Subgroups — C₂×C₆₇×#1895 #30700220

Order 17152.

2310 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1895	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₆₇	—	2	1	no	—
8	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	—	2	4	no	—
11	C₂²×M₁₆×C₆₇	—	2	8	no	—
12	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	complemented
13	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
14	C₂×#121×C₆₇	—	2	4	no	—
15	C₂×#121×C₆₇	—	2	2	no	—
16	C₂×#121×C₆₇	C₄	1	8	yes	complemented
17	C₂×#121×C₆₇	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
22	C₂×#102×C₆₇	—	2	8	no	—
23	C₂×#102×C₆₇	C₂²	1	8	yes	complemented
24	#380×C₆₇	—	2	2	no	—
25	#380×C₆₇	C₂²	1	4	yes	complemented
26	C₂×#95×C₆₇	—	2	1	no	—
27	#340×C₆₇	C₂²	1	8	yes	complemented
28	C₂⁵×C₆₇	—	2	1	no	—
29	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₆₇	—	2	8	no	—
31	C₂²×D₄×C₆₇	—	2	4	no	—
32	C₂²×D₄×C₆₇	—	2	4	no	—
33	C₂²×D₄×C₆₇	—	2	1	no	—
34	C₂²×D₄×C₆₇	—	2	2	no	—
35	C₂²×D₄×C₆₇	—	2	4	no	—
36	C₂²×D₄×C₆₇	—	4	8	no	—
37	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
38	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₆₇	—	2	4	no	—
40	C₂³×C₄×C₆₇	—	2	4	no	—
41	C₂³×C₄×C₆₇	—	2	1	no	—
42	C₂³×C₄×C₆₇	—	2	2	no	—
43	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
44	C₂³×C₄×C₆₇	D₄	1	2	yes	—
45	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	D₄	1	4	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₆₇	—	2	32	no	—
50	C₂×M₁₆×C₆₇	—	2	8	no	—
51	C₂×M₁₆×C₆₇	—	2	16	no	—
52	C₂²×C₈×C₆₇	—	2	4	no	—
53	C₂²×C₈×C₆₇	—	2	4	no	—
54	C₂²×C₈×C₆₇	D₄	1	8	yes	complemented
55	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
56	#121×C₆₇	—	2	16	no	—
57	#121×C₆₇	—	2	8	no	—
58	#121×C₆₇	C₂×C₄	1	16	yes	complemented
59	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
71	#102×C₆₇	—	2	16	no	—
72	#95×C₆₇	—	2	4	no	—
73	C₂⁴×C₆₇	—	2	4	no	—
74	C₂⁴×C₆₇	—	2	2	no	—
75	C₂⁴×C₆₇	—	2	4	no	—
76	C₂⁴×C₆₇	—	2	2	no	—
77	C₂⁴×C₆₇	—	2	4	no	—
78	C₂⁴×C₆₇	—	2	2	no	—
79	C₂⁴×C₆₇	—	4	4	no	—
80	C₂⁴×C₆₇	—	4	4	no	—
81	C₂⁴×C₆₇	—	4	2	no	—
82	C₂⁴×C₆₇	—	4	2	no	—
83	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
84	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
85	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
86	C₂×D₄×C₆₇	—	2	16	no	—
87	C₂×D₄×C₆₇	—	2	4	no	—
88	C₂×D₄×C₆₇	—	2	16	no	—
89	C₂×D₄×C₆₇	—	2	4	no	—
90	C₂×D₄×C₆₇	—	2	2	no	—
91	C₂×D₄×C₆₇	—	2	4	no	—
92	C₂×D₄×C₆₇	—	4	16	no	—
93	C₂×D₄×C₆₇	—	4	32	no	—
94	C₂×D₄×C₆₇	—	4	4	no	—
95	C₂×D₄×C₆₇	—	4	4	no	—
96	C₂×D₄×C₆₇	—	4	4	no	—
97	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	16	no	—
100	C₂²×C₄×C₆₇	—	2	8	no	—
101	C₂²×C₄×C₆₇	—	2	8	no	—
102	C₂²×C₄×C₆₇	—	2	8	no	—
103	C₂²×C₄×C₆₇	—	2	4	no	—
104	C₂²×C₄×C₆₇	—	2	4	no	—
105	C₂²×C₄×C₆₇	—	2	4	no	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	—	2	4	no	—
108	C₂²×C₄×C₆₇	—	4	4	no	—
109	C₂²×C₄×C₆₇	—	4	4	no	—
110	C₂²×C₄×C₆₇	—	4	4	no	—
111	C₂²×C₄×C₆₇	—	4	4	no	—
112	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
114	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₆₇	#41	1	4	yes	—
122	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₆₇	—	2	32	no	—
124	C₂×C₈×C₆₇	—	2	16	no	—
125	C₂×C₈×C₆₇	—	2	4	no	—
126	C₂×C₈×C₆₇	—	2	4	no	—
127	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	complemented
128	C₄⋊C₄×C₆₇	—	2	4	no	—
129	C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	2	4	no	—
131	C₄⋊C₄×C₆₇	—	2	4	no	—
132	C₄⋊C₄×C₆₇	—	4	4	no	—
133	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
134	C₂²⋊C₄×C₆₇	—	2	16	no	—
135	C₂²⋊C₄×C₆₇	—	4	8	no	—
136	C₂³×C₆₇	—	2	4	no	—
137	C₂³×C₆₇	—	2	2	no	—
138	C₂³×C₆₇	—	2	4	no	—
139	C₂³×C₆₇	—	2	2	no	—
140	C₂³×C₆₇	—	2	8	no	—
141	C₂³×C₆₇	—	2	8	no	—
142	C₂³×C₆₇	—	2	8	no	—
143	C₂³×C₆₇	—	2	4	no	—
144	C₂³×C₆₇	—	4	8	no	—
145	C₂³×C₆₇	—	4	8	no	—
146	C₂³×C₆₇	—	4	4	no	—
147	C₂³×C₆₇	—	4	4	no	—
148	C₂³×C₆₇	—	4	2	no	—
149	C₂³×C₆₇	—	4	2	no	—
150	C₂³×C₆₇	—	4	8	no	—
151	C₂³×C₆₇	—	4	8	no	—
152	C₂³×C₆₇	—	4	8	no	—
153	C₂³×C₆₇	—	8	8	no	—
154	C₂³×C₆₇	—	8	8	no	—
155	C₂³×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂³×C₆₇	#121	1	4	yes	—
158	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
159	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
160	C₂³×C₆₇	#137	1	2	yes	—
161	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₆₇	—	2	8	no	—
163	D₄×C₆₇	—	4	32	no	—
164	D₄×C₆₇	—	4	2	no	—
165	D₄×C₆₇	—	4	2	no	—
166	D₄×C₆₇	—	4	8	no	—
167	C₂×C₄×C₆₇	—	2	4	no	—
168	C₂×C₄×C₆₇	—	2	8	no	—
169	C₂×C₄×C₆₇	—	2	8	no	—
170	C₂×C₄×C₆₇	—	2	4	no	—
171	C₂×C₄×C₆₇	—	2	4	no	—
172	C₂×C₄×C₆₇	—	2	16	no	—
173	C₂×C₄×C₆₇	—	2	4	no	—
174	C₂×C₄×C₆₇	—	4	4	no	—
175	C₂×C₄×C₆₇	—	4	8	no	—
176	C₂×C₄×C₆₇	—	4	4	no	—
177	C₂×C₄×C₆₇	—	4	4	no	—
178	C₂×C₄×C₆₇	—	4	4	no	—
179	C₂×C₄×C₆₇	—	8	8	no	—
180	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
183	C₂×C₄×C₆₇	#120	1	4	yes	—
184	C₂×C₄×C₆₇	#121	1	4	yes	—
185	C₂×C₄×C₆₇	#123	1	4	yes	—
186	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
190	C₈×C₆₇	—	2	8	no	—
191	C₂²×C₆₇	—	2	4	no	—
192	C₂²×C₆₇	—	2	4	no	—
193	C₂²×C₆₇	—	2	4	no	—
194	C₂²×C₆₇	—	4	16	no	—
195	C₂²×C₆₇	—	4	4	no	—
196	C₂²×C₆₇	—	4	4	no	—
197	C₂²×C₆₇	—	4	4	no	—
198	C₂²×C₆₇	—	4	4	no	—
199	C₂²×C₆₇	—	4	4	no	—
200	C₂²×C₆₇	—	8	16	no	—
201	C₂²×C₆₇	—	8	4	no	—
202	C₂²×C₆₇	—	8	4	no	—
203	C₂²×C₆₇	#386	1	4	yes	—
204	C₂²×C₆₇	#417	1	4	yes	—
205	C₂²×C₆₇	#418	1	4	yes	—
206	C₂²×C₆₇	#468	1	8	yes	—
207	C₂²×C₆₇	#469	1	8	yes	—
208	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₆₇	C₂×#121	1	2	yes	—
210	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
211	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₆₇	C₂×#137	1	1	yes	characteristic
213	C₄×C₆₇	—	2	4	no	—
214	C₄×C₆₇	—	4	4	no	—
215	C₄×C₆₇	—	8	4	no	—
216	C₄×C₆₇	#386	1	4	yes	—
217	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
218	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
219	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
220	C₂×#1895	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₆₇	—	4	4	no	—
222	C₂×C₆₇	—	8	4	no	—
223	C₂×C₆₇	#1895	1	8	yes	direct product factor
224	C₂×C₆₇	C₂×#386	1	1	yes	characteristic
225	C₂×C₆₇	C₂×#418	1	1	yes	characteristic
226	C₂×C₆₇	C₂×#417	1	1	yes	characteristic
227	C₂×C₆₇	C₂×#468	1	2	yes	—
228	C₂×C₆₇	C₂×#469	1	2	yes	—
229	C₂³×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
230	C₂²×#121	C₂×C₆₇	1	1	yes	characteristic
231	C₂²×#102	C₂×C₆₇	1	2	yes	complemented
232	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
233	#1895	C₂×C₆₇	1	8	yes	direct product factor
234	C₂×#340	C₂×C₆₇	1	2	yes	complemented
235	C₆₇	C₂×#1895	1	1	yes	characteristic, direct product factor, Sylow
236	C₂³×D₄	—	2	1	no	—
237	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
239	C₂²×M₁₆	—	2	4	no	—
240	C₂²×M₁₆	—	2	8	no	—
241	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	complemented
242	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
243	C₂×#121	—	2	4	no	—
244	C₂×#121	—	2	2	no	—
245	C₂×#121	C₄×C₆₇	1	8	yes	complemented
246	C₂×#121	C₂²×C₆₇	1	4	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	—	2	1	no	—
250	C₂²×C₂²⋊C₄	—	2	1	no	—
251	C₂×#102	—	2	8	no	—
252	C₂×#102	C₂²×C₆₇	1	8	yes	complemented
253	#380	—	2	2	no	—
254	#380	C₂²×C₆₇	1	4	yes	complemented
255	C₂×#95	—	2	1	no	—
256	#340	C₂²×C₆₇	1	8	yes	complemented
257	C₂⁵	—	2	1	no	—
258	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
259	C₂²×D₄	—	2	8	no	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	4	8	no	—
266	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
267	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
273	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₆₇	1	2	yes	—
275	C₂³×C₄	D₄×C₆₇	1	4	yes	—
276	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
277	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
278	C₂×M₁₆	—	2	32	no	—
279	C₂×M₁₆	—	2	8	no	—
280	C₂×M₁₆	—	2	16	no	—
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	D₄×C₆₇	1	8	yes	complemented
284	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
285	#121	—	2	16	no	—
286	#121	—	2	8	no	—
287	#121	C₂×C₄×C₆₇	1	16	yes	complemented
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	8	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	4	4	no	—
300	#102	—	2	16	no	—
301	#95	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	2	2	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	4	2	no	—
312	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
313	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
314	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
315	C₂×D₄	—	2	16	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	16	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	4	16	no	—
322	C₂×D₄	—	4	32	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₆₇	1	8	yes	—
343	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
344	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
347	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
350	C₂²×C₄	#41×C₆₇	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
352	M₁₆	—	2	32	no	—
353	C₂×C₈	—	2	16	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	complemented
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
363	C₂²⋊C₄	—	2	16	no	—
364	C₂²⋊C₄	—	4	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	4	8	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	8	8	no	—
383	C₂³	—	8	8	no	—
384	C₂³	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
385	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
386	C₂³	#121×C₆₇	1	4	yes	—
387	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
388	C₂³	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
389	C₂³	#137×C₆₇	1	2	yes	—
390	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
391	D₄	—	2	8	no	—
392	D₄	—	4	32	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	16	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
412	C₂×C₄	#120×C₆₇	1	4	yes	—
413	C₂×C₄	#121×C₆₇	1	4	yes	—
414	C₂×C₄	#123×C₆₇	1	4	yes	—
415	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
417	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
419	C₈	—	2	8	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	16	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	16	no	—
432	C₂²	#386×C₆₇	1	4	yes	—
433	C₂²	#417×C₆₇	1	4	yes	—
434	C₂²	#418×C₆₇	1	4	yes	—
435	C₂²	#468×C₆₇	1	8	yes	—
436	C₂²	#469×C₆₇	1	8	yes	—
437	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
438	C₂²	C₂×#121×C₆₇	1	2	yes	—
439	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
440	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
441	C₂²	C₂×#137×C₆₇	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	4	no	—
445	C₄	#386×C₆₇	1	4	yes	—
446	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
447	C₄	C₂×#120×C₆₇	1	1	yes	characteristic
448	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
449	C₂	—	4	4	no	—
450	C₂	—	8	4	no	—
451	C₂	C₆₇×#1895	1	8	yes	direct product factor
452	C₂	C₂×#386×C₆₇	1	1	yes	characteristic
453	C₂	C₂×#418×C₆₇	1	1	yes	characteristic
454	C₂	C₂×#417×C₆₇	1	1	yes	characteristic
455	C₂	C₂×#468×C₆₇	1	2	yes	—
456	C₂	C₂×#469×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#121×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₆₇	C₂	semidirect
3. C₂²×#102×C₆₇	C₂	semidirect
4. C₂×#380×C₆₇	C₂	semidirect
5. C₆₇×#1895	C₂	direct (N × H)
6. C₂×#340×C₆₇	C₂	semidirect
12. C₂²×M₁₆×C₆₇	C₂²	semidirect
16. C₂×#121×C₆₇	C₄	semidirect
23. C₂×#102×C₆₇	C₂²	semidirect
25. #380×C₆₇	C₂²	semidirect
27. #340×C₆₇	C₂²	semidirect
54. C₂²×C₈×C₆₇	D₄	semidirect
58. #121×C₆₇	C₂×C₄	semidirect
127. C₂×C₈×C₆₇	C₂×D₄	semidirect
220. C₂×#1895	C₆₇	direct (N × H)
223. C₂×C₆₇	#1895	direct (N × H)
229. C₂³×M₁₆	C₂×C₆₇	semidirect
231. C₂²×#102	C₂×C₆₇	semidirect
232. C₂×#380	C₂×C₆₇	semidirect
233. #1895	C₂×C₆₇	direct (N × H)
234. C₂×#340	C₂×C₆₇	semidirect
235. C₆₇	C₂×#1895	direct (N × H)
241. C₂²×M₁₆	C₂²×C₆₇	semidirect
245. C₂×#121	C₄×C₆₇	semidirect
252. C₂×#102	C₂²×C₆₇	semidirect
254. #380	C₂²×C₆₇	semidirect
256. #340	C₂²×C₆₇	semidirect
283. C₂²×C₈	D₄×C₆₇	semidirect
287. #121	C₂×C₄×C₆₇	semidirect
356. C₂×C₈	C₂×D₄×C₆₇	semidirect
451. C₂	C₆₇×#1895	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₆₇	2
C₂²×#121×C₆₇	2
C₂²×#102×C₆₇	2
C₂×#380×C₆₇	2
C₆₇×#1895	2
C₂×#340×C₆₇	2
C₂×#1895	67

Subgroups — C2×C67×#1895 #30700220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1895 #30700220