Subgroups — #30825170

Order 17152.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569334	C₂	1	2	yes	maximal
2	#22558994	C₂	1	2	yes	maximal, complemented
3	#22558989	C₂	1	2	yes	maximal, complemented
4	#22558984	C₂	1	2	yes	maximal, complemented
5	#22558976	C₂	1	2	yes	maximal, complemented
6	#22558972	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558961	C₂	1	2	yes	maximal, complemented
8	C₂×#16863149	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic
10	#16863527	—	2	2	no	—
11	#16863468	—	2	2	no	—
12	#16863468	—	2	2	no	—
13	D₄×C₆₇⋊C₈	—	2	2	no	—
14	#16863453	C₂²	1	2	yes	—
15	#16863453	C₂²	1	2	yes	—
16	#16863449	C₂²	1	2	yes	—
17	#16863420	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
20	#16863149	C₂²	1	1	yes	characteristic
21	#16863149	C₂²	1	2	yes	—
22	#16863149	C₂²	1	1	yes	characteristic
23	#16863149	C₂²	1	2	yes	—
24	#16863149	C₂²	1	2	yes	—
25	#16863149	C₂²	1	1	yes	characteristic
26	#16863149	C₂²	1	1	yes	characteristic
27	#16863147	C₂²	1	2	yes	—
28	#16863147	C₂²	1	2	yes	—
29	#16863147	C₂²	1	2	yes	—
30	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
31	#446×C₆₇	C₄	1	1	yes	characteristic
32	#446×C₆₇	C₄	1	1	yes	characteristic
33	#436×C₆₇	C₄	1	1	yes	characteristic
34	#436×C₆₇	C₄	1	1	yes	characteristic
35	#435×C₆₇	C₄	1	2	yes	—
36	#435×C₆₇	C₄	1	2	yes	—
37	#431×C₆₇	C₂²	1	2	yes	—
38	#431×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#11761612	—	2	2	no	—
42	C₂²×C₆₇⋊C₈	—	2	2	no	—
43	C₂²×C₆₇⋊C₈	—	2	2	no	—
44	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
45	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
46	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
48	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
49	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
50	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
51	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
54	#14523954	—	2	2	no	—
55	#14523954	—	2	2	no	—
56	C₄×C₆₇⋊C₈	—	2	2	no	—
57	C₂×#41×C₆₇	Q₈	1	1	yes	characteristic
58	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
64	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₆₇	D₄	1	2	yes	—
67	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
68	#117×C₆₇	Q₈	1	1	yes	characteristic
69	#117×C₆₇	Q₈	1	2	yes	—
70	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
73	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
74	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
75	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
78	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
79	#97×C₆₇	C₂×C₄	1	2	yes	—
80	#97×C₆₇	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₆₇	C₂³	1	2	yes	—
85	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	#11761612	—	8	2	no	—
87	C₂×C₆₇⋊C₈	—	2	2	no	—
88	C₂×C₆₇⋊C₈	—	2	2	no	—
89	C₂×C₆₇⋊C₈	—	2	2	no	—
90	C₂×C₆₇⋊C₈	—	2	2	no	—
91	C₂×C₆₇⋊C₈	—	8	2	no	—
92	C₂×C₆₇⋊C₈	—	8	2	no	—
93	#41×C₆₇	—	4	2	no	—
94	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
95	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
96	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
103	M₁₆×C₆₇	—	2	4	no	—
104	M₁₆×C₆₇	—	4	2	no	—
105	C₂×C₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	4	1	no	—
107	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
116	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
120	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₆₇	C₂×D₄	1	2	yes	—
123	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
125	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
126	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	Q₈×C₆₇	—	4	1	no	—
130	D₄×C₆₇	—	2	4	no	—
131	D₄×C₆₇	—	4	1	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	1	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	2	1	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
151	C₈×C₆₇	—	2	1	no	—
152	C₈×C₆₇	—	2	2	no	—
153	C₈×C₆₇	—	2	1	no	—
154	C₈×C₆₇	—	2	1	no	—
155	C₈×C₆₇	—	2	2	no	—
156	C₈×C₆₇	#131	1	2	yes	—
157	C₆₇⋊C₈	—	4	2	no	—
158	C₆₇⋊C₈	—	4	2	no	—
159	C₆₇⋊C₈	—	4	2	no	—
160	C₆₇⋊C₈	—	4	2	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	2	2	no	—
165	C₂²×C₆₇	—	2	2	no	—
166	C₂²×C₆₇	#430	1	2	yes	—
167	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	2	no	—
175	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
176	C₄×C₆₇	#568	1	1	yes	characteristic
177	C₄×C₆₇	#576	1	1	yes	characteristic
178	C₄×C₆₇	#578	1	1	yes	characteristic
179	#17840	—	67	1	no	maximal, Sylow
180	C₂×C₆₇	—	2	2	no	—
181	C₂×C₆₇	—	4	2	no	—
182	C₂×C₆₇	#2906	1	1	yes	characteristic
183	C₂×C₆₇	#2913	1	1	yes	characteristic
184	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
185	#2990	—	67	2	no	—
186	#2965	D₆₇	1	1	yes	characteristic
187	#1573	—	67	2	no	—
188	#1572	—	67	2	no	—
189	#1571	—	67	2	no	—
190	#1569	—	67	2	no	—
191	#1568	—	67	1	no	—
192	#1565	—	67	2	no	—
193	C₂×#335	—	67	1	no	—
194	C₆₇	#17840	1	1	yes	characteristic, complemented, Sylow
195	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
196	#446	—	134	2	no	—
197	#446	Dic₆₇	1	1	yes	characteristic
198	#446	Dic₆₇	1	1	yes	characteristic
199	#436	Dic₆₇	1	1	yes	characteristic
200	#436	Dic₆₇	1	1	yes	characteristic
201	#435	—	134	2	no	—
202	#435	—	134	2	no	—
203	#435	Dic₆₇	1	2	yes	—
204	#435	Dic₆₇	1	2	yes	—
205	C₈×D₄	—	134	2	no	—
206	#432	—	67	2	no	—
207	#432	—	67	2	no	—
208	#431	—	67	2	no	—
209	#431	C₂×D₆₇	1	2	yes	—
210	#431	C₂×D₆₇	1	1	yes	characteristic
211	#423	—	67	2	no	—
212	C₂×C₄⋊C₈	—	67	2	no	—
213	C₂×C₄⋊C₈	—	67	2	no	—
214	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
215	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
216	#335	—	67	1	no	—
217	#335	—	67	1	no	—
218	#335	—	67	2	no	—
219	#335	—	67	2	no	—
220	#335	—	67	1	no	—
221	#335	—	67	1	no	—
222	#335	—	67	2	no	—
223	#334	—	67	2	no	—
224	#334	—	67	2	no	—
225	#334	—	67	2	no	—
226	C₂×#41	Dic₁₃₄	1	1	yes	characteristic
227	C₂×M₁₆	—	134	2	no	—
228	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
229	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
230	C₂²×C₈	—	134	2	no	—
231	C₂²×C₈	—	134	2	no	—
232	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
233	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
234	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
236	C₄×D₄	D₂₆₈	1	2	yes	—
237	C₄×D₄	D₂₆₈	1	1	yes	characteristic
238	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
239	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
240	#117	Dic₁₃₄	1	1	yes	characteristic
241	#117	Dic₁₃₄	1	2	yes	—
242	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
244	C₄⋊C₈	—	67	2	no	—
245	C₄⋊C₈	—	67	2	no	—
246	C₄⋊C₈	—	67	2	no	—
247	C₄⋊C₈	—	67	2	no	—
248	C₄⋊C₈	—	134	2	no	—
249	C₄⋊C₈	—	134	2	no	—
250	C₄⋊C₈	—	134	2	no	—
251	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
252	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
253	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
254	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
255	C₂²⋊C₈	—	134	2	no	—
256	C₂²⋊C₈	—	134	2	no	—
257	C₂²⋊C₈	—	134	2	no	—
258	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
259	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
260	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
261	#97	—	134	2	no	—
262	#97	—	134	2	no	—
263	#97	C₂×Dic₆₇	1	2	yes	—
264	#97	C₂×Dic₆₇	1	2	yes	—
265	C₄×C₈	—	134	2	no	—
266	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
267	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
268	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
269	C₄×C₈	C₂²×D₆₇	1	2	yes	—
270	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
271	#41	—	4	2	no	—
272	C₂×Q₈	C₄⋊Dic₆₇	1	1	yes	characteristic
273	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
274	C₂×D₄	C₄⋊Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
277	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
279	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	4	2	no	—
283	M₁₆	—	536	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	536	2	no	—
287	C₂×C₈	—	536	2	no	—
288	C₂×C₈	—	134	2	no	—
289	C₂×C₈	—	134	2	no	—
290	C₂×C₈	—	134	2	no	—
291	C₂×C₈	—	134	2	no	—
292	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
293	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
294	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
295	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
296	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
297	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
298	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
299	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
300	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
301	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
302	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
303	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
304	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
305	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
306	C₄²	C₂²×Dic₆₇	1	2	yes	—
307	C₄²	C₂×D₂₆₈	1	2	yes	—
308	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
309	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
310	C₄²	C₂×Dic₁₃₄	1	2	yes	—
311	C₄²	C₂³×D₆₇	1	1	yes	characteristic
312	C₂³	C₂×C₄⋊Dic₆₇	1	2	yes	—
313	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
314	Q₈	—	4	1	no	—
315	D₄	—	2	4	no	—
316	D₄	—	4	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
329	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
331	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
333	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
335	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
336	C₈	—	2	1	no	—
337	C₈	—	2	2	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	2	no	—
341	C₈	—	268	2	no	—
342	C₈	—	268	2	no	—
343	C₈	—	268	2	no	—
344	C₈	—	268	2	no	—
345	C₈	#14524050	1	2	yes	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	#16863445	1	2	yes	—
352	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	2	no	—
360	C₄	C₂×#14524050	1	1	yes	characteristic
361	C₄	#16864163	1	1	yes	characteristic
362	C₄	#16864201	1	1	yes	characteristic
363	C₄	#16864213	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	2	no	—
366	C₂	#22568777	1	1	yes	characteristic
367	C₂	#22568809	1	1	yes	characteristic
368	C₂	C₂×#16863445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2965	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₆₇	Q₈
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2965	D₆₇
hypocenter	C₆₇	#17840
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
2. #22558994	C₂	semidirect
3. #22558989	C₂	semidirect
4. #22558984	C₂	semidirect
5. #22558976	C₂	semidirect
6. #22558972	C₂	semidirect
7. #22558961	C₂	semidirect
8. C₂×#16863149	C₂	semidirect
194. C₆₇	#17840	semidirect

Maximal subgroups

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

subgroup	index
#22569334	2
#22558994	2
#22558989	2
#22558984	2
#22558976	2
#22558972	2
#22558961	2
C₂×#16863149	2
C₆₇×#2965	2
#17840	67