Subgroups — C₆₇×#60174 #30739425

Order 17152.

2734 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2951	C₂	1	3	yes	maximal, complemented
5	C₆₇×#2949	C₂	1	3	yes	maximal, complemented
6	C₆₇×#2947	C₂	1	3	yes	maximal, complemented
7	C₆₇×#2946	C₂	1	3	yes	maximal, complemented
8	C₄×#137×C₆₇	C₂	1	3	yes	maximal, complemented
9	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	3	yes	maximal, complemented
10	C₆₇×#2943	C₂	1	3	yes	maximal, complemented
11	C₂×#440×C₆₇	C₂	1	3	yes	maximal, complemented
12	C₆₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
18	#577×C₆₇	C₄	1	16	yes	complemented
19	C₂×#137×C₆₇	C₂²	1	3	yes	—
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	3	yes	—
21	C₂×#135×C₆₇	C₂²	1	3	yes	—
22	C₂²×SD₁₆×C₆₇	C₂²	1	3	yes	—
23	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
25	#520×C₆₇	—	2	1	no	—
26	#520×C₆₇	—	2	3	no	—
27	#520×C₆₇	C₂²	1	3	yes	—
28	#520×C₆₇	C₂²	1	1	yes	characteristic
29	#520×C₆₇	C₂²	1	1	yes	characteristic
30	#520×C₆₇	C₂²	1	3	yes	complemented
31	#519×C₆₇	—	2	1	no	—
32	#519×C₆₇	C₂²	1	3	yes	complemented
33	#518×C₆₇	—	2	3	no	—
34	#518×C₆₇	C₂²	1	3	yes	—
35	C₄×#41×C₆₇	—	2	1	no	—
36	C₄×#41×C₆₇	—	2	3	no	—
37	C₄×#41×C₆₇	C₂²	1	3	yes	—
38	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×#41×C₆₇	C₂²	1	3	yes	complemented
40	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
41	C₂×C₄×Q₈×C₆₇	C₂²	1	3	yes	complemented
42	C₂×C₄×D₄×C₆₇	—	2	3	no	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	3	yes	—
44	#442×C₆₇	C₂²	1	3	yes	complemented
45	#442×C₆₇	C₂²	1	3	yes	complemented
46	#441×C₆₇	C₂²	1	3	yes	complemented
47	#441×C₆₇	C₂²	1	3	yes	complemented
48	#440×C₆₇	C₂²	1	3	yes	complemented
49	#440×C₆₇	C₂²	1	6	yes	complemented
50	#440×C₆₇	C₂²	1	6	yes	complemented
51	#440×C₆₇	C₂²	1	6	yes	complemented
52	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#440×C₆₇	C₂²	1	3	yes	complemented
54	#440×C₆₇	C₂²	1	3	yes	complemented
55	C₄×Q₁₆×C₆₇	C₂²	1	6	yes	complemented
56	C₄×SD₁₆×C₆₇	C₂²	1	6	yes	complemented
57	C₄×SD₁₆×C₆₇	C₂²	1	6	yes	complemented
58	C₄×D₈×C₆₇	C₂²	1	6	yes	complemented
59	#428×C₆₇	C₂²	1	3	yes	complemented
60	#428×C₆₇	C₂²	1	3	yes	complemented
61	#427×C₆₇	C₂²	1	3	yes	complemented
62	C₂×#107×C₆₇	C₂²	1	3	yes	complemented
63	#419×C₆₇	C₂²	1	3	yes	complemented
64	#418×C₆₇	C₂²	1	3	yes	—
65	#417×C₆₇	C₂²	1	3	yes	—
66	#417×C₆₇	C₂²	1	3	yes	complemented
67	#416×C₆₇	C₂²	1	3	yes	—
68	#416×C₆₇	C₂²	1	3	yes	complemented
69	C₂×#103×C₆₇	C₂²	1	3	yes	complemented
70	C₂×#102×C₆₇	C₂²	1	3	yes	—
71	#405×C₆₇	C₂²	1	3	yes	complemented
72	#405×C₆₇	C₂²	1	3	yes	complemented
73	C₄×M₁₆×C₆₇	C₂²	1	3	yes	complemented
74	C₂×#97×C₆₇	C₂²	1	3	yes	complemented
75	2₋¹⁺⁴×C₆₇	—	2	4	no	—
76	2₋¹⁺⁴×C₆₇	C₂×C₄	1	8	yes	complemented
77	H(5,𝔽₂)×C₆₇	—	2	4	no	—
78	H(5,𝔽₂)×C₆₇	C₂×C₄	1	8	yes	complemented
79	C₂×#41×C₆₇	—	2	1	no	—
80	C₂×#41×C₆₇	—	2	3	no	—
81	C₂×#41×C₆₇	C₂³	1	3	yes	—
82	C₂×#41×C₆₇	C₂³	1	3	yes	—
83	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₆₇	—	2	1	no	—
85	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
86	C₂²×D₄×C₆₇	—	2	3	no	—
87	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
88	C₂³×C₄×C₆₇	—	2	3	no	—
89	#137×C₆₇	C₂×C₄	1	24	yes	complemented
90	AGL(1,ℤ/8)×C₆₇	C₂×C₄	1	24	yes	complemented
91	#135×C₆₇	C₂×C₄	1	24	yes	complemented
92	C₂×Q₁₆×C₆₇	C₂³	1	3	yes	—
93	C₂×SD₁₆×C₆₇	C₂×C₄	1	24	yes	complemented
94	C₂×SD₁₆×C₆₇	C₂³	1	3	yes	—
95	C₂×SD₁₆×C₆₇	C₂³	1	6	yes	—
96	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
97	C₂×D₈×C₆₇	C₂³	1	3	yes	—
98	#131×C₆₇	—	2	4	no	—
99	#131×C₆₇	C₂×C₄	1	8	yes	complemented
100	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	3	yes	—
102	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
103	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
104	C₄×Q₈×C₆₇	—	2	1	no	—
105	C₄×Q₈×C₆₇	—	2	1	no	—
106	C₄×Q₈×C₆₇	—	2	3	no	—
107	C₄×Q₈×C₆₇	—	2	3	no	—
108	C₄×Q₈×C₆₇	—	2	3	no	—
109	C₄×Q₈×C₆₇	—	2	3	no	—
110	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
112	C₄×Q₈×C₆₇	C₂³	1	3	yes	—
113	C₄×Q₈×C₆₇	C₂³	1	6	yes	—
114	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₆₇	C₂³	1	3	yes	—
116	C₄×Q₈×C₆₇	C₂³	1	3	yes	—
117	C₄×D₄×C₆₇	—	2	3	no	—
118	C₄×D₄×C₆₇	—	2	3	no	—
119	C₄×D₄×C₆₇	—	2	3	no	—
120	C₄×D₄×C₆₇	—	2	3	no	—
121	C₄×D₄×C₆₇	—	2	3	no	—
122	C₄×D₄×C₆₇	—	2	3	no	—
123	C₄×D₄×C₆₇	—	2	3	no	—
124	C₄×D₄×C₆₇	—	2	3	no	—
125	C₄×D₄×C₆₇	—	2	6	no	—
126	C₄×D₄×C₆₇	—	2	6	no	—
127	C₄×D₄×C₆₇	—	2	3	no	—
128	C₄×D₄×C₆₇	—	2	3	no	—
129	C₄×D₄×C₆₇	D₄	1	3	yes	—
130	C₄×D₄×C₆₇	D₄	1	3	yes	—
131	C₄×D₄×C₆₇	C₂³	1	3	yes	—
132	C₄×D₄×C₆₇	C₂³	1	6	yes	—
133	C₄×D₄×C₆₇	C₂³	1	3	yes	—
134	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₆₇	C₂³	1	3	yes	—
136	#117×C₆₇	—	2	3	no	—
137	#117×C₆₇	—	2	3	no	—
138	#117×C₆₇	—	2	6	no	—
139	#117×C₆₇	—	2	3	no	—
140	#117×C₆₇	—	2	3	no	—
141	#117×C₆₇	C₂³	1	3	yes	—
142	#117×C₆₇	C₂³	1	3	yes	—
143	#117×C₆₇	C₂³	1	3	yes	—
144	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
145	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
146	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	6	no	—
151	C₂×C₄²×C₆₇	—	2	3	no	—
152	C₂×C₄²×C₆₇	—	2	3	no	—
153	C₂×C₄²×C₆₇	—	2	3	no	—
154	C₂×C₄²×C₆₇	C₂³	1	3	yes	—
155	#107×C₆₇	C₂³	1	3	yes	—
156	#107×C₆₇	C₂³	1	6	yes	—
157	#107×C₆₇	C₂³	1	1	yes	characteristic
158	#106×C₆₇	C₂³	1	3	yes	—
159	#106×C₆₇	C₂³	1	3	yes	—
160	#103×C₆₇	C₂³	1	3	yes	—
161	#103×C₆₇	C₂³	1	6	yes	—
162	#103×C₆₇	C₂³	1	1	yes	characteristic
163	#103×C₆₇	C₂³	1	3	yes	—
164	#103×C₆₇	C₂³	1	3	yes	—
165	#102×C₆₇	C₂³	1	3	yes	—
166	#102×C₆₇	C₂³	1	6	yes	—
167	#102×C₆₇	C₂³	1	3	yes	—
168	#102×C₆₇	C₂³	1	1	yes	characteristic
169	#102×C₆₇	C₂³	1	3	yes	—
170	#97×C₆₇	C₂³	1	1	yes	characteristic
171	#97×C₆₇	C₂³	1	3	yes	—
172	#97×C₆₇	C₂³	1	3	yes	—
173	#97×C₆₇	C₂³	1	3	yes	—
174	C₄×C₈×C₆₇	C₂³	1	6	yes	—
175	C₂⁴×C₆₇	—	2	3	no	—
176	#41×C₆₇	—	2	8	no	—
177	#41×C₆₇	—	2	24	no	—
178	#41×C₆₇	—	2	6	no	—
179	#41×C₆₇	—	2	6	no	—
180	#41×C₆₇	C₂²×C₄	1	12	yes	—
181	#41×C₆₇	C₂²×C₄	1	4	yes	—
182	#41×C₆₇	C₂²×C₄	1	12	yes	complemented
183	#41×C₆₇	#41	1	4	yes	—
184	C₂×Q₈×C₆₇	—	2	8	no	—
185	C₂×Q₈×C₆₇	—	2	3	no	—
186	C₂×Q₈×C₆₇	—	2	6	no	—
187	C₂×Q₈×C₆₇	C₂²×C₄	1	12	yes	complemented
188	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
190	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂×D₄×C₆₇	—	2	3	no	—
192	C₂×D₄×C₆₇	—	2	3	no	—
193	C₂×D₄×C₆₇	—	2	24	no	—
194	C₂×D₄×C₆₇	—	2	3	no	—
195	C₂×D₄×C₆₇	—	2	6	no	—
196	C₂×D₄×C₆₇	C₂²×C₄	1	12	yes	—
197	C₂×D₄×C₆₇	C₂×D₄	1	3	yes	—
198	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
200	C₂²×C₄×C₆₇	—	2	3	no	—
201	C₂²×C₄×C₆₇	—	2	3	no	—
202	C₂²×C₄×C₆₇	—	2	3	no	—
203	C₂²×C₄×C₆₇	—	2	3	no	—
204	C₂²×C₄×C₆₇	—	2	3	no	—
205	C₂²×C₄×C₆₇	—	2	1	no	—
206	C₂²×C₄×C₆₇	—	2	3	no	—
207	C₂²×C₄×C₆₇	—	2	3	no	—
208	C₂²×C₄×C₆₇	—	2	3	no	—
209	C₂²×C₄×C₆₇	—	2	6	no	—
210	C₂²×C₄×C₆₇	—	8	6	no	—
211	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
212	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
214	Q₁₆×C₆₇	C₂²×C₄	1	12	yes	complemented
215	SD₁₆×C₆₇	C₂²×C₄	1	12	yes	complemented
216	SD₁₆×C₆₇	C₂²×C₄	1	24	yes	complemented
217	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	complemented
218	D₈×C₆₇	C₂²×C₄	1	12	yes	complemented
219	M₁₆×C₆₇	—	2	6	no	—
220	M₁₆×C₆₇	C₂²×C₄	1	12	yes	complemented
221	C₂×C₈×C₆₇	—	2	6	no	—
222	C₂×C₈×C₆₇	C₂²×C₄	1	12	yes	complemented
223	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
225	C₂×C₈×C₆₇	C₂⁴	1	3	yes	—
226	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₆₇	—	2	3	no	—
228	C₄⋊C₄×C₆₇	—	2	3	no	—
229	C₄⋊C₄×C₆₇	—	2	6	no	—
230	C₄⋊C₄×C₆₇	—	2	3	no	—
231	C₄⋊C₄×C₆₇	—	2	3	no	—
232	C₄⋊C₄×C₆₇	—	2	1	no	—
233	C₄⋊C₄×C₆₇	—	2	3	no	—
234	C₄⋊C₄×C₆₇	C₂×D₄	1	3	yes	—
235	C₄⋊C₄×C₆₇	C₂×D₄	1	3	yes	—
236	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
238	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
240	C₂²⋊C₄×C₆₇	—	2	3	no	—
241	C₂²⋊C₄×C₆₇	—	2	3	no	—
242	C₂²⋊C₄×C₆₇	—	2	3	no	—
243	C₂²⋊C₄×C₆₇	—	2	3	no	—
244	C₂²⋊C₄×C₆₇	—	2	6	no	—
245	C₂²⋊C₄×C₆₇	—	2	1	no	—
246	C₂²⋊C₄×C₆₇	—	2	3	no	—
247	C₂²⋊C₄×C₆₇	C₂×D₄	1	6	yes	—
248	C₄²×C₆₇	—	2	1	no	—
249	C₄²×C₆₇	—	2	3	no	—
250	C₄²×C₆₇	—	2	3	no	—
251	C₄²×C₆₇	—	2	3	no	—
252	C₄²×C₆₇	—	2	6	no	—
253	C₄²×C₆₇	—	2	3	no	—
254	C₄²×C₆₇	—	2	3	no	—
255	C₄²×C₆₇	C₂×D₄	1	3	yes	—
256	C₄²×C₆₇	C₂×D₄	1	3	yes	—
257	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₄²×C₆₇	C₂⁴	1	3	yes	—
259	C₂³×C₆₇	—	2	1	no	—
260	C₂³×C₆₇	—	2	3	no	—
261	C₂³×C₆₇	—	2	12	no	—
262	C₂³×C₆₇	—	8	3	no	—
263	C₂³×C₆₇	—	8	3	no	—
264	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
265	Q₈×C₆₇	—	2	12	no	—
266	Q₈×C₆₇	—	2	3	no	—
267	Q₈×C₆₇	—	2	1	no	—
268	Q₈×C₆₇	C₄×D₄	1	4	yes	—
269	Q₈×C₆₇	C₂³×C₄	1	6	yes	—
270	Q₈×C₆₇	C₂³×C₄	1	2	yes	—
271	D₄×C₆₇	—	2	12	no	—
272	D₄×C₆₇	—	2	12	no	—
273	D₄×C₆₇	—	2	12	no	—
274	D₄×C₆₇	—	2	3	no	—
275	D₄×C₆₇	—	2	1	no	—
276	D₄×C₆₇	C₄×D₄	1	12	yes	—
277	D₄×C₆₇	C₂³×C₄	1	2	yes	—
278	D₄×C₆₇	C₂³×C₄	1	6	yes	—
279	C₂×C₄×C₆₇	—	2	12	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	3	no	—
282	C₂×C₄×C₆₇	—	2	12	no	—
283	C₂×C₄×C₆₇	—	2	12	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	3	no	—
287	C₂×C₄×C₆₇	—	2	3	no	—
288	C₂×C₄×C₆₇	—	4	3	no	—
289	C₂×C₄×C₆₇	—	4	3	no	—
290	C₂×C₄×C₆₇	—	4	2	no	—
291	C₂×C₄×C₆₇	—	4	6	no	—
292	C₂×C₄×C₆₇	—	8	3	no	—
293	C₂×C₄×C₆₇	—	8	3	no	—
294	C₂×C₄×C₆₇	—	8	6	no	—
295	C₂×C₄×C₆₇	—	8	3	no	—
296	C₂×C₄×C₆₇	—	8	3	no	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
303	C₂×C₄×C₆₇	C₂×#41	1	6	yes	—
304	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
305	C₈×C₆₇	—	2	1	no	—
306	C₈×C₆₇	—	2	3	no	—
307	C₈×C₆₇	C₂³×C₄	1	2	yes	—
308	C₈×C₆₇	C₂³×C₄	1	6	yes	—
309	C₂²×C₆₇	—	2	3	no	—
310	C₂²×C₆₇	—	2	3	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	6	no	—
313	C₂²×C₆₇	—	4	3	no	—
314	C₂²×C₆₇	—	4	1	no	—
315	C₂²×C₆₇	—	4	1	no	—
316	C₂²×C₆₇	—	4	3	no	—
317	C₂²×C₆₇	—	8	12	no	—
318	C₂²×C₆₇	C₂×C₄×D₄	1	6	yes	—
319	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	3	no	—
322	C₄×C₆₇	—	2	1	no	—
323	C₄×C₆₇	—	2	3	no	—
324	C₄×C₆₇	—	2	2	no	—
325	C₄×C₆₇	—	2	6	no	—
326	C₄×C₆₇	—	4	3	no	—
327	C₄×C₆₇	—	4	3	no	—
328	C₄×C₆₇	—	4	1	no	—
329	C₄×C₆₇	—	4	1	no	—
330	C₄×C₆₇	C₂×C₄×D₄	1	6	yes	—
331	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
332	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
333	#60174	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂×C₆₇	—	2	6	no	—
335	C₂×C₆₇	—	4	2	no	—
336	C₂×C₆₇	—	4	6	no	—
337	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
338	C₂×C₆₇	#3585	1	1	yes	characteristic
339	C₂×C₆₇	#3586	1	1	yes	characteristic
340	C₂×#577	C₂×C₆₇	1	1	yes	characteristic
341	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
342	C₄×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
343	#2951	C₂×C₆₇	1	3	yes	complemented
344	#2949	C₂×C₆₇	1	3	yes	complemented
345	#2947	C₂×C₆₇	1	3	yes	complemented
346	#2946	C₂×C₆₇	1	3	yes	complemented
347	C₄×#137	C₂×C₆₇	1	3	yes	complemented
348	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	3	yes	complemented
349	#2943	C₂×C₆₇	1	3	yes	complemented
350	C₂×#440	C₂×C₆₇	1	3	yes	complemented
351	#2913	C₂×C₆₇	1	1	yes	characteristic, complemented
352	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
353	#2897	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2875	C₂×C₆₇	1	1	yes	characteristic, complemented
355	C₆₇	#60174	1	1	yes	characteristic, direct product factor, Sylow
356	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
357	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
358	#577	C₄×C₆₇	1	16	yes	complemented
359	C₂×#137	C₂²×C₆₇	1	3	yes	—
360	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	3	yes	—
361	C₂×#135	C₂²×C₆₇	1	3	yes	—
362	C₂²×SD₁₆	C₂²×C₆₇	1	3	yes	—
363	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
364	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
365	#520	—	2	1	no	—
366	#520	—	2	3	no	—
367	#520	C₂²×C₆₇	1	3	yes	—
368	#520	C₂²×C₆₇	1	1	yes	characteristic
369	#520	C₂²×C₆₇	1	1	yes	characteristic
370	#520	C₂²×C₆₇	1	3	yes	complemented
371	#519	—	2	1	no	—
372	#519	C₂²×C₆₇	1	3	yes	complemented
373	#518	—	2	3	no	—
374	#518	C₂²×C₆₇	1	3	yes	—
375	C₄×#41	—	2	1	no	—
376	C₄×#41	—	2	3	no	—
377	C₄×#41	C₂²×C₆₇	1	3	yes	—
378	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
379	C₄×#41	C₂²×C₆₇	1	3	yes	complemented
380	C₂×C₄×Q₈	—	2	1	no	—
381	C₂×C₄×Q₈	C₂²×C₆₇	1	3	yes	complemented
382	C₂×C₄×D₄	—	2	3	no	—
383	C₂×C₄×D₄	C₂²×C₆₇	1	3	yes	—
384	#442	C₂²×C₆₇	1	3	yes	complemented
385	#442	C₂²×C₆₇	1	3	yes	complemented
386	#441	C₂²×C₆₇	1	3	yes	complemented
387	#441	C₂²×C₆₇	1	3	yes	complemented
388	#440	C₂²×C₆₇	1	3	yes	complemented
389	#440	C₂²×C₆₇	1	6	yes	complemented
390	#440	C₂²×C₆₇	1	6	yes	complemented
391	#440	C₂²×C₆₇	1	6	yes	complemented
392	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
393	#440	C₂²×C₆₇	1	3	yes	complemented
394	#440	C₂²×C₆₇	1	3	yes	complemented
395	C₄×Q₁₆	C₂²×C₆₇	1	6	yes	complemented
396	C₄×SD₁₆	C₂²×C₆₇	1	6	yes	complemented
397	C₄×SD₁₆	C₂²×C₆₇	1	6	yes	complemented
398	C₄×D₈	C₂²×C₆₇	1	6	yes	complemented
399	#428	C₂²×C₆₇	1	3	yes	complemented
400	#428	C₂²×C₆₇	1	3	yes	complemented
401	#427	C₂²×C₆₇	1	3	yes	complemented
402	C₂×#107	C₂²×C₆₇	1	3	yes	complemented
403	#419	C₂²×C₆₇	1	3	yes	complemented
404	#418	C₂²×C₆₇	1	3	yes	—
405	#417	C₂²×C₆₇	1	3	yes	—
406	#417	C₂²×C₆₇	1	3	yes	complemented
407	#416	C₂²×C₆₇	1	3	yes	—
408	#416	C₂²×C₆₇	1	3	yes	complemented
409	C₂×#103	C₂²×C₆₇	1	3	yes	complemented
410	C₂×#102	C₂²×C₆₇	1	3	yes	—
411	#405	C₂²×C₆₇	1	3	yes	complemented
412	#405	C₂²×C₆₇	1	3	yes	complemented
413	C₄×M₁₆	C₂²×C₆₇	1	3	yes	complemented
414	C₂×#97	C₂²×C₆₇	1	3	yes	complemented
415	2₋¹⁺⁴	—	2	4	no	—
416	2₋¹⁺⁴	C₂×C₄×C₆₇	1	8	yes	complemented
417	H(5,𝔽₂)	—	2	4	no	—
418	H(5,𝔽₂)	C₂×C₄×C₆₇	1	8	yes	complemented
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	3	no	—
421	C₂×#41	C₂³×C₆₇	1	3	yes	—
422	C₂×#41	C₂³×C₆₇	1	3	yes	—
423	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	C₂³×C₆₇	1	3	yes	—
426	C₂²×D₄	—	2	3	no	—
427	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
428	C₂³×C₄	—	2	3	no	—
429	#137	C₂×C₄×C₆₇	1	24	yes	complemented
430	AGL(1,ℤ/8)	C₂×C₄×C₆₇	1	24	yes	complemented
431	#135	C₂×C₄×C₆₇	1	24	yes	complemented
432	C₂×Q₁₆	C₂³×C₆₇	1	3	yes	—
433	C₂×SD₁₆	C₂×C₄×C₆₇	1	24	yes	complemented
434	C₂×SD₁₆	C₂³×C₆₇	1	3	yes	—
435	C₂×SD₁₆	C₂³×C₆₇	1	6	yes	—
436	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
437	C₂×D₈	C₂³×C₆₇	1	3	yes	—
438	#131	—	2	4	no	—
439	#131	C₂×C₄×C₆₇	1	8	yes	complemented
440	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
441	C₂×M₁₆	C₂³×C₆₇	1	3	yes	—
442	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
443	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
444	C₄×Q₈	—	2	1	no	—
445	C₄×Q₈	—	2	1	no	—
446	C₄×Q₈	—	2	3	no	—
447	C₄×Q₈	—	2	3	no	—
448	C₄×Q₈	—	2	3	no	—
449	C₄×Q₈	—	2	3	no	—
450	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
451	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
452	C₄×Q₈	C₂³×C₆₇	1	3	yes	—
453	C₄×Q₈	C₂³×C₆₇	1	6	yes	—
454	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
455	C₄×Q₈	C₂³×C₆₇	1	3	yes	—
456	C₄×Q₈	C₂³×C₆₇	1	3	yes	—
457	C₄×D₄	—	2	3	no	—
458	C₄×D₄	—	2	3	no	—
459	C₄×D₄	—	2	3	no	—
460	C₄×D₄	—	2	3	no	—
461	C₄×D₄	—	2	3	no	—
462	C₄×D₄	—	2	3	no	—
463	C₄×D₄	—	2	3	no	—
464	C₄×D₄	—	2	3	no	—
465	C₄×D₄	—	2	6	no	—
466	C₄×D₄	—	2	6	no	—
467	C₄×D₄	—	2	3	no	—
468	C₄×D₄	—	2	3	no	—
469	C₄×D₄	D₄×C₆₇	1	3	yes	—
470	C₄×D₄	D₄×C₆₇	1	3	yes	—
471	C₄×D₄	C₂³×C₆₇	1	3	yes	—
472	C₄×D₄	C₂³×C₆₇	1	6	yes	—
473	C₄×D₄	C₂³×C₆₇	1	3	yes	—
474	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
475	C₄×D₄	C₂³×C₆₇	1	3	yes	—
476	#117	—	2	3	no	—
477	#117	—	2	3	no	—
478	#117	—	2	6	no	—
479	#117	—	2	3	no	—
480	#117	—	2	3	no	—
481	#117	C₂³×C₆₇	1	3	yes	—
482	#117	C₂³×C₆₇	1	3	yes	—
483	#117	C₂³×C₆₇	1	3	yes	—
484	C₂×C₄⋊C₄	—	2	3	no	—
485	C₂×C₄⋊C₄	—	2	3	no	—
486	C₂×C₄⋊C₄	—	2	3	no	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
489	C₂×C₂²⋊C₄	—	2	3	no	—
490	C₂×C₂²⋊C₄	—	2	6	no	—
491	C₂×C₄²	—	2	3	no	—
492	C₂×C₄²	—	2	3	no	—
493	C₂×C₄²	—	2	3	no	—
494	C₂×C₄²	C₂³×C₆₇	1	3	yes	—
495	#107	C₂³×C₆₇	1	3	yes	—
496	#107	C₂³×C₆₇	1	6	yes	—
497	#107	C₂³×C₆₇	1	1	yes	characteristic
498	#106	C₂³×C₆₇	1	3	yes	—
499	#106	C₂³×C₆₇	1	3	yes	—
500	#103	C₂³×C₆₇	1	3	yes	—
501	#103	C₂³×C₆₇	1	6	yes	—
502	#103	C₂³×C₆₇	1	1	yes	characteristic
503	#103	C₂³×C₆₇	1	3	yes	—
504	#103	C₂³×C₆₇	1	3	yes	—
505	#102	C₂³×C₆₇	1	3	yes	—
506	#102	C₂³×C₆₇	1	6	yes	—
507	#102	C₂³×C₆₇	1	3	yes	—
508	#102	C₂³×C₆₇	1	1	yes	characteristic
509	#102	C₂³×C₆₇	1	3	yes	—
510	#97	C₂³×C₆₇	1	1	yes	characteristic
511	#97	C₂³×C₆₇	1	3	yes	—
512	#97	C₂³×C₆₇	1	3	yes	—
513	#97	C₂³×C₆₇	1	3	yes	—
514	C₄×C₈	C₂³×C₆₇	1	6	yes	—
515	C₂⁴	—	2	3	no	—
516	#41	—	2	8	no	—
517	#41	—	2	24	no	—
518	#41	—	2	6	no	—
519	#41	—	2	6	no	—
520	#41	C₂²×C₄×C₆₇	1	12	yes	—
521	#41	C₂²×C₄×C₆₇	1	4	yes	—
522	#41	C₂²×C₄×C₆₇	1	12	yes	complemented
523	#41	#41×C₆₇	1	4	yes	—
524	C₂×Q₈	—	2	8	no	—
525	C₂×Q₈	—	2	3	no	—
526	C₂×Q₈	—	2	6	no	—
527	C₂×Q₈	C₂²×C₄×C₆₇	1	12	yes	complemented
528	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
529	C₂×Q₈	C₂⁴×C₆₇	1	3	yes	—
530	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
531	C₂×D₄	—	2	3	no	—
532	C₂×D₄	—	2	3	no	—
533	C₂×D₄	—	2	24	no	—
534	C₂×D₄	—	2	3	no	—
535	C₂×D₄	—	2	6	no	—
536	C₂×D₄	C₂²×C₄×C₆₇	1	12	yes	—
537	C₂×D₄	C₂×D₄×C₆₇	1	3	yes	—
538	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
539	C₂×D₄	C₂⁴×C₆₇	1	3	yes	—
540	C₂²×C₄	—	2	3	no	—
541	C₂²×C₄	—	2	3	no	—
542	C₂²×C₄	—	2	3	no	—
543	C₂²×C₄	—	2	3	no	—
544	C₂²×C₄	—	2	3	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	3	no	—
547	C₂²×C₄	—	2	3	no	—
548	C₂²×C₄	—	2	3	no	—
549	C₂²×C₄	—	2	6	no	—
550	C₂²×C₄	—	8	6	no	—
551	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
552	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
554	Q₁₆	C₂²×C₄×C₆₇	1	12	yes	complemented
555	SD₁₆	C₂²×C₄×C₆₇	1	12	yes	complemented
556	SD₁₆	C₂²×C₄×C₆₇	1	24	yes	complemented
557	SD₁₆	C₂²×C₄×C₆₇	1	4	yes	complemented
558	D₈	C₂²×C₄×C₆₇	1	12	yes	complemented
559	M₁₆	—	2	6	no	—
560	M₁₆	C₂²×C₄×C₆₇	1	12	yes	complemented
561	C₂×C₈	—	2	6	no	—
562	C₂×C₈	C₂²×C₄×C₆₇	1	12	yes	complemented
563	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
564	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
565	C₂×C₈	C₂⁴×C₆₇	1	3	yes	—
566	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
567	C₄⋊C₄	—	2	3	no	—
568	C₄⋊C₄	—	2	3	no	—
569	C₄⋊C₄	—	2	6	no	—
570	C₄⋊C₄	—	2	3	no	—
571	C₄⋊C₄	—	2	3	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	3	no	—
574	C₄⋊C₄	C₂×D₄×C₆₇	1	3	yes	—
575	C₄⋊C₄	C₂×D₄×C₆₇	1	3	yes	—
576	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
577	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
578	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₄⋊C₄	C₂⁴×C₆₇	1	3	yes	—
580	C₂²⋊C₄	—	2	3	no	—
581	C₂²⋊C₄	—	2	3	no	—
582	C₂²⋊C₄	—	2	3	no	—
583	C₂²⋊C₄	—	2	3	no	—
584	C₂²⋊C₄	—	2	6	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	3	no	—
587	C₂²⋊C₄	C₂×D₄×C₆₇	1	6	yes	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	3	no	—
590	C₄²	—	2	3	no	—
591	C₄²	—	2	3	no	—
592	C₄²	—	2	6	no	—
593	C₄²	—	2	3	no	—
594	C₄²	—	2	3	no	—
595	C₄²	C₂×D₄×C₆₇	1	3	yes	—
596	C₄²	C₂×D₄×C₆₇	1	3	yes	—
597	C₄²	C₂⁴×C₆₇	1	3	yes	—
598	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
599	C₂³	—	2	1	no	—
600	C₂³	—	2	3	no	—
601	C₂³	—	2	12	no	—
602	C₂³	—	8	3	no	—
603	C₂³	—	8	3	no	—
604	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
605	Q₈	—	2	12	no	—
606	Q₈	—	2	3	no	—
607	Q₈	—	2	1	no	—
608	Q₈	C₄×D₄×C₆₇	1	4	yes	—
609	Q₈	C₂³×C₄×C₆₇	1	6	yes	—
610	Q₈	C₂³×C₄×C₆₇	1	2	yes	—
611	D₄	—	2	12	no	—
612	D₄	—	2	12	no	—
613	D₄	—	2	12	no	—
614	D₄	—	2	3	no	—
615	D₄	—	2	1	no	—
616	D₄	C₄×D₄×C₆₇	1	12	yes	—
617	D₄	C₂³×C₄×C₆₇	1	2	yes	—
618	D₄	C₂³×C₄×C₆₇	1	6	yes	—
619	C₂×C₄	—	2	12	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	3	no	—
622	C₂×C₄	—	2	12	no	—
623	C₂×C₄	—	2	12	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	3	no	—
627	C₂×C₄	—	2	3	no	—
628	C₂×C₄	—	4	3	no	—
629	C₂×C₄	—	4	3	no	—
630	C₂×C₄	—	4	6	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	8	6	no	—
633	C₂×C₄	—	8	3	no	—
634	C₂×C₄	—	8	3	no	—
635	C₂×C₄	—	8	3	no	—
636	C₂×C₄	—	8	3	no	—
637	C₂×C₄	C₂³×C₄×C₆₇	1	6	yes	—
638	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
640	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
642	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
643	C₂×C₄	C₂×#41×C₆₇	1	6	yes	—
644	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
645	C₈	—	2	1	no	—
646	C₈	—	2	3	no	—
647	C₈	C₂³×C₄×C₆₇	1	2	yes	—
648	C₈	C₂³×C₄×C₆₇	1	6	yes	—
649	C₂²	—	2	3	no	—
650	C₂²	—	2	3	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	6	no	—
653	C₂²	—	4	3	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	3	no	—
657	C₂²	—	8	12	no	—
658	C₂²	C₂×C₄×D₄×C₆₇	1	6	yes	—
659	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
660	C₄	—	2	1	no	—
661	C₄	—	2	3	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	3	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	6	no	—
666	C₄	—	4	3	no	—
667	C₄	—	4	3	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	C₂×C₄×D₄×C₆₇	1	6	yes	—
671	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
672	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
673	C₂	—	2	6	no	—
674	C₂	—	4	6	no	—
675	C₂	—	4	2	no	—
676	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
677	C₂	C₆₇×#3585	1	1	yes	characteristic
678	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#577×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₄×H(5,𝔽₂)×C₆₇	C₂	semidirect
4. C₆₇×#2951	C₂	semidirect
5. C₆₇×#2949	C₂	semidirect
6. C₆₇×#2947	C₂	semidirect
7. C₆₇×#2946	C₂	semidirect
8. C₄×#137×C₆₇	C₂	semidirect
9. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
10. C₆₇×#2943	C₂	semidirect
11. C₂×#440×C₆₇	C₂	semidirect
12. C₆₇×#2913	C₂	semidirect
13. C₆₇×#2898	C₂	semidirect
14. C₆₇×#2897	C₂	semidirect
15. C₆₇×#2875	C₂	semidirect
18. #577×C₆₇	C₄	semidirect
30. #520×C₆₇	C₂²	semidirect
32. #519×C₆₇	C₂²	semidirect
39. C₄×#41×C₆₇	C₂²	semidirect
41. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
44. #442×C₆₇	C₂²	semidirect
45. #442×C₆₇	C₂²	semidirect
46. #441×C₆₇	C₂²	semidirect
47. #441×C₆₇	C₂²	semidirect
48. #440×C₆₇	C₂²	semidirect
49. #440×C₆₇	C₂²	semidirect
50. #440×C₆₇	C₂²	semidirect
51. #440×C₆₇	C₂²	semidirect
52. #440×C₆₇	C₂²	semidirect
53. #440×C₆₇	C₂²	semidirect
54. #440×C₆₇	C₂²	semidirect
55. C₄×Q₁₆×C₆₇	C₂²	semidirect
56. C₄×SD₁₆×C₆₇	C₂²	semidirect
57. C₄×SD₁₆×C₆₇	C₂²	semidirect
58. C₄×D₈×C₆₇	C₂²	semidirect
59. #428×C₆₇	C₂²	semidirect
60. #428×C₆₇	C₂²	semidirect
61. #427×C₆₇	C₂²	semidirect
62. C₂×#107×C₆₇	C₂²	semidirect
63. #419×C₆₇	C₂²	semidirect
66. #417×C₆₇	C₂²	semidirect
68. #416×C₆₇	C₂²	semidirect
69. C₂×#103×C₆₇	C₂²	semidirect
71. #405×C₆₇	C₂²	semidirect
72. #405×C₆₇	C₂²	semidirect
73. C₄×M₁₆×C₆₇	C₂²	semidirect
74. C₂×#97×C₆₇	C₂²	semidirect
76. 2₋¹⁺⁴×C₆₇	C₂×C₄	semidirect
78. H(5,𝔽₂)×C₆₇	C₂×C₄	semidirect
89. #137×C₆₇	C₂×C₄	semidirect
90. AGL(1,ℤ/8)×C₆₇	C₂×C₄	semidirect
91. #135×C₆₇	C₂×C₄	semidirect
93. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
99. #131×C₆₇	C₂×C₄	semidirect
182. #41×C₆₇	C₂²×C₄	semidirect
187. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
214. Q₁₆×C₆₇	C₂²×C₄	semidirect
215. SD₁₆×C₆₇	C₂²×C₄	semidirect
216. SD₁₆×C₆₇	C₂²×C₄	semidirect
217. SD₁₆×C₆₇	C₂²×C₄	semidirect
218. D₈×C₆₇	C₂²×C₄	semidirect
220. M₁₆×C₆₇	C₂²×C₄	semidirect
222. C₂×C₈×C₆₇	C₂²×C₄	semidirect
333. #60174	C₆₇	direct (N × H)
341. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
342. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
343. #2951	C₂×C₆₇	semidirect
344. #2949	C₂×C₆₇	semidirect
345. #2947	C₂×C₆₇	semidirect
346. #2946	C₂×C₆₇	semidirect
347. C₄×#137	C₂×C₆₇	semidirect
348. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
349. #2943	C₂×C₆₇	semidirect
350. C₂×#440	C₂×C₆₇	semidirect
351. #2913	C₂×C₆₇	semidirect
352. #2898	C₂×C₆₇	semidirect
353. #2897	C₂×C₆₇	semidirect
354. #2875	C₂×C₆₇	semidirect
355. C₆₇	#60174	direct (N × H)
358. #577	C₄×C₆₇	semidirect
370. #520	C₂²×C₆₇	semidirect
372. #519	C₂²×C₆₇	semidirect
379. C₄×#41	C₂²×C₆₇	semidirect
381. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
384. #442	C₂²×C₆₇	semidirect
385. #442	C₂²×C₆₇	semidirect
386. #441	C₂²×C₆₇	semidirect
387. #441	C₂²×C₆₇	semidirect
388. #440	C₂²×C₆₇	semidirect
389. #440	C₂²×C₆₇	semidirect
390. #440	C₂²×C₆₇	semidirect
391. #440	C₂²×C₆₇	semidirect
392. #440	C₂²×C₆₇	semidirect
393. #440	C₂²×C₆₇	semidirect
394. #440	C₂²×C₆₇	semidirect
395. C₄×Q₁₆	C₂²×C₆₇	semidirect
396. C₄×SD₁₆	C₂²×C₆₇	semidirect
397. C₄×SD₁₆	C₂²×C₆₇	semidirect
398. C₄×D₈	C₂²×C₆₇	semidirect
399. #428	C₂²×C₆₇	semidirect
400. #428	C₂²×C₆₇	semidirect
401. #427	C₂²×C₆₇	semidirect
402. C₂×#107	C₂²×C₆₇	semidirect
403. #419	C₂²×C₆₇	semidirect
406. #417	C₂²×C₆₇	semidirect
408. #416	C₂²×C₆₇	semidirect
409. C₂×#103	C₂²×C₆₇	semidirect
411. #405	C₂²×C₆₇	semidirect
412. #405	C₂²×C₆₇	semidirect
413. C₄×M₁₆	C₂²×C₆₇	semidirect
414. C₂×#97	C₂²×C₆₇	semidirect
416. 2₋¹⁺⁴	C₂×C₄×C₆₇	semidirect
418. H(5,𝔽₂)	C₂×C₄×C₆₇	semidirect
429. #137	C₂×C₄×C₆₇	semidirect
430. AGL(1,ℤ/8)	C₂×C₄×C₆₇	semidirect
431. #135	C₂×C₄×C₆₇	semidirect
433. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
439. #131	C₂×C₄×C₆₇	semidirect
522. #41	C₂²×C₄×C₆₇	semidirect
527. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
554. Q₁₆	C₂²×C₄×C₆₇	semidirect
555. SD₁₆	C₂²×C₄×C₆₇	semidirect
556. SD₁₆	C₂²×C₄×C₆₇	semidirect
557. SD₁₆	C₂²×C₄×C₆₇	semidirect
558. D₈	C₂²×C₄×C₆₇	semidirect
560. M₁₆	C₂²×C₄×C₆₇	semidirect
562. 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
C₂×#577×C₆₇	2
C₄×2₋¹⁺⁴×C₆₇	2
C₄×H(5,𝔽₂)×C₆₇	2
C₆₇×#2951	2
C₆₇×#2949	2
C₆₇×#2947	2
C₆₇×#2946	2
C₄×#137×C₆₇	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2943	2
C₂×#440×C₆₇	2
C₆₇×#2913	2
C₆₇×#2898	2
C₆₇×#2897	2
C₆₇×#2875	2
#60174	67

Subgroups — C67×#60174 #30739425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60174 #30739425