Subgroups — #30745347

Order 17152.

700 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568842	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11761612	C₂	1	1	yes	maximal, characteristic
3	#22558046	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	C₄	1	2	yes	—
6	#16863453	—	2	1	no	—
7	#16863453	C₄	1	2	yes	—
8	#16863449	—	2	1	no	—
9	#16863449	C₂²	1	2	yes	—
10	#16863420	C₄	1	2	yes	—
11	#16863360	—	2	1	no	—
12	C₄×#11761612	—	2	1	no	—
13	C₄×#11761612	—	2	1	no	—
14	C₄×#11761612	—	2	1	no	—
15	C₄×#11761612	C₄	1	2	yes	—
16	C₄×#11761612	C₂²	1	2	yes	—
17	C₂×#14523954	—	2	1	no	—
18	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
19	C₂²×M₁₆×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₆₇	—	2	1	no	—
22	C₄×M₁₆×C₆₇	—	2	1	no	—
23	C₄×M₁₆×C₆₇	C₄	1	2	yes	—
24	C₄×M₁₆×C₆₇	C₄	1	2	yes	—
25	C₂×#97×C₆₇	—	2	1	no	—
26	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
27	C₂×#11761612	—	2	8	no	—
28	C₂×#11761612	—	2	2	no	—
29	C₂×#11761612	—	2	2	no	—
30	C₂×#11761612	C₂×C₄	1	4	yes	—
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
34	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
36	#14523954	—	2	2	no	—
37	#14523954	—	2	2	no	—
38	#14523954	—	2	2	no	—
39	C₄×C₆₇⋊C₈	—	2	2	no	—
40	C₄×C₆₇⋊C₈	—	2	2	no	—
41	C₄×C₆₇⋊C₈	—	2	2	no	—
42	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
45	C₂×M₁₆×C₆₇	—	2	8	no	—
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂²×C₈×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
61	#97×C₆₇	—	2	2	no	—
62	#97×C₆₇	—	2	2	no	—
63	C₄×C₈×C₆₇	—	2	2	no	—
64	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	—
65	#11761612	—	2	8	no	—
66	#11761612	—	2	4	no	—
67	#11761612	—	4	4	no	—
68	#11761612	M₁₆	1	8	yes	complemented
69	C₂×C₆₇⋊C₈	—	2	8	no	—
70	C₂×C₆₇⋊C₈	—	2	4	no	—
71	C₂×C₆₇⋊C₈	—	2	4	no	—
72	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	—	2	4	no	—
74	C₂²×C₄×C₆₇	—	2	4	no	—
75	C₂²×C₄×C₆₇	—	4	2	no	—
76	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
94	M₁₆×C₆₇	—	2	8	no	—
95	M₁₆×C₆₇	—	2	8	no	—
96	C₂×C₈×C₆₇	—	2	8	no	—
97	C₂×C₈×C₆₇	—	2	4	no	—
98	C₄²×C₆₇	C₄²	1	1	yes	characteristic
99	C₄²×C₆₇	C₄²	1	1	yes	characteristic
100	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	2	no	—
116	C₂³×C₆₇	—	4	1	no	—
117	C₂³×C₆₇	#95	1	1	yes	characteristic
118	C₂³×C₆₇	#95	1	1	yes	characteristic
119	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	2	2	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	1	no	—
136	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
137	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#104	1	4	yes	—
143	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
150	C₈×C₆₇	—	2	8	no	—
151	C₆₇⋊C₈	—	2	8	no	—
152	C₆₇⋊C₈	—	4	4	no	—
153	C₂²×C₆₇	—	2	1	no	—
154	C₂²×C₆₇	—	2	1	no	—
155	C₂²×C₆₇	—	2	1	no	—
156	C₂²×C₆₇	—	2	1	no	—
157	C₂²×C₆₇	—	2	1	no	—
158	C₂²×C₆₇	—	2	1	no	—
159	C₂²×C₆₇	—	2	1	no	—
160	C₂²×C₆₇	—	4	4	no	—
161	C₂²×C₆₇	#339	1	2	yes	—
162	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
163	C₂²×C₆₇	#423	1	2	yes	—
164	C₄×C₆₇	—	2	1	no	—
165	C₄×C₆₇	—	2	1	no	—
166	C₄×C₆₇	—	2	1	no	—
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	#339	1	2	yes	—
172	C₄×C₆₇	C₄×M₁₆	1	2	yes	—
173	C₄×C₆₇	#407	1	2	yes	—
174	C₄×C₆₇	C₂×#104	1	2	yes	—
175	C₄×C₆₇	#430	1	2	yes	—
176	#7887	—	67	1	no	maximal, Sylow
177	C₂×C₆₇	—	2	2	no	—
178	C₂×C₆₇	—	2	2	no	—
179	C₂×C₆₇	—	4	1	no	—
180	C₂×C₆₇	#1728	1	1	yes	characteristic
181	C₂×C₆₇	C₂×#339	1	1	yes	characteristic
182	C₂×C₆₇	#1738	1	1	yes	characteristic
183	#2920	—	67	1	no	—
184	C₂×C₄×M₁₆	—	67	1	no	—
185	C₂×C₄×M₁₆	D₆₇	1	1	yes	characteristic
186	#1278	—	67	4	no	—
187	C₆₇	#7887	1	1	yes	characteristic, complemented, Sylow
188	C₂²×M₁₆	—	2	1	no	—
189	C₂²×M₁₆	—	67	2	no	—
190	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
191	#432	—	67	2	no	—
192	#432	—	134	1	no	—
193	#431	—	67	2	no	—
194	#431	—	134	1	no	—
195	#423	—	67	2	no	—
196	#407	—	134	1	no	—
197	C₄×M₁₆	—	2	1	no	—
198	C₄×M₁₆	—	2	1	no	—
199	C₄×M₁₆	—	67	2	no	—
200	C₄×M₁₆	—	67	2	no	—
201	C₄×M₁₆	—	134	1	no	—
202	C₄×M₁₆	—	134	1	no	—
203	C₄×M₁₆	—	134	1	no	—
204	C₄×M₁₆	Dic₆₇	1	2	yes	—
205	C₄×M₁₆	Dic₆₇	1	2	yes	—
206	C₂×#97	—	2	1	no	—
207	C₂×#97	—	134	1	no	—
208	C₂×C₄×C₈	—	134	1	no	—
209	C₂×C₄×C₈	C₂×D₆₇	1	2	yes	—
210	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
211	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	67	4	no	—
217	C₂×M₁₆	—	134	2	no	—
218	C₂×M₁₆	—	134	8	no	—
219	C₂×M₁₆	—	134	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	134	2	no	—
222	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
226	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
227	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
234	C₄⋊C₈	—	67	4	no	—
235	C₄⋊C₈	—	134	2	no	—
236	C₂²⋊C₈	—	134	2	no	—
237	C₂²⋊C₈	—	134	2	no	—
238	#97	—	2	2	no	—
239	#97	—	2	2	no	—
240	#97	—	134	2	no	—
241	#97	—	134	2	no	—
242	#97	—	134	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	134	2	no	—
245	C₄×C₈	—	134	2	no	—
246	C₄×C₈	—	134	2	no	—
247	C₄×C₈	C₂×Dic₆₇	1	4	yes	—
248	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
253	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
254	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
260	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
270	M₁₆	—	2	8	no	—
271	M₁₆	—	2	8	no	—
272	M₁₆	—	268	4	no	—
273	M₁₆	—	67	8	no	—
274	M₁₆	—	134	8	no	—
275	M₁₆	—	134	4	no	—
276	C₂×C₈	—	2	8	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	134	4	no	—
279	C₂×C₈	—	134	8	no	—
280	C₂×C₈	—	134	4	no	—
281	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
282	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
283	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
284	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
285	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
287	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
288	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
289	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
294	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
295	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
296	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	4	1	no	—
300	C₂³	C₆₇⋊#95	1	1	yes	characteristic
301	C₂³	C₆₇⋊#95	1	1	yes	characteristic
302	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
320	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
321	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
324	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
325	C₂×C₄	#14523971	1	4	yes	—
326	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
327	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
332	C₂×C₄	M₁₆×D₆₇	1	4	yes	—
333	C₈	—	2	8	no	—
334	C₈	—	268	4	no	—
335	C₈	—	134	8	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	4	4	no	—
344	C₂²	#16863156	1	2	yes	—
345	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
346	C₂²	#16863419	1	2	yes	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	#16863156	1	2	yes	—
355	C₄	M₁₆×Dic₆₇	1	2	yes	—
356	C₄	#16863359	1	2	yes	—
357	C₄	C₂×#14523971	1	2	yes	—
358	C₄	#16863445	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	4	1	no	—
362	C₂	#22559902	1	1	yes	characteristic
363	C₂	C₂×#16863156	1	1	yes	characteristic
364	C₂	#22559936	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×C₄×M₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×C₄×M₁₆	D₆₇
hypocenter	C₆₇	#7887
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22558046	C₂	semidirect
68. #11761612	M₁₆	semidirect
187. C₆₇	#7887	semidirect

Maximal subgroups

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

subgroup	index
#22568842	2
C₂×C₄×#11761612	2
#22558046	2
C₂×C₄×M₁₆×C₆₇	2
#7887	67