Subgroups — C₂×C₆₇×#1968 #30700472

Order 17152.

1830 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#103×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#391×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#1968	C₂	1	8	yes	maximal, direct product factor
9	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₆₇	—	2	4	no	—
12	C₂²×SD₁₆×C₆₇	—	2	4	no	—
13	C₂²×SD₁₆×C₆₇	C₄	1	8	yes	complemented
14	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	—
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₆₇	—	2	4	no	—
22	C₂×#106×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#103×C₆₇	—	2	4	no	—
24	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#102×C₆₇	—	2	4	no	—
26	C₂×#102×C₆₇	C₂²	1	4	yes	—
27	C₂×C₄×C₈×C₆₇	—	2	4	no	—
28	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
29	#391×C₆₇	—	2	2	no	—
30	#391×C₆₇	C₂²	1	4	yes	complemented
31	#390×C₆₇	—	2	2	no	—
32	#390×C₆₇	C₂²	1	4	yes	—
33	C₂×#95×C₆₇	—	2	2	no	—
34	C₂⁵×C₆₇	—	2	1	no	—
35	C₂²×Q₈×C₆₇	—	2	1	no	—
36	C₂²×Q₈×C₆₇	—	2	2	no	—
37	C₂²×Q₈×C₆₇	—	2	2	no	—
38	C₂²×Q₈×C₆₇	—	2	2	no	—
39	C₂²×Q₈×C₆₇	—	2	2	no	—
40	C₂²×Q₈×C₆₇	—	2	2	no	—
41	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
43	C₂²×D₄×C₆₇	—	2	2	no	—
44	C₂²×D₄×C₆₇	—	2	2	no	—
45	C₂²×D₄×C₆₇	—	2	2	no	—
46	C₂²×D₄×C₆₇	—	2	1	no	—
47	C₂²×D₄×C₆₇	—	2	2	no	—
48	C₂²×D₄×C₆₇	—	2	2	no	—
49	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
50	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₆₇	—	2	1	no	—
52	C₂³×C₄×C₆₇	—	2	1	no	—
53	C₂³×C₄×C₆₇	—	2	1	no	—
54	C₂³×C₄×C₆₇	D₄	1	2	yes	—
55	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₆₇	—	2	32	no	—
57	C₂×SD₁₆×C₆₇	—	2	8	no	—
58	C₂×SD₁₆×C₆₇	—	2	8	no	—
59	C₂×SD₁₆×C₆₇	C₂×C₄	1	16	yes	complemented
60	C₂²×C₈×C₆₇	—	2	2	no	—
61	C₂²×C₈×C₆₇	—	2	2	no	—
62	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
63	C₂²×C₈×C₆₇	D₄	1	4	yes	—
64	C₂²×C₈×C₆₇	D₄	1	4	yes	—
65	C₂²×C₈×C₆₇	D₄	1	4	yes	—
66	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
78	C₂×C₄²×C₆₇	—	2	2	no	—
79	C₂×C₄²×C₆₇	—	2	2	no	—
80	C₂×C₄²×C₆₇	D₄	1	2	yes	—
81	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
82	#106×C₆₇	—	2	8	no	—
83	#103×C₆₇	—	2	8	no	—
84	#102×C₆₇	—	2	8	no	—
85	C₄×C₈×C₆₇	—	2	8	no	—
86	#95×C₆₇	—	2	8	no	—
87	C₂⁴×C₆₇	—	2	4	no	—
88	C₂⁴×C₆₇	—	2	2	no	—
89	C₂⁴×C₆₇	—	4	2	no	—
90	C₂⁴×C₆₇	—	4	2	no	—
91	C₂⁴×C₆₇	—	4	4	no	—
92	C₂⁴×C₆₇	—	4	4	no	—
93	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₆₇	—	2	4	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	—	2	8	no	—
97	C₂×Q₈×C₆₇	—	2	8	no	—
98	C₂×Q₈×C₆₇	—	2	2	no	—
99	C₂×Q₈×C₆₇	—	2	2	no	—
100	C₂×Q₈×C₆₇	—	2	2	no	—
101	C₂×Q₈×C₆₇	—	2	2	no	—
102	C₂×Q₈×C₆₇	—	4	2	no	—
103	C₂×Q₈×C₆₇	—	4	4	no	—
104	C₂×Q₈×C₆₇	—	4	4	no	—
105	C₂×Q₈×C₆₇	—	4	2	no	—
106	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
107	C₂×D₄×C₆₇	—	2	8	no	—
108	C₂×D₄×C₆₇	—	2	8	no	—
109	C₂×D₄×C₆₇	—	2	4	no	—
110	C₂×D₄×C₆₇	—	2	2	no	—
111	C₂×D₄×C₆₇	—	2	2	no	—
112	C₂×D₄×C₆₇	—	2	2	no	—
113	C₂×D₄×C₆₇	—	2	2	no	—
114	C₂×D₄×C₆₇	—	2	2	no	—
115	C₂×D₄×C₆₇	—	4	4	no	—
116	C₂×D₄×C₆₇	—	4	2	no	—
117	C₂×D₄×C₆₇	—	4	4	no	—
118	C₂×D₄×C₆₇	—	4	2	no	—
119	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₆₇	—	2	4	no	—
121	C₂²×C₄×C₆₇	—	2	4	no	—
122	C₂²×C₄×C₆₇	—	2	4	no	—
123	C₂²×C₄×C₆₇	—	2	2	no	—
124	C₂²×C₄×C₆₇	—	2	2	no	—
125	C₂²×C₄×C₆₇	—	2	2	no	—
126	C₂²×C₄×C₆₇	—	4	2	no	—
127	C₂²×C₄×C₆₇	—	4	2	no	—
128	C₂²×C₄×C₆₇	—	4	2	no	—
129	C₂²×C₄×C₆₇	—	4	2	no	—
130	C₂²×C₄×C₆₇	—	4	4	no	—
131	C₂²×C₄×C₆₇	—	4	4	no	—
132	C₂²×C₄×C₆₇	SD₁₆	1	8	yes	complemented
133	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₆₇	#41	1	2	yes	—
140	C₂²×C₄×C₆₇	#41	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₆₇	—	2	32	no	—
143	C₂×C₈×C₆₇	—	2	8	no	—
144	C₂×C₈×C₆₇	—	2	2	no	—
145	C₂×C₈×C₆₇	—	2	2	no	—
146	C₂×C₈×C₆₇	C₂²⋊C₄	1	16	yes	complemented
147	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
148	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
149	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
150	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₆₇	—	2	2	no	—
152	C₄⋊C₄×C₆₇	—	2	2	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₄⋊C₄×C₆₇	—	4	2	no	—
156	C₄⋊C₄×C₆₇	—	4	2	no	—
157	C₂²⋊C₄×C₆₇	—	4	16	no	—
158	C₄²×C₆₇	—	2	4	no	—
159	C₄²×C₆₇	—	2	2	no	—
160	C₄²×C₆₇	—	2	2	no	—
161	C₂³×C₆₇	—	2	4	no	—
162	C₂³×C₆₇	—	4	2	no	—
163	C₂³×C₆₇	—	4	2	no	—
164	C₂³×C₆₇	—	4	4	no	—
165	C₂³×C₆₇	—	4	4	no	—
166	C₂³×C₆₇	—	4	8	no	—
167	C₂³×C₆₇	—	4	16	no	—
168	C₂³×C₆₇	—	8	8	no	—
169	C₂³×C₆₇	—	8	4	no	—
170	C₂³×C₆₇	—	8	4	no	—
171	C₂³×C₆₇	C₄×D₄	1	2	yes	—
172	C₂³×C₆₇	#121	1	2	yes	—
173	C₂³×C₆₇	#127	1	2	yes	—
174	C₂³×C₆₇	C₂×SD₁₆	1	4	yes	—
175	C₂³×C₆₇	#135	1	4	yes	—
176	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₆₇	—	2	4	no	—
178	Q₈×C₆₇	—	2	4	no	—
179	Q₈×C₆₇	—	4	2	no	—
180	Q₈×C₆₇	—	4	2	no	—
181	Q₈×C₆₇	—	4	8	no	—
182	D₄×C₆₇	—	2	4	no	—
183	D₄×C₆₇	—	2	4	no	—
184	D₄×C₆₇	—	4	2	no	—
185	D₄×C₆₇	—	4	2	no	—
186	D₄×C₆₇	—	4	8	no	—
187	C₂×C₄×C₆₇	—	2	4	no	—
188	C₂×C₄×C₆₇	—	2	4	no	—
189	C₂×C₄×C₆₇	—	2	16	no	—
190	C₂×C₄×C₆₇	—	2	4	no	—
191	C₂×C₄×C₆₇	—	4	2	no	—
192	C₂×C₄×C₆₇	—	4	2	no	—
193	C₂×C₄×C₆₇	—	4	8	no	—
194	C₂×C₄×C₆₇	—	4	2	no	—
195	C₂×C₄×C₆₇	—	4	2	no	—
196	C₂×C₄×C₆₇	—	4	4	no	—
197	C₂×C₄×C₆₇	—	4	4	no	—
198	C₂×C₄×C₆₇	—	8	4	no	—
199	C₂×C₄×C₆₇	—	8	4	no	—
200	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
201	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
202	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₆₇	#121	1	4	yes	—
204	C₂×C₄×C₆₇	#121	1	2	yes	—
205	C₂×C₄×C₆₇	#124	1	4	yes	—
206	C₂×C₄×C₆₇	#127	1	2	yes	—
207	C₂×C₄×C₆₇	C₂×SD₁₆	1	8	yes	complemented
208	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂²×D₄	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	C₈×C₆₇	—	2	4	no	—
215	C₈×C₆₇	C₂×C₂²⋊C₄	1	8	yes	complemented
216	C₂²×C₆₇	—	4	8	no	—
217	C₂²×C₆₇	—	4	4	no	—
218	C₂²×C₆₇	—	8	2	no	—
219	C₂²×C₆₇	—	8	2	no	—
220	C₂²×C₆₇	—	8	16	no	—
221	C₂²×C₆₇	—	8	4	no	—
222	C₂²×C₆₇	#390	1	4	yes	—
223	C₂²×C₆₇	C₄×SD₁₆	1	8	yes	—
224	C₂²×C₆₇	#465	1	8	yes	—
225	C₂²×C₆₇	#492	1	4	yes	—
226	C₂²×C₆₇	#495	1	4	yes	—
227	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
229	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
230	C₂²×C₆₇	C₂²×SD₁₆	1	2	yes	—
231	C₂²×C₆₇	C₂×#135	1	2	yes	—
232	C₄×C₆₇	—	2	8	no	—
233	C₄×C₆₇	—	4	4	no	—
234	C₄×C₆₇	—	8	2	no	—
235	C₄×C₆₇	—	8	2	no	—
236	C₄×C₆₇	#390	1	4	yes	—
237	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
240	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
241	C₂×#1968	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₆₇	—	8	4	no	—
243	C₂×C₆₇	#1968	1	8	yes	direct product factor
244	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
245	C₂×C₆₇	C₂×C₄×SD₁₆	1	2	yes	—
246	C₂×C₆₇	C₂×#465	1	2	yes	—
247	C₂×C₆₇	C₂×#492	1	1	yes	characteristic
248	C₂×C₆₇	C₂×#495	1	1	yes	characteristic
249	C₂³×SD₁₆	C₂×C₆₇	1	1	yes	characteristic
250	C₂²×#106	C₂×C₆₇	1	1	yes	characteristic, complemented
251	C₂²×#103	C₂×C₆₇	1	1	yes	characteristic, complemented
252	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic
253	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
254	C₂×#391	C₂×C₆₇	1	1	yes	characteristic, complemented
255	C₂×#390	C₂×C₆₇	1	1	yes	characteristic
256	#1968	C₂×C₆₇	1	8	yes	direct product factor
257	C₆₇	C₂×#1968	1	1	yes	characteristic, direct product factor, Sylow
258	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
260	C₂²×SD₁₆	—	2	4	no	—
261	C₂²×SD₁₆	—	2	4	no	—
262	C₂²×SD₁₆	C₄×C₆₇	1	8	yes	complemented
263	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	—
264	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	—	2	2	no	—
269	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
270	C₂×#106	—	2	4	no	—
271	C₂×#106	C₂²×C₆₇	1	4	yes	complemented
272	C₂×#103	—	2	4	no	—
273	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
274	C₂×#102	—	2	4	no	—
275	C₂×#102	C₂²×C₆₇	1	4	yes	—
276	C₂×C₄×C₈	—	2	4	no	—
277	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
278	#391	—	2	2	no	—
279	#391	C₂²×C₆₇	1	4	yes	complemented
280	#390	—	2	2	no	—
281	#390	C₂²×C₆₇	1	4	yes	—
282	C₂×#95	—	2	2	no	—
283	C₂⁵	—	2	1	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	—
291	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
299	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	D₄×C₆₇	1	2	yes	—
304	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
305	C₂×SD₁₆	—	2	32	no	—
306	C₂×SD₁₆	—	2	8	no	—
307	C₂×SD₁₆	—	2	8	no	—
308	C₂×SD₁₆	C₂×C₄×C₆₇	1	16	yes	complemented
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
312	C₂²×C₈	D₄×C₆₇	1	4	yes	—
313	C₂²×C₈	D₄×C₆₇	1	4	yes	—
314	C₂²×C₈	D₄×C₆₇	1	4	yes	—
315	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
316	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	4	8	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	D₄×C₆₇	1	2	yes	—
330	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
331	#106	—	2	8	no	—
332	#103	—	2	8	no	—
333	#102	—	2	8	no	—
334	C₄×C₈	—	2	8	no	—
335	#95	—	2	8	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	—	4	2	no	—
339	C₂⁴	—	4	2	no	—
340	C₂⁴	—	4	4	no	—
341	C₂⁴	—	4	4	no	—
342	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	8	no	—
346	C₂×Q₈	—	2	8	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	4	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	4	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	SD₁₆×C₆₇	1	8	yes	complemented
382	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
384	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
388	C₂²×C₄	#41×C₆₇	1	2	yes	—
389	C₂²×C₄	#41×C₆₇	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
391	SD₁₆	—	2	32	no	—
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	C₂²⋊C₄×C₆₇	1	16	yes	complemented
396	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
397	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
398	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
399	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	16	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	—	4	4	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	16	no	—
417	C₂³	—	8	8	no	—
418	C₂³	—	8	4	no	—
419	C₂³	—	8	4	no	—
420	C₂³	C₄×D₄×C₆₇	1	2	yes	—
421	C₂³	#121×C₆₇	1	2	yes	—
422	C₂³	#127×C₆₇	1	2	yes	—
423	C₂³	C₂×SD₁₆×C₆₇	1	4	yes	—
424	C₂³	#135×C₆₇	1	4	yes	—
425	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	2	4	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	8	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	8	no	—
436	C₂×C₄	—	2	16	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
450	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
451	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
452	C₂×C₄	#121×C₆₇	1	4	yes	—
453	C₂×C₄	#121×C₆₇	1	2	yes	—
454	C₂×C₄	#124×C₆₇	1	4	yes	—
455	C₂×C₄	#127×C₆₇	1	2	yes	—
456	C₂×C₄	C₂×SD₁₆×C₆₇	1	8	yes	complemented
457	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
463	C₈	—	2	4	no	—
464	C₈	C₂×C₂²⋊C₄×C₆₇	1	8	yes	complemented
465	C₂²	—	4	4	no	—
466	C₂²	—	4	8	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	16	no	—
471	C₂²	#390×C₆₇	1	4	yes	—
472	C₂²	C₄×SD₁₆×C₆₇	1	8	yes	—
473	C₂²	#465×C₆₇	1	8	yes	—
474	C₂²	#492×C₆₇	1	4	yes	—
475	C₂²	#495×C₆₇	1	4	yes	—
476	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
477	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
478	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
479	C₂²	C₂²×SD₁₆×C₆₇	1	2	yes	—
480	C₂²	C₂×#135×C₆₇	1	2	yes	—
481	C₄	—	2	8	no	—
482	C₄	—	4	4	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	2	no	—
485	C₄	#390×C₆₇	1	4	yes	—
486	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
487	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
488	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
489	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
490	C₂	—	8	4	no	—
491	C₂	C₆₇×#1968	1	8	yes	direct product factor
492	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
493	C₂	C₂×C₄×SD₁₆×C₆₇	1	2	yes	—
494	C₂	C₂×#465×C₆₇	1	2	yes	—
495	C₂	C₂×#492×C₆₇	1	1	yes	characteristic
496	C₂	C₂×#495×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#106×C₆₇	C₂	semidirect
3. C₂²×#103×C₆₇	C₂	semidirect
5. C₂²×C₄×C₈×C₆₇	C₂	semidirect
6. C₂×#391×C₆₇	C₂	semidirect
8. C₆₇×#1968	C₂	direct (N × H)
13. C₂²×SD₁₆×C₆₇	C₄	semidirect
22. C₂×#106×C₆₇	C₂²	semidirect
24. C₂×#103×C₆₇	C₂²	semidirect
28. C₂×C₄×C₈×C₆₇	C₂²	semidirect
30. #391×C₆₇	C₂²	semidirect
59. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
132. C₂²×C₄×C₆₇	SD₁₆	semidirect
146. C₂×C₈×C₆₇	C₂²⋊C₄	semidirect
207. C₂×C₄×C₆₇	C₂×SD₁₆	semidirect
215. C₈×C₆₇	C₂×C₂²⋊C₄	semidirect
241. C₂×#1968	C₆₇	direct (N × H)
243. C₂×C₆₇	#1968	direct (N × H)
250. C₂²×#106	C₂×C₆₇	semidirect
251. C₂²×#103	C₂×C₆₇	semidirect
253. C₂²×C₄×C₈	C₂×C₆₇	semidirect
254. C₂×#391	C₂×C₆₇	semidirect
256. #1968	C₂×C₆₇	direct (N × H)
257. C₆₇	C₂×#1968	direct (N × H)
262. C₂²×SD₁₆	C₄×C₆₇	semidirect
271. C₂×#106	C₂²×C₆₇	semidirect
273. C₂×#103	C₂²×C₆₇	semidirect
277. C₂×C₄×C₈	C₂²×C₆₇	semidirect
279. #391	C₂²×C₆₇	semidirect
308. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
381. C₂²×C₄	SD₁₆×C₆₇	semidirect
395. C₂×C₈	C₂²⋊C₄×C₆₇	semidirect
456. C₂×C₄	C₂×SD₁₆×C₆₇	semidirect
464. C₈	C₂×C₂²⋊C₄×C₆₇	semidirect
491. C₂	C₆₇×#1968	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×SD₁₆×C₆₇	2
C₂²×#106×C₆₇	2
C₂²×#103×C₆₇	2
C₂²×#102×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×#391×C₆₇	2
C₂×#390×C₆₇	2
C₆₇×#1968	2
C₂×#1968	67

Subgroups — C2×C67×#1968 #30700472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1968 #30700472