Subgroups — #1589×D₆₇ #30825555

Order 17152.

822 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#436×D₆₇	C₂	1	2	yes	maximal, complemented
3	#22559095	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559094	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559093	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559092	C₂	1	2	yes	maximal, complemented
7	#22559091	C₂	1	2	yes	maximal, complemented
8	#335×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄⋊C₈×D₆₇	C₂	1	2	yes	maximal, complemented
10	C₈²×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₆₇	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₆₇	—	2	2	no	—
14	C₄×D₄×D₆₇	C₂²	1	2	yes	—
15	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
16	D₈×Dic₆₇	C₄	1	1	yes	characteristic
17	#16863478	C₄	1	1	yes	characteristic
18	C₄×#11761613	C₂²	1	2	yes	—
19	#16863476	C₄	1	2	yes	—
20	#16863475	C₂²	1	2	yes	complemented
21	#16863474	C₂²	1	2	yes	complemented
22	#16863473	C₂²	1	2	yes	complemented
23	#16863472	—	2	2	no	—
24	#16863471	—	2	2	no	—
25	#107×D₆₇	C₄	1	1	yes	characteristic
26	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
27	#102×D₆₇	C₄	1	2	yes	—
28	C₂²⋊C₈×D₆₇	—	2	2	no	—
29	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic, complemented
33	#16863148	C₂²	1	2	yes	complemented
34	#16863125	C₂²	1	2	yes	complemented
35	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
36	#16863123	C₂²	1	2	yes	complemented
37	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
41	#436×C₆₇	C₂²	1	2	yes	complemented
42	#335×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₆₇	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₆₇	—	2	2	no	—
47	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761613	C₂×C₄	1	2	yes	—
49	D₈×D₆₇	—	2	4	no	—
50	C₂×#11761612	—	2	2	no	—
51	C₂×#11761611	—	2	2	no	—
52	C₂×#11761611	—	2	2	no	—
53	M₁₆×D₆₇	—	4	8	no	—
54	C₂×C₈×D₆₇	—	2	1	no	—
55	C₂×C₈×D₆₇	—	2	2	no	—
56	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
59	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
60	C₄×D₂₆₈	C₂³	1	2	yes	—
61	D₄×Dic₆₇	C₂×C₄	1	2	yes	—
62	#14524005	C₂×C₄	1	2	yes	—
63	C₄×C₂²⋊D₆₇	—	2	2	no	—
64	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
65	C₄⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
66	C₂²⋊C₄×D₆₇	—	2	2	no	—
67	C₄²×D₆₇	C₂³	1	1	yes	characteristic
68	#14523977	C₂×C₄	1	1	yes	characteristic
69	#14523976	C₂×C₄	1	2	yes	—
70	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
71	Dic₆₇⋊C₈	—	2	2	no	—
72	#14523965	C₂×C₄	1	2	yes	—
73	#14523964	C₂×C₄	1	2	yes	—
74	#14523963	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
76	(C₂×D₆₇)⋊C₈	—	2	2	no	—
77	(C₂×D₆₇)⋊C₈	—	2	2	no	—
78	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₈×Dic₆₇	—	2	1	no	—
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₇	D₄	1	1	yes	characteristic
85	C₈×Dic₆₇	D₄	1	1	yes	characteristic
86	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂×M₁₆×C₆₇	—	2	2	no	—
88	C₄×D₄×C₆₇	C₂³	1	2	yes	—
89	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
91	#102×C₆₇	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₆₇	—	2	2	no	—
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×D₆₇	—	2	2	no	—
97	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₆₇	—	2	2	no	—
99	D₄×D₆₇	—	2	4	no	—
100	D₄×D₆₇	—	2	4	no	—
101	C₂²×Dic₆₇	—	2	2	no	—
102	C₂×C₄×D₆₇	—	2	2	no	—
103	C₂×C₄×D₆₇	—	2	2	no	—
104	C₂×C₄×D₆₇	—	2	2	no	—
105	C₂×C₄×D₆₇	—	4	4	no	—
106	C₂×C₄×D₆₇	—	4	4	no	—
107	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
110	D₅₃₆	—	2	2	no	—
111	#11761613	—	2	4	no	—
112	#11761612	—	4	4	no	—
113	#11761611	—	4	4	no	—
114	#11761611	—	4	4	no	—
115	C₂×C₆₇⋊C₈	—	2	1	no	—
116	C₂×C₆₇⋊C₈	—	2	2	no	—
117	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₈×D₆₇	—	2	4	no	—
122	C₈×D₆₇	—	2	2	no	—
123	C₈×D₆₇	—	2	2	no	—
124	C₈×D₆₇	—	4	4	no	—
125	C₈×D₆₇	M₁₆	1	4	yes	complemented
126	C₈×D₆₇	D₈	1	4	yes	complemented
127	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
128	Dic₆₇⋊C₄	—	2	2	no	—
129	C₂²⋊Dic₆₇	—	2	2	no	—
130	(C₂×D₆₇)⋊C₄	—	2	2	no	—
131	(C₂×D₆₇)⋊C₄	—	2	2	no	—
132	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₆₇	#41	1	1	yes	characteristic
135	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₆₇	—	2	2	no	—
137	D₈×C₆₇	—	2	2	no	—
138	M₁₆×C₆₇	—	4	4	no	—
139	C₂×C₈×C₆₇	—	2	1	no	—
140	C₂×C₈×C₆₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
148	C₂³×C₆₇	—	2	2	no	—
149	C₂²×D₆₇	—	2	2	no	—
150	C₂²×D₆₇	—	4	4	no	—
151	C₂²×D₆₇	—	4	4	no	—
152	C₂²×D₆₇	—	4	4	no	—
153	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
154	D₄×C₆₇	—	2	2	no	—
155	D₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₆₇	—	4	4	no	—
163	C₂×Dic₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	4	4	no	—
165	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
167	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
168	D₂₆₈	—	2	2	no	—
169	D₂₆₈	—	2	2	no	—
170	C₄×D₆₇	—	2	2	no	—
171	C₄×D₆₇	—	4	4	no	—
172	C₄×D₆₇	—	4	2	no	—
173	C₄×D₆₇	—	4	2	no	—
174	C₄×D₆₇	—	4	4	no	—
175	C₄×D₆₇	C₂×M₁₆	1	2	yes	—
176	C₄×D₆₇	#131	1	2	yes	—
177	C₄×D₆₇	C₂×D₈	1	2	yes	—
178	C₄×D₆₇	#135	1	2	yes	—
179	C₈×C₆₇	—	2	2	no	—
180	C₈×C₆₇	—	2	1	no	—
181	C₈×C₆₇	—	2	1	no	—
182	C₈×C₆₇	—	4	2	no	—
183	C₈×C₆₇	C₂×M₁₆	1	2	yes	complemented
184	C₈×C₆₇	C₂×D₈	1	2	yes	complemented
185	C₆₇⋊C₈	—	2	2	no	—
186	C₆₇⋊C₈	—	2	1	no	—
187	C₆₇⋊C₈	—	2	1	no	—
188	C₆₇⋊C₈	—	4	2	no	—
189	C₆₇⋊C₈	C₂×M₁₆	1	2	yes	complemented
190	C₆₇⋊C₈	C₂×D₈	1	2	yes	complemented
191	C₂²×C₆₇	—	4	2	no	—
192	C₂²×C₆₇	—	4	2	no	—
193	C₂²×C₆₇	—	4	2	no	—
194	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₆₇	—	4	2	no	—
196	C₂×D₆₇	—	4	2	no	—
197	C₂×D₆₇	—	4	2	no	—
198	C₂×D₆₇	—	8	8	no	—
199	C₂×D₆₇	#436	1	2	yes	—
200	C₂×D₆₇	C₄×D₈	1	2	yes	—
201	C₂×D₆₇	#443	1	2	yes	—
202	C₄×C₆₇	—	2	1	no	—
203	C₄×C₆₇	—	4	2	no	—
204	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
205	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
206	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
207	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
208	Dic₆₇	—	2	1	no	—
209	Dic₆₇	—	4	2	no	—
210	Dic₆₇	#436	1	2	yes	—
211	Dic₆₇	C₄×D₈	1	2	yes	—
212	C₂×#1589	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	8	2	no	—
214	C₂×C₆₇	C₂×#436	1	1	yes	characteristic
215	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
216	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
217	D₆₇	—	8	2	no	—
218	D₆₇	#1589	1	4	yes	direct product factor
219	C₂×C₄×D₈	—	67	1	no	—
220	C₂×#436	—	67	2	no	—
221	#1589	—	67	1	no	—
222	#1589	—	67	2	no	—
223	#1589	—	67	1	no	—
224	#1589	—	67	2	no	—
225	#1589	—	67	1	no	—
226	#1589	D₆₇	1	1	yes	characteristic, direct product factor
227	C₂×#335	—	67	1	no	—
228	C₂×D₄⋊C₈	—	67	2	no	—
229	C₂×C₈²	—	67	1	no	—
230	C₆₇	C₂×#1589	1	1	yes	characteristic, complemented, Sylow
231	C₂²×D₈	—	67	1	no	—
232	C₂²×M₁₆	—	134	2	no	—
233	C₂×C₄×D₄	—	67	2	no	—
234	C₄×D₈	—	67	1	no	—
235	C₄×D₈	—	67	2	no	—
236	C₄×D₈	—	67	1	no	—
237	C₄×D₈	—	67	2	no	—
238	C₄×D₈	—	67	1	no	—
239	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
240	#436	—	67	2	no	—
241	#436	—	67	2	no	—
242	#436	—	67	2	no	—
243	#436	—	134	2	no	—
244	#436	—	134	2	no	—
245	#436	C₂×D₆₇	1	2	yes	complemented
246	C₂×#107	—	67	1	no	—
247	C₂×C₄⋊C₈	—	67	2	no	—
248	C₂×#102	—	67	2	no	—
249	C₂×C₂²⋊C₈	—	134	2	no	—
250	C₂×C₄×C₈	—	67	1	no	—
251	C₂×C₄×C₈	—	67	1	no	—
252	C₂×C₄×C₈	—	67	1	no	—
253	#335	—	67	2	no	—
254	#335	—	67	1	no	—
255	#335	C₂×D₆₇	1	1	yes	characteristic, complemented
256	D₄⋊C₈	—	67	2	no	—
257	D₄⋊C₈	—	67	2	no	—
258	D₄⋊C₈	—	67	2	no	—
259	D₄⋊C₈	C₂×D₆₇	1	2	yes	complemented
260	C₈²	—	67	1	no	—
261	C₈²	—	67	1	no	—
262	C₈²	—	67	1	no	—
263	C₈²	C₂×D₆₇	1	1	yes	characteristic, complemented
264	C₂²×D₄	—	67	2	no	—
265	C₂³×C₄	—	134	2	no	—
266	C₂×D₈	—	67	2	no	—
267	C₂×D₈	—	67	1	no	—
268	C₂×D₈	—	134	4	no	—
269	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	268	8	no	—
272	C₂×M₁₆	—	134	2	no	—
273	C₂×M₁₆	—	134	2	no	—
274	C₂×M₁₆	—	134	2	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	—	134	2	no	—
280	C₂²×C₈	—	134	1	no	—
281	C₄×D₄	—	67	2	no	—
282	C₄×D₄	—	67	2	no	—
283	C₄×D₄	—	67	2	no	—
284	C₄×D₄	—	134	2	no	—
285	C₄×D₄	—	134	2	no	—
286	C₄×D₄	C₂²×D₆₇	1	2	yes	—
287	C₂×C₄⋊C₄	—	67	2	no	—
288	C₂×C₂²⋊C₄	—	134	2	no	—
289	C₂×C₄²	—	67	1	no	—
290	#107	—	67	1	no	—
291	#107	—	67	2	no	—
292	#107	C₄×D₆₇	1	1	yes	characteristic
293	C₄⋊C₈	—	67	2	no	—
294	C₄⋊C₈	—	134	2	no	—
295	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
296	#102	—	67	2	no	—
297	#102	—	67	2	no	—
298	#102	—	67	2	no	—
299	#102	C₄×D₆₇	1	2	yes	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	134	2	no	—
302	C₂²⋊C₈	—	134	2	no	—
303	C₂²⋊C₈	—	134	2	no	—
304	C₄×C₈	—	67	1	no	—
305	C₄×C₈	—	67	1	no	—
306	C₄×C₈	—	67	1	no	—
307	C₄×C₈	—	67	1	no	—
308	C₄×C₈	—	67	1	no	—
309	C₄×C₈	—	67	1	no	—
310	C₄×C₈	—	67	1	no	—
311	C₄×C₈	—	134	1	no	—
312	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
315	C₂⁴	—	134	2	no	—
316	C₂×D₄	—	67	2	no	—
317	C₂×D₄	—	134	4	no	—
318	C₂×D₄	—	134	4	no	—
319	C₂×D₄	—	134	2	no	—
320	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	268	4	no	—
323	C₂²×C₄	—	268	4	no	—
324	C₂²×C₄	—	67	1	no	—
325	C₂²×C₄	—	67	1	no	—
326	C₂²×C₄	—	67	1	no	—
327	C₂²×C₄	—	134	2	no	—
328	C₂²×C₄	—	134	2	no	—
329	C₂²×C₄	—	134	2	no	—
330	C₂²×C₄	—	134	2	no	—
331	D₈	—	2	2	no	—
332	D₈	—	134	4	no	—
333	D₈	—	134	2	no	—
334	M₁₆	—	4	4	no	—
335	M₁₆	—	268	4	no	—
336	M₁₆	—	268	4	no	—
337	M₁₆	—	268	4	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	268	4	no	—
341	C₂×C₈	—	67	1	no	—
342	C₂×C₈	—	67	1	no	—
343	C₂×C₈	—	67	4	no	—
344	C₂×C₈	—	67	4	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	1	no	—
347	C₂×C₈	—	134	2	no	—
348	C₂×C₈	—	134	2	no	—
349	C₂×C₈	—	134	4	no	—
350	C₂×C₈	—	134	2	no	—
351	C₂×C₈	—	134	1	no	—
352	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
353	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
354	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
355	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
356	C₄⋊C₄	—	67	2	no	—
357	C₄⋊C₄	—	134	2	no	—
358	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	134	2	no	—
361	C₂²⋊C₄	—	134	2	no	—
362	C₂²⋊C₄	—	134	2	no	—
363	C₄²	—	67	1	no	—
364	C₄²	—	67	1	no	—
365	C₄²	—	67	1	no	—
366	C₄²	C₂³×D₆₇	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	268	4	no	—
369	C₂³	—	268	4	no	—
370	C₂³	—	268	4	no	—
371	C₂³	—	67	1	no	—
372	C₂³	—	134	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	268	4	no	—
376	D₄	—	134	2	no	—
377	D₄	—	134	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	268	4	no	—
382	C₂×C₄	—	268	4	no	—
383	C₂×C₄	—	268	4	no	—
384	C₂×C₄	—	268	2	no	—
385	C₂×C₄	—	268	2	no	—
386	C₂×C₄	—	67	1	no	—
387	C₂×C₄	—	67	1	no	—
388	C₂×C₄	—	67	2	no	—
389	C₂×C₄	—	67	2	no	—
390	C₂×C₄	—	67	2	no	—
391	C₂×C₄	—	67	2	no	—
392	C₂×C₄	—	67	1	no	—
393	C₂×C₄	—	134	2	no	—
394	C₂×C₄	—	134	2	no	—
395	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
397	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	268	2	no	—
403	C₈	—	67	2	no	—
404	C₈	—	67	2	no	—
405	C₈	—	134	2	no	—
406	C₈	—	134	1	no	—
407	C₈	—	134	1	no	—
408	C₈	M₁₆×D₆₇	1	2	yes	complemented
409	C₈	D₈×D₆₇	1	2	yes	complemented
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	268	2	no	—
414	C₂²	—	268	2	no	—
415	C₂²	—	268	2	no	—
416	C₂²	—	536	8	no	—
417	C₂²	—	67	2	no	—
418	C₂²	—	67	2	no	—
419	C₂²	—	67	2	no	—
420	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	268	2	no	—
424	C₄	—	67	2	no	—
425	C₄	—	67	2	no	—
426	C₄	—	134	1	no	—
427	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
428	C₄	#131×D₆₇	1	1	yes	characteristic
429	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
430	C₄	#135×D₆₇	1	1	yes	characteristic
431	C₂	—	8	2	no	—
432	C₂	—	536	2	no	—
433	C₂	—	67	4	no	—
434	C₂	#436×D₆₇	1	1	yes	characteristic
435	C₂	C₄×D₈×D₆₇	1	1	yes	characteristic
436	C₂	#443×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1589	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×D₈×D₆₇	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1589	D₆₇
hypocenter	C₆₇	C₂×#1589
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #436×D₆₇	C₂	semidirect
3. #22559095	C₂	semidirect
4. #22559094	C₂	semidirect
5. #22559093	C₂	semidirect
6. #22559092	C₂	semidirect
7. #22559091	C₂	semidirect
8. #335×D₆₇	C₂	semidirect
9. D₄⋊C₈×D₆₇	C₂	semidirect
10. C₈²×D₆₇	C₂	semidirect
11. C₆₇×#1589	C₂	semidirect
20. #16863475	C₂²	semidirect
21. #16863474	C₂²	semidirect
22. #16863473	C₂²	semidirect
32. #16863149	C₂²	semidirect
33. #16863148	C₂²	semidirect
34. #16863125	C₂²	semidirect
35. D₄⋊(C₆₇⋊C₈)	C₂²	semidirect
36. #16863123	C₂²	semidirect
37. C₈×C₆₇⋊C₈	C₂²	semidirect
38. C₈×C₆₇⋊C₈	C₂²	semidirect
39. C₈×C₆₇⋊C₈	C₂²	semidirect
41. #436×C₆₇	C₂²	semidirect
42. #335×C₆₇	C₂²	semidirect
43. D₄⋊C₈×C₆₇	C₂²	semidirect
44. C₈²×C₆₇	C₂²	semidirect
125. C₈×D₆₇	M₁₆	semidirect
126. C₈×D₆₇	D₈	semidirect
183. C₈×C₆₇	C₂×M₁₆	semidirect
184. C₈×C₆₇	C₂×D₈	semidirect
189. C₆₇⋊C₈	C₂×M₁₆	semidirect
190. C₆₇⋊C₈	C₂×D₈	semidirect
218. D₆₇	#1589	direct (N × H)
226. #1589	D₆₇	direct (N × H)
230. C₆₇	C₂×#1589	semidirect
245. #436	C₂×D₆₇	semidirect
255. #335	C₂×D₆₇	semidirect
259. D₄⋊C₈	C₂×D₆₇	semidirect
263. C₈²	C₂×D₆₇	semidirect
408. C₈	M₁₆×D₆₇	semidirect
409. C₈	D₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₆₇	2
#436×D₆₇	2
#22559095	2
#22559094	2
#22559093	2
#22559092	2
#22559091	2
#335×D₆₇	2
D₄⋊C₈×D₆₇	2
C₈²×D₆₇	2
C₆₇×#1589	2
C₂×#1589	67

Subgroups — #1589×D67 #30825555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1589×D₆₇ #30825555