Subgroups — C₂×C₆₇×#1924 #30700296

Order 17152.

1398 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₆₇×#1924	C₂	1	8	yes	maximal, direct product factor
7	C₂×#336×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#336×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₆₇	C₄	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₆₇	C₄	1	1	yes	characteristic
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₆₇	—	2	4	no	—
19	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊C₈×C₆₇	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₆₇	—	2	4	no	—
22	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
24	C₂×#97×C₆₇	—	2	4	no	—
25	C₂×#97×C₆₇	C₂²	1	4	yes	complemented
26	C₄×C₂²⋊C₄×C₆₇	C₄	1	4	yes	—
27	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
28	C₂×#95×C₆₇	C₄	1	1	yes	characteristic
29	C₂×#95×C₆₇	C₄	1	1	yes	characteristic
30	#336×C₆₇	C₂²	1	4	yes	complemented
31	#336×C₆₇	C₂²	1	4	yes	complemented
32	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₇	—	2	2	no	—
34	C₂³×C₄×C₆₇	—	2	2	no	—
35	C₂³×C₄×C₆₇	—	2	2	no	—
36	C₂³×C₄×C₆₇	—	2	2	no	—
37	C₂³×C₄×C₆₇	—	2	2	no	—
38	C₂³×C₄×C₆₇	—	2	2	no	—
39	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₇	—	2	2	no	—
48	C₂²×C₈×C₆₇	—	2	2	no	—
49	C₂²×C₈×C₆₇	—	2	2	no	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
52	C₂²×C₈×C₆₇	—	2	2	no	—
53	C₂²×C₈×C₆₇	—	2	2	no	—
54	C₂²×C₈×C₆₇	—	2	2	no	—
55	C₂²×C₈×C₆₇	—	2	2	no	—
56	C₂²×C₈×C₆₇	—	2	2	no	—
57	C₂²×C₈×C₆₇	D₄	1	4	yes	—
58	C₂²×C₈×C₆₇	D₄	1	4	yes	—
59	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
62	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	—	2	2	no	—
69	C₂×C₄²×C₆₇	—	2	2	no	—
70	C₂×C₄²×C₆₇	—	2	2	no	—
71	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₆₇	—	2	8	no	—
76	C₂²⋊C₈×C₆₇	—	2	8	no	—
77	C₂²⋊C₈×C₆₇	—	2	8	no	—
78	#97×C₆₇	—	2	8	no	—
79	#95×C₆₇	C₂×C₄	1	4	yes	—
80	#95×C₆₇	C₂×C₄	1	4	yes	—
81	C₂⁴×C₆₇	—	2	2	no	—
82	C₂⁴×C₆₇	—	2	2	no	—
83	C₂⁴×C₆₇	—	2	2	no	—
84	C₂⁴×C₆₇	—	2	2	no	—
85	C₂⁴×C₆₇	—	2	2	no	—
86	C₂⁴×C₆₇	—	2	2	no	—
87	C₂⁴×C₆₇	M₁₆	1	4	yes	—
88	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
89	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	—	2	2	no	—
93	C₂²×C₄×C₆₇	—	2	2	no	—
94	C₂²×C₄×C₆₇	—	2	2	no	—
95	C₂²×C₄×C₆₇	—	2	2	no	—
96	C₂²×C₄×C₆₇	—	2	2	no	—
97	C₂²×C₄×C₆₇	—	2	2	no	—
98	C₂²×C₄×C₆₇	—	2	2	no	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	2	2	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	4	no	—
105	C₂²×C₄×C₆₇	—	2	4	no	—
106	C₂²×C₄×C₆₇	—	2	4	no	—
107	C₂²×C₄×C₆₇	—	2	2	no	—
108	C₂²×C₄×C₆₇	—	2	2	no	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	2	no	—
113	C₂²×C₄×C₆₇	—	4	4	no	—
114	C₂²×C₄×C₆₇	—	4	4	no	—
115	C₂²×C₄×C₆₇	—	4	4	no	—
116	C₂²×C₄×C₆₇	—	4	4	no	—
117	C₂²×C₄×C₆₇	M₁₆	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₆₇	#41	1	2	yes	—
127	C₂²×C₄×C₆₇	#41	1	2	yes	—
128	C₂²×C₄×C₆₇	#41	1	2	yes	—
129	C₂²×C₄×C₆₇	#41	1	2	yes	—
130	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₆₇	—	2	8	no	—
132	C₂×C₈×C₆₇	—	2	8	no	—
133	C₂×C₈×C₆₇	—	2	2	no	—
134	C₂×C₈×C₆₇	—	2	2	no	—
135	C₂×C₈×C₆₇	—	2	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	—	2	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	4	4	no	—
144	C₂×C₈×C₆₇	—	4	4	no	—
145	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
147	C₂²⋊C₄×C₆₇	—	2	8	no	—
148	C₂²⋊C₄×C₆₇	—	2	8	no	—
149	C₄²×C₆₇	—	2	4	no	—
150	C₄²×C₆₇	—	2	4	no	—
151	C₄²×C₆₇	—	2	2	no	—
152	C₄²×C₆₇	—	2	2	no	—
153	C₄²×C₆₇	—	2	2	no	—
154	C₄²×C₆₇	—	2	2	no	—
155	C₂³×C₆₇	—	2	2	no	—
156	C₂³×C₆₇	—	2	2	no	—
157	C₂³×C₆₇	—	2	2	no	—
158	C₂³×C₆₇	—	2	2	no	—
159	C₂³×C₆₇	—	2	2	no	—
160	C₂³×C₆₇	—	2	2	no	—
161	C₂³×C₆₇	—	2	8	no	—
162	C₂³×C₆₇	—	2	8	no	—
163	C₂³×C₆₇	—	2	8	no	—
164	C₂³×C₆₇	—	4	4	no	—
165	C₂³×C₆₇	—	4	4	no	—
166	C₂³×C₆₇	—	4	4	no	—
167	C₂³×C₆₇	—	4	4	no	—
168	C₂³×C₆₇	#117	1	2	yes	—
169	C₂³×C₆₇	C₄×D₄	1	2	yes	—
170	C₂³×C₆₇	C₄×D₄	1	2	yes	—
171	C₂³×C₆₇	C₂×M₁₆	1	4	yes	—
172	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
173	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
174	C₂³×C₆₇	#131	1	2	yes	—
175	C₂³×C₆₇	#131	1	2	yes	—
176	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	2	no	—
179	C₂×C₄×C₆₇	—	2	8	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	2	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	2	no	—
185	C₂×C₄×C₆₇	—	2	2	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	—	2	2	no	—
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	4	4	no	—
193	C₂×C₄×C₆₇	—	4	4	no	—
194	C₂×C₄×C₆₇	—	4	4	no	—
195	C₂×C₄×C₆₇	—	4	4	no	—
196	C₂×C₄×C₆₇	—	4	2	no	—
197	C₂×C₄×C₆₇	—	4	2	no	—
198	C₂×C₄×C₆₇	—	4	2	no	—
199	C₂×C₄×C₆₇	—	4	2	no	—
200	C₂×C₄×C₆₇	—	4	8	no	—
201	C₂×C₄×C₆₇	#117	1	2	yes	—
202	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₆₇	#121	1	4	yes	—
205	C₂×C₄×C₆₇	#123	1	4	yes	—
206	C₂×C₄×C₆₇	#124	1	4	yes	—
207	C₂×C₄×C₆₇	#126	1	4	yes	—
208	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
209	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
215	C₈×C₆₇	—	2	4	no	—
216	C₈×C₆₇	—	2	4	no	—
217	C₈×C₆₇	—	4	2	no	—
218	C₈×C₆₇	—	4	2	no	—
219	C₂²×C₆₇	—	2	4	no	—
220	C₂²×C₆₇	—	2	4	no	—
221	C₂²×C₆₇	—	2	4	no	—
222	C₂²×C₆₇	—	4	2	no	—
223	C₂²×C₆₇	—	4	2	no	—
224	C₂²×C₆₇	—	4	2	no	—
225	C₂²×C₆₇	—	4	16	no	—
226	C₂²×C₆₇	—	4	2	no	—
227	C₂²×C₆₇	#388	1	4	yes	—
228	C₂²×C₆₇	#432	1	4	yes	—
229	C₂²×C₆₇	#433	1	4	yes	—
230	C₂²×C₆₇	#435	1	4	yes	—
231	C₂²×C₆₇	#435	1	4	yes	—
232	C₂²×C₆₇	#435	1	4	yes	—
233	C₂²×C₆₇	#436	1	4	yes	—
234	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
235	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
238	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
239	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
240	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
241	C₄×C₆₇	—	2	4	no	—
242	C₄×C₆₇	—	4	2	no	—
243	C₄×C₆₇	—	4	2	no	—
244	C₄×C₆₇	—	4	2	no	—
245	C₄×C₆₇	—	4	2	no	—
246	C₄×C₆₇	#388	1	4	yes	—
247	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
248	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
249	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
250	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
251	C₂×#1924	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂×C₆₇	—	4	4	no	—
253	C₂×C₆₇	#1924	1	8	yes	direct product factor
254	C₂×C₆₇	C₂×#388	1	1	yes	characteristic
255	C₂×C₆₇	C₂×#432	1	1	yes	characteristic
256	C₂×C₆₇	C₂×#433	1	1	yes	characteristic
257	C₂×C₆₇	C₂×#435	1	1	yes	characteristic
258	C₂×C₆₇	C₂×#435	1	1	yes	characteristic
259	C₂×C₆₇	C₂×#435	1	1	yes	characteristic
260	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
261	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
262	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic
263	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic
264	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
265	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
266	#1924	C₂×C₆₇	1	8	yes	direct product factor
267	C₂×#336	C₂×C₆₇	1	1	yes	characteristic, complemented
268	C₂×#336	C₂×C₆₇	1	1	yes	characteristic, complemented
269	C₆₇	C₂×#1924	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
271	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₄×C₆₇	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₄×C₆₇	1	1	yes	characteristic
277	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
279	C₂×C₄⋊C₈	—	2	4	no	—
280	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
281	C₂×C₂²⋊C₈	—	2	4	no	—
282	C₂×C₂²⋊C₈	—	2	4	no	—
283	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
285	C₂×#97	—	2	4	no	—
286	C₂×#97	C₂²×C₆₇	1	4	yes	complemented
287	C₄×C₂²⋊C₄	C₄×C₆₇	1	4	yes	—
288	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
289	C₂×#95	C₄×C₆₇	1	1	yes	characteristic
290	C₂×#95	C₄×C₆₇	1	1	yes	characteristic
291	#336	C₂²×C₆₇	1	4	yes	complemented
292	#336	C₂²×C₆₇	1	4	yes	complemented
293	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
301	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
302	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
303	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
304	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
305	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
307	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	D₄×C₆₇	1	4	yes	—
319	C₂²×C₈	D₄×C₆₇	1	4	yes	—
320	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
321	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
322	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
323	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
333	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
334	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
335	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
336	C₄⋊C₈	—	2	8	no	—
337	C₂²⋊C₈	—	2	8	no	—
338	C₂²⋊C₈	—	2	8	no	—
339	#97	—	2	8	no	—
340	#95	C₂×C₄×C₆₇	1	4	yes	—
341	#95	C₂×C₄×C₆₇	1	4	yes	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	2	no	—
348	C₂⁴	M₁₆×C₆₇	1	4	yes	—
349	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
350	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	M₁₆×C₆₇	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
380	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
381	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
382	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
383	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
387	C₂²×C₄	#41×C₆₇	1	2	yes	—
388	C₂²×C₄	#41×C₆₇	1	2	yes	—
389	C₂²×C₄	#41×C₆₇	1	2	yes	—
390	C₂²×C₄	#41×C₆₇	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	—	2	8	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	4	4	no	—
405	C₂×C₈	—	4	4	no	—
406	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
407	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	#117×C₆₇	1	2	yes	—
430	C₂³	C₄×D₄×C₆₇	1	2	yes	—
431	C₂³	C₄×D₄×C₆₇	1	2	yes	—
432	C₂³	C₂×M₁₆×C₆₇	1	4	yes	—
433	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
434	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
435	C₂³	#131×C₆₇	1	2	yes	—
436	C₂³	#131×C₆₇	1	2	yes	—
437	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	#117×C₆₇	1	2	yes	—
463	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
464	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
465	C₂×C₄	#121×C₆₇	1	4	yes	—
466	C₂×C₄	#123×C₆₇	1	4	yes	—
467	C₂×C₄	#124×C₆₇	1	4	yes	—
468	C₂×C₄	#126×C₆₇	1	4	yes	—
469	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	2	4	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	16	no	—
488	C₂²	#388×C₆₇	1	4	yes	—
489	C₂²	#432×C₆₇	1	4	yes	—
490	C₂²	#433×C₆₇	1	4	yes	—
491	C₂²	#435×C₆₇	1	4	yes	—
492	C₂²	#435×C₆₇	1	4	yes	—
493	C₂²	#435×C₆₇	1	4	yes	—
494	C₂²	#436×C₆₇	1	4	yes	—
495	C₂²	C₂×#117×C₆₇	1	1	yes	characteristic
496	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
497	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
498	C₂²	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
499	C₂²	C₂²×M₁₆×C₆₇	1	1	yes	characteristic
500	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
501	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	#388×C₆₇	1	4	yes	—
508	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
509	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
510	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
511	C₄	C₂×#126×C₆₇	1	1	yes	characteristic
512	C₂	—	4	4	no	—
513	C₂	C₆₇×#1924	1	8	yes	direct product factor
514	C₂	C₂×#388×C₆₇	1	1	yes	characteristic
515	C₂	C₂×#432×C₆₇	1	1	yes	characteristic
516	C₂	C₂×#433×C₆₇	1	1	yes	characteristic
517	C₂	C₂×#435×C₆₇	1	1	yes	characteristic
518	C₂	C₂×#435×C₆₇	1	1	yes	characteristic
519	C₂	C₂×#435×C₆₇	1	1	yes	characteristic
520	C₂	C₂×#436×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊C₈×C₆₇	C₂	semidirect
4. C₂²×#97×C₆₇	C₂	semidirect
6. C₆₇×#1924	C₂	direct (N × H)
7. C₂×#336×C₆₇	C₂	semidirect
8. C₂×#336×C₆₇	C₂	semidirect
19. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
25. C₂×#97×C₆₇	C₂²	semidirect
30. #336×C₆₇	C₂²	semidirect
31. #336×C₆₇	C₂²	semidirect
251. C₂×#1924	C₆₇	direct (N × H)
253. C₂×C₆₇	#1924	direct (N × H)
261. C₂²×C₄⋊C₈	C₂×C₆₇	semidirect
264. C₂²×#97	C₂×C₆₇	semidirect
266. #1924	C₂×C₆₇	direct (N × H)
267. C₂×#336	C₂×C₆₇	semidirect
268. C₂×#336	C₂×C₆₇	semidirect
269. C₆₇	C₂×#1924	direct (N × H)
280. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
286. C₂×#97	C₂²×C₆₇	semidirect
291. #336	C₂²×C₆₇	semidirect
292. #336	C₂²×C₆₇	semidirect
513. C₂	C₆₇×#1924	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⋊C₈×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂²×#97×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₆₇×#1924	2
C₂×#336×C₆₇	2
C₂×#1924	67

Subgroups — C2×C67×#1924 #30700296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1924 #30700296