Subgroups — #1387×D₆₇ #30770752

Order 17152.

614 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#107×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22558319	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558318	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	—	2	1	no	—
9	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×D₆₇	—	2	1	no	—
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523982	—	2	1	no	—
13	M₃₂×D₆₇	—	2	2	no	—
14	M₃₂×D₆₇	C₄	1	4	yes	complemented
15	C₂×C₁₆×D₆₇	—	2	1	no	—
16	C₂×#14523979	C₂²	1	1	yes	characteristic
17	C₂×#14523978	—	2	1	no	—
18	#108×D₆₇	—	2	2	no	—
19	#108×D₆₇	C₄	1	4	yes	complemented
20	C₂×#14523977	C₂²	1	1	yes	characteristic
21	C₂×#14523976	—	2	1	no	—
22	#107×D₆₇	—	2	1	no	—
23	#107×D₆₇	—	2	1	no	—
24	#107×D₆₇	C₄	1	2	yes	—
25	#107×D₆₇	C₄	1	2	yes	—
26	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₆₇	—	4	1	no	—
30	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
31	C₂×#11761612	—	2	1	no	—
32	C₂×#11761611	—	4	1	no	—
33	M₁₆×D₆₇	—	2	4	no	—
34	M₁₆×D₆₇	—	4	2	no	—
35	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
36	C₂×C₈×D₆₇	—	4	1	no	—
37	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
41	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
42	C₂×C₈×D₆₇	D₄	1	2	yes	—
43	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
44	C₂×C₈×D₆₇	Q₈	1	2	yes	—
45	C₂×C₄⋊Dic₆₇	—	2	1	no	—
46	C₂×Dic₆₇⋊C₄	—	4	1	no	—
47	C₄⋊C₄×D₆₇	—	2	2	no	—
48	C₄⋊C₄×D₆₇	—	2	2	no	—
49	C₄⋊C₄×D₆₇	—	4	1	no	—
50	C₄⋊C₄×D₆₇	—	4	1	no	—
51	#14523983	—	2	1	no	—
52	#14523983	C₂×C₄	1	2	yes	complemented
53	#14523982	—	2	4	no	—
54	C₂×C₆₇⋊C₁₆	—	2	1	no	—
55	C₁₆×D₆₇	—	2	4	no	—
56	#14523979	—	2	1	no	—
57	#14523979	C₂×C₄	1	2	yes	complemented
58	#14523978	—	2	4	no	—
59	#14523977	—	2	1	no	—
60	#14523977	C₂×C₄	1	2	yes	—
61	#14523976	—	2	2	no	—
62	#14523976	—	2	2	no	—
63	C₂×M₁₆×C₆₇	—	2	1	no	—
64	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
66	M₃₂×C₆₇	—	2	1	no	—
67	M₃₂×C₆₇	C₂×C₄	1	2	yes	complemented
68	C₂×C₁₆×C₆₇	—	2	1	no	—
69	#108×C₆₇	—	2	1	no	—
70	#108×C₆₇	C₂×C₄	1	2	yes	complemented
71	#107×C₆₇	—	2	1	no	—
72	#107×C₆₇	C₂×C₄	1	2	yes	—
73	C₂³×D₆₇	SD₁₆	1	1	yes	characteristic
74	C₂²×Dic₆₇	—	4	1	no	—
75	C₂²×Dic₆₇	SD₁₆	1	1	yes	characteristic
76	C₂×C₄×D₆₇	—	4	2	no	—
77	C₂×C₄×D₆₇	—	4	2	no	—
78	C₂×C₄×D₆₇	—	8	4	no	—
79	C₂×C₄×D₆₇	C₂²⋊C₄	1	2	yes	—
80	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
83	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
84	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
85	C₂×C₄×D₆₇	SD₁₆	1	2	yes	—
86	C₂×C₄×D₆₇	Q₁₆	1	2	yes	—
87	#11761612	—	2	2	no	—
88	#11761612	—	4	1	no	—
89	#11761611	—	4	4	no	—
90	C₂×C₆₇⋊C₈	—	4	1	no	—
91	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	2	yes	—
94	C₂×C₆₇⋊C₈	C₄⋊C₄	1	2	yes	—
95	C₈×D₆₇	—	4	4	no	—
96	C₈×D₆₇	C₄²	1	2	yes	—
97	C₈×D₆₇	C₄²	1	2	yes	—
98	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
99	C₈×D₆₇	C₂²⋊C₄	1	2	yes	—
100	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
101	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
102	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
103	C₈×D₆₇	C₄⋊C₄	1	2	yes	—
104	C₄⋊Dic₆₇	—	2	2	no	—
105	C₄⋊Dic₆₇	—	4	1	no	—
106	Dic₆₇⋊C₄	—	4	2	no	—
107	Dic₆₇⋊C₄	—	4	2	no	—
108	C₆₇⋊C₁₆	—	2	2	no	—
109	C₂²×C₄×C₆₇	—	4	1	no	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	M₁₆×C₆₇	—	2	2	no	—
112	M₁₆×C₆₇	—	4	1	no	—
113	C₂×C₈×C₆₇	—	4	1	no	—
114	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	4	1	no	—
122	C₁₆×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
124	C₂²×D₆₇	—	2	2	no	—
125	C₂²×D₆₇	—	2	2	no	—
126	C₂²×D₆₇	#102	1	1	yes	characteristic
127	C₂²×D₆₇	#102	1	1	yes	characteristic
128	C₂²×D₆₇	#103	1	2	yes	—
129	C₂²×D₆₇	#106	1	2	yes	—
130	C₂×C₄×C₆₇	—	4	2	no	—
131	C₂×C₄×C₆₇	—	8	2	no	—
132	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
138	C₂×Dic₆₇	—	4	2	no	—
139	C₂×Dic₆₇	—	8	2	no	—
140	C₂×Dic₆₇	#102	1	1	yes	characteristic
141	C₂×Dic₆₇	#102	1	1	yes	characteristic
142	C₂×Dic₆₇	#103	1	2	yes	—
143	C₂×Dic₆₇	#106	1	2	yes	—
144	C₄×D₆₇	—	8	4	no	—
145	C₄×D₆₇	—	8	4	no	—
146	C₄×D₆₇	#95	1	2	yes	—
147	C₄×D₆₇	#95	1	2	yes	—
148	C₄×D₆₇	#102	1	2	yes	—
149	C₄×D₆₇	#102	1	2	yes	—
150	C₄×D₆₇	#103	1	2	yes	—
151	C₄×D₆₇	#103	1	2	yes	—
152	C₄×D₆₇	#107	1	2	yes	—
153	C₄×D₆₇	#107	1	2	yes	—
154	C₈×C₆₇	—	4	2	no	—
155	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
156	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₆₇⋊C₈	—	4	2	no	—
160	C₆₇⋊C₈	#95	1	2	yes	—
161	C₆₇⋊C₈	#95	1	2	yes	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	1	no	—
164	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
165	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
167	C₂×D₆₇	—	2	1	no	—
168	C₂×D₆₇	—	2	1	no	—
169	C₂×D₆₇	—	2	4	no	—
170	C₂×D₆₇	—	2	4	no	—
171	C₂×D₆₇	#340	1	2	yes	—
172	C₂×D₆₇	#340	1	2	yes	—
173	C₂×D₆₇	#361	1	2	yes	—
174	C₂×D₆₇	#362	1	2	yes	—
175	C₄×C₆₇	—	8	2	no	—
176	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
177	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
178	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
179	C₄×C₆₇	C₂×#107	1	1	yes	characteristic
180	Dic₆₇	—	8	2	no	—
181	Dic₆₇	#340	1	2	yes	—
182	Dic₆₇	#340	1	2	yes	—
183	C₂×#1387	—	67	1	no	maximal, Sylow
184	C₂×C₆₇	—	2	1	no	—
185	C₂×C₆₇	—	2	1	no	—
186	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
187	C₂×C₆₇	C₂×#361	1	1	yes	characteristic
188	C₂×C₆₇	C₂×#362	1	1	yes	characteristic
189	D₆₇	—	2	2	no	—
190	D₆₇	#1387	1	4	yes	direct product factor
191	C₂²×M₃₂	—	67	1	no	—
192	C₂²×#108	—	67	1	no	—
193	C₂²×#107	—	67	1	no	—
194	#1387	—	67	1	no	—
195	#1387	—	67	1	no	—
196	#1387	—	67	1	no	—
197	#1387	D₆₇	1	1	yes	characteristic, direct product factor
198	C₆₇	C₂×#1387	1	1	yes	characteristic, complemented, Sylow
199	C₂²×M₁₆	—	134	1	no	—
200	C₂³×C₈	—	67	1	no	—
201	C₂²×C₄⋊C₄	—	134	1	no	—
202	C₂×M₃₂	—	67	1	no	—
203	C₂×M₃₂	—	67	4	no	—
204	C₂×M₃₂	—	134	1	no	—
205	C₂×M₃₂	—	134	2	no	—
206	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
207	C₂²×C₁₆	—	134	1	no	—
208	C₂×#108	—	67	1	no	—
209	C₂×#108	—	67	4	no	—
210	C₂×#108	—	134	2	no	—
211	C₂×#108	—	134	1	no	—
212	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
213	C₂×#107	—	67	1	no	—
214	C₂×#107	—	67	2	no	—
215	C₂×#107	—	67	2	no	—
216	C₂×#107	—	134	1	no	—
217	C₂×#107	—	134	1	no	—
218	C₂×#107	—	134	1	no	—
219	C₂×#107	C₂×D₆₇	1	1	yes	characteristic
220	C₂³×C₄	—	268	1	no	—
221	C₂³×C₄	—	67	1	no	—
222	C₂×M₁₆	—	2	1	no	—
223	C₂×M₁₆	—	268	1	no	—
224	C₂×M₁₆	—	268	2	no	—
225	C₂×M₁₆	—	134	4	no	—
226	C₂×M₁₆	—	134	1	no	—
227	C₂²×C₈	—	268	1	no	—
228	C₂²×C₈	—	67	1	no	—
229	C₂²×C₈	—	67	1	no	—
230	C₂²×C₈	—	67	1	no	—
231	C₂²×C₈	—	67	2	no	—
232	C₂²×C₈	—	67	2	no	—
233	C₂²×C₈	—	67	1	no	—
234	C₂²×C₈	—	67	1	no	—
235	C₂²×C₈	—	67	2	no	—
236	C₂²×C₈	—	67	2	no	—
237	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	268	1	no	—
240	C₂×C₄⋊C₄	—	268	1	no	—
241	C₂×C₄⋊C₄	—	268	1	no	—
242	C₂×C₄⋊C₄	—	134	2	no	—
243	C₂×C₄⋊C₄	—	134	2	no	—
244	C₂×C₄⋊C₄	—	134	1	no	—
245	M₃₂	—	2	1	no	—
246	M₃₂	—	67	2	no	—
247	M₃₂	—	134	4	no	—
248	M₃₂	—	134	1	no	—
249	M₃₂	C₄×D₆₇	1	2	yes	complemented
250	C₂×C₁₆	—	2	1	no	—
251	C₂×C₁₆	—	134	4	no	—
252	C₂×C₁₆	—	134	1	no	—
253	#108	—	2	1	no	—
254	#108	—	67	2	no	—
255	#108	—	134	4	no	—
256	#108	—	134	1	no	—
257	#108	C₄×D₆₇	1	2	yes	complemented
258	#107	—	2	1	no	—
259	#107	—	67	2	no	—
260	#107	—	134	2	no	—
261	#107	—	134	2	no	—
262	#107	—	134	1	no	—
263	#107	C₄×D₆₇	1	2	yes	—
264	C₂⁴	—	67	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	268	2	no	—
267	C₂²×C₄	—	268	2	no	—
268	C₂²×C₄	—	268	1	no	—
269	C₂²×C₄	—	536	4	no	—
270	C₂²×C₄	—	67	1	no	—
271	C₂²×C₄	—	67	1	no	—
272	C₂²×C₄	—	67	1	no	—
273	C₂²×C₄	—	67	2	no	—
274	C₂²×C₄	—	67	2	no	—
275	C₂²×C₄	—	67	1	no	—
276	C₂²×C₄	—	67	1	no	—
277	C₂²×C₄	—	67	2	no	—
278	C₂²×C₄	—	67	2	no	—
279	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
280	M₁₆	—	2	2	no	—
281	M₁₆	—	4	1	no	—
282	M₁₆	—	268	4	no	—
283	M₁₆	—	268	1	no	—
284	M₁₆	—	134	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	268	4	no	—
287	C₂×C₈	—	268	1	no	—
288	C₂×C₈	—	67	1	no	—
289	C₂×C₈	—	67	1	no	—
290	C₂×C₈	—	67	2	no	—
291	C₂×C₈	—	67	2	no	—
292	C₂×C₈	—	67	2	no	—
293	C₂×C₈	—	67	2	no	—
294	C₂×C₈	—	67	2	no	—
295	C₂×C₈	—	67	2	no	—
296	C₂×C₈	—	67	2	no	—
297	C₂×C₈	—	67	2	no	—
298	C₂×C₈	—	67	2	no	—
299	C₂×C₈	—	67	2	no	—
300	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
301	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
302	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
303	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
304	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
305	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	268	2	no	—
309	C₄⋊C₄	—	268	2	no	—
310	C₄⋊C₄	—	268	1	no	—
311	C₄⋊C₄	—	134	2	no	—
312	C₁₆	—	2	2	no	—
313	C₁₆	—	134	2	no	—
314	C₂³	—	67	1	no	—
315	C₂³	—	67	1	no	—
316	C₂³	—	67	2	no	—
317	C₂³	—	67	2	no	—
318	C₂³	—	134	2	no	—
319	C₂³	—	134	2	no	—
320	C₂³	SD₁₆×D₆₇	1	1	yes	characteristic
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	8	2	no	—
323	C₂×C₄	—	268	2	no	—
324	C₂×C₄	—	536	4	no	—
325	C₂×C₄	—	536	4	no	—
326	C₂×C₄	—	536	2	no	—
327	C₂×C₄	—	67	1	no	—
328	C₂×C₄	—	67	1	no	—
329	C₂×C₄	—	67	2	no	—
330	C₂×C₄	—	67	2	no	—
331	C₂×C₄	—	67	2	no	—
332	C₂×C₄	—	67	2	no	—
333	C₂×C₄	—	67	2	no	—
334	C₂×C₄	—	67	2	no	—
335	C₂×C₄	—	67	2	no	—
336	C₂×C₄	—	67	2	no	—
337	C₂×C₄	—	67	2	no	—
338	C₂×C₄	—	67	2	no	—
339	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
341	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
342	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
343	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
344	C₂×C₄	Q₁₆×D₆₇	1	1	yes	characteristic
345	C₈	—	4	2	no	—
346	C₈	—	268	2	no	—
347	C₈	—	67	2	no	—
348	C₈	—	67	2	no	—
349	C₈	C₄²×D₆₇	1	1	yes	characteristic
350	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
351	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
352	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	67	2	no	—
356	C₂²	—	67	2	no	—
357	C₂²	—	67	2	no	—
358	C₂²	—	67	2	no	—
359	C₂²	—	134	4	no	—
360	C₂²	—	134	4	no	—
361	C₂²	—	134	1	no	—
362	C₂²	—	134	1	no	—
363	C₂²	#102×D₆₇	1	1	yes	characteristic
364	C₂²	#103×D₆₇	1	1	yes	characteristic
365	C₂²	#106×D₆₇	1	1	yes	characteristic
366	C₄	—	8	2	no	—
367	C₄	—	536	2	no	—
368	C₄	—	67	2	no	—
369	C₄	—	67	2	no	—
370	C₄	#95×D₆₇	1	1	yes	characteristic
371	C₄	#102×D₆₇	1	1	yes	characteristic
372	C₄	#103×D₆₇	1	1	yes	characteristic
373	C₄	#107×D₆₇	1	1	yes	characteristic
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	67	4	no	—
377	C₂	—	134	2	no	—
378	C₂	#340×D₆₇	1	1	yes	characteristic
379	C₂	#361×D₆₇	1	1	yes	characteristic
380	C₂	#362×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#102×D₆₇
commutator	C₈×C₆₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1387	C₂
socle	C₂²×C₆₇	C₂×#102
prime radical	C₂³×D₆₇	SD₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1387	D₆₇
hypocenter	C₆₇	C₂×#1387
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1387

Complements

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

N	H ≅ G/N	type
4. #22558319	C₂	semidirect
5. #22558318	C₂	semidirect
6. #22558317	C₂	semidirect
7. C₆₇×#1387	C₂	semidirect
14. M₃₂×D₆₇	C₄	semidirect
19. #108×D₆₇	C₄	semidirect
52. #14523983	C₂×C₄	semidirect
57. #14523979	C₂×C₄	semidirect
67. M₃₂×C₆₇	C₂×C₄	semidirect
70. #108×C₆₇	C₂×C₄	semidirect
190. D₆₇	#1387	direct (N × H)
197. #1387	D₆₇	direct (N × H)
198. C₆₇	C₂×#1387	semidirect
249. M₃₂	C₄×D₆₇	semidirect
257. #108	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₆₇	2
C₂×#108×D₆₇	2
C₂×#107×D₆₇	2
#22558319	2
#22558318	2
#22558317	2
C₆₇×#1387	2
C₂×#1387	67

Subgroups — #1387×D67 #30770752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1387×D₆₇ #30770752