Subgroups — C₆₇×#60373 #30739624

Order 17152.

5058 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3012	C₂	1	6	yes	maximal, complemented
5	C₆₇×#3009	C₂	1	6	yes	maximal, complemented
6	C₆₇×#3007	C₂	1	3	yes	maximal, complemented
7	C₆₇×#3003	C₂	1	3	yes	maximal, complemented
8	C₆₇×#3002	C₂	1	3	yes	maximal, complemented
9	C₂×#450×C₆₇	C₂	1	3	yes	maximal, complemented
10	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
13	C₂×H(5,𝔽₂)×C₆₇	—	2	16	no	—
14	C₂×H(5,𝔽₂)×C₆₇	—	2	3	no	—
15	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	6	yes	—
17	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
18	C₂²×#41×C₆₇	—	2	1	no	—
19	C₂²×#41×C₆₇	C₂²	1	3	yes	—
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₆₇	—	2	3	no	—
22	C₂³×D₄×C₆₇	C₂²	1	3	yes	—
23	#577×C₆₇	—	2	16	no	—
24	C₂×#137×C₆₇	C₂²	1	6	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	6	yes	complemented
26	C₂×#135×C₆₇	C₂²	1	6	yes	complemented
27	C₂²×SD₁₆×C₆₇	C₂²	1	6	yes	complemented
28	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
29	D₄×Q₈×C₆₇	—	2	1	no	—
30	#548×C₆₇	—	2	1	no	—
31	#547×C₆₇	—	2	3	no	—
32	#546×C₆₇	—	2	3	no	—
33	#537×C₆₇	C₂²	1	3	yes	complemented
34	#536×C₆₇	C₂²	1	3	yes	complemented
35	#525×C₆₇	C₂²	1	3	yes	complemented
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	3	yes	complemented
37	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#452×C₆₇	C₂²	1	6	yes	complemented
39	#452×C₆₇	C₂²	1	12	yes	complemented
40	#451×C₆₇	C₂²	1	3	yes	complemented
41	#450×C₆₇	C₂²	1	3	yes	complemented
42	#450×C₆₇	C₂²	1	6	yes	complemented
43	#450×C₆₇	C₂²	1	6	yes	complemented
44	#450×C₆₇	C₂²	1	12	yes	complemented
45	#449×C₆₇	C₂²	1	6	yes	complemented
46	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#447×C₆₇	C₂²	1	3	yes	complemented
48	#447×C₆₇	C₂²	1	6	yes	complemented
49	#418×C₆₇	C₂²	1	6	yes	complemented
50	#417×C₆₇	C₂²	1	6	yes	complemented
51	#416×C₆₇	C₂²	1	6	yes	complemented
52	C₂×#102×C₆₇	C₂²	1	6	yes	complemented
53	#408×C₆₇	C₂²	1	6	yes	complemented
54	#407×C₆₇	C₂²	1	3	yes	complemented
55	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
56	C₂⁵×C₆₇	—	2	3	no	—
57	2₋¹⁺⁴×C₆₇	—	2	8	no	—
58	H(5,𝔽₂)×C₆₇	—	2	16	no	—
59	H(5,𝔽₂)×C₆₇	—	2	48	no	—
60	H(5,𝔽₂)×C₆₇	—	2	24	no	—
61	H(5,𝔽₂)×C₆₇	—	2	8	no	—
62	H(5,𝔽₂)×C₆₇	—	2	24	no	—
63	H(5,𝔽₂)×C₆₇	D₄	1	16	yes	complemented
64	C₂×#41×C₆₇	—	2	16	no	—
65	C₂×#41×C₆₇	—	2	24	no	—
66	C₂×#41×C₆₇	—	2	8	no	—
67	C₂×#41×C₆₇	—	2	6	no	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	—	2	3	no	—
70	C₂×#41×C₆₇	—	2	3	no	—
71	C₂×#41×C₆₇	—	2	3	no	—
72	C₂×#41×C₆₇	D₄	1	3	yes	—
73	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
74	C₂×#41×C₆₇	C₂³	1	6	yes	—
75	C₂×#41×C₆₇	C₂³	1	6	yes	—
76	C₂×#41×C₆₇	C₂³	1	3	yes	—
77	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
78	C₂×#41×C₆₇	C₂³	1	3	yes	complemented
79	C₂²×Q₈×C₆₇	—	2	1	no	—
80	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
81	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₆₇	C₂³	1	3	yes	complemented
83	C₂²×D₄×C₆₇	—	2	48	no	—
84	C₂²×D₄×C₆₇	—	2	3	no	—
85	C₂²×D₄×C₆₇	—	2	12	no	—
86	C₂²×D₄×C₆₇	—	2	6	no	—
87	C₂²×D₄×C₆₇	—	2	6	no	—
88	C₂²×D₄×C₆₇	—	2	24	no	—
89	C₂²×D₄×C₆₇	—	2	3	no	—
90	C₂²×D₄×C₆₇	—	2	3	no	—
91	C₂²×D₄×C₆₇	—	2	3	no	—
92	C₂²×D₄×C₆₇	D₄	1	3	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
96	C₂³×C₄×C₆₇	—	2	3	no	—
97	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
98	#137×C₆₇	—	2	24	no	—
99	AGL(1,ℤ/8)×C₆₇	—	2	24	no	—
100	#135×C₆₇	—	2	24	no	—
101	C₂×Q₁₆×C₆₇	C₂³	1	6	yes	complemented
102	C₂×SD₁₆×C₆₇	—	2	24	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
104	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	complemented
105	C₂×SD₁₆×C₆₇	C₂³	1	12	yes	complemented
106	C₂×D₈×C₆₇	C₂³	1	6	yes	complemented
107	#131×C₆₇	—	2	8	no	—
108	C₂×M₁₆×C₆₇	C₂³	1	6	yes	complemented
109	C₂²×C₈×C₆₇	C₂³	1	6	yes	complemented
110	C₄⋊Q₈×C₆₇	—	2	3	no	—
111	#124×C₆₇	—	2	3	no	—
112	#123×C₆₇	—	2	6	no	—
113	#123×C₆₇	—	2	3	no	—
114	C₂²⋊Q₈×C₆₇	—	2	3	no	—
115	C₂²⋊Q₈×C₆₇	—	2	3	no	—
116	C₂²⋊Q₈×C₆₇	—	2	3	no	—
117	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	—
118	C₂²⋊Q₈×C₆₇	C₂³	1	6	yes	complemented
119	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	complemented
120	#121×C₆₇	—	2	6	no	—
121	#121×C₆₇	—	2	3	no	—
122	#121×C₆₇	C₂³	1	1	yes	characteristic
123	#121×C₆₇	C₂³	1	3	yes	complemented
124	#120×C₆₇	—	2	3	no	—
125	C₄×Q₈×C₆₇	—	2	1	no	—
126	C₄×D₄×C₆₇	—	2	3	no	—
127	C₄×D₄×C₆₇	—	2	3	no	—
128	C₄×D₄×C₆₇	—	2	3	no	—
129	#117×C₆₇	C₂³	1	3	yes	complemented
130	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	complemented
132	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
133	#103×C₆₇	C₂³	1	2	yes	complemented
134	#103×C₆₇	C₂³	1	6	yes	complemented
135	#102×C₆₇	C₂³	1	6	yes	complemented
136	#102×C₆₇	C₂³	1	12	yes	complemented
137	#102×C₆₇	C₂³	1	6	yes	complemented
138	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²⋊C₈×C₆₇	C₂³	1	3	yes	—
140	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	complemented
141	C₂²⋊C₈×C₆₇	C₂³	1	6	yes	complemented
142	C₂⁴×C₆₇	—	2	24	no	—
143	C₂⁴×C₆₇	—	2	3	no	—
144	C₂⁴×C₆₇	—	2	6	no	—
145	C₂⁴×C₆₇	—	2	6	no	—
146	C₂⁴×C₆₇	—	8	6	no	—
147	C₂⁴×C₆₇	—	8	6	no	—
148	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
149	#41×C₆₇	—	2	24	no	—
150	#41×C₆₇	—	2	48	no	—
151	#41×C₆₇	—	2	24	no	—
152	#41×C₆₇	—	2	16	no	—
153	#41×C₆₇	—	2	4	no	—
154	#41×C₆₇	—	2	12	no	—
155	#41×C₆₇	—	2	12	no	—
156	#41×C₆₇	—	2	12	no	—
157	#41×C₆₇	—	2	12	no	—
158	#41×C₆₇	—	2	12	no	—
159	#41×C₆₇	—	2	12	no	—
160	#41×C₆₇	—	4	12	no	—
161	#41×C₆₇	C₂×D₄	1	24	yes	—
162	#41×C₆₇	C₂×D₄	1	8	yes	—
163	C₂×Q₈×C₆₇	—	2	4	no	—
164	C₂×Q₈×C₆₇	—	2	4	no	—
165	C₂×Q₈×C₆₇	—	2	1	no	—
166	C₂×Q₈×C₆₇	—	2	3	no	—
167	C₂×Q₈×C₆₇	—	2	12	no	—
168	C₂×Q₈×C₆₇	—	4	4	no	—
169	C₂×Q₈×C₆₇	C₂×D₄	1	3	yes	—
170	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
172	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
173	C₂×D₄×C₆₇	—	2	24	no	—
174	C₂×D₄×C₆₇	—	2	24	no	—
175	C₂×D₄×C₆₇	—	2	96	no	—
176	C₂×D₄×C₆₇	—	2	24	no	—
177	C₂×D₄×C₆₇	—	2	48	no	—
178	C₂×D₄×C₆₇	—	2	24	no	—
179	C₂×D₄×C₆₇	—	2	6	no	—
180	C₂×D₄×C₆₇	—	2	6	no	—
181	C₂×D₄×C₆₇	—	2	12	no	—
182	C₂×D₄×C₆₇	—	2	48	no	—
183	C₂×D₄×C₆₇	—	2	12	no	—
184	C₂×D₄×C₆₇	—	2	24	no	—
185	C₂×D₄×C₆₇	—	2	1	no	—
186	C₂×D₄×C₆₇	—	2	3	no	—
187	C₂×D₄×C₆₇	—	2	3	no	—
188	C₂×D₄×C₆₇	—	2	6	no	—
189	C₂×D₄×C₆₇	—	2	3	no	—
190	C₂×D₄×C₆₇	—	2	6	no	—
191	C₂×D₄×C₆₇	—	2	12	no	—
192	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
193	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
194	C₂×D₄×C₆₇	C₂×D₄	1	24	yes	—
195	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
196	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
198	C₂²×C₄×C₆₇	—	2	24	no	—
199	C₂²×C₄×C₆₇	—	2	1	no	—
200	C₂²×C₄×C₆₇	—	2	6	no	—
201	C₂²×C₄×C₆₇	—	2	6	no	—
202	C₂²×C₄×C₆₇	—	2	12	no	—
203	C₂²×C₄×C₆₇	—	2	3	no	—
204	C₂²×C₄×C₆₇	—	2	3	no	—
205	C₂²×C₄×C₆₇	—	2	3	no	—
206	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
207	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
208	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
212	Q₁₆×C₆₇	—	2	12	no	—
213	SD₁₆×C₆₇	—	2	4	no	—
214	SD₁₆×C₆₇	—	2	12	no	—
215	SD₁₆×C₆₇	—	2	24	no	—
216	D₈×C₆₇	—	2	12	no	—
217	M₁₆×C₆₇	—	2	12	no	—
218	C₂×C₈×C₆₇	—	2	12	no	—
219	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
220	C₂×C₈×C₆₇	C₂⁴	1	6	yes	—
221	C₄⋊C₄×C₆₇	—	2	3	no	—
222	C₄⋊C₄×C₆₇	—	2	6	no	—
223	C₄⋊C₄×C₆₇	—	2	3	no	—
224	C₄⋊C₄×C₆₇	—	2	3	no	—
225	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
226	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²⋊C₄×C₆₇	—	2	3	no	—
228	C₂²⋊C₄×C₆₇	—	2	6	no	—
229	C₂²⋊C₄×C₆₇	—	2	3	no	—
230	C₂²⋊C₄×C₆₇	—	2	3	no	—
231	C₂²⋊C₄×C₆₇	—	2	1	no	—
232	C₂²⋊C₄×C₆₇	—	2	3	no	—
233	C₄²×C₆₇	—	2	3	no	—
234	C₂³×C₆₇	—	2	12	no	—
235	C₂³×C₆₇	—	2	24	no	—
236	C₂³×C₆₇	—	2	6	no	—
237	C₂³×C₆₇	—	2	6	no	—
238	C₂³×C₆₇	—	2	6	no	—
239	C₂³×C₆₇	—	2	24	no	—
240	C₂³×C₆₇	—	2	1	no	—
241	C₂³×C₆₇	—	4	3	no	—
242	C₂³×C₆₇	—	4	6	no	—
243	C₂³×C₆₇	—	4	6	no	—
244	C₂³×C₆₇	—	8	6	no	—
245	C₂³×C₆₇	—	8	6	no	—
246	C₂³×C₆₇	—	8	6	no	—
247	C₂³×C₆₇	—	8	6	no	—
248	C₂³×C₆₇	—	8	48	no	—
249	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
250	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
251	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₆₇	—	2	4	no	—
253	Q₈×C₆₇	—	2	6	no	—
254	Q₈×C₆₇	—	2	2	no	—
255	Q₈×C₆₇	—	2	6	no	—
256	Q₈×C₆₇	—	4	6	no	—
257	Q₈×C₆₇	#120	1	4	yes	—
258	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
259	D₄×C₆₇	—	2	24	no	—
260	D₄×C₆₇	—	2	24	no	—
261	D₄×C₆₇	—	2	12	no	—
262	D₄×C₆₇	—	2	24	no	—
263	D₄×C₆₇	—	2	12	no	—
264	D₄×C₆₇	—	2	6	no	—
265	D₄×C₆₇	—	2	24	no	—
266	D₄×C₆₇	—	2	6	no	—
267	D₄×C₆₇	—	2	2	no	—
268	D₄×C₆₇	—	4	6	no	—
269	D₄×C₆₇	—	4	2	no	—
270	D₄×C₆₇	—	8	3	no	—
271	D₄×C₆₇	#120	1	12	yes	—
272	D₄×C₆₇	C₂²×D₄	1	12	yes	—
273	C₂×C₄×C₆₇	—	2	4	no	—
274	C₂×C₄×C₆₇	—	2	24	no	—
275	C₂×C₄×C₆₇	—	2	6	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	6	no	—
278	C₂×C₄×C₆₇	—	2	24	no	—
279	C₂×C₄×C₆₇	—	2	6	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	6	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	3	no	—
284	C₂×C₄×C₆₇	—	2	3	no	—
285	C₂×C₄×C₆₇	—	4	6	no	—
286	C₂×C₄×C₆₇	—	4	6	no	—
287	C₂×C₄×C₆₇	—	8	3	no	—
288	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
289	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
291	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
292	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
293	C₈×C₆₇	—	2	2	no	—
294	C₈×C₆₇	—	2	6	no	—
295	C₂²×C₆₇	—	2	3	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	1	no	—
298	C₂²×C₆₇	—	2	3	no	—
299	C₂²×C₆₇	—	2	3	no	—
300	C₂²×C₆₇	—	2	3	no	—
301	C₂²×C₆₇	—	2	12	no	—
302	C₂²×C₆₇	—	2	3	no	—
303	C₂²×C₆₇	—	4	12	no	—
304	C₂²×C₆₇	—	4	24	no	—
305	C₂²×C₆₇	—	4	6	no	—
306	C₂²×C₆₇	—	4	6	no	—
307	C₂²×C₆₇	—	4	1	no	—
308	C₂²×C₆₇	—	4	1	no	—
309	C₂²×C₆₇	—	4	1	no	—
310	C₂²×C₆₇	—	8	24	no	—
311	C₂²×C₆₇	—	8	24	no	—
312	C₂²×C₆₇	C₂×#120	1	6	yes	—
313	C₂²×C₆₇	#577	1	2	yes	complemented
314	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
315	C₄×C₆₇	—	2	4	no	—
316	C₄×C₆₇	—	2	3	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	4	3	no	—
319	C₄×C₆₇	—	4	3	no	—
320	C₄×C₆₇	—	4	1	no	—
321	C₄×C₆₇	C₂×#120	1	6	yes	—
322	C₄×C₆₇	C₂³×D₄	1	2	yes	—
323	#60373	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂×C₆₇	—	2	2	no	—
325	C₂×C₆₇	—	2	6	no	—
326	C₂×C₆₇	—	4	3	no	—
327	C₂×C₆₇	—	4	12	no	—
328	C₂×C₆₇	—	8	1	no	—
329	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
330	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
331	C₂×C₆₇	#3585	1	1	yes	characteristic
332	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
333	C₂×#577	C₂×C₆₇	1	2	yes	complemented
334	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
335	#3012	C₂×C₆₇	1	6	yes	complemented
336	#3009	C₂×C₆₇	1	6	yes	complemented
337	#3007	C₂×C₆₇	1	3	yes	complemented
338	#3003	C₂×C₆₇	1	3	yes	complemented
339	#3002	C₂×C₆₇	1	3	yes	complemented
340	C₂×#450	C₂×C₆₇	1	3	yes	complemented
341	#2897	C₂×C₆₇	1	2	yes	complemented
342	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
343	C₆₇	#60373	1	1	yes	characteristic, direct product factor, Sylow
344	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
345	C₂×H(5,𝔽₂)	—	2	16	no	—
346	C₂×H(5,𝔽₂)	—	2	3	no	—
347	C₂×H(5,𝔽₂)	—	2	1	no	—
348	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	6	yes	—
349	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
350	C₂²×#41	—	2	1	no	—
351	C₂²×#41	C₂²×C₆₇	1	3	yes	—
352	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
353	C₂³×D₄	—	2	3	no	—
354	C₂³×D₄	C₂²×C₆₇	1	3	yes	—
355	#577	—	2	16	no	—
356	C₂×#137	C₂²×C₆₇	1	6	yes	complemented
357	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	6	yes	complemented
358	C₂×#135	C₂²×C₆₇	1	6	yes	complemented
359	C₂²×SD₁₆	C₂²×C₆₇	1	6	yes	complemented
360	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
361	D₄×Q₈	—	2	1	no	—
362	#548	—	2	1	no	—
363	#547	—	2	3	no	—
364	#546	—	2	3	no	—
365	#537	C₂²×C₆₇	1	3	yes	complemented
366	#536	C₂²×C₆₇	1	3	yes	complemented
367	#525	C₂²×C₆₇	1	3	yes	complemented
368	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	3	yes	complemented
369	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
370	#452	C₂²×C₆₇	1	6	yes	complemented
371	#452	C₂²×C₆₇	1	12	yes	complemented
372	#451	C₂²×C₆₇	1	3	yes	complemented
373	#450	C₂²×C₆₇	1	3	yes	complemented
374	#450	C₂²×C₆₇	1	6	yes	complemented
375	#450	C₂²×C₆₇	1	12	yes	complemented
376	#450	C₂²×C₆₇	1	6	yes	complemented
377	#449	C₂²×C₆₇	1	6	yes	complemented
378	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
379	#447	C₂²×C₆₇	1	3	yes	complemented
380	#447	C₂²×C₆₇	1	6	yes	complemented
381	#418	C₂²×C₆₇	1	6	yes	complemented
382	#417	C₂²×C₆₇	1	6	yes	complemented
383	#416	C₂²×C₆₇	1	6	yes	complemented
384	C₂×#102	C₂²×C₆₇	1	6	yes	complemented
385	#408	C₂²×C₆₇	1	6	yes	complemented
386	#407	C₂²×C₆₇	1	3	yes	complemented
387	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
388	C₂⁵	—	2	3	no	—
389	2₋¹⁺⁴	—	2	8	no	—
390	H(5,𝔽₂)	—	2	16	no	—
391	H(5,𝔽₂)	—	2	48	no	—
392	H(5,𝔽₂)	—	2	24	no	—
393	H(5,𝔽₂)	—	2	8	no	—
394	H(5,𝔽₂)	—	2	24	no	—
395	H(5,𝔽₂)	D₄×C₆₇	1	16	yes	complemented
396	C₂×#41	—	2	16	no	—
397	C₂×#41	—	2	24	no	—
398	C₂×#41	—	2	8	no	—
399	C₂×#41	—	2	6	no	—
400	C₂×#41	—	2	2	no	—
401	C₂×#41	—	2	3	no	—
402	C₂×#41	—	2	3	no	—
403	C₂×#41	—	2	3	no	—
404	C₂×#41	D₄×C₆₇	1	3	yes	—
405	C₂×#41	D₄×C₆₇	1	1	yes	characteristic
406	C₂×#41	C₂³×C₆₇	1	6	yes	—
407	C₂×#41	C₂³×C₆₇	1	6	yes	—
408	C₂×#41	C₂³×C₆₇	1	3	yes	—
409	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
410	C₂×#41	C₂³×C₆₇	1	3	yes	complemented
411	C₂²×Q₈	—	2	1	no	—
412	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₆₇	1	3	yes	complemented
415	C₂²×D₄	—	2	48	no	—
416	C₂²×D₄	—	2	3	no	—
417	C₂²×D₄	—	2	12	no	—
418	C₂²×D₄	—	2	6	no	—
419	C₂²×D₄	—	2	6	no	—
420	C₂²×D₄	—	2	24	no	—
421	C₂²×D₄	—	2	3	no	—
422	C₂²×D₄	—	2	3	no	—
423	C₂²×D₄	—	2	3	no	—
424	C₂²×D₄	D₄×C₆₇	1	3	yes	—
425	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
426	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
427	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
428	C₂³×C₄	—	2	3	no	—
429	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
430	#137	—	2	24	no	—
431	AGL(1,ℤ/8)	—	2	24	no	—
432	#135	—	2	24	no	—
433	C₂×Q₁₆	C₂³×C₆₇	1	6	yes	complemented
434	C₂×SD₁₆	—	2	24	no	—
435	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	complemented
436	C₂×SD₁₆	C₂³×C₆₇	1	12	yes	complemented
437	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
438	C₂×D₈	C₂³×C₆₇	1	6	yes	complemented
439	#131	—	2	8	no	—
440	C₂×M₁₆	C₂³×C₆₇	1	6	yes	complemented
441	C₂²×C₈	C₂³×C₆₇	1	6	yes	complemented
442	C₄⋊Q₈	—	2	3	no	—
443	#124	—	2	3	no	—
444	#123	—	2	6	no	—
445	#123	—	2	3	no	—
446	C₂²⋊Q₈	—	2	3	no	—
447	C₂²⋊Q₈	—	2	3	no	—
448	C₂²⋊Q₈	—	2	3	no	—
449	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	—
450	C₂²⋊Q₈	C₂³×C₆₇	1	6	yes	complemented
451	C₂²⋊Q₈	C₂³×C₆₇	1	3	yes	complemented
452	#121	—	2	6	no	—
453	#121	—	2	3	no	—
454	#121	C₂³×C₆₇	1	1	yes	characteristic
455	#121	C₂³×C₆₇	1	3	yes	complemented
456	#120	—	2	3	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×D₄	—	2	3	no	—
459	C₄×D₄	—	2	3	no	—
460	C₄×D₄	—	2	3	no	—
461	#117	C₂³×C₆₇	1	3	yes	complemented
462	C₂×C₄⋊C₄	—	2	3	no	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	complemented
464	C₂×C₂²⋊C₄	—	2	3	no	—
465	#103	C₂³×C₆₇	1	2	yes	complemented
466	#103	C₂³×C₆₇	1	6	yes	complemented
467	#102	C₂³×C₆₇	1	6	yes	complemented
468	#102	C₂³×C₆₇	1	12	yes	complemented
469	#102	C₂³×C₆₇	1	6	yes	complemented
470	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²⋊C₈	C₂³×C₆₇	1	3	yes	—
472	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	complemented
473	C₂²⋊C₈	C₂³×C₆₇	1	6	yes	complemented
474	C₂⁴	—	2	24	no	—
475	C₂⁴	—	2	3	no	—
476	C₂⁴	—	2	6	no	—
477	C₂⁴	—	2	6	no	—
478	C₂⁴	—	8	6	no	—
479	C₂⁴	—	8	6	no	—
480	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
481	#41	—	2	24	no	—
482	#41	—	2	48	no	—
483	#41	—	2	24	no	—
484	#41	—	2	16	no	—
485	#41	—	2	4	no	—
486	#41	—	2	12	no	—
487	#41	—	2	12	no	—
488	#41	—	2	12	no	—
489	#41	—	2	12	no	—
490	#41	—	2	12	no	—
491	#41	—	2	12	no	—
492	#41	—	4	12	no	—
493	#41	C₂×D₄×C₆₇	1	24	yes	—
494	#41	C₂×D₄×C₆₇	1	8	yes	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	4	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	3	no	—
499	C₂×Q₈	—	2	12	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	C₂×D₄×C₆₇	1	3	yes	—
502	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴×C₆₇	1	3	yes	—
504	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
505	C₂×D₄	—	2	24	no	—
506	C₂×D₄	—	2	24	no	—
507	C₂×D₄	—	2	96	no	—
508	C₂×D₄	—	2	24	no	—
509	C₂×D₄	—	2	48	no	—
510	C₂×D₄	—	2	24	no	—
511	C₂×D₄	—	2	6	no	—
512	C₂×D₄	—	2	6	no	—
513	C₂×D₄	—	2	12	no	—
514	C₂×D₄	—	2	48	no	—
515	C₂×D₄	—	2	12	no	—
516	C₂×D₄	—	2	24	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	3	no	—
519	C₂×D₄	—	2	3	no	—
520	C₂×D₄	—	2	6	no	—
521	C₂×D₄	—	2	3	no	—
522	C₂×D₄	—	2	6	no	—
523	C₂×D₄	—	2	12	no	—
524	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
525	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
526	C₂×D₄	C₂×D₄×C₆₇	1	24	yes	—
527	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
528	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
529	C₂×D₄	C₂⁴×C₆₇	1	6	yes	—
530	C₂²×C₄	—	2	24	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	6	no	—
533	C₂²×C₄	—	2	6	no	—
534	C₂²×C₄	—	2	12	no	—
535	C₂²×C₄	—	2	3	no	—
536	C₂²×C₄	—	2	3	no	—
537	C₂²×C₄	—	2	3	no	—
538	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
539	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
540	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
544	Q₁₆	—	2	12	no	—
545	SD₁₆	—	2	4	no	—
546	SD₁₆	—	2	12	no	—
547	SD₁₆	—	2	24	no	—
548	D₈	—	2	12	no	—
549	M₁₆	—	2	12	no	—
550	C₂×C₈	—	2	12	no	—
551	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
552	C₂×C₈	C₂⁴×C₆₇	1	6	yes	—
553	C₄⋊C₄	—	2	3	no	—
554	C₄⋊C₄	—	2	6	no	—
555	C₄⋊C₄	—	2	3	no	—
556	C₄⋊C₄	—	2	3	no	—
557	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
558	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
559	C₂²⋊C₄	—	2	3	no	—
560	C₂²⋊C₄	—	2	6	no	—
561	C₂²⋊C₄	—	2	3	no	—
562	C₂²⋊C₄	—	2	3	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	3	no	—
565	C₄²	—	2	3	no	—
566	C₂³	—	2	12	no	—
567	C₂³	—	2	24	no	—
568	C₂³	—	2	6	no	—
569	C₂³	—	2	6	no	—
570	C₂³	—	2	6	no	—
571	C₂³	—	2	24	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	4	3	no	—
574	C₂³	—	4	6	no	—
575	C₂³	—	4	6	no	—
576	C₂³	—	8	6	no	—
577	C₂³	—	8	6	no	—
578	C₂³	—	8	6	no	—
579	C₂³	—	8	6	no	—
580	C₂³	—	8	48	no	—
581	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
582	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
583	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
584	Q₈	—	2	4	no	—
585	Q₈	—	2	6	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	6	no	—
588	Q₈	—	4	6	no	—
589	Q₈	#120×C₆₇	1	4	yes	—
590	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
591	D₄	—	2	24	no	—
592	D₄	—	2	24	no	—
593	D₄	—	2	12	no	—
594	D₄	—	2	24	no	—
595	D₄	—	2	12	no	—
596	D₄	—	2	6	no	—
597	D₄	—	2	24	no	—
598	D₄	—	2	6	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	6	no	—
601	D₄	—	4	2	no	—
602	D₄	—	8	3	no	—
603	D₄	#120×C₆₇	1	12	yes	—
604	D₄	C₂²×D₄×C₆₇	1	12	yes	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	24	no	—
607	C₂×C₄	—	2	6	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	6	no	—
610	C₂×C₄	—	2	24	no	—
611	C₂×C₄	—	2	6	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	6	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	3	no	—
616	C₂×C₄	—	2	3	no	—
617	C₂×C₄	—	4	6	no	—
618	C₂×C₄	—	4	6	no	—
619	C₂×C₄	—	8	3	no	—
620	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
621	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
623	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
624	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	6	no	—
627	C₂²	—	2	3	no	—
628	C₂²	—	2	3	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	3	no	—
632	C₂²	—	2	3	no	—
633	C₂²	—	2	3	no	—
634	C₂²	—	2	12	no	—
635	C₂²	—	4	12	no	—
636	C₂²	—	4	24	no	—
637	C₂²	—	4	6	no	—
638	C₂²	—	4	6	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	8	24	no	—
643	C₂²	—	8	24	no	—
644	C₂²	C₂×#120×C₆₇	1	6	yes	—
645	C₂²	#577×C₆₇	1	2	yes	complemented
646	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
647	C₄	—	2	4	no	—
648	C₄	—	2	3	no	—
649	C₄	—	2	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	3	no	—
652	C₄	—	4	3	no	—
653	C₄	C₂×#120×C₆₇	1	6	yes	—
654	C₄	C₂³×D₄×C₆₇	1	2	yes	—
655	C₂	—	2	2	no	—
656	C₂	—	2	6	no	—
657	C₂	—	4	3	no	—
658	C₂	—	4	12	no	—
659	C₂	—	8	1	no	—
660	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
661	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
662	C₂	C₆₇×#3585	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 ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₇	C₂	semidirect
2. C₂×#577×C₆₇	C₂	semidirect
3. C₆₇×#3489	C₂	semidirect
4. C₆₇×#3012	C₂	semidirect
5. C₆₇×#3009	C₂	semidirect
6. C₆₇×#3007	C₂	semidirect
7. C₆₇×#3003	C₂	semidirect
8. C₆₇×#3002	C₂	semidirect
9. C₂×#450×C₆₇	C₂	semidirect
10. C₆₇×#2897	C₂	semidirect
11. C₆₇×#2880	C₂	semidirect
12. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×#135×C₆₇	C₂²	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
28. C₂×#131×C₆₇	C₂²	semidirect
33. #537×C₆₇	C₂²	semidirect
34. #536×C₆₇	C₂²	semidirect
35. #525×C₆₇	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
37. #520×C₆₇	C₂²	semidirect
38. #452×C₆₇	C₂²	semidirect
39. #452×C₆₇	C₂²	semidirect
40. #451×C₆₇	C₂²	semidirect
41. #450×C₆₇	C₂²	semidirect
42. #450×C₆₇	C₂²	semidirect
43. #450×C₆₇	C₂²	semidirect
44. #450×C₆₇	C₂²	semidirect
45. #449×C₆₇	C₂²	semidirect
46. #448×C₆₇	C₂²	semidirect
47. #447×C₆₇	C₂²	semidirect
48. #447×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. #408×C₆₇	C₂²	semidirect
54. #407×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
63. H(5,𝔽₂)×C₆₇	D₄	semidirect
78. C₂×#41×C₆₇	C₂³	semidirect
82. C₂²×Q₈×C₆₇	C₂³	semidirect
101. C₂×Q₁₆×C₆₇	C₂³	semidirect
103. C₂×SD₁₆×C₆₇	C₂³	semidirect
104. C₂×SD₁₆×C₆₇	C₂³	semidirect
105. C₂×SD₁₆×C₆₇	C₂³	semidirect
106. C₂×D₈×C₆₇	C₂³	semidirect
108. C₂×M₁₆×C₆₇	C₂³	semidirect
109. C₂²×C₈×C₆₇	C₂³	semidirect
118. C₂²⋊Q₈×C₆₇	C₂³	semidirect
119. C₂²⋊Q₈×C₆₇	C₂³	semidirect
123. #121×C₆₇	C₂³	semidirect
129. #117×C₆₇	C₂³	semidirect
131. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
133. #103×C₆₇	C₂³	semidirect
134. #103×C₆₇	C₂³	semidirect
135. #102×C₆₇	C₂³	semidirect
136. #102×C₆₇	C₂³	semidirect
137. #102×C₆₇	C₂³	semidirect
140. C₂²⋊C₈×C₆₇	C₂³	semidirect
141. C₂²⋊C₈×C₆₇	C₂³	semidirect
313. C₂²×C₆₇	#577	semidirect
323. #60373	C₆₇	direct (N × H)
332. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
333. C₂×#577	C₂×C₆₇	semidirect
334. #3489	C₂×C₆₇	semidirect
335. #3012	C₂×C₆₇	semidirect
336. #3009	C₂×C₆₇	semidirect
337. #3007	C₂×C₆₇	semidirect
338. #3003	C₂×C₆₇	semidirect
339. #3002	C₂×C₆₇	semidirect
340. C₂×#450	C₂×C₆₇	semidirect
341. #2897	C₂×C₆₇	semidirect
342. #2880	C₂×C₆₇	semidirect
343. C₆₇	#60373	direct (N × H)
344. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
356. C₂×#137	C₂²×C₆₇	semidirect
357. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
358. C₂×#135	C₂²×C₆₇	semidirect
359. C₂²×SD₁₆	C₂²×C₆₇	semidirect
360. C₂×#131	C₂²×C₆₇	semidirect
365. #537	C₂²×C₆₇	semidirect
366. #536	C₂²×C₆₇	semidirect
367. #525	C₂²×C₆₇	semidirect
368. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
369. #520	C₂²×C₆₇	semidirect
370. #452	C₂²×C₆₇	semidirect
371. #452	C₂²×C₆₇	semidirect
372. #451	C₂²×C₆₇	semidirect
373. #450	C₂²×C₆₇	semidirect
374. #450	C₂²×C₆₇	semidirect
375. #450	C₂²×C₆₇	semidirect
376. #450	C₂²×C₆₇	semidirect
377. #449	C₂²×C₆₇	semidirect
378. #448	C₂²×C₆₇	semidirect
379. #447	C₂²×C₆₇	semidirect
380. #447	C₂²×C₆₇	semidirect
381. #418	C₂²×C₆₇	semidirect
382. #417	C₂²×C₆₇	semidirect
383. #416	C₂²×C₆₇	semidirect
384. C₂×#102	C₂²×C₆₇	semidirect
385. #408	C₂²×C₆₇	semidirect
386. #407	C₂²×C₆₇	semidirect
387. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
395. H(5,𝔽₂)	D₄×C₆₇	semidirect
410. C₂×#41	C₂³×C₆₇	semidirect
414. C₂²×Q₈	C₂³×C₆₇	semidirect
433. C₂×Q₁₆	C₂³×C₆₇	semidirect
435. C₂×SD₁₆	C₂³×C₆₇	semidirect
436. C₂×SD₁₆	C₂³×C₆₇	semidirect
437. C₂×SD₁₆	C₂³×C₆₇	semidirect
438. C₂×D₈	C₂³×C₆₇	semidirect
440. C₂×M₁₆	C₂³×C₆₇	semidirect
441. C₂²×C₈	C₂³×C₆₇	semidirect
450. C₂²⋊Q₈	C₂³×C₆₇	semidirect
451. C₂²⋊Q₈	C₂³×C₆₇	semidirect
455. #121	C₂³×C₆₇	semidirect
461. #117	C₂³×C₆₇	semidirect
463. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
465. #103	C₂³×C₆₇	semidirect
466. #103	C₂³×C₆₇	semidirect
467. #102	C₂³×C₆₇	semidirect
468. #102	C₂³×C₆₇	semidirect
469. #102	C₂³×C₆₇	semidirect
472. C₂²⋊C₈	C₂³×C₆₇	semidirect
473. C₂²⋊C₈	C₂³×C₆₇	semidirect
645. C₂²	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₆₇	2
C₂×#577×C₆₇	2
C₆₇×#3489	2
C₆₇×#3012	2
C₆₇×#3009	2
C₆₇×#3007	2
C₆₇×#3003	2
C₆₇×#3002	2
C₂×#450×C₆₇	2
C₆₇×#2897	2
C₆₇×#2880	2
#60373	67

Subgroups — C67×#60373 #30739624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60373 #30739624