Subgroups — #30826344

Order 17152.

750 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570785	C₂	1	1	yes	maximal, characteristic
2	#22568918	C₂	1	2	yes	maximal, complemented
3	#22559095	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559092	C₂	1	2	yes	maximal, complemented
5	D₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559003	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559001	C₂	1	2	yes	maximal, complemented
8	#22558966	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558658	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×#14524051	—	2	2	no	—
13	#16863943	C₂²	1	2	yes	—
14	#16863800	C₄	1	1	yes	characteristic
15	#16863771	C₄	1	1	yes	characteristic
16	#16863741	C₄	1	2	yes	—
17	#16863633	C₄	1	1	yes	characteristic
18	#16863631	C₄	1	2	yes	—
19	#16863629	C₄	1	1	yes	characteristic
20	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
21	C₄×#11761613	C₂²	1	2	yes	—
22	#16863475	C₂²	1	2	yes	—
23	#16863472	—	2	2	no	—
24	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
25	#16863461	C₂²	1	2	yes	—
26	(C₂²⋊D₆₇)⋊C₈	—	2	2	no	—
27	#16863418	C₂²	1	2	yes	—
28	#16863361	—	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
33	#16863148	C₂²	1	2	yes	—
34	#16863125	C₂²	1	2	yes	—
35	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
36	#16863123	C₂²	1	2	yes	—
37	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
41	#436×C₆₇	C₂²	1	2	yes	—
42	#335×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761628	—	2	2	no	—
46	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#11761613	C₂×C₄	1	2	yes	—
48	#14524051	—	4	8	no	—
49	C₂×#11761611	—	2	2	no	—
50	C₂×#11761611	—	2	2	no	—
51	C₂²×C₆₇⋊C₈	—	2	2	no	—
52	C₂×C₈×D₆₇	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	2	no	—
54	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
57	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
58	#14524042	C₂×C₄	1	2	yes	—
59	#14524039	C₂×C₄	1	2	yes	—
60	#14524029	—	2	2	no	—
61	#14524018	C₂×C₄	1	2	yes	—
62	#14524016	—	2	2	no	—
63	#14524014	C₂×C₄	1	2	yes	—
64	C₄×D₂₆₈	C₂³	1	2	yes	—
65	C₄×C₂²⋊D₆₇	—	2	2	no	—
66	C₄²×D₆₇	C₂³	1	1	yes	characteristic
67	#14523977	C₂×C₄	1	1	yes	characteristic
68	#14523976	C₂×C₄	1	2	yes	—
69	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₆₇⋊C₈	—	2	2	no	—
71	#14523965	C₂×C₄	1	2	yes	—
72	#14523964	C₂×C₄	1	2	yes	—
73	#14523963	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
75	(C₂×D₆₇)⋊C₈	—	2	2	no	—
76	(C₂×D₆₇)⋊C₈	—	2	2	no	—
77	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₆₇	—	2	1	no	—
81	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	D₄	1	1	yes	characteristic
84	C₈×Dic₆₇	D₄	1	1	yes	characteristic
85	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₂×M₁₆×C₆₇	—	2	2	no	—
87	C₄×D₄×C₆₇	C₂³	1	2	yes	—
88	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
90	#102×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₆₇	—	2	2	no	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#11761628	—	4	4	no	—
96	#11761628	—	4	4	no	—
97	C₂×Dic₁₃₄	—	2	2	no	—
98	C₂×D₂₆₈	—	2	2	no	—
99	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
100	C₂×C₂²⋊D₆₇	—	2	2	no	—
101	C₂×C₂²⋊D₆₇	—	2	2	no	—
102	C₂×C₂²⋊D₆₇	—	2	2	no	—
103	C₂×C₄×D₆₇	—	2	2	no	—
104	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
107	D₅₃₆	—	2	2	no	—
108	#11761613	—	2	4	no	—
109	#11761611	—	4	4	no	—
110	#11761611	—	4	4	no	—
111	C₂×C₆₇⋊C₈	—	2	1	no	—
112	C₂×C₆₇⋊C₈	—	2	2	no	—
113	C₂×C₆₇⋊C₈	—	4	4	no	—
114	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₈×D₆₇	—	2	4	no	—
119	C₈×D₆₇	—	2	2	no	—
120	C₈×D₆₇	—	2	2	no	—
121	C₈×D₆₇	—	2	2	no	—
122	C₈×D₆₇	—	4	4	no	—
123	C₈×D₆₇	D₈	1	4	yes	complemented
124	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
125	Dic₆₇⋊C₄	—	2	2	no	—
126	C₂²⋊Dic₆₇	—	2	2	no	—
127	(C₂×D₆₇)⋊C₄	—	2	2	no	—
128	(C₂×D₆₇)⋊C₄	—	2	2	no	—
129	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₆₇	#41	1	1	yes	characteristic
132	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₆₇	—	2	2	no	—
134	D₈×C₆₇	—	2	2	no	—
135	M₁₆×C₆₇	—	4	4	no	—
136	C₂×C₈×C₆₇	—	2	1	no	—
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
143	C₂²⋊C₄×C₆₇	—	2	2	no	—
144	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₆₇	—	2	2	no	—
146	C₂²×D₆₇	—	2	2	no	—
147	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
148	D₄×C₆₇	—	2	2	no	—
149	D₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
156	C₂²⋊D₆₇	—	4	4	no	—
157	C₂²⋊D₆₇	—	4	4	no	—
158	C₂²⋊D₆₇	—	4	4	no	—
159	C₂×Dic₆₇	—	2	2	no	—
160	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
163	D₂₆₈	—	2	2	no	—
164	D₂₆₈	—	2	2	no	—
165	D₂₆₈	—	4	4	no	—
166	C₄×D₆₇	—	2	1	no	—
167	C₄×D₆₇	—	2	1	no	—
168	C₄×D₆₇	—	2	2	no	—
169	C₄×D₆₇	—	4	2	no	—
170	C₄×D₆₇	—	4	2	no	—
171	C₄×D₆₇	C₂×D₈	1	2	yes	—
172	C₄×D₆₇	#135	1	2	yes	—
173	Dic₁₃₄	—	4	4	no	—
174	C₈×C₆₇	—	2	2	no	—
175	C₈×C₆₇	—	2	1	no	—
176	C₈×C₆₇	—	2	1	no	—
177	C₈×C₆₇	—	4	2	no	—
178	C₈×C₆₇	#131	1	2	yes	complemented
179	C₈×C₆₇	C₂×D₈	1	2	yes	—
180	C₆₇⋊C₈	—	2	2	no	—
181	C₆₇⋊C₈	—	2	1	no	—
182	C₆₇⋊C₈	—	2	1	no	—
183	C₆₇⋊C₈	—	4	2	no	—
184	C₆₇⋊C₈	#131	1	2	yes	complemented
185	C₆₇⋊C₈	C₂×D₈	1	2	yes	—
186	C₂²×C₆₇	—	4	2	no	—
187	C₂²×C₆₇	—	4	2	no	—
188	C₂²×C₆₇	—	4	2	no	—
189	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂×D₆₇	—	2	1	no	—
191	C₂×D₆₇	—	2	1	no	—
192	C₂×D₆₇	—	4	2	no	—
193	C₂×D₆₇	—	4	2	no	—
194	C₂×D₆₇	—	4	2	no	—
195	C₂×D₆₇	C₄×D₈	1	2	yes	—
196	C₄×C₆₇	—	2	1	no	—
197	C₄×C₆₇	—	4	2	no	—
198	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
199	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
200	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
201	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
202	Dic₆₇	—	2	1	no	—
203	Dic₆₇	—	4	2	no	—
204	Dic₆₇	C₄×D₈	1	2	yes	—
205	Dic₆₇	#443	1	2	yes	—
206	#17956	—	67	1	no	maximal, Sylow
207	C₂×C₆₇	—	8	2	no	—
208	C₂×C₆₇	#2931	1	1	yes	characteristic
209	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
210	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
211	D₆₇	—	2	2	no	—
212	D₆₇	—	8	2	no	—
213	#3169	—	67	1	no	—
214	#2931	—	67	2	no	—
215	#1589	—	67	2	no	—
216	#1589	—	67	1	no	—
217	#1589	D₆₇	1	1	yes	characteristic, complemented
218	C₈×D₈	—	67	1	no	—
219	C₈×D₈	—	67	1	no	—
220	C₈×D₈	—	67	2	no	—
221	#1567	—	67	1	no	—
222	#1492	—	67	2	no	—
223	C₂×C₈²	—	67	1	no	—
224	C₆₇	#17956	1	1	yes	characteristic, complemented, Sylow
225	C₂×#131	—	134	2	no	—
226	#532	—	67	2	no	—
227	#500	—	67	1	no	—
228	#493	—	67	1	no	—
229	#486	—	67	2	no	—
230	#466	—	67	1	no	—
231	#466	—	67	1	no	—
232	#466	—	67	2	no	—
233	C₄×D₈	—	67	2	no	—
234	C₄×D₈	—	67	1	no	—
235	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
236	#436	—	67	2	no	—
237	#436	—	134	2	no	—
238	#436	C₂×D₆₇	1	2	yes	—
239	C₈×D₄	—	67	2	no	—
240	C₈×D₄	—	67	2	no	—
241	C₈×D₄	—	134	2	no	—
242	#423	—	67	2	no	—
243	#408	—	134	2	no	—
244	C₂×C₄×C₈	—	67	1	no	—
245	C₂×C₄×C₈	—	67	1	no	—
246	C₂×C₄×C₈	—	67	1	no	—
247	#335	—	67	2	no	—
248	#335	—	67	1	no	—
249	#335	C₂×D₆₇	1	1	yes	characteristic
250	D₄⋊C₈	—	67	2	no	—
251	D₄⋊C₈	—	67	2	no	—
252	D₄⋊C₈	—	67	2	no	—
253	D₄⋊C₈	C₂×D₆₇	1	2	yes	—
254	C₈²	—	67	1	no	—
255	C₈²	—	67	1	no	—
256	C₈²	—	67	1	no	—
257	C₈²	C₂×D₆₇	1	1	yes	characteristic
258	C₂×#41	—	134	2	no	—
259	C₂×D₈	—	67	2	no	—
260	C₂×D₈	—	67	1	no	—
261	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
262	#131	—	268	8	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	134	2	no	—
265	C₂×M₁₆	—	134	2	no	—
266	C₂²×C₈	—	67	1	no	—
267	C₂²×C₈	—	67	1	no	—
268	C₂²×C₈	—	67	1	no	—
269	C₂²×C₈	—	67	1	no	—
270	C₂²×C₈	—	134	2	no	—
271	C₂²×C₈	—	134	1	no	—
272	C₂²×C₈	—	134	2	no	—
273	C₄⋊Q₈	—	67	2	no	—
274	#127	—	67	2	no	—
275	#124	—	134	2	no	—
276	#121	—	67	2	no	—
277	#121	—	67	2	no	—
278	#121	—	134	2	no	—
279	C₄×D₄	—	67	2	no	—
280	C₄×D₄	—	134	2	no	—
281	C₄×D₄	C₂²×D₆₇	1	2	yes	—
282	C₂×C₄²	—	67	1	no	—
283	#107	—	67	1	no	—
284	#107	—	67	2	no	—
285	#107	C₄×D₆₇	1	1	yes	characteristic
286	C₄⋊C₈	—	67	2	no	—
287	C₄⋊C₈	—	134	2	no	—
288	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
289	#102	—	67	2	no	—
290	#102	—	67	2	no	—
291	#102	—	67	2	no	—
292	#102	C₄×D₆₇	1	2	yes	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	134	2	no	—
295	C₂²⋊C₈	—	134	2	no	—
296	C₂²⋊C₈	—	134	2	no	—
297	C₄×C₈	—	67	1	no	—
298	C₄×C₈	—	67	1	no	—
299	C₄×C₈	—	67	1	no	—
300	C₄×C₈	—	67	1	no	—
301	C₄×C₈	—	67	1	no	—
302	C₄×C₈	—	67	1	no	—
303	C₄×C₈	—	67	1	no	—
304	C₄×C₈	—	134	1	no	—
305	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
308	#41	—	268	4	no	—
309	#41	—	268	4	no	—
310	C₂×Q₈	—	134	2	no	—
311	C₂×D₄	—	67	2	no	—
312	C₂×D₄	—	134	2	no	—
313	C₂×D₄	—	134	2	no	—
314	C₂×D₄	—	134	2	no	—
315	C₂×D₄	—	134	2	no	—
316	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	67	1	no	—
319	C₂²×C₄	—	67	1	no	—
320	C₂²×C₄	—	67	1	no	—
321	C₂²×C₄	—	134	2	no	—
322	D₈	—	2	2	no	—
323	D₈	—	134	4	no	—
324	D₈	—	134	2	no	—
325	M₁₆	—	4	4	no	—
326	M₁₆	—	268	4	no	—
327	M₁₆	—	268	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	268	4	no	—
331	C₂×C₈	—	268	4	no	—
332	C₂×C₈	—	67	1	no	—
333	C₂×C₈	—	67	1	no	—
334	C₂×C₈	—	67	4	no	—
335	C₂×C₈	—	67	1	no	—
336	C₂×C₈	—	67	1	no	—
337	C₂×C₈	—	134	2	no	—
338	C₂×C₈	—	134	2	no	—
339	C₂×C₈	—	134	4	no	—
340	C₂×C₈	—	134	2	no	—
341	C₂×C₈	—	134	1	no	—
342	C₂×C₈	—	134	2	no	—
343	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
345	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
346	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
347	C₄⋊C₄	—	67	2	no	—
348	C₄⋊C₄	—	134	2	no	—
349	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	134	2	no	—
352	C₂²⋊C₄	—	134	2	no	—
353	C₂²⋊C₄	—	134	2	no	—
354	C₄²	—	67	1	no	—
355	C₄²	—	67	1	no	—
356	C₄²	—	67	1	no	—
357	C₄²	C₂³×D₆₇	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	67	1	no	—
360	C₂³	—	134	2	no	—
361	Q₈	—	268	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	268	4	no	—
365	D₄	—	268	4	no	—
366	D₄	—	268	4	no	—
367	D₄	—	268	4	no	—
368	D₄	—	134	2	no	—
369	D₄	—	134	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	268	2	no	—
374	C₂×C₄	—	268	2	no	—
375	C₂×C₄	—	67	1	no	—
376	C₂×C₄	—	67	1	no	—
377	C₂×C₄	—	67	2	no	—
378	C₂×C₄	—	67	2	no	—
379	C₂×C₄	—	67	1	no	—
380	C₂×C₄	—	134	2	no	—
381	C₂×C₄	—	134	2	no	—
382	C₂×C₄	—	134	1	no	—
383	C₂×C₄	—	134	1	no	—
384	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
386	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	268	2	no	—
392	C₈	—	67	2	no	—
393	C₈	—	67	2	no	—
394	C₈	—	134	2	no	—
395	C₈	—	134	1	no	—
396	C₈	—	134	1	no	—
397	C₈	#14524051	1	2	yes	complemented
398	C₈	D₈×D₆₇	1	2	yes	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	268	2	no	—
403	C₂²	—	268	2	no	—
404	C₂²	—	268	2	no	—
405	C₂²	—	67	2	no	—
406	C₂²	—	134	1	no	—
407	C₂²	—	134	1	no	—
408	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	268	2	no	—
412	C₄	—	67	2	no	—
413	C₄	—	67	2	no	—
414	C₄	—	134	1	no	—
415	C₄	#131×D₆₇	1	1	yes	characteristic
416	C₄	C₂×#14524051	1	1	yes	characteristic
417	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
418	C₄	#135×D₆₇	1	1	yes	characteristic
419	C₂	—	8	2	no	—
420	C₂	—	536	2	no	—
421	C₂	—	134	2	no	—
422	C₂	#22568918	1	1	yes	characteristic
423	C₂	C₄×D₈×D₆₇	1	1	yes	characteristic
424	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	#22570785	C₂
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1589	D₆₇
hypocenter	C₆₇	#17956
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. #22568918	C₂	semidirect
3. #22559095	C₂	semidirect
4. #22559092	C₂	semidirect
5. D₈×C₆₇⋊C₈	C₂	semidirect
6. #22559003	C₂	semidirect
7. #22559001	C₂	semidirect
8. #22558966	C₂	semidirect
9. #22558658	C₂	semidirect
10. C₈²×D₆₇	C₂	semidirect
11. C₆₇×#1589	C₂	semidirect
123. C₈×D₆₇	D₈	semidirect
178. C₈×C₆₇	#131	semidirect
184. C₆₇⋊C₈	#131	semidirect
217. #1589	D₆₇	semidirect
224. C₆₇	#17956	semidirect
397. C₈	#14524051	semidirect

Maximal subgroups

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

subgroup	index
#22570785	2
#22568918	2
#22559095	2
#22559092	2
D₈×C₆₇⋊C₈	2
#22559003	2
#22559001	2
#22558966	2
#22558658	2
C₈²×D₆₇	2
C₆₇×#1589	2
#17956	67