Subgroups — #30827618

Order 17152.

600 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569214	C₂	1	2	yes	maximal, complemented
2	#22559106	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559094	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559053	C₂	1	2	yes	maximal, complemented
5	#22559046	C₂	1	2	yes	maximal, complemented
6	Q₁₆×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558617	C₂	1	2	yes	maximal, complemented
10	C₈×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic
12	#16863527	C₂²	1	2	yes	—
13	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	—
14	#16863474	—	2	2	no	—
15	#16863474	C₂²	1	2	yes	—
16	#16863468	—	2	2	no	—
17	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
18	#16863457	—	2	2	no	—
19	#16863449	C₂²	1	2	yes	—
20	#16863449	C₂²	1	1	yes	characteristic
21	#16863352	—	2	2	no	—
22	C₄×#11761612	C₂²	1	1	yes	characteristic
23	#16863149	C₂²	1	1	yes	characteristic
24	#16863149	C₂²	1	1	yes	characteristic
25	#16863147	C₂²	1	2	yes	—
26	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
27	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
28	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
30	#16863118	C₂²	1	1	yes	characteristic
31	#16863118	C₂²	1	1	yes	characteristic
32	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
34	#529×C₆₇	C₂²	1	2	yes	—
35	#499×C₆₇	C₄	1	1	yes	characteristic
36	#495×C₆₇	C₄	1	1	yes	characteristic
37	#488×C₆₇	C₄	1	2	yes	—
38	#467×C₆₇	C₄	1	1	yes	characteristic
39	#466×C₆₇	C₄	1	1	yes	characteristic
40	#465×C₆₇	C₄	1	2	yes	—
41	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
43	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761612	—	2	2	no	—
46	C₂×#11761612	D₄	1	1	yes	characteristic
47	C₂×#11761612	D₄	1	1	yes	characteristic
48	C₂²×C₆₇⋊C₈	—	2	2	no	—
49	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
50	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
53	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
54	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
58	#14523954	—	2	2	no	—
59	#14523954	D₄	1	1	yes	characteristic
60	#14523954	D₄	1	1	yes	characteristic
61	C₄×C₆₇⋊C₈	—	2	2	no	—
62	C₄×C₆₇⋊C₈	—	2	2	no	—
63	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
69	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
72	#126×C₆₇	—	2	2	no	—
73	#125×C₆₇	C₂×C₄	1	2	yes	—
74	#124×C₆₇	C₂×C₄	1	2	yes	—
75	#123×C₆₇	—	2	2	no	—
76	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
77	#121×C₆₇	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
79	C₄×D₄×C₆₇	—	2	2	no	—
80	C₄×D₄×C₆₇	C₂³	1	2	yes	—
81	#117×C₆₇	—	2	2	no	—
82	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
83	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
84	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
85	#106×C₆₇	C₂×C₄	1	2	yes	—
86	#103×C₆₇	C₂×C₄	1	2	yes	—
87	#103×C₆₇	C₂×C₄	1	2	yes	—
88	#102×C₆₇	C₂×C₄	1	2	yes	—
89	#102×C₆₇	C₂×C₄	1	2	yes	—
90	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#11761612	—	2	2	no	—
95	#11761612	—	2	2	no	—
96	#11761612	—	4	4	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	2	no	—
99	C₂×C₆₇⋊C₈	—	2	1	no	—
100	C₂×C₆₇⋊C₈	—	2	1	no	—
101	C₂×C₆₇⋊C₈	—	4	4	no	—
102	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
103	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
104	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₆₇	—	2	2	no	—
108	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
113	Q₁₆×C₆₇	—	2	2	no	—
114	SD₁₆×C₆₇	—	4	2	no	—
115	D₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	4	1	no	—
118	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₆₇	—	2	2	no	—
129	C₂²⋊C₄×C₆₇	—	2	2	no	—
130	C₂²⋊C₄×C₆₇	—	2	2	no	—
131	C₂²⋊C₄×C₆₇	—	2	2	no	—
132	C₂²⋊C₄×C₆₇	—	2	2	no	—
133	C₄²×C₆₇	—	2	2	no	—
134	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₆₇	#41	1	1	yes	characteristic
137	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
138	C₂³×C₆₇	—	2	2	no	—
139	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
140	Q₈×C₆₇	—	2	2	no	—
141	Q₈×C₆₇	—	2	2	no	—
142	D₄×C₆₇	—	2	2	no	—
143	D₄×C₆₇	—	2	2	no	—
144	D₄×C₆₇	—	8	2	no	—
145	C₂×C₄×C₆₇	—	2	1	no	—
146	C₂×C₄×C₆₇	—	2	1	no	—
147	C₂×C₄×C₆₇	—	2	1	no	—
148	C₂×C₄×C₆₇	—	2	1	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	4	1	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₆₇	—	2	1	no	—
162	C₈×C₆₇	—	2	1	no	—
163	C₈×C₆₇	—	2	1	no	—
164	C₈×C₆₇	#131	1	2	yes	—
165	C₆₇⋊C₈	—	2	1	no	—
166	C₆₇⋊C₈	—	2	1	no	—
167	C₆₇⋊C₈	—	4	1	no	—
168	C₆₇⋊C₈	—	4	1	no	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₆₇⋊C₈	—	4	2	no	—
171	C₆₇⋊C₈	#135	1	2	yes	—
172	C₆₇⋊C₈	#135	1	2	yes	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	2	1	no	—
175	C₂²×C₆₇	—	2	1	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	—	4	2	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	—	4	2	no	—
187	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
188	C₄×C₆₇	#568	1	1	yes	characteristic
189	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
190	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
191	#18069	—	67	1	no	maximal, Sylow
192	C₂×C₆₇	—	4	1	no	—
193	C₂×C₆₇	—	8	2	no	—
194	C₂×C₆₇	#2935	1	1	yes	characteristic
195	C₂×C₆₇	C₄×#135	1	1	yes	characteristic
196	C₂×C₆₇	#2957	1	1	yes	characteristic
197	#3168	D₆₇	1	1	yes	characteristic
198	#2969	—	67	2	no	—
199	#1591	—	67	1	no	—
200	#1589	—	67	1	no	—
201	#1583	—	67	2	no	—
202	#1582	—	67	2	no	—
203	C₈×Q₁₆	—	67	1	no	—
204	C₈×D₈	—	67	1	no	—
205	#1564	—	67	1	no	—
206	#1482	—	67	2	no	—
207	C₈×M₁₆	—	67	1	no	—
208	C₆₇	#18069	1	1	yes	characteristic, complemented, Sylow
209	#529	C₂×D₆₇	1	2	yes	—
210	#499	Dic₆₇	1	1	yes	characteristic
211	#495	Dic₆₇	1	1	yes	characteristic
212	#488	Dic₆₇	1	2	yes	—
213	#467	Dic₆₇	1	1	yes	characteristic
214	#466	Dic₆₇	1	1	yes	characteristic
215	#465	Dic₆₇	1	2	yes	—
216	#446	—	67	2	no	—
217	C₈×Q₈	—	67	2	no	—
218	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
219	C₄×SD₁₆	C₂×D₆₇	1	2	yes	—
220	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
221	#436	—	67	2	no	—
222	#436	—	134	2	no	—
223	#435	—	134	2	no	—
224	C₈×D₄	—	67	2	no	—
225	#433	—	134	2	no	—
226	#431	—	67	1	no	—
227	#431	—	67	2	no	—
228	#405	—	134	2	no	—
229	C₄×M₁₆	—	67	1	no	—
230	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
231	#335	—	67	1	no	—
232	#335	—	67	1	no	—
233	#334	—	67	2	no	—
234	Q₈⋊C₈	—	67	2	no	—
235	Q₈⋊C₈	—	67	2	no	—
236	D₄⋊C₈	—	67	2	no	—
237	D₄⋊C₈	—	67	2	no	—
238	#322	—	67	1	no	—
239	#322	—	67	1	no	—
240	C₈²	—	67	1	no	—
241	C₈²	—	67	1	no	—
242	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
244	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
245	C₂×M₁₆	—	67	1	no	—
246	C₂×M₁₆	—	67	1	no	—
247	C₂×M₁₆	—	134	2	no	—
248	C₂²×C₈	—	134	2	no	—
249	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
250	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
251	#126	—	2	2	no	—
252	#125	C₂×Dic₆₇	1	2	yes	—
253	#124	C₂×Dic₆₇	1	2	yes	—
254	#123	—	2	2	no	—
255	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
256	#121	C₂×Dic₆₇	1	2	yes	—
257	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂²×D₆₇	1	2	yes	—
260	#117	—	2	2	no	—
261	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
262	#107	C₂×Dic₆₇	1	1	yes	characteristic
263	#107	C₂×Dic₆₇	1	1	yes	characteristic
264	#106	C₂×Dic₆₇	1	2	yes	—
265	C₄⋊C₈	—	67	2	no	—
266	C₄⋊C₈	—	67	2	no	—
267	C₄⋊C₈	—	134	2	no	—
268	C₄⋊C₈	—	134	2	no	—
269	C₄⋊C₈	—	134	1	no	—
270	#103	C₂×Dic₆₇	1	2	yes	—
271	#103	C₂×Dic₆₇	1	2	yes	—
272	#102	C₂×Dic₆₇	1	2	yes	—
273	#102	C₂×Dic₆₇	1	2	yes	—
274	C₂²⋊C₈	—	134	2	no	—
275	C₂²⋊C₈	—	134	2	no	—
276	C₂²⋊C₈	—	134	2	no	—
277	C₂²⋊C₈	—	134	1	no	—
278	#97	—	67	1	no	—
279	#97	—	67	1	no	—
280	#97	—	134	2	no	—
281	C₄×C₈	—	67	1	no	—
282	C₄×C₈	—	67	1	no	—
283	C₄×C₈	—	67	1	no	—
284	C₄×C₈	—	67	1	no	—
285	C₄×C₈	—	134	2	no	—
286	C₄×C₈	—	134	2	no	—
287	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
288	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
291	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
297	C₂²×C₄	#11761627	1	1	yes	characteristic
298	Q₁₆	—	2	2	no	—
299	SD₁₆	—	4	2	no	—
300	D₈	—	2	2	no	—
301	M₁₆	—	268	4	no	—
302	M₁₆	—	134	2	no	—
303	M₁₆	—	134	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	268	4	no	—
307	C₂×C₈	—	67	1	no	—
308	C₂×C₈	—	67	1	no	—
309	C₂×C₈	—	67	1	no	—
310	C₂×C₈	—	67	1	no	—
311	C₂×C₈	—	134	2	no	—
312	C₂×C₈	—	134	2	no	—
313	C₂×C₈	—	134	1	no	—
314	C₂×C₈	—	134	1	no	—
315	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
316	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
317	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
318	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
324	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
332	C₄²	D₄×D₆₇	1	1	yes	characteristic
333	C₄²	#11761627	1	1	yes	characteristic
334	C₄²	C₂³×D₆₇	1	1	yes	characteristic
335	C₂³	—	2	2	no	—
336	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
337	Q₈	—	2	2	no	—
338	Q₈	—	2	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	8	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
353	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
354	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	268	1	no	—
362	C₈	—	268	1	no	—
363	C₈	—	268	2	no	—
364	C₈	—	268	2	no	—
365	C₈	—	67	2	no	—
366	C₈	—	67	2	no	—
367	C₈	—	134	1	no	—
368	C₈	—	134	1	no	—
369	C₈	#14524050	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₂×#14524050	1	1	yes	characteristic
385	C₄	#16864163	1	1	yes	characteristic
386	C₄	#135×D₆₇	1	1	yes	characteristic
387	C₄	#135×D₆₇	1	1	yes	characteristic
388	C₂	—	4	1	no	—
389	C₂	—	8	2	no	—
390	C₂	#22568953	1	1	yes	characteristic
391	C₂	#135×Dic₆₇	1	1	yes	characteristic
392	C₂	#22569126	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×#3168	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#466×C₆₇	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#3168	D₆₇
hypocenter	C₆₇	#18069
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #22569214	C₂	semidirect
2. #22559106	C₂	semidirect
3. #22559094	C₂	semidirect
4. #22559053	C₂	semidirect
5. #22559046	C₂	semidirect
6. Q₁₆×C₆₇⋊C₈	C₂	semidirect
7. D₈×C₆₇⋊C₈	C₂	semidirect
8. #22558957	C₂	semidirect
9. #22558617	C₂	semidirect
10. C₈×#11761612	C₂	semidirect
208. C₆₇	#18069	semidirect

Maximal subgroups

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

subgroup	index
#22569214	2
#22559106	2
#22559094	2
#22559053	2
#22559046	2
Q₁₆×C₆₇⋊C₈	2
D₈×C₆₇⋊C₈	2
#22558957	2
#22558617	2
C₈×#11761612	2
C₆₇×#3168	2
#18069	67