Subgroups — C₂×C₆₇×#1954 #30700436

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊C₈×C₆₇	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1954	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₄×C₆₇	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
8	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
9	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₆₇	—	2	4	no	—
11	C₂×C₄×D₄×C₆₇	—	2	4	no	—
12	C₂×C₄×D₄×C₆₇	C₄	1	4	yes	—
13	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₆₇	C₄	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₆₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₆₇	—	2	4	no	—
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
19	C₂×C₂²⋊C₈×C₆₇	—	2	16	no	—
20	C₂×C₂²⋊C₈×C₆₇	C₂²	1	16	yes	complemented
21	C₂×C₄×C₈×C₆₇	—	2	4	no	—
22	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
23	C₂⁵×C₆₇	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₆₇	—	2	4	no	—
25	C₂²×D₄×C₆₇	—	2	4	no	—
26	C₂²×D₄×C₆₇	C₈	1	8	yes	complemented
27	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
28	C₂³×C₄×C₆₇	—	2	4	no	—
29	C₂³×C₄×C₆₇	—	2	4	no	—
30	C₂³×C₄×C₆₇	—	2	8	no	—
31	C₂³×C₄×C₆₇	—	2	8	no	—
32	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
37	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₆₇	—	2	4	no	—
39	C₂²×C₈×C₆₇	—	2	4	no	—
40	C₂²×C₈×C₆₇	—	2	8	no	—
41	C₂²×C₈×C₆₇	—	2	4	no	—
42	C₂²×C₈×C₆₇	D₄	1	8	yes	complemented
43	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
44	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
45	C₄×D₄×C₆₇	—	2	16	no	—
46	C₄×D₄×C₆₇	—	2	8	no	—
47	C₄×D₄×C₆₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
52	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₆₇	D₄	1	4	yes	—
54	C₂×C₄²×C₆₇	D₄	1	4	yes	—
55	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
56	C₄⋊C₈×C₆₇	—	2	8	no	—
57	C₂²⋊C₈×C₆₇	—	2	32	no	—
58	C₄×C₈×C₆₇	—	2	8	no	—
59	C₂⁴×C₆₇	—	2	4	no	—
60	C₂⁴×C₆₇	—	2	8	no	—
61	C₂⁴×C₆₇	—	2	4	no	—
62	C₂⁴×C₆₇	—	2	8	no	—
63	C₂⁴×C₆₇	C₂×C₈	1	8	yes	—
64	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
65	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×D₄×C₆₇	—	2	32	no	—
67	C₂×D₄×C₆₇	—	2	8	no	—
68	C₂×D₄×C₆₇	—	2	8	no	—
69	C₂×D₄×C₆₇	C₂×C₈	1	16	yes	complemented
70	C₂²×C₄×C₆₇	—	2	4	no	—
71	C₂²×C₄×C₆₇	—	2	4	no	—
72	C₂²×C₄×C₆₇	—	2	8	no	—
73	C₂²×C₄×C₆₇	—	2	8	no	—
74	C₂²×C₄×C₆₇	—	2	16	no	—
75	C₂²×C₄×C₆₇	—	2	4	no	—
76	C₂²×C₄×C₆₇	—	2	4	no	—
77	C₂²×C₄×C₆₇	—	2	8	no	—
78	C₂²×C₄×C₆₇	—	2	8	no	—
79	C₂²×C₄×C₆₇	—	4	16	no	—
80	C₂²×C₄×C₆₇	—	4	8	no	—
81	C₂²×C₄×C₆₇	—	4	8	no	—
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₆₇	C₂×C₈	1	4	yes	—
85	C₂²×C₄×C₆₇	M₁₆	1	4	yes	—
86	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₆₇	#41	1	4	yes	—
94	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₆₇	—	2	16	no	—
96	C₂×C₈×C₆₇	—	2	4	no	—
97	C₂×C₈×C₆₇	—	2	4	no	—
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	8	no	—
100	C₂×C₈×C₆₇	—	4	8	no	—
101	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	complemented
102	C₄⋊C₄×C₆₇	—	2	8	no	—
103	C₂²⋊C₄×C₆₇	—	2	16	no	—
104	C₄²×C₆₇	C₂²⋊C₄	1	8	yes	—
105	C₄²×C₆₇	C₂×D₄	1	4	yes	—
106	C₄²×C₆₇	C₂×D₄	1	4	yes	—
107	C₂³×C₆₇	—	2	4	no	—
108	C₂³×C₆₇	—	2	8	no	—
109	C₂³×C₆₇	—	2	4	no	—
110	C₂³×C₆₇	—	2	8	no	—
111	C₂³×C₆₇	—	2	16	no	—
112	C₂³×C₆₇	—	2	32	no	—
113	C₂³×C₆₇	—	4	8	no	—
114	C₂³×C₆₇	—	4	8	no	—
115	C₂³×C₆₇	—	4	16	no	—
116	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₆₇	C₄×D₄	1	4	yes	—
118	C₂³×C₆₇	C₂²×C₈	1	8	yes	—
119	C₂³×C₆₇	C₂²×C₈	1	2	yes	—
120	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
121	C₂³×C₆₇	#131	1	4	yes	—
122	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
123	D₄×C₆₇	—	2	32	no	—
124	C₂×C₄×C₆₇	—	2	4	no	—
125	C₂×C₄×C₆₇	—	2	8	no	—
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	4	8	no	—
129	C₂×C₄×C₆₇	—	4	8	no	—
130	C₂×C₄×C₆₇	—	4	4	no	—
131	C₂×C₄×C₆₇	—	4	4	no	—
132	C₂×C₄×C₆₇	—	4	16	no	—
133	C₂×C₄×C₆₇	C₂²⋊C₈	1	16	yes	complemented
134	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
137	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₆₇	#121	1	8	yes	—
139	C₂×C₄×C₆₇	#124	1	4	yes	—
140	C₂×C₄×C₆₇	#127	1	4	yes	—
141	C₂×C₄×C₆₇	C₂²×C₈	1	4	yes	—
142	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
145	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
147	C₈×C₆₇	—	2	8	no	—
148	C₈×C₆₇	—	4	4	no	—
149	C₂²×C₆₇	—	2	8	no	—
150	C₂²×C₆₇	—	2	16	no	—
151	C₂²×C₆₇	—	4	4	no	—
152	C₂²×C₆₇	—	4	8	no	—
153	C₂²×C₆₇	—	4	32	no	—
154	C₂²×C₆₇	—	4	4	no	—
155	C₂²×C₆₇	#390	1	4	yes	—
156	C₂²×C₆₇	C₂×C₂²⋊C₈	1	4	yes	—
157	C₂²×C₆₇	#408	1	4	yes	—
158	C₂²×C₆₇	C₈×D₄	1	8	yes	—
159	C₂²×C₆₇	#436	1	8	yes	—
160	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
162	C₂²×C₆₇	C₂³×C₈	1	1	yes	characteristic
163	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
164	C₂²×C₆₇	C₂×#131	1	2	yes	—
165	C₄×C₆₇	—	2	4	no	—
166	C₄×C₆₇	—	4	4	no	—
167	C₄×C₆₇	#390	1	4	yes	—
168	C₄×C₆₇	C₂×C₂²⋊C₈	1	8	yes	complemented
169	C₄×C₆₇	C₂×#121	1	2	yes	—
170	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
171	C₄×C₆₇	C₂×#127	1	1	yes	characteristic
172	C₂×#1954	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₆₇	—	4	8	no	—
174	C₂×C₆₇	#1954	1	8	yes	direct product factor
175	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
176	C₂×C₆₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
177	C₂×C₆₇	C₂×#408	1	1	yes	characteristic
178	C₂×C₆₇	C₂×C₈×D₄	1	2	yes	—
179	C₂×C₆₇	C₂×#436	1	2	yes	—
180	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic
181	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
182	C₂²×C₂²⋊C₈	C₂×C₆₇	1	4	yes	complemented
183	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
184	#1954	C₂×C₆₇	1	8	yes	direct product factor
185	C₆₇	C₂×#1954	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³×D₄	C₄×C₆₇	1	1	yes	characteristic
187	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
188	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
189	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
190	C₂×C₄×D₄	—	2	4	no	—
191	C₂×C₄×D₄	—	2	4	no	—
192	C₂×C₄×D₄	C₄×C₆₇	1	4	yes	—
193	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
194	C₂²×C₄⋊C₄	C₄×C₆₇	1	1	yes	characteristic
195	C₂²×C₂²⋊C₄	C₄×C₆₇	1	2	yes	—
196	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×C₄⋊C₈	—	2	4	no	—
198	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
199	C₂×C₂²⋊C₈	—	2	16	no	—
200	C₂×C₂²⋊C₈	C₂²×C₆₇	1	16	yes	complemented
201	C₂×C₄×C₈	—	2	4	no	—
202	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
203	C₂⁵	C₂×C₄×C₆₇	1	2	yes	—
204	C₂²×D₄	—	2	4	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	C₈×C₆₇	1	8	yes	complemented
207	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	8	no	—
211	C₂³×C₄	—	2	8	no	—
212	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
213	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
214	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
217	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	2	8	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	D₄×C₆₇	1	8	yes	complemented
223	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
224	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
225	C₄×D₄	—	2	16	no	—
226	C₄×D₄	—	2	8	no	—
227	C₄×D₄	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
230	C₂×C₂²⋊C₄	—	2	8	no	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
232	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
233	C₂×C₄²	D₄×C₆₇	1	4	yes	—
234	C₂×C₄²	D₄×C₆₇	1	4	yes	—
235	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
236	C₄⋊C₈	—	2	8	no	—
237	C₂²⋊C₈	—	2	32	no	—
238	C₄×C₈	—	2	8	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	—	2	8	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	8	no	—
243	C₂⁴	C₂×C₈×C₆₇	1	8	yes	—
244	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
245	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
246	C₂×D₄	—	2	8	no	—
247	C₂×D₄	—	2	8	no	—
248	C₂×D₄	—	2	32	no	—
249	C₂×D₄	C₂×C₈×C₆₇	1	16	yes	complemented
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	16	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	16	no	—
260	C₂²×C₄	—	4	8	no	—
261	C₂²×C₄	—	4	8	no	—
262	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
264	C₂²×C₄	C₂×C₈×C₆₇	1	4	yes	—
265	C₂²×C₄	M₁₆×C₆₇	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
271	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
273	C₂²×C₄	#41×C₆₇	1	4	yes	—
274	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
275	C₂×C₈	—	2	16	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	8	no	—
281	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	complemented
282	C₄⋊C₄	—	2	8	no	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₄²	C₂²⋊C₄×C₆₇	1	8	yes	—
285	C₄²	C₂×D₄×C₆₇	1	4	yes	—
286	C₄²	C₂×D₄×C₆₇	1	4	yes	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	2	32	no	—
293	C₂³	—	4	8	no	—
294	C₂³	—	4	8	no	—
295	C₂³	—	4	16	no	—
296	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
297	C₂³	C₄×D₄×C₆₇	1	4	yes	—
298	C₂³	C₂²×C₈×C₆₇	1	8	yes	—
299	C₂³	C₂²×C₈×C₆₇	1	2	yes	—
300	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
301	C₂³	#131×C₆₇	1	4	yes	—
302	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
303	D₄	—	2	32	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	16	no	—
313	C₂×C₄	C₂²⋊C₈×C₆₇	1	16	yes	complemented
314	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
315	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
316	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
317	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
318	C₂×C₄	#121×C₆₇	1	8	yes	—
319	C₂×C₄	#124×C₆₇	1	4	yes	—
320	C₂×C₄	#127×C₆₇	1	4	yes	—
321	C₂×C₄	C₂²×C₈×C₆₇	1	4	yes	—
322	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
324	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
325	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
327	C₈	—	2	8	no	—
328	C₈	—	4	4	no	—
329	C₂²	—	2	8	no	—
330	C₂²	—	2	16	no	—
331	C₂²	—	4	4	no	—
332	C₂²	—	4	4	no	—
333	C₂²	—	4	8	no	—
334	C₂²	—	4	32	no	—
335	C₂²	#390×C₆₇	1	4	yes	—
336	C₂²	C₂×C₂²⋊C₈×C₆₇	1	4	yes	—
337	C₂²	#408×C₆₇	1	4	yes	—
338	C₂²	C₈×D₄×C₆₇	1	8	yes	—
339	C₂²	#436×C₆₇	1	8	yes	—
340	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
341	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
342	C₂²	C₂³×C₈×C₆₇	1	1	yes	characteristic
343	C₂²	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
344	C₂²	C₂×#131×C₆₇	1	2	yes	—
345	C₄	—	2	4	no	—
346	C₄	—	4	4	no	—
347	C₄	#390×C₆₇	1	4	yes	—
348	C₄	C₂×C₂²⋊C₈×C₆₇	1	8	yes	complemented
349	C₄	C₂×#121×C₆₇	1	2	yes	—
350	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
351	C₄	C₂×#127×C₆₇	1	1	yes	characteristic
352	C₂	—	4	8	no	—
353	C₂	C₆₇×#1954	1	8	yes	direct product factor
354	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
355	C₂	C₂²×C₂²⋊C₈×C₆₇	1	1	yes	characteristic
356	C₂	C₂×#408×C₆₇	1	1	yes	characteristic
357	C₂	C₂×C₈×D₄×C₆₇	1	2	yes	—
358	C₂	C₂×#436×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂²	C₂³×C₈×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂⁴×C₆₇	C₂²×C₄
prime radical	C₂³×D₄×C₆₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₆₇	C₂	semidirect
3. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
4. C₂²×C₄×C₈×C₆₇	C₂	semidirect
5. C₆₇×#1954	C₂	direct (N × H)
18. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
20. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
22. C₂×C₄×C₈×C₆₇	C₂²	semidirect
26. C₂²×D₄×C₆₇	C₈	semidirect
42. C₂²×C₈×C₆₇	D₄	semidirect
69. C₂×D₄×C₆₇	C₂×C₈	semidirect
101. C₂×C₈×C₆₇	C₂×D₄	semidirect
133. C₂×C₄×C₆₇	C₂²⋊C₈	semidirect
168. C₄×C₆₇	C₂×C₂²⋊C₈	semidirect
172. C₂×#1954	C₆₇	direct (N × H)
174. C₂×C₆₇	#1954	direct (N × H)
181. C₂²×C₄⋊C₈	C₂×C₆₇	semidirect
182. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
183. C₂²×C₄×C₈	C₂×C₆₇	semidirect
184. #1954	C₂×C₆₇	direct (N × H)
185. C₆₇	C₂×#1954	direct (N × H)
198. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
200. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
202. C₂×C₄×C₈	C₂²×C₆₇	semidirect
206. C₂²×D₄	C₈×C₆₇	semidirect
222. C₂²×C₈	D₄×C₆₇	semidirect
249. C₂×D₄	C₂×C₈×C₆₇	semidirect
281. C₂×C₈	C₂×D₄×C₆₇	semidirect
313. C₂×C₄	C₂²⋊C₈×C₆₇	semidirect
348. C₄	C₂×C₂²⋊C₈×C₆₇	semidirect
353. C₂	C₆₇×#1954	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₆₇	2
C₂²×C₄⋊C₈×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₆₇×#1954	2
C₂×#1954	67

Subgroups — C2×C67×#1954 #30700436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1954 #30700436