Subgroups — C₂×C₆₇×#2486 #30714006

Order 17152.

3678 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₆₇	C₂	1	2	yes	maximal
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2486	C₂	1	16	yes	maximal, direct product factor
5	C₂×#398×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#397×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#389×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#381×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#380×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#123×C₆₇	—	2	16	no	—
16	C₂×#123×C₆₇	C₂²	1	16	yes	—
17	C₂×C₄×D₄×C₆₇	—	2	8	no	—
18	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₆₇	—	2	8	no	—
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₆₇	C₂²	1	8	yes	complemented
26	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
28	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
31	#398×C₆₇	C₂²	1	16	yes	complemented
32	#397×C₆₇	C₂²	1	16	yes	complemented
33	#389×C₆₇	C₂²	1	16	yes	complemented
34	#381×C₆₇	C₂²	1	16	yes	complemented
35	#380×C₆₇	C₂²	1	8	yes	complemented
36	#380×C₆₇	C₂²	1	16	yes	complemented
37	C₂×#95×C₆₇	C₂²	1	4	yes	—
38	C₂×#95×C₆₇	C₂²	1	2	yes	—
39	C₂×#95×C₆₇	C₂²	1	4	yes	—
40	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
41	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₆₇	—	2	4	no	—
43	C₂²×D₄×C₆₇	—	2	4	no	—
44	C₂²×D₄×C₆₇	D₄	1	8	yes	—
45	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
46	C₂³×C₄×C₆₇	—	2	8	no	—
47	C₂³×C₄×C₆₇	—	2	8	no	—
48	C₂³×C₄×C₆₇	—	2	8	no	—
49	C₂³×C₄×C₆₇	—	2	8	no	—
50	C₂³×C₄×C₆₇	—	2	4	no	—
51	C₂³×C₄×C₆₇	—	2	8	no	—
52	C₂³×C₄×C₆₇	D₄	1	8	yes	—
53	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
54	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
60	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
63	#123×C₆₇	—	2	64	no	—
64	C₄×D₄×C₆₇	—	2	32	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	32	no	—
68	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
69	C₂×C₄⋊C₄×C₆₇	—	2	16	no	—
70	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
71	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
75	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
79	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
84	C₂×C₄²×C₆₇	—	2	4	no	—
85	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
86	#95×C₆₇	C₂³	1	16	yes	—
87	#95×C₆₇	C₂³	1	8	yes	—
88	#95×C₆₇	C₂³	1	16	yes	—
89	C₂⁴×C₆₇	—	2	4	no	—
90	C₂⁴×C₆₇	—	2	4	no	—
91	C₂⁴×C₆₇	—	2	2	no	—
92	C₂⁴×C₆₇	—	2	4	no	—
93	C₂⁴×C₆₇	—	2	2	no	—
94	C₂⁴×C₆₇	—	2	4	no	—
95	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
96	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
97	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
98	C₂⁴×C₆₇	#41	1	4	yes	—
99	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
100	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
101	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
102	C₂×D₄×C₆₇	—	2	32	no	—
103	C₂×D₄×C₆₇	—	2	8	no	—
104	C₂×D₄×C₆₇	—	2	8	no	—
105	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	—	2	4	no	—
108	C₂²×C₄×C₆₇	—	2	2	no	—
109	C₂²×C₄×C₆₇	—	2	32	no	—
110	C₂²×C₄×C₆₇	—	2	16	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	8	no	—
113	C₂²×C₄×C₆₇	—	2	8	no	—
114	C₂²×C₄×C₆₇	—	2	2	no	—
115	C₂²×C₄×C₆₇	—	2	16	no	—
116	C₂²×C₄×C₆₇	—	2	8	no	—
117	C₂²×C₄×C₆₇	—	2	16	no	—
118	C₂²×C₄×C₆₇	—	2	8	no	—
119	C₂²×C₄×C₆₇	—	2	16	no	—
120	C₂²×C₄×C₆₇	—	2	8	no	—
121	C₂²×C₄×C₆₇	—	2	4	no	—
122	C₂²×C₄×C₆₇	—	2	4	no	—
123	C₂²×C₄×C₆₇	—	2	8	no	—
124	C₂²×C₄×C₆₇	—	2	8	no	—
125	C₂²×C₄×C₆₇	—	2	16	no	—
126	C₂²×C₄×C₆₇	—	4	32	no	—
127	C₂²×C₄×C₆₇	—	4	16	no	—
128	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₆₇	C₂×D₄	1	16	yes	—
131	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₆₇	#41	1	8	yes	—
133	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
135	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
140	C₄⋊C₄×C₆₇	—	2	16	no	—
141	C₄⋊C₄×C₆₇	—	2	16	no	—
142	C₄⋊C₄×C₆₇	—	2	8	no	—
143	C₄⋊C₄×C₆₇	—	2	32	no	—
144	C₄⋊C₄×C₆₇	—	2	16	no	—
145	C₂²⋊C₄×C₆₇	—	2	8	no	—
146	C₂²⋊C₄×C₆₇	—	2	16	no	—
147	C₂²⋊C₄×C₆₇	—	2	32	no	—
148	C₂²⋊C₄×C₆₇	—	2	8	no	—
149	C₄²×C₆₇	—	2	8	no	—
150	C₂³×C₆₇	—	2	8	no	—
151	C₂³×C₆₇	—	2	8	no	—
152	C₂³×C₆₇	—	2	16	no	—
153	C₂³×C₆₇	—	2	16	no	—
154	C₂³×C₆₇	—	2	4	no	—
155	C₂³×C₆₇	—	2	4	no	—
156	C₂³×C₆₇	—	2	8	no	—
157	C₂³×C₆₇	—	2	16	no	—
158	C₂³×C₆₇	—	2	2	no	—
159	C₂³×C₆₇	—	2	4	no	—
160	C₂³×C₆₇	—	2	2	no	—
161	C₂³×C₆₇	—	2	4	no	—
162	C₂³×C₆₇	—	4	4	no	—
163	C₂³×C₆₇	—	4	4	no	—
164	C₂³×C₆₇	—	4	8	no	—
165	C₂³×C₆₇	#121	1	16	yes	—
166	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
167	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
168	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
169	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
170	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
171	C₂³×C₆₇	C₂×#41	1	4	yes	—
172	C₂³×C₆₇	C₂×#41	1	2	yes	—
173	C₂³×C₆₇	C₂×#41	1	4	yes	—
174	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
175	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
176	D₄×C₆₇	—	2	32	no	—
177	C₂×C₄×C₆₇	—	2	8	no	—
178	C₂×C₄×C₆₇	—	2	8	no	—
179	C₂×C₄×C₆₇	—	2	2	no	—
180	C₂×C₄×C₆₇	—	2	4	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	32	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	8	no	—
185	C₂×C₄×C₆₇	—	2	8	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	8	no	—
188	C₂×C₄×C₆₇	—	2	8	no	—
189	C₂×C₄×C₆₇	—	2	8	no	—
190	C₂×C₄×C₆₇	—	2	4	no	—
191	C₂×C₄×C₆₇	—	2	4	no	—
192	C₂×C₄×C₆₇	—	2	8	no	—
193	C₂×C₄×C₆₇	—	4	32	no	—
194	C₂×C₄×C₆₇	—	4	16	no	—
195	C₂×C₄×C₆₇	—	4	4	no	—
196	C₂×C₄×C₆₇	—	4	4	no	—
197	C₂×C₄×C₆₇	—	4	16	no	—
198	C₂×C₄×C₆₇	—	4	16	no	—
199	C₂×C₄×C₆₇	#123	1	16	yes	complemented
200	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
204	C₂²×C₆₇	—	2	4	no	—
205	C₂²×C₆₇	—	2	4	no	—
206	C₂²×C₆₇	—	2	8	no	—
207	C₂²×C₆₇	—	2	8	no	—
208	C₂²×C₆₇	—	2	32	no	—
209	C₂²×C₆₇	—	2	4	no	—
210	C₂²×C₆₇	—	2	8	no	—
211	C₂²×C₆₇	—	4	2	no	—
212	C₂²×C₆₇	—	4	2	no	—
213	C₂²×C₆₇	—	4	4	no	—
214	C₂²×C₆₇	—	4	16	no	—
215	C₂²×C₆₇	C₂×#121	1	8	yes	—
216	C₂²×C₆₇	C₂×#121	1	4	yes	—
217	C₂²×C₆₇	C₂×#123	1	4	yes	—
218	C₂²×C₆₇	#536	1	4	yes	—
219	C₂²×C₆₇	#547	1	8	yes	—
220	C₂²×C₆₇	#552	1	8	yes	—
221	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
222	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
223	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
224	C₂²×C₆₇	C₂²×#41	1	2	yes	—
225	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
226	C₄×C₆₇	—	2	4	no	—
227	C₄×C₆₇	—	2	4	no	—
228	C₄×C₆₇	—	4	8	no	—
229	C₄×C₆₇	—	4	2	no	—
230	C₄×C₆₇	—	4	2	no	—
231	C₄×C₆₇	—	4	8	no	—
232	C₄×C₆₇	C₂×#123	1	8	yes	complemented
233	C₂×#2486	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₆₇	—	2	8	no	—
235	C₂×C₆₇	—	4	4	no	—
236	C₂×C₆₇	#2486	1	8	yes	direct product factor
237	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
238	C₂×C₆₇	C₂²×#123	1	1	yes	characteristic
239	C₂×C₆₇	C₂×#536	1	1	yes	characteristic
240	C₂×C₆₇	C₂×#547	1	2	yes	—
241	C₂×C₆₇	C₂×#552	1	2	yes	—
242	C₂²×#123	C₂×C₆₇	1	2	yes	—
243	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic
244	C₂³×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
245	#2486	C₂×C₆₇	1	16	yes	direct product factor
246	C₂×#398	C₂×C₆₇	1	2	yes	complemented
247	C₂×#397	C₂×C₆₇	1	2	yes	complemented
248	C₂×#389	C₂×C₆₇	1	2	yes	complemented
249	C₂×#381	C₂×C₆₇	1	2	yes	complemented
250	C₂×#380	C₂×C₆₇	1	2	yes	complemented
251	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
252	C₆₇	C₂×#2486	1	1	yes	characteristic, direct product factor, Sylow
253	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
255	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
257	C₂×#123	—	2	16	no	—
258	C₂×#123	C₂²×C₆₇	1	16	yes	—
259	C₂×C₄×D₄	—	2	8	no	—
260	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
261	C₂²×C₄⋊C₄	—	2	8	no	—
262	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
266	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₆₇	1	8	yes	complemented
268	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
270	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
272	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
273	#398	C₂²×C₆₇	1	16	yes	complemented
274	#397	C₂²×C₆₇	1	16	yes	complemented
275	#389	C₂²×C₆₇	1	16	yes	complemented
276	#381	C₂²×C₆₇	1	16	yes	complemented
277	#380	C₂²×C₆₇	1	16	yes	complemented
278	#380	C₂²×C₆₇	1	8	yes	complemented
279	C₂×#95	C₂²×C₆₇	1	2	yes	—
280	C₂×#95	C₂²×C₆₇	1	4	yes	—
281	C₂×#95	C₂²×C₆₇	1	4	yes	—
282	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
283	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
284	C₂²×D₄	—	2	4	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	D₄×C₆₇	1	8	yes	—
287	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
288	C₂³×C₄	—	2	8	no	—
289	C₂³×C₄	—	2	8	no	—
290	C₂³×C₄	—	2	8	no	—
291	C₂³×C₄	—	2	8	no	—
292	C₂³×C₄	—	2	4	no	—
293	C₂³×C₄	—	2	8	no	—
294	C₂³×C₄	D₄×C₆₇	1	8	yes	—
295	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
296	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
298	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
300	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
301	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
304	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
305	#123	—	2	64	no	—
306	C₄×D₄	—	2	32	no	—
307	C₂×C₄⋊C₄	—	2	8	no	—
308	C₂×C₄⋊C₄	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	32	no	—
310	C₂×C₄⋊C₄	—	2	4	no	—
311	C₂×C₄⋊C₄	—	2	16	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
317	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	8	no	—
320	C₂×C₂²⋊C₄	—	2	16	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
326	C₂×C₄²	—	2	4	no	—
327	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
328	#95	C₂³×C₆₇	1	16	yes	—
329	#95	C₂³×C₆₇	1	8	yes	—
330	#95	C₂³×C₆₇	1	16	yes	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
338	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
339	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
340	C₂⁴	#41×C₆₇	1	4	yes	—
341	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
342	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
343	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
344	C₂×D₄	—	2	32	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	32	no	—
352	C₂²×C₄	—	2	16	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	16	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	16	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	16	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	16	no	—
368	C₂²×C₄	—	4	32	no	—
369	C₂²×C₄	—	4	16	no	—
370	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	—
373	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
374	C₂²×C₄	#41×C₆₇	1	8	yes	—
375	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
378	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
379	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	16	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	32	no	—
386	C₄⋊C₄	—	2	16	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	16	no	—
389	C₂²⋊C₄	—	2	32	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₄²	—	2	8	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	16	no	—
395	C₂³	—	2	16	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	8	no	—
407	C₂³	#121×C₆₇	1	16	yes	—
408	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
409	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
410	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
411	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
412	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
413	C₂³	C₂×#41×C₆₇	1	4	yes	—
414	C₂³	C₂×#41×C₆₇	1	2	yes	—
415	C₂³	C₂×#41×C₆₇	1	4	yes	—
416	C₂³	2₋¹⁺⁴×C₆₇	1	4	yes	—
417	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
418	D₄	—	2	32	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	32	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	4	32	no	—
436	C₂×C₄	—	4	16	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	16	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	#123×C₆₇	1	16	yes	complemented
442	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
444	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
445	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	8	no	—
449	C₂²	—	2	8	no	—
450	C₂²	—	2	32	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	16	no	—
457	C₂²	C₂×#121×C₆₇	1	8	yes	—
458	C₂²	C₂×#121×C₆₇	1	4	yes	—
459	C₂²	C₂×#123×C₆₇	1	4	yes	—
460	C₂²	#536×C₆₇	1	4	yes	—
461	C₂²	#547×C₆₇	1	8	yes	—
462	C₂²	#552×C₆₇	1	8	yes	—
463	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
464	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
465	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
466	C₂²	C₂²×#41×C₆₇	1	2	yes	—
467	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	8	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	8	no	—
474	C₄	C₂×#123×C₆₇	1	8	yes	complemented
475	C₂	—	2	8	no	—
476	C₂	—	4	4	no	—
477	C₂	C₆₇×#2486	1	8	yes	direct product factor
478	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
479	C₂	C₂²×#123×C₆₇	1	1	yes	characteristic
480	C₂	C₂×#536×C₆₇	1	1	yes	characteristic
481	C₂	C₂×#547×C₆₇	1	2	yes	—
482	C₂	C₂×#552×C₆₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂³×C₄⋊C₄×C₆₇	C₂	semidirect
4. C₆₇×#2486	C₂	direct (N × H)
5. C₂×#398×C₆₇	C₂	semidirect
6. C₂×#397×C₆₇	C₂	semidirect
7. C₂×#389×C₆₇	C₂	semidirect
8. C₂×#381×C₆₇	C₂	semidirect
9. C₂×#380×C₆₇	C₂	semidirect
10. C₂×#380×C₆₇	C₂	semidirect
25. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
31. #398×C₆₇	C₂²	semidirect
32. #397×C₆₇	C₂²	semidirect
33. #389×C₆₇	C₂²	semidirect
34. #381×C₆₇	C₂²	semidirect
35. #380×C₆₇	C₂²	semidirect
36. #380×C₆₇	C₂²	semidirect
199. C₂×C₄×C₆₇	#123	semidirect
232. C₄×C₆₇	C₂×#123	semidirect
233. C₂×#2486	C₆₇	direct (N × H)
236. C₂×C₆₇	#2486	direct (N × H)
244. C₂³×C₄⋊C₄	C₂×C₆₇	semidirect
245. #2486	C₂×C₆₇	direct (N × H)
246. C₂×#398	C₂×C₆₇	semidirect
247. C₂×#397	C₂×C₆₇	semidirect
248. C₂×#389	C₂×C₆₇	semidirect
249. C₂×#381	C₂×C₆₇	semidirect
250. C₂×#380	C₂×C₆₇	semidirect
251. C₂×#380	C₂×C₆₇	semidirect
252. C₆₇	C₂×#2486	direct (N × H)
267. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
273. #398	C₂²×C₆₇	semidirect
274. #397	C₂²×C₆₇	semidirect
275. #389	C₂²×C₆₇	semidirect
276. #381	C₂²×C₆₇	semidirect
277. #380	C₂²×C₆₇	semidirect
278. #380	C₂²×C₆₇	semidirect
441. C₂×C₄	#123×C₆₇	semidirect
474. C₄	C₂×#123×C₆₇	semidirect
477. C₂	C₆₇×#2486	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×#123×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂³×C₄⋊C₄×C₆₇	2
C₆₇×#2486	2
C₂×#398×C₆₇	2
C₂×#397×C₆₇	2
C₂×#389×C₆₇	2
C₂×#381×C₆₇	2
C₂×#380×C₆₇	2
C₂×#2486	67

Subgroups — C2×C67×#2486 #30714006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2486 #30714006