Subgroups — C₆₇×#10834 #30690085

Order 17152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 346 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
2	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#336×C₆₇	C₂	1	4	yes	maximal
5	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
6	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
8	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
9	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₆₇	—	2	2	no	—
11	C₂×C₄⋊C₈×C₆₇	—	2	2	no	—
12	C₂×C₄⋊C₈×C₆₇	C₄	1	4	yes	complemented
13	C₂×C₄×C₈×C₆₇	—	2	2	no	—
14	C₂×C₄×C₈×C₆₇	—	2	2	no	—
15	C₂×C₄×C₈×C₆₇	C₄	1	4	yes	complemented
16	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
17	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
18	C₂×#95×C₆₇	C₄	1	2	yes	—
19	#336×C₆₇	—	2	8	no	—
20	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
21	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₆₇	—	2	2	no	—
25	C₂²×C₈×C₆₇	—	2	2	no	—
26	C₂²×C₈×C₆₇	—	2	2	no	—
27	C₂²×C₈×C₆₇	—	2	2	no	—
28	C₂²×C₈×C₆₇	—	2	4	no	—
29	C₂²×C₈×C₆₇	—	2	2	no	—
30	C₂²×C₈×C₆₇	—	2	2	no	—
31	C₂²×C₈×C₆₇	—	2	4	no	—
32	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₆₇	D₄	1	4	yes	—
35	C₂²×C₈×C₆₇	Q₈	1	4	yes	—
36	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
37	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
38	C₂×C₄⋊C₄×C₆₇	C₈	1	8	yes	complemented
39	C₂×C₄²×C₆₇	—	2	4	no	—
40	C₂×C₄²×C₆₇	—	2	2	no	—
41	C₂×C₄²×C₆₇	—	2	2	no	—
42	C₂×C₄²×C₆₇	—	2	4	no	—
43	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₆₇	D₄	1	2	yes	—
46	C₂×C₄²×C₆₇	D₄	1	2	yes	—
47	C₂×C₄²×C₆₇	D₄	1	2	yes	—
48	C₂×C₄²×C₆₇	Q₈	1	2	yes	—
49	C₄⋊C₈×C₆₇	—	2	8	no	—
50	C₄×C₈×C₆₇	—	2	8	no	—
51	#95×C₆₇	—	2	4	no	—
52	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₆₇	—	2	4	no	—
54	C₂²×C₄×C₆₇	—	2	4	no	—
55	C₂²×C₄×C₆₇	—	2	8	no	—
56	C₂²×C₄×C₆₇	—	2	4	no	—
57	C₂²×C₄×C₆₇	—	2	8	no	—
58	C₂²×C₄×C₆₇	C₄²	1	2	yes	—
59	C₂²×C₄×C₆₇	C₄²	1	2	yes	—
60	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₆₇	C₂×C₈	1	8	yes	—
65	C₂²×C₄×C₆₇	C₂×C₈	1	4	yes	—
66	C₂²×C₄×C₆₇	M₁₆	1	4	yes	—
67	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₆₇	#41	1	2	yes	—
76	C₂²×C₄×C₆₇	#41	1	2	yes	—
77	C₂×C₈×C₆₇	—	2	4	no	—
78	C₂×C₈×C₆₇	—	2	4	no	—
79	C₂×C₈×C₆₇	—	2	4	no	—
80	C₂×C₈×C₆₇	—	2	4	no	—
81	C₂×C₈×C₆₇	—	2	4	no	—
82	C₂×C₈×C₆₇	—	2	4	no	—
83	C₂×C₈×C₆₇	—	2	4	no	—
84	C₂×C₈×C₆₇	—	2	8	no	—
85	C₂×C₈×C₆₇	—	4	4	no	—
86	C₂×C₈×C₆₇	—	4	2	no	—
87	C₂×C₈×C₆₇	—	4	2	no	—
88	C₂×C₈×C₆₇	C₄⋊C₄	1	8	yes	complemented
89	C₄⋊C₄×C₆₇	—	2	16	no	—
90	C₄²×C₆₇	—	4	4	no	—
91	C₄²×C₆₇	—	4	2	no	—
92	C₄²×C₆₇	—	4	2	no	—
93	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
94	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
95	C₄²×C₆₇	C₄⋊C₄	1	4	yes	—
96	C₄²×C₆₇	C₄⋊C₄	1	4	yes	—
97	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
98	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂³×C₆₇	C₄×D₄	1	2	yes	—
101	C₂³×C₆₇	C₄×Q₈	1	2	yes	—
102	C₂³×C₆₇	C₂²×C₈	1	2	yes	—
103	C₂³×C₆₇	C₂×M₁₆	1	2	yes	—
104	C₂³×C₆₇	#131	1	4	yes	—
105	C₂×C₄×C₆₇	—	2	4	no	—
106	C₂×C₄×C₆₇	—	2	4	no	—
107	C₂×C₄×C₆₇	—	2	4	no	—
108	C₂×C₄×C₆₇	—	2	8	no	—
109	C₂×C₄×C₆₇	—	2	16	no	—
110	C₂×C₄×C₆₇	—	4	4	no	—
111	C₂×C₄×C₆₇	—	4	4	no	—
112	C₂×C₄×C₆₇	—	4	8	no	—
113	C₂×C₄×C₆₇	#95	1	4	yes	—
114	C₂×C₄×C₆₇	#95	1	4	yes	—
115	C₂×C₄×C₆₇	C₄×C₈	1	4	yes	—
116	C₂×C₄×C₆₇	#97	1	4	yes	—
117	C₂×C₄×C₆₇	C₂²⋊C₈	1	8	yes	—
118	C₂×C₄×C₆₇	C₄⋊C₈	1	8	yes	—
119	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₆₇	#117	1	2	yes	—
125	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
127	C₂×C₄×C₆₇	#121	1	2	yes	—
128	C₂×C₄×C₆₇	#121	1	2	yes	—
129	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
132	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
133	C₂×C₄×C₆₇	#125	1	2	yes	—
134	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
136	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
137	C₈×C₆₇	—	2	8	no	—
138	C₈×C₆₇	—	4	4	no	—
139	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
140	C₂²×C₆₇	C₄×C₄⋊C₄	1	2	yes	—
141	C₂²×C₆₇	#389	1	2	yes	—
142	C₂²×C₆₇	#390	1	1	yes	characteristic
143	C₂²×C₆₇	#391	1	1	yes	characteristic
144	C₂²×C₆₇	C₂×C₄×C₈	1	1	yes	characteristic
145	C₂²×C₆₇	C₂×#97	1	1	yes	characteristic
146	C₂²×C₆₇	#405	1	2	yes	—
147	C₂²×C₆₇	C₂×C₂²⋊C₈	1	2	yes	—
148	C₂²×C₆₇	#408	1	2	yes	—
149	C₂²×C₆₇	C₂×C₄⋊C₈	1	2	yes	—
150	C₂²×C₆₇	#424	1	2	yes	—
151	C₂²×C₆₇	C₈×D₄	1	4	yes	—
152	C₂²×C₆₇	#436	1	4	yes	—
153	C₂²×C₆₇	C₈×Q₈	1	4	yes	—
154	C₂²×C₆₇	#446	1	4	yes	—
155	C₄×C₆₇	—	2	4	no	—
156	C₄×C₆₇	—	4	8	no	—
157	C₄×C₆₇	#336	1	8	yes	complemented
158	C₄×C₆₇	#380	1	2	yes	—
159	C₄×C₆₇	#382	1	1	yes	characteristic
160	C₄×C₆₇	#384	1	1	yes	characteristic
161	C₄×C₆₇	#389	1	2	yes	—
162	C₄×C₆₇	#390	1	1	yes	characteristic
163	C₄×C₆₇	#391	1	1	yes	characteristic
164	#10834	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₆₇	C₄⋊#95	1	1	yes	characteristic
166	C₂×C₆₇	C₂×#336	1	1	yes	characteristic
167	C₂×C₆₇	#1729	1	1	yes	characteristic
168	C₂×C₆₇	C₈×C₄⋊C₄	1	2	yes	—
169	C₂×C₆₇	#1770	1	2	yes	—
170	C₂×C₆₇	#1939	1	4	yes	—
171	C₂×C₆₇	#1954	1	2	yes	—
172	C₂×C₆₇	#1984	1	2	yes	—
173	C₂²×C₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
174	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic
175	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
176	C₂×#336	C₂×C₆₇	1	4	yes	—
177	C₆₇	#10834	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
179	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
180	C₂²×C₄⋊C₄	C₄×C₆₇	1	2	yes	—
181	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
182	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
183	C₂×C₄⋊C₈	—	2	2	no	—
184	C₂×C₄⋊C₈	—	2	2	no	—
185	C₂×C₄⋊C₈	C₄×C₆₇	1	4	yes	complemented
186	C₂×C₄×C₈	—	2	2	no	—
187	C₂×C₄×C₈	—	2	2	no	—
188	C₂×C₄×C₈	C₄×C₆₇	1	4	yes	complemented
189	C₄×C₄⋊C₄	—	2	2	no	—
190	C₄×C₄⋊C₄	—	2	2	no	—
191	C₂×#95	C₄×C₆₇	1	2	yes	—
192	#336	—	2	8	no	—
193	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
194	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
195	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	—	2	2	no	—
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
206	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
207	C₂²×C₈	D₄×C₆₇	1	4	yes	—
208	C₂²×C₈	Q₈×C₆₇	1	4	yes	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	C₈×C₆₇	1	8	yes	complemented
212	C₂×C₄²	—	2	4	no	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	—	2	4	no	—
216	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
217	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
218	C₂×C₄²	D₄×C₆₇	1	2	yes	—
219	C₂×C₄²	D₄×C₆₇	1	2	yes	—
220	C₂×C₄²	D₄×C₆₇	1	2	yes	—
221	C₂×C₄²	Q₈×C₆₇	1	2	yes	—
222	C₄⋊C₈	—	2	8	no	—
223	C₄×C₈	—	2	8	no	—
224	#95	—	2	4	no	—
225	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	8	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	C₄²×C₆₇	1	2	yes	—
232	C₂²×C₄	C₄²×C₆₇	1	2	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
234	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
235	C₂²×C₄	C₄⋊C₄×C₆₇	1	2	yes	—
236	C₂²×C₄	C₄⋊C₄×C₆₇	1	2	yes	—
237	C₂²×C₄	C₂×C₈×C₆₇	1	8	yes	—
238	C₂²×C₄	C₂×C₈×C₆₇	1	4	yes	—
239	C₂²×C₄	M₁₆×C₆₇	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
246	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
247	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
248	C₂²×C₄	#41×C₆₇	1	2	yes	—
249	C₂²×C₄	#41×C₆₇	1	2	yes	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	2	8	no	—
258	C₂×C₈	—	4	4	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	C₄⋊C₄×C₆₇	1	8	yes	complemented
262	C₄⋊C₄	—	2	16	no	—
263	C₄²	—	4	4	no	—
264	C₄²	—	4	2	no	—
265	C₄²	—	4	2	no	—
266	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
267	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
268	C₄²	C₄⋊C₄×C₆₇	1	4	yes	—
269	C₄²	C₄⋊C₄×C₆₇	1	4	yes	—
270	C₂³	C₂×C₄²×C₆₇	1	1	yes	characteristic
271	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
272	C₂³	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
273	C₂³	C₄×D₄×C₆₇	1	2	yes	—
274	C₂³	C₄×Q₈×C₆₇	1	2	yes	—
275	C₂³	C₂²×C₈×C₆₇	1	2	yes	—
276	C₂³	C₂×M₁₆×C₆₇	1	2	yes	—
277	C₂³	#131×C₆₇	1	4	yes	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	16	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	8	no	—
286	C₂×C₄	#95×C₆₇	1	4	yes	—
287	C₂×C₄	#95×C₆₇	1	4	yes	—
288	C₂×C₄	C₄×C₈×C₆₇	1	4	yes	—
289	C₂×C₄	#97×C₆₇	1	4	yes	—
290	C₂×C₄	C₂²⋊C₈×C₆₇	1	8	yes	—
291	C₂×C₄	C₄⋊C₈×C₆₇	1	8	yes	—
292	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
293	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
294	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
295	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
296	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
297	C₂×C₄	#117×C₆₇	1	2	yes	—
298	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
299	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
300	C₂×C₄	#121×C₆₇	1	2	yes	—
301	C₂×C₄	#121×C₆₇	1	2	yes	—
302	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
303	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
304	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
305	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
306	C₂×C₄	#125×C₆₇	1	2	yes	—
307	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
308	C₂×C₄	C₄⋊Q₈×C₆₇	1	2	yes	—
309	C₂×C₄	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
310	C₈	—	2	8	no	—
311	C₈	—	4	4	no	—
312	C₂²	C₂×#95×C₆₇	1	1	yes	characteristic
313	C₂²	C₄×C₄⋊C₄×C₆₇	1	2	yes	—
314	C₂²	#389×C₆₇	1	2	yes	—
315	C₂²	#390×C₆₇	1	1	yes	characteristic
316	C₂²	#391×C₆₇	1	1	yes	characteristic
317	C₂²	C₂×C₄×C₈×C₆₇	1	1	yes	characteristic
318	C₂²	C₂×#97×C₆₇	1	1	yes	characteristic
319	C₂²	#405×C₆₇	1	2	yes	—
320	C₂²	C₂×C₂²⋊C₈×C₆₇	1	2	yes	—
321	C₂²	#408×C₆₇	1	2	yes	—
322	C₂²	C₂×C₄⋊C₈×C₆₇	1	2	yes	—
323	C₂²	#424×C₆₇	1	2	yes	—
324	C₂²	C₈×D₄×C₆₇	1	4	yes	—
325	C₂²	#436×C₆₇	1	4	yes	—
326	C₂²	C₈×Q₈×C₆₇	1	4	yes	—
327	C₂²	#446×C₆₇	1	4	yes	—
328	C₄	—	2	4	no	—
329	C₄	—	4	8	no	—
330	C₄	#336×C₆₇	1	8	yes	complemented
331	C₄	#380×C₆₇	1	2	yes	—
332	C₄	#382×C₆₇	1	1	yes	characteristic
333	C₄	#384×C₆₇	1	1	yes	characteristic
334	C₄	#389×C₆₇	1	2	yes	—
335	C₄	#390×C₆₇	1	1	yes	characteristic
336	C₄	#391×C₆₇	1	1	yes	characteristic
337	C₂	C₆₇×C₄⋊#95	1	1	yes	characteristic
338	C₂	C₂×#336×C₆₇	1	1	yes	characteristic
339	C₂	C₆₇×#1729	1	1	yes	characteristic
340	C₂	C₈×C₄⋊C₄×C₆₇	1	2	yes	—
341	C₂	C₆₇×#1770	1	2	yes	—
342	C₂	C₆₇×#1939	1	4	yes	—
343	C₂	C₆₇×#1954	1	2	yes	—
344	C₂	C₆₇×#1984	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂²	C₂×C₄×C₈×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
socle, prime radical	C₂⁴×C₆₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₄⋊C₈×C₆₇	C₄	semidirect
15. C₂×C₄×C₈×C₆₇	C₄	semidirect
38. C₂×C₄⋊C₄×C₆₇	C₈	semidirect
88. C₂×C₈×C₆₇	C₄⋊C₄	semidirect
157. C₄×C₆₇	#336	semidirect
164. #10834	C₆₇	direct (N × H)
177. C₆₇	#10834	direct (N × H)
185. C₂×C₄⋊C₈	C₄×C₆₇	semidirect
188. C₂×C₄×C₈	C₄×C₆₇	semidirect
211. C₂×C₄⋊C₄	C₈×C₆₇	semidirect
261. C₂×C₈	C₄⋊C₄×C₆₇	semidirect
330. C₄	#336×C₆₇	semidirect

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×C₄×C₈×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×#336×C₆₇	2
#10834	67

Subgroups — C67×#10834 #30690085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10834 #30690085