Subgroups — #30854396

Order 17152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863518	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863513	C₂	1	1	yes	maximal, characteristic
3	C₄×#14524050	C₂	1	2	yes	maximal, complemented
4	#22560115	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560095	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560056	C₂	1	2	yes	maximal, complemented
8	#22560049	C₂	1	2	yes	maximal, complemented
9	#22560019	C₂	1	2	yes	maximal, complemented
10	#22559897	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	C₂×#14524050	C₂²	1	2	yes	—
14	#16863518	C₄	1	8	yes	complemented
15	#16863513	C₄	1	8	yes	complemented
16	C₂×#14523979	C₂²	1	1	yes	characteristic
17	C₂×#14523979	C₂²	1	1	yes	characteristic
18	C₂×#14523970	C₂²	1	2	yes	—
19	C₂×#14523970	C₂²	1	2	yes	—
20	#16863352	—	2	2	no	—
21	#16863352	—	2	2	no	—
22	#16863352	C₂²	1	2	yes	—
23	#16863352	C₂²	1	2	yes	—
24	C₄×#11761612	—	2	2	no	—
25	C₄×#11761612	C₂²	1	2	yes	—
26	C₂×#14523953	C₂²	1	1	yes	characteristic
27	C₂×#14523953	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₆₇⋊C₈	—	2	2	no	—
29	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
32	#16863242	C₂²	1	1	yes	characteristic
33	#16863161	C₂²	1	2	yes	—
34	#16863155	C₂²	1	2	yes	—
35	#16863155	C₂²	1	2	yes	—
36	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
37	C₄×#41×C₆₇	C₂²	1	2	yes	—
38	#442×C₆₇	C₄	1	2	yes	complemented
39	#441×C₆₇	C₄	1	2	yes	complemented
40	#440×C₆₇	C₄	1	4	yes	complemented
41	#427×C₆₇	C₂²	1	1	yes	characteristic
42	#416×C₆₇	C₂²	1	2	yes	—
43	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
44	#14524050	—	2	4	no	—
45	#14524050	—	2	4	no	—
46	#14524050	C₂×C₄	1	8	yes	complemented
47	#14524050	C₂×C₄	1	8	yes	complemented
48	C₂×#11761612	—	2	2	no	—
49	C₂×#11761612	—	2	2	no	—
50	C₂×#11761612	C₂³	1	2	yes	—
51	C₂×#11761612	C₂³	1	2	yes	—
52	C₂²×C₆₇⋊C₈	—	2	2	no	—
53	C₂²×C₆₇⋊C₈	—	2	2	no	—
54	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
58	#14523979	C₂×C₄	1	4	yes	complemented
59	#14523979	C₂×C₄	1	4	yes	complemented
60	#14523970	C₂×C₄	1	8	yes	complemented
61	#14523970	C₂×C₄	1	8	yes	complemented
62	#14523954	—	2	2	no	—
63	#14523954	—	2	2	no	—
64	#14523954	—	2	2	no	—
65	#14523953	—	2	2	no	—
66	#14523953	C₂×C₄	1	4	yes	complemented
67	C₄×C₆₇⋊C₈	—	2	2	no	—
68	C₄×C₆₇⋊C₈	—	2	2	no	—
69	C₄×C₆₇⋊C₈	—	2	2	no	—
70	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
71	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
72	C₈×Dic₆₇	—	2	2	no	—
73	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
74	C₆₇⋊#95	—	2	2	no	—
75	C₂×#41×C₆₇	C₂³	1	2	yes	—
76	#135×C₆₇	C₂×C₄	1	4	yes	—
77	#135×C₆₇	C₂×C₄	1	4	yes	—
78	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
80	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₆₇	—	2	4	no	—
85	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
86	#117×C₆₇	—	2	2	no	—
87	#117×C₆₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₆₇	—	2	2	no	—
89	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
90	#107×C₆₇	C₂×C₄	1	2	yes	—
91	#106×C₆₇	C₂×C₄	1	2	yes	—
92	#103×C₆₇	C₂×C₄	1	4	yes	—
93	#102×C₆₇	C₂×C₄	1	4	yes	—
94	#97×C₆₇	C₂×C₄	1	2	yes	—
95	#97×C₆₇	C₂×C₄	1	2	yes	—
96	C₂²×Dic₆₇	—	2	1	no	—
97	C₂²×Dic₆₇	—	2	1	no	—
98	#11761612	—	2	2	no	—
99	#11761612	—	2	2	no	—
100	#11761612	—	2	8	no	—
101	#11761612	—	2	8	no	—
102	#11761612	C₂²×C₄	1	4	yes	—
103	#11761612	C₂²×C₄	1	4	yes	—
104	C₂×C₆₇⋊C₈	—	2	2	no	—
105	C₂×C₆₇⋊C₈	—	2	2	no	—
106	C₂×C₆₇⋊C₈	—	2	8	no	—
107	C₂×C₆₇⋊C₈	—	2	8	no	—
108	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
109	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
110	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
112	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₆₇⋊C₈	#41	1	2	yes	—
114	C₂×C₆₇⋊C₈	#41	1	2	yes	—
115	C₄×Dic₆₇	—	2	1	no	—
116	C₄×Dic₆₇	—	2	1	no	—
117	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
118	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
119	#41×C₆₇	—	2	2	no	—
120	#41×C₆₇	—	2	2	no	—
121	#41×C₆₇	C₂²×C₄	1	4	yes	—
122	#41×C₆₇	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
124	C₂×D₄×C₆₇	—	2	2	no	—
125	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₆₇	—	2	2	no	—
127	C₂²×C₄×C₆₇	—	2	4	no	—
128	C₂²×C₄×C₆₇	#41	1	2	yes	—
129	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₆₇	C₄²	1	4	yes	—
131	SD₁₆×C₆₇	C₄²	1	8	yes	—
132	D₈×C₆₇	C₄²	1	4	yes	—
133	C₂×C₈×C₆₇	—	2	1	no	—
134	C₂×C₈×C₆₇	—	2	1	no	—
135	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₆₇	—	2	4	no	—
141	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
142	C₂²⋊C₄×C₆₇	—	2	2	no	—
143	C₂²⋊C₄×C₆₇	—	2	4	no	—
144	C₄²×C₆₇	—	2	4	no	—
145	C₄²×C₆₇	—	2	2	no	—
146	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₆₇	C₂×D₄	1	2	yes	—
148	C₂³×C₆₇	—	2	2	no	—
149	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
150	Q₈×C₆₇	—	2	2	no	—
151	Q₈×C₆₇	C₂×C₄²	1	4	yes	—
152	D₄×C₆₇	—	2	4	no	—
153	D₄×C₆₇	—	2	4	no	—
154	D₄×C₆₇	—	2	2	no	—
155	D₄×C₆₇	C₂×C₄²	1	4	yes	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	—	4	8	no	—
162	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₆₇	—	2	2	no	—
170	C₂×Dic₆₇	—	2	2	no	—
171	C₂×Dic₆₇	—	4	2	no	—
172	C₂×Dic₆₇	—	4	2	no	—
173	C₈×C₆₇	—	2	2	no	—
174	C₈×C₆₇	C₂×C₄²	1	2	yes	—
175	C₈×C₆₇	C₂×C₄²	1	2	yes	—
176	C₆₇⋊C₈	—	2	4	no	—
177	C₆₇⋊C₈	—	2	4	no	—
178	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
179	C₆₇⋊C₈	C₄×D₄	1	4	yes	—
180	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	—	2	4	no	—
183	C₂²×C₆₇	—	4	4	no	—
184	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
186	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
187	C₄×C₆₇	—	2	4	no	—
188	C₄×C₆₇	—	2	4	no	—
189	C₄×C₆₇	—	4	4	no	—
190	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
194	Dic₆₇	—	4	2	no	—
195	Dic₆₇	—	4	2	no	—
196	#20510	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	—	2	1	no	—
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	—	4	4	no	—
200	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
201	C₂×C₆₇	#2955	1	2	yes	—
202	C₂×#444	—	67	1	no	—
203	C₂×#443	—	67	1	no	—
204	#2943	D₆₇	1	1	yes	characteristic
205	C₄×#131	—	67	2	no	—
206	#1778	—	67	1	no	—
207	#1773	—	67	1	no	—
208	#1772	—	67	1	no	—
209	#1765	—	67	2	no	—
210	#1764	—	67	2	no	—
211	#1759	—	67	2	no	—
212	#1726	—	67	1	no	—
213	C₆₇	#20510	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
215	C₂×#131	—	67	2	no	—
216	C₂×#131	—	67	2	no	—
217	C₄×#41	C₂×D₆₇	1	2	yes	—
218	#444	—	67	8	no	—
219	#443	—	67	8	no	—
220	#442	Dic₆₇	1	2	yes	complemented
221	#441	Dic₆₇	1	2	yes	complemented
222	#440	Dic₆₇	1	4	yes	complemented
223	C₂×#108	—	67	1	no	—
224	C₂×#108	—	67	1	no	—
225	#427	C₂×D₆₇	1	1	yes	characteristic
226	C₂×#104	—	67	2	no	—
227	C₂×#104	—	67	2	no	—
228	#416	C₂×D₆₇	1	2	yes	—
229	#405	—	67	2	no	—
230	#405	—	67	2	no	—
231	#405	—	134	2	no	—
232	#405	—	134	2	no	—
233	C₄×M₁₆	—	67	2	no	—
234	C₄×M₁₆	—	134	2	no	—
235	C₂×#97	—	67	1	no	—
236	C₂×#97	—	67	1	no	—
237	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
238	C₂×C₄×C₈	—	67	1	no	—
239	C₂×C₄×C₈	—	67	1	no	—
240	C₂×C₄×C₈	—	67	1	no	—
241	C₂×C₄×C₈	—	134	2	no	—
242	#376	—	67	1	no	—
243	#341	—	67	2	no	—
244	#339	—	67	2	no	—
245	#339	—	67	2	no	—
246	C₂×#41	C₂²×D₆₇	1	2	yes	—
247	#135	C₄×D₆₇	1	4	yes	—
248	#135	C₄×D₆₇	1	4	yes	—
249	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
251	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
252	#131	—	67	8	no	—
253	#131	—	67	8	no	—
254	#131	—	134	4	no	—
255	#131	—	134	4	no	—
256	C₂×M₁₆	—	67	2	no	—
257	C₂×M₁₆	—	67	2	no	—
258	C₂×M₁₆	—	134	2	no	—
259	C₂×M₁₆	—	134	2	no	—
260	C₂²×C₈	—	67	1	no	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	134	2	no	—
263	C₂²×C₈	—	134	2	no	—
264	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
266	C₄×Q₈	C₂×Dic₆₇	1	4	yes	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	C₂×Dic₆₇	1	4	yes	—
269	#117	—	2	2	no	—
270	#117	C₂²×D₆₇	1	2	yes	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	67	1	no	—
273	C₂×C₄²	—	67	1	no	—
274	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
275	#108	—	67	4	no	—
276	#108	—	67	4	no	—
277	#107	C₂×Dic₆₇	1	2	yes	—
278	#106	C₂×Dic₆₇	1	2	yes	—
279	#104	—	67	8	no	—
280	#104	—	67	8	no	—
281	#103	C₂×Dic₆₇	1	4	yes	—
282	#102	C₂×Dic₆₇	1	4	yes	—
283	#97	—	67	4	no	—
284	#97	—	134	2	no	—
285	#97	—	134	2	no	—
286	#97	—	134	2	no	—
287	#97	—	134	2	no	—
288	#97	C₂×Dic₆₇	1	2	yes	—
289	#97	C₂×Dic₆₇	1	2	yes	—
290	C₄×C₈	—	67	4	no	—
291	C₄×C₈	—	67	2	no	—
292	C₄×C₈	—	67	2	no	—
293	C₄×C₈	—	134	2	no	—
294	C₄×C₈	—	134	2	no	—
295	C₄×C₈	—	134	2	no	—
296	C₄×C₈	—	134	2	no	—
297	#95	—	134	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	C₂×C₄×D₆₇	1	4	yes	—
301	#41	C₂×C₄×D₆₇	1	4	yes	—
302	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	134	1	no	—
308	C₂²×C₄	—	134	1	no	—
309	C₂²×C₄	#11761627	1	2	yes	—
310	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
311	Q₁₆	C₄×Dic₆₇	1	4	yes	—
312	SD₁₆	C₄×Dic₆₇	1	8	yes	—
313	D₈	C₄×Dic₆₇	1	4	yes	—
314	M₁₆	—	67	4	no	—
315	M₁₆	—	67	4	no	—
316	M₁₆	—	134	8	no	—
317	M₁₆	—	134	8	no	—
318	M₁₆	—	134	2	no	—
319	M₁₆	—	134	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	67	2	no	—
323	C₂×C₈	—	67	2	no	—
324	C₂×C₈	—	67	1	no	—
325	C₂×C₈	—	67	2	no	—
326	C₂×C₈	—	67	1	no	—
327	C₂×C₈	—	67	2	no	—
328	C₂×C₈	—	67	2	no	—
329	C₂×C₈	—	134	8	no	—
330	C₂×C₈	—	134	8	no	—
331	C₂×C₈	—	134	2	no	—
332	C₂×C₈	—	134	2	no	—
333	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
334	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
335	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
336	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
337	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	67	2	no	—
345	C₄²	—	67	2	no	—
346	C₄²	—	134	1	no	—
347	C₄²	—	134	1	no	—
348	C₄²	C₂²×Dic₆₇	1	2	yes	—
349	C₄²	D₄×D₆₇	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	C₂×#11761627	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	C₂×C₄×Dic₆₇	1	4	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂×C₄×Dic₆₇	1	4	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	268	2	no	—
365	C₂×C₄	—	268	2	no	—
366	C₂×C₄	—	134	2	no	—
367	C₂×C₄	—	134	2	no	—
368	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
371	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
374	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	67	2	no	—
377	C₈	—	67	4	no	—
378	C₈	—	67	2	no	—
379	C₈	—	134	4	no	—
380	C₈	—	134	4	no	—
381	C₈	C₂×C₄×Dic₆₇	1	2	yes	—
382	C₈	C₂×C₄×Dic₆₇	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
387	C₂²	C₄×#11761627	1	1	yes	characteristic
388	C₂²	C₄×#11761627	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	4	no	—
392	C₄	—	268	2	no	—
393	C₄	—	268	2	no	—
394	C₄	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
395	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
396	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
397	C₄	#41×Dic₆₇	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	C₄×D₄×Dic₆₇	1	1	yes	characteristic
402	C₂	#22569112	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2943	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2943	D₆₇
hypocenter	C₆₇	#20510
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. C₄×#14524050	C₂	semidirect
4. #22560115	C₂	semidirect
5. #22560095	C₂	semidirect
6. #22560090	C₂	semidirect
7. #22560056	C₂	semidirect
8. #22560049	C₂	semidirect
9. #22560019	C₂	semidirect
10. #22559897	C₂	semidirect
14. #16863518	C₄	semidirect
15. #16863513	C₄	semidirect
38. #442×C₆₇	C₄	semidirect
39. #441×C₆₇	C₄	semidirect
40. #440×C₆₇	C₄	semidirect
46. #14524050	C₂×C₄	semidirect
47. #14524050	C₂×C₄	semidirect
58. #14523979	C₂×C₄	semidirect
59. #14523979	C₂×C₄	semidirect
60. #14523970	C₂×C₄	semidirect
61. #14523970	C₂×C₄	semidirect
66. #14523953	C₂×C₄	semidirect
73. C₈×Dic₆₇	C₂×C₄	semidirect
213. C₆₇	#20510	semidirect
220. #442	Dic₆₇	semidirect
221. #441	Dic₆₇	semidirect
222. #440	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863518	2
C₂×#16863513	2
C₄×#14524050	2
#22560115	2
#22560095	2
#22560090	2
#22560056	2
#22560049	2
#22560019	2
#22559897	2
C₆₇×#2943	2
#20510	67