Subgroups — C₂×C₆₇×#1545 #30696952

Order 17152.

1934 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1545	C₂	1	8	yes	maximal, direct product factor
5	C₂×#331×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₆₇	—	2	1	no	—
7	C₂³×D₄×C₆₇	—	2	1	no	—
8	C₂³×D₄×C₆₇	C₄	1	2	yes	—
9	C₂²×M₁₆×C₆₇	—	2	1	no	—
10	C₂×#127×C₆₇	—	2	1	no	—
11	C₂×#127×C₆₇	—	2	1	no	—
12	C₂×#127×C₆₇	—	2	2	no	—
13	C₂×#127×C₆₇	—	2	2	no	—
14	C₂×#127×C₆₇	C₄	1	4	yes	—
15	C₂×#127×C₆₇	C₄	1	2	yes	—
16	C₂×#127×C₆₇	C₂²	1	2	yes	—
17	C₂×#127×C₆₇	C₂²	1	4	yes	—
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	#431×C₆₇	—	2	2	no	—
20	#431×C₆₇	C₂²	1	4	yes	complemented
21	#423×C₆₇	—	2	2	no	—
22	#423×C₆₇	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊C₈×C₆₇	—	2	1	no	—
27	C₂×C₄×C₈×C₆₇	—	2	1	no	—
28	#331×C₆₇	C₂²	1	16	yes	complemented
29	C₂⁵×C₆₇	—	2	2	no	—
30	C₂²×D₄×C₆₇	—	2	4	no	—
31	C₂²×D₄×C₆₇	—	2	2	no	—
32	C₂²×D₄×C₆₇	—	2	4	no	—
33	C₂²×D₄×C₆₇	—	2	2	no	—
34	C₂²×D₄×C₆₇	—	2	4	no	—
35	C₂²×D₄×C₆₇	—	2	2	no	—
36	C₂²×D₄×C₆₇	—	2	4	no	—
37	C₂²×D₄×C₆₇	—	2	4	no	—
38	C₂²×D₄×C₆₇	—	2	2	no	—
39	C₂²×D₄×C₆₇	—	2	2	no	—
40	C₂²×D₄×C₆₇	—	4	8	no	—
41	C₂²×D₄×C₆₇	—	4	8	no	—
42	C₂²×D₄×C₆₇	—	4	4	no	—
43	C₂²×D₄×C₆₇	—	4	4	no	—
44	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
45	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₆₇	—	2	4	no	—
50	C₂×M₁₆×C₆₇	—	4	4	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
52	C₂²×C₈×C₆₇	—	2	2	no	—
53	#127×C₆₇	—	2	4	no	—
54	#127×C₆₇	—	2	4	no	—
55	#127×C₆₇	—	2	4	no	—
56	#127×C₆₇	—	2	2	no	—
57	#127×C₆₇	—	2	2	no	—
58	#127×C₆₇	—	2	4	no	—
59	#127×C₆₇	—	2	4	no	—
60	#127×C₆₇	C₂×C₄	1	4	yes	—
61	#127×C₆₇	C₂×C₄	1	8	yes	—
62	#127×C₆₇	C₂³	1	4	yes	—
63	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	D₄	1	2	yes	—
68	C₂×C₄²×C₆₇	D₄	1	2	yes	—
69	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
71	C₄⋊C₈×C₆₇	—	2	4	no	—
72	C₄⋊C₈×C₆₇	—	2	2	no	—
73	C₄⋊C₈×C₆₇	—	2	2	no	—
74	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
75	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
76	C₂²⋊C₈×C₆₇	—	2	4	no	—
77	C₄×C₈×C₆₇	—	2	4	no	—
78	C₂⁴×C₆₇	—	2	8	no	—
79	C₂⁴×C₆₇	—	2	4	no	—
80	C₂⁴×C₆₇	—	4	8	no	—
81	C₂⁴×C₆₇	—	4	8	no	—
82	C₂⁴×C₆₇	—	4	8	no	—
83	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₆₇	—	2	4	no	—
85	C₂×D₄×C₆₇	—	2	8	no	—
86	C₂×D₄×C₆₇	—	2	8	no	—
87	C₂×D₄×C₆₇	—	2	4	no	—
88	C₂×D₄×C₆₇	—	2	8	no	—
89	C₂×D₄×C₆₇	—	2	4	no	—
90	C₂×D₄×C₆₇	—	2	4	no	—
91	C₂×D₄×C₆₇	—	2	4	no	—
92	C₂×D₄×C₆₇	—	4	8	no	—
93	C₂×D₄×C₆₇	—	4	8	no	—
94	C₂×D₄×C₆₇	—	4	16	no	—
95	C₂×D₄×C₆₇	—	4	16	no	—
96	C₂×D₄×C₆₇	—	4	16	no	—
97	C₂×D₄×C₆₇	—	4	16	no	—
98	C₂×D₄×C₆₇	—	4	8	no	—
99	C₂×D₄×C₆₇	—	4	16	no	—
100	C₂×D₄×C₆₇	—	4	8	no	—
101	C₂×D₄×C₆₇	—	4	4	no	—
102	C₂×D₄×C₆₇	—	4	8	no	—
103	C₂×D₄×C₆₇	—	4	8	no	—
104	C₂×D₄×C₆₇	—	4	4	no	—
105	C₂×D₄×C₆₇	—	4	8	no	—
106	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
107	C₂²×C₄×C₆₇	—	2	4	no	—
108	C₂²×C₄×C₆₇	—	2	4	no	—
109	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	D₈	1	4	yes	—
116	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
117	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	M₁₆×C₆₇	—	4	8	no	—
124	C₂×C₈×C₆₇	—	2	4	no	—
125	C₂×C₈×C₆₇	—	2	4	no	—
126	C₂×C₈×C₆₇	—	4	4	no	—
127	C₂×C₈×C₆₇	—	4	4	no	—
128	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₇	C₂×D₄	1	2	yes	—
134	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₆₇	C₂×D₄	1	2	yes	—
137	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
138	C₂³×C₆₇	—	2	2	no	—
139	C₂³×C₆₇	—	2	2	no	—
140	C₂³×C₆₇	—	2	8	no	—
141	C₂³×C₆₇	—	4	16	no	—
142	C₂³×C₆₇	—	4	16	no	—
143	C₂³×C₆₇	—	4	8	no	—
144	C₂³×C₆₇	—	4	16	no	—
145	C₂³×C₆₇	—	4	8	no	—
146	C₂³×C₆₇	—	4	8	no	—
147	C₂³×C₆₇	—	8	32	no	—
148	C₂³×C₆₇	#102	1	4	yes	—
149	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	D₄×C₆₇	—	4	8	no	—
152	D₄×C₆₇	—	4	8	no	—
153	D₄×C₆₇	—	4	16	no	—
154	D₄×C₆₇	—	4	4	no	—
155	D₄×C₆₇	—	4	4	no	—
156	D₄×C₆₇	—	4	8	no	—
157	D₄×C₆₇	—	4	16	no	—
158	D₄×C₆₇	—	4	8	no	—
159	D₄×C₆₇	—	4	16	no	—
160	D₄×C₆₇	—	4	8	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	4	no	—
164	C₂×C₄×C₆₇	—	2	4	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	#100	1	4	yes	—
168	C₂×C₄×C₆₇	#102	1	8	yes	—
169	C₂×C₄×C₆₇	#102	1	4	yes	—
170	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
177	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
178	C₂×C₄×C₆₇	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
181	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₆₇	—	4	4	no	—
185	C₈×C₆₇	—	4	4	no	—
186	C₂²×C₆₇	—	2	8	no	—
187	C₂²×C₆₇	—	2	2	no	—
188	C₂²×C₆₇	—	2	2	no	—
189	C₂²×C₆₇	—	4	8	no	—
190	C₂²×C₆₇	—	4	8	no	—
191	C₂²×C₆₇	—	4	8	no	—
192	C₂²×C₆₇	—	8	32	no	—
193	C₂²×C₆₇	—	8	16	no	—
194	C₂²×C₆₇	C₂×#100	1	2	yes	—
195	C₂²×C₆₇	C₂×#102	1	4	yes	—
196	C₂²×C₆₇	C₂×#102	1	2	yes	—
197	C₂²×C₆₇	#418	1	2	yes	—
198	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	—	2	1	no	—
201	C₄×C₆₇	—	2	2	no	—
202	C₄×C₆₇	C₂×#100	1	4	yes	—
203	C₄×C₆₇	C₂×#102	1	2	yes	—
204	C₄×C₆₇	C₂×#102	1	4	yes	—
205	C₄×C₆₇	#418	1	2	yes	—
206	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
207	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
208	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
209	C₂×#1545	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂×C₆₇	—	2	4	no	—
211	C₂×C₆₇	—	8	8	no	—
212	C₂×C₆₇	#1545	1	4	yes	direct product factor
213	C₂×C₆₇	C₂²×#100	1	1	yes	characteristic
214	C₂×C₆₇	C₂²×#102	1	1	yes	characteristic
215	C₂×C₆₇	C₂×#418	1	1	yes	characteristic
216	C₂²×#127	C₂×C₆₇	1	1	yes	characteristic
217	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
218	C₂×#423	C₂×C₆₇	1	1	yes	characteristic, complemented
219	#1545	C₂×C₆₇	1	8	yes	direct product factor
220	C₂×#331	C₂×C₆₇	1	4	yes	complemented
221	C₆₇	C₂×#1545	1	1	yes	characteristic, direct product factor, Sylow
222	C₂³×D₄	—	2	1	no	—
223	C₂³×D₄	—	2	1	no	—
224	C₂³×D₄	C₄×C₆₇	1	2	yes	—
225	C₂²×M₁₆	—	2	1	no	—
226	C₂×#127	—	2	1	no	—
227	C₂×#127	—	2	1	no	—
228	C₂×#127	—	2	2	no	—
229	C₂×#127	—	2	2	no	—
230	C₂×#127	C₄×C₆₇	1	4	yes	—
231	C₂×#127	C₄×C₆₇	1	2	yes	—
232	C₂×#127	C₂²×C₆₇	1	2	yes	—
233	C₂×#127	C₂²×C₆₇	1	4	yes	—
234	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
235	#431	—	2	2	no	—
236	#431	C₂²×C₆₇	1	4	yes	complemented
237	#423	—	2	2	no	—
238	#423	C₂²×C₆₇	1	4	yes	complemented
239	C₂×C₄⋊C₈	—	2	1	no	—
240	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
242	C₂×C₂²⋊C₈	—	2	1	no	—
243	C₂×C₄×C₈	—	2	1	no	—
244	#331	C₂²×C₆₇	1	16	yes	complemented
245	C₂⁵	—	2	2	no	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	4	no	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	4	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	4	8	no	—
257	C₂²×D₄	—	4	8	no	—
258	C₂²×D₄	—	4	4	no	—
259	C₂²×D₄	—	4	4	no	—
260	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
261	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
262	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	4	4	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	#127	—	2	4	no	—
270	#127	—	2	4	no	—
271	#127	—	2	4	no	—
272	#127	—	2	4	no	—
273	#127	—	2	2	no	—
274	#127	—	2	2	no	—
275	#127	—	2	4	no	—
276	#127	C₂×C₄×C₆₇	1	4	yes	—
277	#127	C₂×C₄×C₆₇	1	8	yes	—
278	#127	C₂³×C₆₇	1	4	yes	—
279	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
280	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
281	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₆₇	1	2	yes	—
284	C₂×C₄²	D₄×C₆₇	1	2	yes	—
285	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
287	C₄⋊C₈	—	2	4	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
291	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
292	C₂²⋊C₈	—	2	4	no	—
293	C₄×C₈	—	2	4	no	—
294	C₂⁴	—	2	8	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	4	8	no	—
297	C₂⁴	—	4	8	no	—
298	C₂⁴	—	4	8	no	—
299	C₂⁴	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	4	8	no	—
309	C₂×D₄	—	4	8	no	—
310	C₂×D₄	—	4	16	no	—
311	C₂×D₄	—	4	16	no	—
312	C₂×D₄	—	4	16	no	—
313	C₂×D₄	—	4	16	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	16	no	—
316	C₂×D₄	—	4	8	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	8	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	8	no	—
322	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
327	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
328	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
331	C₂²×C₄	D₈×C₆₇	1	4	yes	—
332	C₂²×C₄	SD₁₆×C₆₇	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
339	M₁₆	—	4	8	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	4	4	no	—
343	C₂×C₈	—	4	4	no	—
344	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
345	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
346	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
347	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
348	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₆₇	1	2	yes	—
350	C₄²	C₂×D₄×C₆₇	1	2	yes	—
351	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
353	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	16	no	—
359	C₂³	—	4	8	no	—
360	C₂³	—	4	16	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	8	32	no	—
364	C₂³	#102×C₆₇	1	4	yes	—
365	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
366	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	D₄	—	4	16	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	8	no	—
373	D₄	—	4	16	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	16	no	—
376	D₄	—	4	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	#100×C₆₇	1	4	yes	—
384	C₂×C₄	#102×C₆₇	1	8	yes	—
385	C₂×C₄	#102×C₆₇	1	4	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
388	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
393	C₂×C₄	C₂×D₈×C₆₇	1	4	yes	—
394	C₂×C₄	C₂×SD₁₆×C₆₇	1	4	yes	—
395	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
396	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
397	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
400	C₈	—	4	4	no	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	4	8	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	8	32	no	—
409	C₂²	—	8	16	no	—
410	C₂²	C₂×#100×C₆₇	1	2	yes	—
411	C₂²	C₂×#102×C₆₇	1	4	yes	—
412	C₂²	C₂×#102×C₆₇	1	2	yes	—
413	C₂²	#418×C₆₇	1	2	yes	—
414	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	C₂×#100×C₆₇	1	4	yes	—
419	C₄	C₂×#102×C₆₇	1	2	yes	—
420	C₄	C₂×#102×C₆₇	1	4	yes	—
421	C₄	#418×C₆₇	1	2	yes	—
422	C₄	C₂²×D₈×C₆₇	1	1	yes	characteristic
423	C₄	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
424	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
425	C₂	—	2	4	no	—
426	C₂	—	8	8	no	—
427	C₂	C₆₇×#1545	1	4	yes	direct product factor
428	C₂	C₂²×#100×C₆₇	1	1	yes	characteristic
429	C₂	C₂²×#102×C₆₇	1	1	yes	characteristic
430	C₂	C₂×#418×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₂²×#127×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₆₇	C₂	semidirect
3. C₂×#423×C₆₇	C₂	semidirect
4. C₆₇×#1545	C₂	direct (N × H)
5. C₂×#331×C₆₇	C₂	semidirect
20. #431×C₆₇	C₂²	semidirect
22. #423×C₆₇	C₂²	semidirect
24. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
25. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
28. #331×C₆₇	C₂²	semidirect
74. C₄⋊C₈×C₆₇	C₂³	semidirect
75. C₄⋊C₈×C₆₇	C₂³	semidirect
209. C₂×#1545	C₆₇	direct (N × H)
212. C₂×C₆₇	#1545	direct (N × H)
217. C₂×#431	C₂×C₆₇	semidirect
218. C₂×#423	C₂×C₆₇	semidirect
219. #1545	C₂×C₆₇	direct (N × H)
220. C₂×#331	C₂×C₆₇	semidirect
221. C₆₇	C₂×#1545	direct (N × H)
236. #431	C₂²×C₆₇	semidirect
238. #423	C₂²×C₆₇	semidirect
240. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
241. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
244. #331	C₂²×C₆₇	semidirect
290. C₄⋊C₈	C₂³×C₆₇	semidirect
291. C₄⋊C₈	C₂³×C₆₇	semidirect
427. C₂	C₆₇×#1545	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×#127×C₆₇	2
C₂×#431×C₆₇	2
C₂×#423×C₆₇	2
C₆₇×#1545	2
C₂×#331×C₆₇	2
C₂×#1545	67

Subgroups — C2×C67×#1545 #30696952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1545 #30696952