Subgroups — #1389×D₆₇ #30770764

Order 17152.

570 conjugacy classes of subgroups.

The subgroup lattice has 466 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	#427×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22558325	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558324	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558323	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₆₇	—	2	1	no	—
9	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	#117×D₆₇	—	2	1	no	—
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	C₂×#14523982	—	2	1	no	—
13	M₃₂×D₆₇	—	2	1	no	—
14	M₃₂×D₆₇	—	2	1	no	—
15	M₃₂×D₆₇	C₄	1	2	yes	complemented
16	M₃₂×D₆₇	C₄	1	2	yes	complemented
17	C₂×C₁₆×D₆₇	—	2	1	no	—
18	C₂×#14523979	C₂²	1	1	yes	characteristic
19	C₂×#14523978	—	2	1	no	—
20	#108×D₆₇	—	2	1	no	—
21	#108×D₆₇	—	2	1	no	—
22	#108×D₆₇	C₄	1	2	yes	complemented
23	#108×D₆₇	C₄	1	2	yes	complemented
24	#16863434	C₂²	1	1	yes	characteristic
25	#16863433	—	2	1	no	—
26	#16863432	—	2	1	no	—
27	#16863431	C₄	1	2	yes	—
28	#107×D₆₇	—	2	1	no	—
29	#106×D₆₇	C₄	1	2	yes	—
30	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
32	#427×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
34	C₂×#11761612	—	2	1	no	—
35	C₂×#11761611	—	4	1	no	—
36	M₁₆×D₆₇	—	2	2	no	—
37	M₁₆×D₆₇	—	2	2	no	—
38	M₁₆×D₆₇	—	4	1	no	—
39	M₁₆×D₆₇	—	4	1	no	—
40	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
41	C₂×C₈×D₆₇	—	4	1	no	—
42	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
49	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
50	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
53	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
54	#14524002	—	2	1	no	—
55	#14524001	—	2	2	no	—
56	#14524000	—	4	1	no	—
57	#14523999	—	4	1	no	—
58	C₄⋊C₄×D₆₇	—	2	2	no	—
59	C₂²⋊C₄×D₆₇	—	4	1	no	—
60	C₄²×D₆₇	—	4	1	no	—
61	#14523983	—	2	1	no	—
62	#14523983	C₂×C₄	1	2	yes	complemented
63	#14523982	—	2	2	no	—
64	#14523982	—	2	2	no	—
65	C₂×C₆₇⋊C₁₆	—	2	1	no	—
66	C₁₆×D₆₇	—	2	2	no	—
67	C₁₆×D₆₇	—	2	2	no	—
68	#14523979	—	2	1	no	—
69	#14523979	C₂×C₄	1	2	yes	complemented
70	#14523978	—	2	2	no	—
71	#14523978	—	2	2	no	—
72	#14523977	—	2	1	no	—
73	#14523976	—	2	2	no	—
74	#14523975	C₂×C₄	1	2	yes	—
75	#14523974	—	2	2	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
78	#117×C₆₇	—	2	1	no	—
79	M₃₂×C₆₇	—	2	1	no	—
80	M₃₂×C₆₇	C₂×C₄	1	2	yes	complemented
81	C₂×C₁₆×C₆₇	—	2	1	no	—
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	C₂×C₄	1	2	yes	complemented
84	#107×C₆₇	—	2	1	no	—
85	#106×C₆₇	C₂×C₄	1	2	yes	—
86	C₂³×D₆₇	SD₁₆	1	1	yes	characteristic
87	C₂²×Dic₆₇	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₆₇	—	4	2	no	—
89	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
96	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
97	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
98	C₂×C₄×D₆₇	SD₁₆	1	1	yes	characteristic
99	C₂×C₄×D₆₇	Q₁₆	1	1	yes	characteristic
100	C₂×C₄×D₆₇	Q₁₆	1	1	yes	characteristic
101	#11761612	—	2	2	no	—
102	#11761612	—	4	1	no	—
103	#11761611	—	4	2	no	—
104	#11761611	—	4	2	no	—
105	C₂×C₆₇⋊C₈	—	4	1	no	—
106	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
112	C₈×D₆₇	—	4	2	no	—
113	C₈×D₆₇	—	4	2	no	—
114	C₈×D₆₇	C₄²	1	1	yes	characteristic
115	C₈×D₆₇	C₄²	1	1	yes	characteristic
116	C₈×D₆₇	C₄²	1	1	yes	characteristic
117	C₈×D₆₇	C₄²	1	1	yes	characteristic
118	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₈×D₆₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
123	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
124	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
125	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₆₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊Dic₆₇	—	2	2	no	—
131	Dic₆₇⋊C₄	—	4	2	no	—
132	C₂²⋊Dic₆₇	—	4	1	no	—
133	(C₂×D₆₇)⋊C₄	—	4	2	no	—
134	C₄×Dic₆₇	—	4	1	no	—
135	C₄×Dic₆₇	—	4	2	no	—
136	C₆₇⋊C₁₆	—	2	2	no	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	M₁₆×C₆₇	—	2	2	no	—
139	M₁₆×C₆₇	—	4	1	no	—
140	C₂×C₈×C₆₇	—	4	1	no	—
141	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
147	C₄⋊C₄×C₆₇	—	2	2	no	—
148	C₂²⋊C₄×C₆₇	—	4	1	no	—
149	C₄²×C₆₇	—	4	1	no	—
150	C₁₆×C₆₇	—	2	2	no	—
151	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
152	C₂²×D₆₇	—	4	2	no	—
153	C₂²×D₆₇	#102	1	1	yes	characteristic
154	C₂²×D₆₇	#102	1	1	yes	characteristic
155	C₂²×D₆₇	#103	1	1	yes	characteristic
156	C₂²×D₆₇	#103	1	1	yes	characteristic
157	C₂²×D₆₇	#106	1	1	yes	characteristic
158	C₂²×D₆₇	#106	1	1	yes	characteristic
159	C₂×C₄×C₆₇	—	4	2	no	—
160	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
166	C₂×Dic₆₇	—	4	2	no	—
167	C₂×Dic₆₇	#102	1	1	yes	characteristic
168	C₂×Dic₆₇	#102	1	1	yes	characteristic
169	C₂×Dic₆₇	#103	1	1	yes	characteristic
170	C₂×Dic₆₇	#103	1	1	yes	characteristic
171	C₂×Dic₆₇	#106	1	1	yes	characteristic
172	C₂×Dic₆₇	#106	1	1	yes	characteristic
173	C₄×D₆₇	—	8	4	no	—
174	C₄×D₆₇	#95	1	1	yes	characteristic
175	C₄×D₆₇	#95	1	1	yes	characteristic
176	C₄×D₆₇	#95	1	1	yes	characteristic
177	C₄×D₆₇	#95	1	1	yes	characteristic
178	C₄×D₆₇	#102	1	1	yes	characteristic
179	C₄×D₆₇	#102	1	1	yes	characteristic
180	C₄×D₆₇	#102	1	1	yes	characteristic
181	C₄×D₆₇	#102	1	1	yes	characteristic
182	C₄×D₆₇	#103	1	1	yes	characteristic
183	C₄×D₆₇	#103	1	1	yes	characteristic
184	C₄×D₆₇	#103	1	1	yes	characteristic
185	C₄×D₆₇	#103	1	1	yes	characteristic
186	C₄×D₆₇	#107	1	1	yes	characteristic
187	C₄×D₆₇	#107	1	1	yes	characteristic
188	C₄×D₆₇	#107	1	1	yes	characteristic
189	C₄×D₆₇	#107	1	1	yes	characteristic
190	C₈×C₆₇	—	4	2	no	—
191	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
192	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₆₇⋊C₈	—	4	2	no	—
196	C₆₇⋊C₈	#95	1	1	yes	characteristic
197	C₆₇⋊C₈	#95	1	1	yes	characteristic
198	C₆₇⋊C₈	#95	1	1	yes	characteristic
199	C₆₇⋊C₈	#95	1	1	yes	characteristic
200	C₂²×C₆₇	—	4	1	no	—
201	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
202	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
203	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
204	C₂×D₆₇	—	2	2	no	—
205	C₂×D₆₇	—	2	2	no	—
206	C₂×D₆₇	—	2	2	no	—
207	C₂×D₆₇	—	4	1	no	—
208	C₂×D₆₇	—	4	1	no	—
209	C₂×D₆₇	—	4	1	no	—
210	C₂×D₆₇	#340	1	1	yes	characteristic
211	C₂×D₆₇	#340	1	1	yes	characteristic
212	C₂×D₆₇	#340	1	1	yes	characteristic
213	C₂×D₆₇	#340	1	1	yes	characteristic
214	C₄×C₆₇	—	8	2	no	—
215	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
216	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
217	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
218	C₄×C₆₇	C₂×#107	1	1	yes	characteristic
219	Dic₆₇	—	8	2	no	—
220	Dic₆₇	#340	1	1	yes	characteristic
221	Dic₆₇	#340	1	1	yes	characteristic
222	Dic₆₇	#340	1	1	yes	characteristic
223	Dic₆₇	#340	1	1	yes	characteristic
224	C₂×#1389	—	67	1	no	maximal, Sylow
225	C₂×C₆₇	—	2	1	no	—
226	C₂×C₆₇	—	2	1	no	—
227	C₂×C₆₇	—	2	1	no	—
228	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
229	D₆₇	—	2	1	no	—
230	D₆₇	—	2	1	no	—
231	D₆₇	—	2	1	no	—
232	D₆₇	#1389	1	2	yes	direct product factor
233	C₂²×M₃₂	—	67	1	no	—
234	C₂²×#108	—	67	1	no	—
235	C₂×#427	—	67	1	no	—
236	#1389	—	67	1	no	—
237	#1389	—	67	1	no	—
238	#1389	—	67	1	no	—
239	#1389	D₆₇	1	1	yes	characteristic, direct product factor
240	C₆₇	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	134	1	no	—
242	C₂³×C₈	—	67	1	no	—
243	C₂×#117	—	134	1	no	—
244	C₂×M₃₂	—	67	1	no	—
245	C₂×M₃₂	—	67	2	no	—
246	C₂×M₃₂	—	67	2	no	—
247	C₂×M₃₂	—	134	1	no	—
248	C₂×M₃₂	—	134	1	no	—
249	C₂×M₃₂	—	134	1	no	—
250	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
251	C₂²×C₁₆	—	134	1	no	—
252	C₂×#108	—	67	1	no	—
253	C₂×#108	—	67	2	no	—
254	C₂×#108	—	67	2	no	—
255	C₂×#108	—	134	1	no	—
256	C₂×#108	—	134	1	no	—
257	C₂×#108	—	134	1	no	—
258	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
259	#427	—	67	1	no	—
260	#427	—	67	2	no	—
261	#427	—	134	1	no	—
262	#427	—	134	1	no	—
263	#427	C₂×D₆₇	1	1	yes	characteristic
264	C₂×#107	—	134	1	no	—
265	C₂×#106	—	67	2	no	—
266	C₂³×C₄	—	67	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	268	1	no	—
269	C₂×M₁₆	—	268	1	no	—
270	C₂×M₁₆	—	268	1	no	—
271	C₂×M₁₆	—	134	2	no	—
272	C₂×M₁₆	—	134	2	no	—
273	C₂×M₁₆	—	134	1	no	—
274	C₂²×C₈	—	268	1	no	—
275	C₂²×C₈	—	67	1	no	—
276	C₂²×C₈	—	67	1	no	—
277	C₂²×C₈	—	67	1	no	—
278	C₂²×C₈	—	67	1	no	—
279	C₂²×C₈	—	67	1	no	—
280	C₂²×C₈	—	67	1	no	—
281	C₂²×C₈	—	67	1	no	—
282	C₂²×C₈	—	67	1	no	—
283	C₂²×C₈	—	67	1	no	—
284	C₂²×C₈	—	67	1	no	—
285	C₂²×C₈	—	67	1	no	—
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	—	67	1	no	—
288	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	—	268	1	no	—
291	#117	—	268	1	no	—
292	#117	—	134	2	no	—
293	#117	—	134	1	no	—
294	C₂×C₄⋊C₄	—	134	2	no	—
295	C₂×C₂²⋊C₄	—	268	1	no	—
296	C₂×C₄²	—	268	1	no	—
297	M₃₂	—	2	1	no	—
298	M₃₂	—	67	2	no	—
299	M₃₂	—	134	2	no	—
300	M₃₂	—	134	2	no	—
301	M₃₂	—	134	1	no	—
302	M₃₂	C₄×D₆₇	1	2	yes	complemented
303	C₂×C₁₆	—	2	1	no	—
304	C₂×C₁₆	—	134	2	no	—
305	C₂×C₁₆	—	134	2	no	—
306	C₂×C₁₆	—	134	1	no	—
307	#108	—	2	1	no	—
308	#108	—	67	2	no	—
309	#108	—	134	2	no	—
310	#108	—	134	2	no	—
311	#108	—	134	1	no	—
312	#108	C₄×D₆₇	1	2	yes	complemented
313	#107	—	2	1	no	—
314	#107	—	134	2	no	—
315	#107	—	134	1	no	—
316	#106	—	67	2	no	—
317	#106	—	134	2	no	—
318	#106	C₄×D₆₇	1	2	yes	—
319	C₂⁴	—	67	1	no	—
320	C₂²×C₄	—	268	2	no	—
321	C₂²×C₄	—	67	1	no	—
322	C₂²×C₄	—	67	1	no	—
323	C₂²×C₄	—	67	1	no	—
324	C₂²×C₄	—	67	1	no	—
325	C₂²×C₄	—	67	1	no	—
326	C₂²×C₄	—	67	1	no	—
327	C₂²×C₄	—	67	1	no	—
328	C₂²×C₄	—	67	1	no	—
329	C₂²×C₄	—	67	1	no	—
330	C₂²×C₄	—	67	1	no	—
331	C₂²×C₄	—	67	1	no	—
332	C₂²×C₄	—	67	1	no	—
333	C₂²×C₄	—	67	1	no	—
334	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
335	M₁₆	—	2	2	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	268	2	no	—
338	M₁₆	—	268	2	no	—
339	M₁₆	—	268	1	no	—
340	M₁₆	—	134	2	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	268	2	no	—
343	C₂×C₈	—	268	2	no	—
344	C₂×C₈	—	268	1	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	1	no	—
347	C₂×C₈	—	67	1	no	—
348	C₂×C₈	—	67	1	no	—
349	C₂×C₈	—	67	1	no	—
350	C₂×C₈	—	67	1	no	—
351	C₂×C₈	—	67	1	no	—
352	C₂×C₈	—	67	1	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	67	1	no	—
356	C₂×C₈	—	67	1	no	—
357	C₂×C₈	—	67	1	no	—
358	C₂×C₈	—	67	1	no	—
359	C₂×C₈	—	67	1	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	67	1	no	—
362	C₂×C₈	—	67	1	no	—
363	C₂×C₈	—	67	1	no	—
364	C₂×C₈	—	67	1	no	—
365	C₂×C₈	—	67	1	no	—
366	C₂×C₈	—	67	1	no	—
367	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
369	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
370	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
371	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
372	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	268	2	no	—
375	C₄⋊C₄	—	134	2	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	268	2	no	—
378	C₂²⋊C₄	—	268	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	268	2	no	—
381	C₄²	—	268	1	no	—
382	C₁₆	—	2	2	no	—
383	C₁₆	—	134	2	no	—
384	C₂³	—	268	2	no	—
385	C₂³	—	67	1	no	—
386	C₂³	—	67	1	no	—
387	C₂³	—	67	1	no	—
388	C₂³	—	67	1	no	—
389	C₂³	—	67	1	no	—
390	C₂³	—	67	1	no	—
391	C₂³	SD₁₆×D₆₇	1	1	yes	characteristic
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	268	2	no	—
394	C₂×C₄	—	536	4	no	—
395	C₂×C₄	—	67	1	no	—
396	C₂×C₄	—	67	1	no	—
397	C₂×C₄	—	67	1	no	—
398	C₂×C₄	—	67	1	no	—
399	C₂×C₄	—	67	1	no	—
400	C₂×C₄	—	67	1	no	—
401	C₂×C₄	—	67	1	no	—
402	C₂×C₄	—	67	1	no	—
403	C₂×C₄	—	67	1	no	—
404	C₂×C₄	—	67	1	no	—
405	C₂×C₄	—	67	1	no	—
406	C₂×C₄	—	67	1	no	—
407	C₂×C₄	—	67	1	no	—
408	C₂×C₄	—	67	1	no	—
409	C₂×C₄	—	67	1	no	—
410	C₂×C₄	—	67	1	no	—
411	C₂×C₄	—	67	1	no	—
412	C₂×C₄	—	67	1	no	—
413	C₂×C₄	—	67	1	no	—
414	C₂×C₄	—	67	1	no	—
415	C₂×C₄	—	67	1	no	—
416	C₂×C₄	—	67	1	no	—
417	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
418	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
420	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
421	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
422	C₂×C₄	Q₁₆×D₆₇	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	268	2	no	—
425	C₈	—	67	1	no	—
426	C₈	—	67	1	no	—
427	C₈	—	67	1	no	—
428	C₈	—	67	1	no	—
429	C₈	C₄²×D₆₇	1	1	yes	characteristic
430	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
431	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
432	C₈	C₄⋊C₄×D₆₇	1	1	yes	characteristic
433	C₂²	—	4	1	no	—
434	C₂²	—	268	1	no	—
435	C₂²	—	268	1	no	—
436	C₂²	—	268	1	no	—
437	C₂²	—	67	1	no	—
438	C₂²	—	67	1	no	—
439	C₂²	—	67	1	no	—
440	C₂²	—	67	1	no	—
441	C₂²	—	134	2	no	—
442	C₂²	—	134	2	no	—
443	C₂²	—	134	2	no	—
444	C₂²	#102×D₆₇	1	1	yes	characteristic
445	C₂²	#103×D₆₇	1	1	yes	characteristic
446	C₂²	#106×D₆₇	1	1	yes	characteristic
447	C₄	—	8	2	no	—
448	C₄	—	536	2	no	—
449	C₄	—	67	1	no	—
450	C₄	—	67	1	no	—
451	C₄	—	67	1	no	—
452	C₄	—	67	1	no	—
453	C₄	#95×D₆₇	1	1	yes	characteristic
454	C₄	#102×D₆₇	1	1	yes	characteristic
455	C₄	#103×D₆₇	1	1	yes	characteristic
456	C₄	#107×D₆₇	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	67	2	no	—
461	C₂	—	134	1	no	—
462	C₂	—	134	1	no	—
463	C₂	—	134	1	no	—
464	C₂	#340×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#102×D₆₇
commutator	C₈×C₆₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1389	C₂
socle	C₂×C₆₇	C₂×#340
prime radical	C₂³×D₆₇	SD₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1389	D₆₇
hypocenter	C₆₇	C₂×#1389
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1389

Complements

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

N	H ≅ G/N	type
4. #22558325	C₂	semidirect
5. #22558324	C₂	semidirect
6. #22558323	C₂	semidirect
7. C₆₇×#1389	C₂	semidirect
15. M₃₂×D₆₇	C₄	semidirect
16. M₃₂×D₆₇	C₄	semidirect
22. #108×D₆₇	C₄	semidirect
23. #108×D₆₇	C₄	semidirect
62. #14523983	C₂×C₄	semidirect
69. #14523979	C₂×C₄	semidirect
80. M₃₂×C₆₇	C₂×C₄	semidirect
83. #108×C₆₇	C₂×C₄	semidirect
232. D₆₇	#1389	direct (N × H)
239. #1389	D₆₇	direct (N × H)
240. C₆₇	C₂×#1389	semidirect
302. M₃₂	C₄×D₆₇	semidirect
312. #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
#427×D₆₇	2
#22558325	2
#22558324	2
#22558323	2
C₆₇×#1389	2
C₂×#1389	67

Subgroups — #1389×D67 #30770764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1389×D₆₇ #30770764