Subgroups — #30825174

Order 17152.

592 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	#22569338	C₂	1	1	yes	maximal, characteristic
2	#22569330	C₂	1	1	yes	maximal, characteristic
3	#22569175	C₂	1	1	yes	maximal, characteristic
4	#22558997	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558997	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558986	C₂	1	2	yes	maximal, complemented
7	#22558978	C₂	1	2	yes	maximal, complemented
8	#22558975	C₂	1	2	yes	maximal, complemented
9	#22558965	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558960	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11761628	C₂²	1	1	yes	characteristic
13	#16863526	—	2	1	no	—
14	#16863526	C₄	1	1	yes	characteristic
15	#16863526	C₄	1	1	yes	characteristic
16	C₈×Dic₁₃₄	—	2	1	no	—
17	#16863475	—	2	1	no	—
18	#16863475	C₄	1	1	yes	characteristic
19	#16863475	C₄	1	1	yes	characteristic
20	#16863471	—	2	2	no	—
21	#16863470	—	2	2	no	—
22	#16863467	C₄	1	2	yes	—
23	#16863467	C₄	1	2	yes	—
24	C₈×D₂₆₈	—	2	1	no	—
25	#16863452	C₂²	1	2	yes	—
26	#16863449	C₂²	1	1	yes	characteristic
27	#16863448	C₂²	1	2	yes	—
28	#16863447	C₂²	1	2	yes	—
29	#16863420	C₂²	1	1	yes	characteristic
30	#16863420	C₂²	1	1	yes	characteristic
31	#16863418	C₂²	1	2	yes	—
32	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
33	C₄×#11761611	C₂²	1	2	yes	—
34	#16863148	C₂²	1	2	yes	—
35	#16863148	C₂²	1	2	yes	—
36	#16863147	C₂²	1	2	yes	—
37	#16863147	C₂²	1	2	yes	—
38	#16863146	C₂²	1	2	yes	—
39	#16863146	C₂²	1	2	yes	—
40	#431×C₆₇	C₂²	1	1	yes	characteristic
41	#431×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
43	#335×C₆₇	C₂²	1	1	yes	characteristic
44	#335×C₆₇	C₂²	1	1	yes	characteristic
45	#334×C₆₇	C₂²	1	1	yes	characteristic
46	#334×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	Q₈	1	1	yes	characteristic
48	C₂×#11761612	—	2	1	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761611	—	2	2	no	—
51	C₂×#11761611	C₂×C₄	1	2	yes	—
52	C₂×#11761611	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₆₇	—	2	2	no	—
54	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
56	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
57	C₄×D₂₆₈	D₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₆₇	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₆₇	D₄	1	2	yes	—
60	#14524002	Q₈	1	1	yes	characteristic
61	#14524000	Q₈	1	2	yes	—
62	C₄²×D₆₇	C₂³	1	2	yes	—
63	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
69	Dic₆₇⋊C₈	—	2	2	no	—
70	Dic₆₇⋊C₈	—	2	2	no	—
71	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
72	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
74	(C₂×D₆₇)⋊C₈	—	2	2	no	—
75	(C₂×D₆₇)⋊C₈	—	2	2	no	—
76	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
78	#14523953	—	2	2	no	—
79	#14523953	C₂×C₄	1	2	yes	—
80	#14523953	C₂×C₄	1	2	yes	—
81	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
82	C₈×Dic₆₇	—	2	2	no	—
83	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²⋊C₈×C₆₇	—	2	1	no	—
91	C₂²⋊C₈×C₆₇	—	2	1	no	—
92	C₄×C₈×C₆₇	—	2	1	no	—
93	C₄×C₈×C₆₇	—	2	1	no	—
94	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	#11761628	—	4	2	no	—
99	C₂×Dic₁₃₄	C₄⋊C₄	1	1	yes	characteristic
100	C₂×D₂₆₈	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₆₇	C₄⋊C₄	1	2	yes	—
102	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₆₇	C₂×Q₈	1	2	yes	—
105	#11761612	—	8	1	no	—
106	#11761612	—	8	1	no	—
107	#11761611	—	2	4	no	—
108	#11761611	—	4	2	no	—
109	#11761611	—	8	2	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	2	2	no	—
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
114	C₈×D₆₇	—	8	2	no	—
115	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
117	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
118	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₂²⋊Dic₆₇	C₄⋊C₄	1	2	yes	—
120	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	2	yes	—
121	(C₂×D₆₇)⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
123	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
124	C₄×Dic₆₇	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	1	no	—
130	C₂×C₈×C₆₇	—	2	1	no	—
131	C₂×C₈×C₆₇	—	2	1	no	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	—	4	1	no	—
134	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
141	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₆₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₆₇	—	2	1	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	2	no	—
149	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂²⋊D₆₇	—	4	2	no	—
156	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
159	D₂₆₈	—	2	2	no	—
160	C₄×D₆₇	—	2	2	no	—
161	C₄×D₆₇	—	2	2	no	—
162	C₄×D₆₇	—	2	2	no	—
163	C₄×D₆₇	—	2	2	no	—
164	C₄×D₆₇	—	4	2	no	—
165	Dic₁₃₄	—	2	2	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	1	no	—
168	C₈×C₆₇	—	2	1	no	—
169	C₈×C₆₇	—	4	1	no	—
170	C₈×C₆₇	—	4	1	no	—
171	C₈×C₆₇	—	4	1	no	—
172	C₈×C₆₇	—	4	1	no	—
173	C₈×C₆₇	#131	1	2	yes	—
174	C₆₇⋊C₈	—	2	2	no	—
175	C₆₇⋊C₈	—	2	2	no	—
176	C₆₇⋊C₈	—	4	2	no	—
177	C₆₇⋊C₈	—	4	2	no	—
178	C₂²×C₆₇	—	2	1	no	—
179	C₂²×C₆₇	—	2	1	no	—
180	C₂²×C₆₇	—	2	1	no	—
181	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₂×D₆₇	—	2	2	no	—
183	C₂×D₆₇	—	2	2	no	—
184	C₂×D₆₇	—	2	2	no	—
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	—	2	1	no	—
188	C₄×C₆₇	#430	1	2	yes	—
189	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
190	C₄×C₆₇	#568	1	1	yes	characteristic
191	C₄×C₆₇	#577	1	1	yes	characteristic
192	C₄×C₆₇	#577	1	1	yes	characteristic
193	Dic₆₇	—	2	2	no	—
194	Dic₆₇	—	2	2	no	—
195	Dic₆₇	—	2	2	no	—
196	#17841	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	—	4	1	no	—
198	C₂×C₆₇	#2906	1	1	yes	characteristic
199	C₂×C₆₇	#2912	1	1	yes	characteristic
200	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
201	D₆₇	—	4	2	no	—
202	#2991	—	67	1	no	—
203	#2990	—	67	1	no	—
204	#2965	—	67	1	no	—
205	#1574	—	67	1	no	—
206	#1574	—	67	1	no	—
207	#1572	—	67	2	no	—
208	#1570	—	67	2	no	—
209	#1569	—	67	2	no	—
210	#1566	—	67	1	no	—
211	#1565	—	67	2	no	—
212	#1564	D₆₇	1	1	yes	characteristic, complemented
213	C₆₇	#17841	1	1	yes	characteristic, complemented, Sylow
214	C₄×#41	—	67	1	no	—
215	#446	—	67	1	no	—
216	#446	—	67	1	no	—
217	#446	—	134	1	no	—
218	C₈×Q₈	—	134	1	no	—
219	#436	—	67	1	no	—
220	#436	—	67	1	no	—
221	#436	—	134	1	no	—
222	#436	—	134	2	no	—
223	#435	—	67	2	no	—
224	#435	—	67	2	no	—
225	#435	—	134	2	no	—
226	C₈×D₄	—	134	1	no	—
227	#432	—	67	2	no	—
228	#431	—	67	1	no	—
229	#431	—	67	2	no	—
230	#431	—	67	2	no	—
231	#431	C₂×D₆₇	1	1	yes	characteristic
232	#431	C₂×D₆₇	1	1	yes	characteristic
233	#423	—	67	1	no	—
234	#423	—	67	1	no	—
235	#423	—	67	2	no	—
236	C₂×C₄⋊C₈	—	67	2	no	—
237	C₄×M₁₆	—	67	2	no	—
238	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
239	#335	—	67	2	no	—
240	#335	—	67	2	no	—
241	#335	C₂×D₆₇	1	1	yes	characteristic
242	#335	C₂×D₆₇	1	1	yes	characteristic
243	#334	—	67	2	no	—
244	#334	—	67	2	no	—
245	#334	—	67	2	no	—
246	#334	—	67	2	no	—
247	#334	C₂×D₆₇	1	1	yes	characteristic
248	#334	C₂×D₆₇	1	1	yes	characteristic
249	C₂×#41	—	67	1	no	—
250	C₂×M₁₆	—	67	2	no	—
251	C₂×M₁₆	—	67	2	no	—
252	C₂×M₁₆	—	134	2	no	—
253	C₂×M₁₆	—	134	1	no	—
254	C₂×M₁₆	—	134	1	no	—
255	C₂²×C₈	—	134	2	no	—
256	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
257	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
258	C₄×Q₈	—	67	1	no	—
259	C₄×Q₈	—	67	1	no	—
260	C₄×D₄	—	67	2	no	—
261	C₄×D₄	—	67	2	no	—
262	C₄×D₄	—	67	1	no	—
263	C₄×D₄	—	67	1	no	—
264	#117	—	67	1	no	—
265	#117	—	67	2	no	—
266	C₂×C₄²	—	67	2	no	—
267	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
268	C₄⋊C₈	—	67	2	no	—
269	C₄⋊C₈	—	67	2	no	—
270	C₄⋊C₈	—	67	1	no	—
271	C₄⋊C₈	—	67	1	no	—
272	C₄⋊C₈	—	67	2	no	—
273	C₄⋊C₈	—	67	2	no	—
274	C₄⋊C₈	—	134	2	no	—
275	C₄⋊C₈	—	134	2	no	—
276	C₄⋊C₈	—	134	1	no	—
277	C₄⋊C₈	—	134	1	no	—
278	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
279	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	67	2	no	—
285	C₂²⋊C₈	—	67	2	no	—
286	C₂²⋊C₈	—	67	2	no	—
287	C₂²⋊C₈	—	134	2	no	—
288	C₂²⋊C₈	—	134	2	no	—
289	#97	—	67	2	no	—
290	#97	—	67	2	no	—
291	#97	—	134	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	67	2	no	—
295	C₄×C₈	—	134	2	no	—
296	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
297	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
300	#41	—	268	2	no	—
301	C₂×Q₈	—	67	1	no	—
302	C₂×D₄	—	67	2	no	—
303	C₂×D₄	—	67	1	no	—
304	C₂²×C₄	—	67	2	no	—
305	C₂²×C₄	—	67	2	no	—
306	C₂²×C₄	—	67	2	no	—
307	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
309	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
310	M₁₆	—	268	2	no	—
311	M₁₆	—	536	2	no	—
312	M₁₆	—	536	1	no	—
313	M₁₆	—	536	1	no	—
314	M₁₆	—	134	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	536	2	no	—
322	C₂×C₈	—	67	2	no	—
323	C₂×C₈	—	67	2	no	—
324	C₂×C₈	—	134	2	no	—
325	C₂×C₈	—	134	2	no	—
326	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
330	C₄⋊C₄	—	67	2	no	—
331	C₄⋊C₄	—	67	2	no	—
332	C₄⋊C₄	—	67	1	no	—
333	C₄⋊C₄	—	67	1	no	—
334	C₂²⋊C₄	—	67	2	no	—
335	C₂²⋊C₄	—	67	2	no	—
336	C₂²⋊C₄	—	67	2	no	—
337	C₄²	—	67	2	no	—
338	C₄²	—	67	2	no	—
339	C₄²	—	67	2	no	—
340	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
341	C₄²	D₄×D₆₇	1	1	yes	characteristic
342	C₄²	Q₈×D₆₇	1	1	yes	characteristic
343	C₄²	C₂³×D₆₇	1	1	yes	characteristic
344	C₂³	—	67	2	no	—
345	C₂³	C₄⋊C₄×D₆₇	1	1	yes	characteristic
346	Q₈	—	134	2	no	—
347	D₄	—	268	2	no	—
348	D₄	—	134	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	268	2	no	—
355	C₂×C₄	—	67	2	no	—
356	C₂×C₄	—	67	2	no	—
357	C₂×C₄	—	67	2	no	—
358	C₂×C₄	—	134	2	no	—
359	C₂×C₄	—	134	2	no	—
360	C₂×C₄	—	134	2	no	—
361	C₂×C₄	—	134	2	no	—
362	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
367	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	268	2	no	—
376	C₈	—	268	2	no	—
377	C₈	—	134	2	no	—
378	C₈	—	134	2	no	—
379	C₈	#14524049	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	134	2	no	—
384	C₂²	—	134	2	no	—
385	C₂²	—	134	2	no	—
386	C₂²	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	134	2	no	—
391	C₄	—	134	2	no	—
392	C₄	—	134	2	no	—
393	C₄	#16863443	1	2	yes	—
394	C₄	C₂×#14524049	1	1	yes	characteristic
395	C₄	#16864162	1	1	yes	characteristic
396	C₄	#16864203	1	1	yes	characteristic
397	C₄	#16864203	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	268	2	no	—
400	C₂	#22568774	1	1	yes	characteristic
401	C₂	#22568801	1	1	yes	characteristic
402	C₂	C₂×#16863443	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×#1564	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#11761628	Q₈
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1564	D₆₇
hypocenter	C₆₇	#17841
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #22558997	C₂	semidirect
5. #22558997	C₂	semidirect
6. #22558986	C₂	semidirect
7. #22558978	C₂	semidirect
8. #22558975	C₂	semidirect
9. #22558965	C₂	semidirect
10. #22558960	C₂	semidirect
11. C₆₇×#1564	C₂	semidirect
212. #1564	D₆₇	semidirect
213. C₆₇	#17841	semidirect

Maximal subgroups

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

subgroup	index
#22569338	2
#22569330	2
#22569175	2
#22558997	2
#22558986	2
#22558978	2
#22558975	2
#22558965	2
#22558960	2
C₆₇×#1564	2
#17841	67