Subgroups — C₂×C₆₇×#3371 #30740565

Order 17152.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#557×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3371	C₂	1	16	yes	maximal, direct product factor
4	C₂×#490×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#489×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#488×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#478×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#476×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#464×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic
13	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	#559×C₆₇	—	2	4	no	—
21	#559×C₆₇	C₂²	1	8	yes	—
22	#557×C₆₇	—	2	4	no	—
23	#557×C₆₇	C₂²	1	8	yes	complemented
24	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	—	2	1	no	—
28	C₂×#125×C₆₇	—	2	1	no	—
29	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₇	—	2	1	no	—
32	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#123×C₆₇	—	2	1	no	—
35	C₂×#123×C₆₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	—	2	1	no	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	#490×C₆₇	C₂²	1	8	yes	—
46	#489×C₆₇	C₂²	1	8	yes	complemented
47	#488×C₆₇	C₂²	1	8	yes	complemented
48	#479×C₆₇	C₂²	1	8	yes	complemented
49	#478×C₆₇	C₂²	1	8	yes	complemented
50	#476×C₆₇	C₂²	1	8	yes	complemented
51	#464×C₆₇	C₂²	1	8	yes	complemented
52	#464×C₆₇	C₂²	1	8	yes	complemented
53	#460×C₆₇	C₂²	1	8	yes	—
54	#446×C₆₇	C₂²	1	8	yes	complemented
55	#441×C₆₇	C₂²	1	8	yes	complemented
56	#440×C₆₇	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₆₇	—	2	1	no	—
78	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₆₇	—	2	1	no	—
82	C₂²×D₄×C₆₇	—	2	1	no	—
83	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂×Q₁₆×C₆₇	—	2	4	no	—
88	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₆₇	—	2	4	no	—
90	C₂×SD₁₆×C₆₇	—	2	4	no	—
91	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₇	—	2	8	no	—
98	C₄⋊Q₈×C₆₇	—	2	2	no	—
99	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
100	#127×C₆₇	—	2	2	no	—
101	#127×C₆₇	C₂³	1	4	yes	—
102	#125×C₆₇	—	2	8	no	—
103	#125×C₆₇	—	2	8	no	—
104	#125×C₆₇	—	2	2	no	—
105	#125×C₆₇	—	2	2	no	—
106	#125×C₆₇	C₂³	1	4	yes	—
107	#125×C₆₇	C₂³	1	4	yes	—
108	#124×C₆₇	—	2	8	no	—
109	#124×C₆₇	—	2	2	no	—
110	#124×C₆₇	—	2	2	no	—
111	#124×C₆₇	C₂³	1	4	yes	—
112	#124×C₆₇	C₂³	1	4	yes	—
113	#123×C₆₇	—	2	8	no	—
114	#123×C₆₇	—	2	8	no	—
115	C₄×Q₈×C₆₇	—	2	8	no	—
116	C₄×Q₈×C₆₇	—	2	2	no	—
117	C₄×Q₈×C₆₇	—	2	2	no	—
118	C₄×Q₈×C₆₇	—	2	2	no	—
119	C₄×Q₈×C₆₇	—	2	2	no	—
120	C₄×Q₈×C₆₇	D₄	1	4	yes	—
121	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
122	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
123	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
124	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
125	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	C₄×D₄×C₆₇	—	2	2	no	—
128	C₄×D₄×C₆₇	—	2	2	no	—
129	C₄×D₄×C₆₇	C₂³	1	4	yes	—
130	C₄×D₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂×C₄²×C₆₇	—	2	1	no	—
154	C₂×C₄²×C₆₇	—	2	1	no	—
155	C₂×C₄²×C₆₇	—	2	1	no	—
156	C₂×C₄²×C₆₇	—	2	1	no	—
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	#107×C₆₇	C₂³	1	4	yes	—
161	#106×C₆₇	C₂³	1	4	yes	—
162	#106×C₆₇	C₂³	1	4	yes	—
163	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
165	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
166	#103×C₆₇	C₂³	1	4	yes	—
167	#103×C₆₇	C₂³	1	4	yes	—
168	#103×C₆₇	C₂³	1	4	yes	—
169	#103×C₆₇	C₂³	1	4	yes	—
170	#102×C₆₇	C₂³	1	4	yes	—
171	#102×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	#102×C₆₇	C₂³	1	4	yes	—
174	#102×C₆₇	C₂³	1	4	yes	—
175	#102×C₆₇	C₂³	1	4	yes	—
176	#97×C₆₇	C₂³	1	4	yes	—
177	#97×C₆₇	C₂³	1	4	yes	—
178	C₄×C₈×C₆₇	C₂³	1	4	yes	—
179	C₂⁴×C₆₇	—	2	1	no	—
180	C₂⁴×C₆₇	—	2	1	no	—
181	C₂×Q₈×C₆₇	—	2	1	no	—
182	C₂×Q₈×C₆₇	—	2	1	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	—	2	2	no	—
187	C₂×Q₈×C₆₇	—	4	2	no	—
188	C₂×Q₈×C₆₇	—	4	4	no	—
189	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
190	C₂×Q₈×C₆₇	#41	1	4	yes	—
191	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
192	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
193	C₂×D₄×C₆₇	—	2	1	no	—
194	C₂×D₄×C₆₇	—	2	1	no	—
195	C₂×D₄×C₆₇	—	2	4	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	2	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	2	2	no	—
200	C₂×D₄×C₆₇	—	2	2	no	—
201	C₂×D₄×C₆₇	—	4	4	no	—
202	C₂×D₄×C₆₇	—	8	2	no	—
203	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	—	2	1	no	—
206	C₂²×C₄×C₆₇	—	2	1	no	—
207	C₂²×C₄×C₆₇	—	2	1	no	—
208	C₂²×C₄×C₆₇	—	2	1	no	—
209	C₂²×C₄×C₆₇	—	2	1	no	—
210	C₂²×C₄×C₆₇	—	2	1	no	—
211	C₂²×C₄×C₆₇	—	2	4	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	8	2	no	—
214	C₂²×C₄×C₆₇	—	8	2	no	—
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₆₇	—	2	8	no	—
223	SD₁₆×C₆₇	—	2	8	no	—
224	SD₁₆×C₆₇	—	2	8	no	—
225	C₂×C₈×C₆₇	—	2	2	no	—
226	C₂×C₈×C₆₇	—	2	2	no	—
227	C₂×C₈×C₆₇	—	2	2	no	—
228	C₂×C₈×C₆₇	—	2	2	no	—
229	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
230	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
232	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	1	no	—
243	C₄⋊C₄×C₆₇	—	2	1	no	—
244	C₄⋊C₄×C₆₇	—	2	1	no	—
245	C₄⋊C₄×C₆₇	—	2	1	no	—
246	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
249	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²⋊C₄×C₆₇	—	2	4	no	—
254	C₂²⋊C₄×C₆₇	—	2	4	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₄²×C₆₇	—	2	4	no	—
260	C₄²×C₆₇	—	2	4	no	—
261	C₄²×C₆₇	—	2	4	no	—
262	C₄²×C₆₇	—	2	4	no	—
263	C₄²×C₆₇	C₂×D₄	1	2	yes	—
264	C₄²×C₆₇	C₂×D₄	1	2	yes	—
265	C₄²×C₆₇	C₂×D₄	1	2	yes	—
266	C₄²×C₆₇	C₂⁴	1	2	yes	—
267	C₄²×C₆₇	C₂⁴	1	2	yes	—
268	C₄²×C₆₇	C₂⁴	1	2	yes	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	4	2	no	—
272	C₂³×C₆₇	—	4	2	no	—
273	C₂³×C₆₇	—	4	2	no	—
274	C₂³×C₆₇	—	4	2	no	—
275	C₂³×C₆₇	—	4	2	no	—
276	C₂³×C₆₇	—	4	2	no	—
277	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₆₇	—	2	4	no	—
279	Q₈×C₆₇	—	2	2	no	—
280	Q₈×C₆₇	—	2	2	no	—
281	Q₈×C₆₇	—	2	2	no	—
282	Q₈×C₆₇	—	4	4	no	—
283	Q₈×C₆₇	—	4	8	no	—
284	Q₈×C₆₇	—	4	2	no	—
285	Q₈×C₆₇	C₂×#41	1	4	yes	—
286	D₄×C₆₇	—	2	2	no	—
287	D₄×C₆₇	—	2	2	no	—
288	D₄×C₆₇	—	2	2	no	—
289	D₄×C₆₇	—	2	2	no	—
290	D₄×C₆₇	—	4	8	no	—
291	D₄×C₆₇	—	4	2	no	—
292	D₄×C₆₇	—	4	2	no	—
293	D₄×C₆₇	—	8	4	no	—
294	C₂×C₄×C₆₇	—	2	4	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	4	2	no	—
308	C₂×C₄×C₆₇	—	4	2	no	—
309	C₂×C₄×C₆₇	—	4	2	no	—
310	C₂×C₄×C₆₇	—	4	2	no	—
311	C₂×C₄×C₆₇	—	4	2	no	—
312	C₂×C₄×C₆₇	—	8	4	no	—
313	C₂×C₄×C₆₇	—	8	4	no	—
314	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
322	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
323	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
324	C₈×C₆₇	—	2	2	no	—
325	C₈×C₆₇	—	2	2	no	—
326	C₈×C₆₇	—	2	2	no	—
327	C₈×C₆₇	—	2	2	no	—
328	C₂²×C₆₇	—	4	2	no	—
329	C₂²×C₆₇	—	4	2	no	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	8	4	no	—
335	C₂²×C₆₇	—	8	4	no	—
336	C₂²×C₆₇	#548	1	2	yes	—
337	C₂²×C₆₇	#575	1	2	yes	—
338	C₂²×C₆₇	#577	1	2	yes	—
339	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
340	C₄×C₆₇	—	2	4	no	—
341	C₄×C₆₇	—	2	2	no	—
342	C₄×C₆₇	—	2	2	no	—
343	C₄×C₆₇	—	2	2	no	—
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	4	2	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	—	4	2	no	—
351	C₄×C₆₇	—	4	2	no	—
352	C₄×C₆₇	#548	1	2	yes	—
353	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
354	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂×#3371	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂×C₆₇	—	8	2	no	—
357	C₂×C₆₇	—	8	2	no	—
358	C₂×C₆₇	#3371	1	4	yes	direct product factor
359	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
360	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
361	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
362	C₂×#559	C₂×C₆₇	1	1	yes	characteristic
363	C₂×#557	C₂×C₆₇	1	1	yes	characteristic, complemented
364	#3371	C₂×C₆₇	1	16	yes	direct product factor
365	C₂×#490	C₂×C₆₇	1	1	yes	characteristic
366	C₂×#489	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₂×#488	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
369	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
370	C₂×#476	C₂×C₆₇	1	1	yes	characteristic, complemented
371	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
372	C₂×#464	C₂×C₆₇	1	1	yes	characteristic, complemented
373	C₂×#460	C₂×C₆₇	1	1	yes	characteristic
374	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
376	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
377	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₆₇	C₂×#3371	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
380	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
381	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
382	#559	—	2	4	no	—
383	#559	C₂²×C₆₇	1	8	yes	—
384	#557	—	2	4	no	—
385	#557	C₂²×C₆₇	1	8	yes	complemented
386	C₂×C₄⋊Q₈	—	2	1	no	—
387	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×#125	—	2	1	no	—
390	C₂×#125	—	2	1	no	—
391	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
392	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×#124	—	2	1	no	—
394	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
395	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×#123	—	2	1	no	—
397	C₂×#123	—	2	1	no	—
398	C₂×C₄×Q₈	—	2	1	no	—
399	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
402	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×C₄×D₄	—	2	1	no	—
405	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
407	#490	C₂²×C₆₇	1	8	yes	—
408	#489	C₂²×C₆₇	1	8	yes	complemented
409	#488	C₂²×C₆₇	1	8	yes	complemented
410	#479	C₂²×C₆₇	1	8	yes	complemented
411	#478	C₂²×C₆₇	1	8	yes	complemented
412	#476	C₂²×C₆₇	1	8	yes	complemented
413	#464	C₂²×C₆₇	1	8	yes	complemented
414	#464	C₂²×C₆₇	1	8	yes	complemented
415	#460	C₂²×C₆₇	1	8	yes	—
416	#446	C₂²×C₆₇	1	8	yes	complemented
417	#441	C₂²×C₆₇	1	8	yes	complemented
418	#440	C₂²×C₆₇	1	8	yes	complemented
419	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
420	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	—	2	1	no	—
449	C₂×Q₁₆	—	2	4	no	—
450	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
451	C₂×SD₁₆	—	2	4	no	—
452	C₂×SD₁₆	—	2	4	no	—
453	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
454	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
455	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
459	C₄⋊Q₈	—	2	8	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
462	#127	—	2	2	no	—
463	#127	C₂³×C₆₇	1	4	yes	—
464	#125	—	2	8	no	—
465	#125	—	2	8	no	—
466	#125	—	2	2	no	—
467	#125	—	2	2	no	—
468	#125	C₂³×C₆₇	1	4	yes	—
469	#125	C₂³×C₆₇	1	4	yes	—
470	#124	—	2	8	no	—
471	#124	—	2	2	no	—
472	#124	—	2	2	no	—
473	#124	C₂³×C₆₇	1	4	yes	—
474	#124	C₂³×C₆₇	1	4	yes	—
475	#123	—	2	8	no	—
476	#123	—	2	8	no	—
477	C₄×Q₈	—	2	8	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	D₄×C₆₇	1	4	yes	—
483	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
484	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
485	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
486	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
487	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	C₂³×C₆₇	1	4	yes	—
492	C₄×D₄	C₂³×C₆₇	1	4	yes	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
504	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
522	#107	C₂³×C₆₇	1	4	yes	—
523	#106	C₂³×C₆₇	1	4	yes	—
524	#106	C₂³×C₆₇	1	4	yes	—
525	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
526	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
527	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
528	#103	C₂³×C₆₇	1	4	yes	—
529	#103	C₂³×C₆₇	1	4	yes	—
530	#103	C₂³×C₆₇	1	4	yes	—
531	#103	C₂³×C₆₇	1	4	yes	—
532	#102	C₂³×C₆₇	1	4	yes	—
533	#102	C₂³×C₆₇	1	4	yes	—
534	#102	C₂³×C₆₇	1	4	yes	—
535	#102	C₂³×C₆₇	1	4	yes	—
536	#102	C₂³×C₆₇	1	4	yes	—
537	#102	C₂³×C₆₇	1	4	yes	—
538	#97	C₂³×C₆₇	1	4	yes	—
539	#97	C₂³×C₆₇	1	4	yes	—
540	C₄×C₈	C₂³×C₆₇	1	4	yes	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	4	2	no	—
550	C₂×Q₈	—	4	4	no	—
551	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
552	C₂×Q₈	#41×C₆₇	1	4	yes	—
553	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
554	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	8	2	no	—
565	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
566	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	—	8	2	no	—
577	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
584	Q₁₆	—	2	8	no	—
585	SD₁₆	—	2	8	no	—
586	SD₁₆	—	2	8	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	—	2	2	no	—
591	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
592	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
593	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
594	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
609	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
610	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
611	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	C₂×D₄×C₆₇	1	2	yes	—
626	C₄²	C₂×D₄×C₆₇	1	2	yes	—
627	C₄²	C₂×D₄×C₆₇	1	2	yes	—
628	C₄²	C₂⁴×C₆₇	1	2	yes	—
629	C₄²	C₂⁴×C₆₇	1	2	yes	—
630	C₄²	C₂⁴×C₆₇	1	2	yes	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	—	4	2	no	—
636	C₂³	—	4	2	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	2	no	—
639	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
640	Q₈	—	2	4	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	8	no	—
646	Q₈	—	4	2	no	—
647	Q₈	C₂×#41×C₆₇	1	4	yes	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	8	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	2	no	—
655	D₄	—	8	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
683	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
684	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
685	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₈	—	2	2	no	—
689	C₈	—	2	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	8	4	no	—
697	C₂²	—	8	4	no	—
698	C₂²	#548×C₆₇	1	2	yes	—
699	C₂²	#575×C₆₇	1	2	yes	—
700	C₂²	#577×C₆₇	1	2	yes	—
701	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	#548×C₆₇	1	2	yes	—
715	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
716	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
717	C₂	—	8	2	no	—
718	C₂	—	8	2	no	—
719	C₂	C₆₇×#3371	1	4	yes	direct product factor
720	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
721	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
722	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#557×C₆₇	C₂	semidirect
3. C₆₇×#3371	C₂	direct (N × H)
5. C₂×#489×C₆₇	C₂	semidirect
6. C₂×#488×C₆₇	C₂	semidirect
7. C₂×#479×C₆₇	C₂	semidirect
8. C₂×#478×C₆₇	C₂	semidirect
9. C₂×#476×C₆₇	C₂	semidirect
10. C₂×#464×C₆₇	C₂	semidirect
11. C₂×#464×C₆₇	C₂	semidirect
13. C₂×#446×C₆₇	C₂	semidirect
14. C₂×#441×C₆₇	C₂	semidirect
15. C₂×#440×C₆₇	C₂	semidirect
16. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
23. #557×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #488×C₆₇	C₂²	semidirect
48. #479×C₆₇	C₂²	semidirect
49. #478×C₆₇	C₂²	semidirect
50. #476×C₆₇	C₂²	semidirect
51. #464×C₆₇	C₂²	semidirect
52. #464×C₆₇	C₂²	semidirect
54. #446×C₆₇	C₂²	semidirect
55. #441×C₆₇	C₂²	semidirect
56. #440×C₆₇	C₂²	semidirect
57. C₄×SD₁₆×C₆₇	C₂²	semidirect
355. C₂×#3371	C₆₇	direct (N × H)
358. C₂×C₆₇	#3371	direct (N × H)
363. C₂×#557	C₂×C₆₇	semidirect
364. #3371	C₂×C₆₇	direct (N × H)
366. C₂×#489	C₂×C₆₇	semidirect
367. C₂×#488	C₂×C₆₇	semidirect
368. C₂×#479	C₂×C₆₇	semidirect
369. C₂×#478	C₂×C₆₇	semidirect
370. C₂×#476	C₂×C₆₇	semidirect
371. C₂×#464	C₂×C₆₇	semidirect
372. C₂×#464	C₂×C₆₇	semidirect
374. C₂×#446	C₂×C₆₇	semidirect
375. C₂×#441	C₂×C₆₇	semidirect
376. C₂×#440	C₂×C₆₇	semidirect
377. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
378. C₆₇	C₂×#3371	direct (N × H)
385. #557	C₂²×C₆₇	semidirect
408. #489	C₂²×C₆₇	semidirect
409. #488	C₂²×C₆₇	semidirect
410. #479	C₂²×C₆₇	semidirect
411. #478	C₂²×C₆₇	semidirect
412. #476	C₂²×C₆₇	semidirect
413. #464	C₂²×C₆₇	semidirect
414. #464	C₂²×C₆₇	semidirect
416. #446	C₂²×C₆₇	semidirect
417. #441	C₂²×C₆₇	semidirect
418. #440	C₂²×C₆₇	semidirect
419. C₄×SD₁₆	C₂²×C₆₇	semidirect
719. C₂	C₆₇×#3371	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×#559×C₆₇	2
C₂×#557×C₆₇	2
C₆₇×#3371	2
C₂×#490×C₆₇	2
C₂×#489×C₆₇	2
C₂×#488×C₆₇	2
C₂×#479×C₆₇	2
C₂×#478×C₆₇	2
C₂×#476×C₆₇	2
C₂×#464×C₆₇	2
C₂×#460×C₆₇	2
C₂×#446×C₆₇	2
C₂×#441×C₆₇	2
C₂×#440×C₆₇	2
C₂×C₄×SD₁₆×C₆₇	2
C₂×#3371	67

Subgroups — C2×C67×#3371 #30740565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3371 #30740565