
84	C₄³×C₆₇	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₆₇	—	2	8	no	—
92	C₄⋊Q₈×C₆₇	—	2	4	no	—
93	C₄⋊Q₈×C₆₇	D₄	1	8	yes	—
94	#126×C₆₇	—	2	16	no	—
95	#125×C₆₇	—	2	16	no	—
96	#125×C₆₇	—	2	8	no	—
97	#124×C₆₇	—	2	8	no	—
98	#124×C₆₇	—	2	4	no	—
99	C₂²⋊Q₈×C₆₇	—	2	8	no	—
100	C₂²⋊Q₈×C₆₇	—	2	8	no	—
101	C₄×Q₈×C₆₇	—	2	8	no	—
102	C₄×Q₈×C₆₇	—	2	8	no	—
103	C₄×Q₈×C₆₇	—	2	8	no	—
104	C₄×Q₈×C₆₇	—	2	4	no	—
105	C₄×Q₈×C₆₇	—	2	4	no	—
106	C₄×Q₈×C₆₇	—	2	4	no	—
107	C₄×Q₈×C₆₇	—	2	8	no	—
108	C₄×D₄×C₆₇	—	2	4	no	—
109	#117×C₆₇	—	2	8	no	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
146	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	#95×C₆₇	C₂³	1	2	yes	—
156	#95×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	4	yes	—
164	#95×C₆₇	C₂³	1	2	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	4	yes	—
167	#95×C₆₇	C₂³	1	4	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₆₇	—	2	2	no	—
171	C₂×Q₈×C₆₇	—	2	2	no	—
172	C₂×Q₈×C₆₇	—	2	2	no	—
173	C₂×Q₈×C₆₇	—	2	4	no	—
174	C₂×Q₈×C₆₇	—	2	2	no	—
175	C₂×Q₈×C₆₇	—	2	2	no	—
176	C₂×Q₈×C₆₇	—	2	4	no	—
177	C₂×Q₈×C₆₇	—	2	2	no	—
178	C₂×Q₈×C₆₇	—	2	2	no	—
179	C₂×Q₈×C₆₇	—	2	2	no	—
180	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
181	C₂×Q₈×C₆₇	#41	1	4	yes	—
182	C₂×D₄×C₆₇	—	2	2	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	4	no	—
186	C₂²×C₄×C₆₇	—	2	4	no	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₄⋊C₄×C₆₇	—	2	2	no	—
205	C₄⋊C₄×C₆₇	—	2	2	no	—
206	C₄⋊C₄×C₆₇	—	2	2	no	—
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	8	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	2	no	—
212	C₄⋊C₄×C₆₇	—	2	8	no	—
213	C₄⋊C₄×C₆₇	—	2	4	no	—
214	C₄⋊C₄×C₆₇	—	2	8	no	—
215	C₄⋊C₄×C₆₇	—	2	8	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	2	8	no	—
219	C₄⋊C₄×C₆₇	—	2	4	no	—
220	C₄⋊C₄×C₆₇	—	2	4	no	—
221	C₄⋊C₄×C₆₇	—	2	4	no	—
222	C₄⋊C₄×C₆₇	—	4	2	no	—
223	C₄⋊C₄×C₆₇	—	4	2	no	—
224	C₄⋊C₄×C₆₇	—	4	4	no	—
225	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
226	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
227	C₂²⋊C₄×C₆₇	—	2	8	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	8	no	—
230	C₂²⋊C₄×C₆₇	—	2	8	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	2	4	no	—
233	C₂²⋊C₄×C₆₇	—	2	4	no	—
234	C₂²⋊C₄×C₆₇	—	4	2	no	—
235	C₂²⋊C₄×C₆₇	—	4	4	no	—
236	C₄²×C₆₇	—	2	8	no	—
237	C₄²×C₆₇	—	2	4	no	—
238	C₄²×C₆₇	—	2	8	no	—
239	C₄²×C₆₇	—	2	4	no	—
240	C₄²×C₆₇	—	2	4	no	—
241	C₄²×C₆₇	—	2	8	no	—
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	—	2	2	no	—
244	C₄²×C₆₇	—	2	2	no	—
245	C₄²×C₆₇	—	2	2	no	—
246	C₄²×C₆₇	—	4	1	no	—
247	C₄²×C₆₇	C₂×D₄	1	4	yes	—
248	C₄²×C₆₇	#41	1	4	yes	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
257	Q₈×C₆₇	—	2	16	no	—
258	Q₈×C₆₇	—	2	8	no	—
259	Q₈×C₆₇	—	4	4	no	—
260	Q₈×C₆₇	—	4	4	no	—
261	D₄×C₆₇	—	4	4	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	1	no	—
264	C₂×C₄×C₆₇	—	2	1	no	—
265	C₂×C₄×C₆₇	—	2	4	no	—
266	C₂×C₄×C₆₇	—	2	1	no	—
267	C₂×C₄×C₆₇	—	2	1	no	—
268	C₂×C₄×C₆₇	—	2	1	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	4	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	4	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	4	8	no	—
299	C₂×C₄×C₆₇	C₂²×D₄	1	8	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	2	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
305	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
306	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
307	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
308	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
309	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
310	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
311	C₂²×C₆₇	—	4	2	no	—
312	C₂²×C₆₇	—	4	2	no	—
313	C₂²×C₆₇	—	4	2	no	—
314	C₂²×C₆₇	—	4	2	no	—
315	C₂²×C₆₇	—	4	2	no	—
316	C₂²×C₆₇	—	4	2	no	—
317	C₂²×C₆₇	—	4	2	no	—
318	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
319	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
320	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
322	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₂²×C₆₇	#585	1	1	yes	characteristic
325	C₄×C₆₇	—	2	8	no	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	—	2	2	no	—
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	4	2	no	—
332	C₄×C₆₇	—	4	2	no	—
333	C₄×C₆₇	—	4	2	no	—
334	C₄×C₆₇	—	4	4	no	—
335	C₄×C₆₇	—	4	2	no	—
336	C₄×C₆₇	—	4	2	no	—
337	C₄×C₆₇	—	4	2	no	—
338	C₄×C₆₇	—	4	1	no	—
339	C₄×C₆₇	#547	1	4	yes	—
340	C₄×C₆₇	#548	1	4	yes	—
341	#59653	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂×C₆₇	—	8	2	no	—
343	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
344	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
345	C₂×C₆₇	#3480	1	1	yes	characteristic
346	C₂×C₆₇	#3497	1	1	yes	characteristic
347	C₂×C₆₇	#3509	1	1	yes	characteristic
348	C₂×C₆₇	#3523	1	1	yes	characteristic
349	C₂×C₆₇	#3555	1	1	yes	characteristic
350	C₂×#557	C₂×C₆₇	1	1	yes	characteristic, complemented
351	C₂×#556	C₂×C₆₇	1	1	yes	characteristic
352	#2725	C₂×C₆₇	1	4	yes	complemented
353	#2582	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2545	C₂×C₆₇	1	2	yes	—
355	#2538	C₂×C₆₇	1	1	yes	characteristic
356	#2519	C₂×C₆₇	1	4	yes	complemented
357	#2489	C₂×C₆₇	1	2	yes	complemented
358	#2448	C₂×C₆₇	1	2	yes	—
359	#2446	C₂×C₆₇	1	2	yes	complemented
360	#2441	C₂×C₆₇	1	2	yes	complemented
361	#2429	C₂×C₆₇	1	2	yes	complemented
362	#2362	C₂×C₆₇	1	2	yes	complemented
363	#2351	C₂×C₆₇	1	2	yes	complemented
364	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
365	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
366	C₄×#124	C₂×C₆₇	1	1	yes	characteristic
367	C₆₇	#59653	1	1	yes	characteristic, direct product factor, Sylow
368	#557	—	2	8	no	—
369	#556	—	2	8	no	—
370	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
371	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
372	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
373	C₂×#126	C₂²×C₆₇	1	4	yes	—
374	C₂×#125	C₂²×C₆₇	1	2	yes	—
375	C₂×#125	C₂²×C₆₇	1	4	yes	—
376	C₂×#124	C₂²×C₆₇	1	2	yes	—
377	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
379	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
385	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
386	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×#117	C₂²×C₆₇	1	2	yes	—
389	#400	C₂²×C₆₇	1	4	yes	—
390	#399	C₂²×C₆₇	1	4	yes	—
391	#398	C₂²×C₆₇	1	4	yes	—
392	#398	C₂²×C₆₇	1	4	yes	—
393	#397	C₂²×C₆₇	1	4	yes	—
394	#396	C₂²×C₆₇	1	4	yes	—
395	#396	C₂²×C₆₇	1	4	yes	—
396	#396	C₂²×C₆₇	1	4	yes	—
397	#391	C₂²×C₆₇	1	1	yes	characteristic
398	#391	C₂²×C₆₇	1	2	yes	—
399	#391	C₂²×C₆₇	1	1	yes	characteristic
400	#391	C₂²×C₆₇	1	2	yes	—
401	#391	C₂²×C₆₇	1	2	yes	—
402	#391	C₂²×C₆₇	1	1	yes	characteristic
403	#390	C₂²×C₆₇	1	1	yes	characteristic
404	#390	C₂²×C₆₇	1	2	yes	—
405	#389	C₂²×C₆₇	1	2	yes	—
406	#389	C₂²×C₆₇	1	2	yes	—
407	#389	C₂²×C₆₇	1	2	yes	—
408	#389	C₂²×C₆₇	1	2	yes	—
409	#389	C₂²×C₆₇	1	2	yes	—
410	#389	C₂²×C₆₇	1	2	yes	—
411	#389	C₂²×C₆₇	1	4	yes	—
412	#389	C₂²×C₆₇	1	4	yes	—
413	#389	C₂²×C₆₇	1	2	yes	—
414	#388	C₂²×C₆₇	1	4	yes	—
415	#388	C₂²×C₆₇	1	4	yes	—
416	#388	C₂²×C₆₇	1	4	yes	—
417	#388	C₂²×C₆₇	1	2	yes	—
418	#388	C₂²×C₆₇	1	4	yes	—
419	#388	C₂²×C₆₇	1	2	yes	—
420	#387	C₂²×C₆₇	1	4	yes	—
421	#387	C₂²×C₆₇	1	4	yes	—
422	#384	C₂²×C₆₇	1	1	yes	characteristic
423	#384	C₂²×C₆₇	1	1	yes	characteristic
424	#382	C₂²×C₆₇	1	1	yes	characteristic
425	#382	C₂²×C₆₇	1	4	yes	—
426	#380	C₂²×C₆₇	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
434	C₄³	C₂²×C₆₇	1	1	yes	characteristic
435	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
438	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
439	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
441	C₄⋊Q₈	—	2	8	no	—
442	C₄⋊Q₈	—	2	4	no	—
443	C₄⋊Q₈	D₄×C₆₇	1	8	yes	—
444	#126	—	2	16	no	—
445	#125	—	2	16	no	—
446	#125	—	2	8	no	—
447	#124	—	2	8	no	—
448	#124	—	2	4	no	—
449	C₂²⋊Q₈	—	2	8	no	—
450	C₂²⋊Q₈	—	2	8	no	—
451	C₄×Q₈	—	2	8	no	—
452	C₄×Q₈	—	2	8	no	—
453	C₄×Q₈	—	2	8	no	—
454	C₄×Q₈	—	2	4	no	—
455	C₄×Q₈	—	2	4	no	—
456	C₄×Q₈	—	2	4	no	—
457	C₄×Q₈	—	2	8	no	—
458	C₄×D₄	—	2	4	no	—
459	#117	—	2	8	no	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	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	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
492	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
493	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
494	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
496	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
505	#95	C₂³×C₆₇	1	2	yes	—
506	#95	C₂³×C₆₇	1	2	yes	—
507	#95	C₂³×C₆₇	1	2	yes	—
508	#95	C₂³×C₆₇	1	2	yes	—
509	#95	C₂³×C₆₇	1	2	yes	—
510	#95	C₂³×C₆₇	1	2	yes	—
511	#95	C₂³×C₆₇	1	2	yes	—
512	#95	C₂³×C₆₇	1	4	yes	—
513	#95	C₂³×C₆₇	1	4	yes	—
514	#95	C₂³×C₆₇	1	2	yes	—
515	#95	C₂³×C₆₇	1	4	yes	—
516	#95	C₂³×C₆₇	1	4	yes	—
517	#95	C₂³×C₆₇	1	4	yes	—
518	#95	C₂³×C₆₇	1	4	yes	—
519	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
531	C₂×Q₈	#41×C₆₇	1	4	yes	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
576	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	4	no	—
586	C₄²	—	2	8	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	8	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	8	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	4	1	no	—
597	C₄²	C₂×D₄×C₆₇	1	4	yes	—
598	C₄²	#41×C₆₇	1	4	yes	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
607	Q₈	—	2	16	no	—
608	Q₈	—	2	8	no	—
609	Q₈	—	4	4	no	—
610	Q₈	—	4	4	no	—
611	D₄	—	4	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
650	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
653	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
654	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
655	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
656	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
657	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
658	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
659	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
660	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
669	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
670	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
671	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
672	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
673	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
674	C₂²	#585×C₆₇	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	8	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	#547×C₆₇	1	4	yes	—
690	C₄	#548×C₆₇	1	4	yes	—
691	C₂	—	8	2	no	—
692	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
693	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
694	C₂	C₆₇×#3480	1	1	yes	characteristic
695	C₂	C₆₇×#3497	1	1	yes	characteristic
696	C₂	C₆₇×#3509	1	1	yes	characteristic
697	C₂	C₆₇×#3523	1	1	yes	characteristic
698	C₂	C₆₇×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#557×C₆₇	C₂	semidirect
3. C₆₇×#2725	C₂	semidirect
4. C₆₇×#2582	C₂	semidirect
7. C₆₇×#2519	C₂	semidirect
8. C₆₇×#2489	C₂	semidirect
10. C₆₇×#2446	C₂	semidirect
11. C₆₇×#2441	C₂	semidirect
12. C₆₇×#2429	C₂	semidirect
13. C₆₇×#2362	C₂	semidirect
14. C₆₇×#2351	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
341. #59653	C₆₇	direct (N × H)
350. C₂×#557	C₂×C₆₇	semidirect
352. #2725	C₂×C₆₇	semidirect
353. #2582	C₂×C₆₇	semidirect
356. #2519	C₂×C₆₇	semidirect
357. #2489	C₂×C₆₇	semidirect
359. #2446	C₂×C₆₇	semidirect
360. #2441	C₂×C₆₇	semidirect
361. #2429	C₂×C₆₇	semidirect
362. #2362	C₂×C₆₇	semidirect
363. #2351	C₂×C₆₇	semidirect
364. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
365. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
367. C₆₇	#59653	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×#557×C₆₇	2
C₂×#556×C₆₇	2
C₆₇×#2725	2
C₆₇×#2582	2
C₆₇×#2545	2
C₆₇×#2538	2
C₆₇×#2519	2
C₆₇×#2489	2
C₆₇×#2448	2
C₆₇×#2446	2
C₆₇×#2441	2
C₆₇×#2429	2
C₆₇×#2362	2
C₆₇×#2351	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#124×C₆₇	2
#59653	67

Subgroups — C67×#59653 #30738904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59653 #30738904