Subgroups — #31009081

Order 17152.

648 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573310	C₂	1	2	yes	maximal, complemented
2	#443×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22562049	C₂	1	2	yes	maximal, complemented
4	#22562048	C₂	1	2	yes	maximal, complemented
5	#22562047	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562046	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562045	C₂	1	1	yes	maximal, characteristic, complemented
8	#364×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#22561835	C₂	1	2	yes	maximal, complemented
10	C₄×#14523982	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₆₇	C₄	1	1	yes	characteristic
13	#131×D₆₇	C₂²	1	2	yes	—
14	#16863814	—	2	2	no	—
15	#16863814	C₂²	1	2	yes	complemented
16	#16863813	C₂²	1	2	yes	complemented
17	#16863812	—	2	2	no	—
18	#16863812	C₂²	1	2	yes	complemented
19	C₂×#14523982	—	2	2	no	—
20	C₂×#14523982	C₂²	1	1	yes	characteristic
21	C₂×#14523982	C₂²	1	1	yes	characteristic
22	M₃₂×D₆₇	—	2	2	no	—
23	M₃₂×D₆₇	C₂²	1	2	yes	—
24	#16863514	C₂²	1	1	yes	characteristic
25	#16863513	C₄	1	1	yes	characteristic
26	#16863512	C₄	1	1	yes	characteristic
27	#16863511	C₂²	1	2	yes	—
28	#16863510	C₄	1	2	yes	—
29	#108×D₆₇	C₄	1	1	yes	characteristic
30	#104×D₆₇	C₄	1	2	yes	—
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863217	C₂²	1	1	yes	characteristic, complemented
33	#16863216	C₂²	1	2	yes	complemented
34	#16863181	C₂²	1	2	yes	complemented
35	#16863180	C₂²	1	2	yes	complemented
36	#16863179	C₂²	1	2	yes	complemented
37	#16863171	C₂²	1	1	yes	characteristic, complemented
38	#16863171	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	#504×C₆₇	C₂²	1	2	yes	complemented
41	#443×C₆₇	C₂²	1	1	yes	characteristic
42	#364×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#350×C₆₇	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#41×D₆₇	C₂×C₄	1	2	yes	—
46	#14524066	C₈	1	1	yes	characteristic
47	#14524065	C₂×C₄	1	1	yes	characteristic
48	#14524064	C₈	1	2	yes	—
49	#14524063	C₂×C₄	1	2	yes	—
50	#14524062	C₈	1	1	yes	characteristic
51	Q₁₆×D₆₇	C₈	1	1	yes	characteristic
52	SD₁₆×D₆₇	C₈	1	2	yes	—
53	D₈×D₆₇	C₈	1	1	yes	characteristic
54	#14524051	—	2	2	no	—
55	#14524051	C₂×C₄	1	2	yes	—
56	#14524050	C₂×C₄	1	2	yes	—
57	#14524049	—	2	2	no	—
58	#14524049	C₂³	1	2	yes	—
59	M₁₆×D₆₇	—	2	2	no	—
60	M₁₆×D₆₇	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₆₇	—	2	2	no	—
62	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
64	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
65	#14523983	—	2	2	no	—
66	#14523983	C₂³	1	2	yes	—
67	#14523982	—	2	2	no	—
68	#14523982	—	2	1	no	—
69	#14523982	—	2	1	no	—
70	#14523982	—	2	2	no	—
71	#14523982	—	2	2	no	—
72	#14523982	D₄	1	1	yes	characteristic
73	#14523982	D₄	1	1	yes	characteristic
74	#14523982	D₄	1	1	yes	characteristic
75	#14523982	D₄	1	1	yes	characteristic
76	C₂×C₆₇⋊C₁₆	—	2	2	no	—
77	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
79	C₁₆×D₆₇	—	2	2	no	—
80	C₁₆×D₆₇	—	2	2	no	—
81	C₁₆×D₆₇	—	2	2	no	—
82	#14523979	C₂×C₄	1	1	yes	characteristic
83	#14523978	C₂×C₄	1	2	yes	—
84	#14523971	C₂×C₄	1	2	yes	—
85	#14523970	C₂×C₄	1	2	yes	—
86	#14523969	C₂×C₄	1	2	yes	—
87	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
90	#135×C₆₇	C₂×C₄	1	1	yes	characteristic
91	#131×C₆₇	C₂³	1	2	yes	—
92	M₃₂×C₆₇	—	2	2	no	—
93	M₃₂×C₆₇	C₂³	1	2	yes	—
94	C₂×C₁₆×C₆₇	—	2	2	no	—
95	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
97	#108×C₆₇	C₂×C₄	1	1	yes	characteristic
98	#104×C₆₇	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	#11761629	C₂×C₈	1	2	yes	—
101	#11761628	—	2	2	no	—
102	#11761628	C₂²×C₄	1	2	yes	—
103	#11761627	—	2	2	no	—
104	#11761627	C₂×C₈	1	2	yes	—
105	Q₈×D₆₇	C₂×C₈	1	2	yes	—
106	D₄×D₆₇	—	2	2	no	—
107	D₄×D₆₇	C₂×C₈	1	2	yes	—
108	C₂×C₄×D₆₇	—	2	2	no	—
109	C₂×C₄×D₆₇	—	2	1	no	—
110	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
111	Dic₂₆₈	C₂×C₈	1	1	yes	characteristic
112	#11761618	C₂×C₈	1	2	yes	—
113	#11761617	C₂×C₈	1	2	yes	—
114	#11761616	C₂×C₈	1	2	yes	—
115	#11761615	C₂×C₈	1	2	yes	—
116	D₅₃₆	C₂×C₈	1	1	yes	characteristic
117	#11761613	C₂×C₈	1	2	yes	—
118	#11761612	—	2	2	no	—
119	#11761612	C₂²×C₄	1	2	yes	—
120	#11761611	—	2	2	no	—
121	#11761611	—	2	2	no	—
122	#11761611	—	2	2	no	—
123	C₂×C₆₇⋊C₈	—	2	2	no	—
124	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₆₇	—	2	2	no	—
127	C₈×D₆₇	—	2	2	no	—
128	C₈×D₆₇	—	2	2	no	—
129	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
130	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
131	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
132	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
133	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
134	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
135	C₈×D₆₇	#41	1	1	yes	characteristic
136	C₈×D₆₇	#41	1	1	yes	characteristic
137	C₄×Dic₆₇	—	2	1	no	—
138	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₆₇⋊C₁₆	—	2	2	no	—
140	C₆₇⋊C₁₆	—	2	1	no	—
141	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
142	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
143	#41×C₆₇	C₂²×C₄	1	2	yes	—
144	Q₁₆×C₆₇	C₂×C₈	1	1	yes	characteristic
145	SD₁₆×C₆₇	C₂×C₈	1	2	yes	—
146	D₈×C₆₇	C₂×C₈	1	1	yes	characteristic
147	M₁₆×C₆₇	—	2	2	no	—
148	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₆₇	—	2	2	no	—
150	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
152	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₆₇	—	2	2	no	—
154	C₁₆×C₆₇	—	2	1	no	—
155	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₆₇	—	2	2	no	—
158	C₂²×D₆₇	#131	1	1	yes	characteristic
159	Q₈×C₆₇	C₂²×C₈	1	2	yes	—
160	D₄×C₆₇	—	2	2	no	—
161	D₄×C₆₇	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₆₇	—	2	2	no	—
166	C₂²⋊D₆₇	—	2	2	no	—
167	C₂²⋊D₆₇	—	2	2	no	—
168	C₂×Dic₆₇	—	2	2	no	—
169	C₂×Dic₆₇	—	2	1	no	—
170	C₂×Dic₆₇	#131	1	1	yes	characteristic
171	D₂₆₈	—	2	2	no	—
172	D₂₆₈	C₂²×C₈	1	2	yes	—
173	C₄×D₆₇	—	2	2	no	—
174	C₄×D₆₇	—	2	2	no	—
175	C₄×D₆₇	—	2	2	no	—
176	C₄×D₆₇	—	4	2	no	—
177	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
178	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
179	C₄×D₆₇	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₆₇	C₂²×C₈	1	1	yes	characteristic
181	Dic₁₃₄	—	2	2	no	—
182	Dic₁₃₄	C₂²×C₈	1	2	yes	—
183	C₈×C₆₇	—	2	2	no	—
184	C₈×C₆₇	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₆₇	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
188	C₆₇⋊C₈	—	2	2	no	—
189	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
190	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
191	C₆₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
192	C₆₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
193	C₂²×C₆₇	—	2	2	no	—
194	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
195	C₂×D₆₇	—	2	2	no	—
196	C₂×D₆₇	—	4	1	no	—
197	C₂×D₆₇	—	8	2	no	—
198	C₂×D₆₇	C₈×D₄	1	1	yes	characteristic
199	C₂×D₆₇	C₈×D₄	1	1	yes	characteristic
200	C₄×C₆₇	—	2	2	no	—
201	C₄×C₆₇	—	2	2	no	—
202	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₆₇	C₂³×C₈	1	1	yes	characteristic
204	Dic₆₇	—	2	2	no	—
205	Dic₆₇	—	4	1	no	—
206	Dic₆₇	C₈×D₄	1	1	yes	characteristic
207	Dic₆₇	C₈×D₄	1	1	yes	characteristic
208	#33443	—	67	1	no	maximal, Sylow
209	C₂×C₆₇	—	2	1	no	—
210	C₂×C₆₇	—	4	2	no	—
211	C₂×C₆₇	C₂×C₈×D₄	1	1	yes	characteristic
212	D₆₇	—	2	1	no	—
213	D₆₇	—	2	1	no	—
214	D₆₇	—	4	2	no	—
215	#3407	—	67	2	no	—
216	C₂×#443	—	67	1	no	—
217	#2171	—	67	2	no	—
218	#2171	—	67	2	no	—
219	#2170	—	67	1	no	—
220	#2170	—	67	1	no	—
221	#2170	—	67	1	no	—
222	#2170	D₆₇	1	1	yes	characteristic, complemented
223	C₂×#364	—	67	1	no	—
224	#2117	—	67	2	no	—
225	C₄×M₃₂	—	67	1	no	—
226	C₆₇	#33443	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	—	67	1	no	—
228	C₂×#131	—	67	2	no	—
229	#504	—	67	2	no	—
230	#504	—	67	2	no	—
231	#504	—	67	2	no	—
232	#504	—	134	2	no	—
233	#504	—	134	2	no	—
234	#504	C₂×D₆₇	1	2	yes	complemented
235	C₂×M₃₂	—	67	1	no	—
236	C₂×M₃₂	—	67	1	no	—
237	C₂×M₃₂	—	67	2	no	—
238	C₂×M₃₂	—	134	2	no	—
239	C₂×M₃₂	—	134	2	no	—
240	#443	—	67	1	no	—
241	#443	—	67	2	no	—
242	#443	—	67	1	no	—
243	#443	—	67	2	no	—
244	#443	—	67	1	no	—
245	#443	C₂×D₆₇	1	1	yes	characteristic
246	C₂×#108	—	67	1	no	—
247	C₂×#104	—	67	2	no	—
248	C₂×C₄×C₈	—	67	1	no	—
249	#364	—	67	2	no	—
250	#364	—	67	1	no	—
251	#364	C₂×D₆₇	1	1	yes	characteristic, complemented
252	#350	—	67	2	no	—
253	#350	—	67	2	no	—
254	#350	—	67	2	no	—
255	#350	C₂×D₆₇	1	2	yes	complemented
256	#346	—	67	1	no	—
257	#346	—	67	1	no	—
258	C₄×C₁₆	—	67	1	no	—
259	C₄×C₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
260	C₂×#41	—	67	2	no	—
261	#135	—	67	2	no	—
262	#135	—	67	1	no	—
263	#135	—	67	2	no	—
264	#135	—	67	1	no	—
265	#135	—	67	1	no	—
266	#135	C₄×D₆₇	1	1	yes	characteristic
267	C₂×Q₁₆	—	67	1	no	—
268	C₂×SD₁₆	—	67	2	no	—
269	C₂×D₈	—	67	1	no	—
270	#131	—	67	2	no	—
271	#131	—	67	2	no	—
272	#131	—	67	2	no	—
273	#131	—	134	2	no	—
274	#131	—	134	2	no	—
275	#131	C₂²×D₆₇	1	2	yes	—
276	C₂×M₁₆	—	67	2	no	—
277	C₂×M₁₆	—	134	2	no	—
278	C₂²×C₈	—	67	1	no	—
279	C₂²×C₈	—	67	1	no	—
280	C₂²×C₈	—	134	2	no	—
281	C₂×C₄²	—	67	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	67	1	no	—
284	M₃₂	—	67	1	no	—
285	M₃₂	—	67	1	no	—
286	M₃₂	—	67	1	no	—
287	M₃₂	—	67	2	no	—
288	M₃₂	—	134	2	no	—
289	M₃₂	—	134	1	no	—
290	M₃₂	—	134	1	no	—
291	M₃₂	—	134	2	no	—
292	M₃₂	—	134	2	no	—
293	M₃₂	—	134	2	no	—
294	M₃₂	C₂²×D₆₇	1	2	yes	—
295	C₂×C₁₆	—	2	2	no	—
296	C₂×C₁₆	—	67	1	no	—
297	C₂×C₁₆	—	67	1	no	—
298	C₂×C₁₆	—	134	2	no	—
299	C₂×C₁₆	—	134	2	no	—
300	C₂×C₁₆	—	134	2	no	—
301	C₂×C₁₆	—	134	2	no	—
302	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
304	#108	—	67	2	no	—
305	#108	—	67	1	no	—
306	#108	C₄×D₆₇	1	1	yes	characteristic
307	#104	—	67	2	no	—
308	#104	—	67	2	no	—
309	#104	—	67	2	no	—
310	#104	C₄×D₆₇	1	2	yes	—
311	C₄×C₈	—	67	1	no	—
312	C₄×C₈	—	67	1	no	—
313	C₄×C₈	—	67	1	no	—
314	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
315	#41	—	67	2	no	—
316	#41	—	67	2	no	—
317	#41	—	67	2	no	—
318	#41	—	134	2	no	—
319	#41	—	134	2	no	—
320	#41	C₂×C₄×D₆₇	1	2	yes	—
321	C₂×Q₈	—	67	2	no	—
322	C₂×D₄	—	67	2	no	—
323	C₂×D₄	—	134	2	no	—
324	C₂²×C₄	—	67	1	no	—
325	C₂²×C₄	—	134	1	no	—
326	C₂²×C₄	—	134	2	no	—
327	Q₁₆	—	67	2	no	—
328	Q₁₆	—	67	1	no	—
329	Q₁₆	C₈×D₆₇	1	1	yes	characteristic
330	SD₁₆	—	67	2	no	—
331	SD₁₆	—	67	2	no	—
332	SD₁₆	—	67	2	no	—
333	SD₁₆	C₈×D₆₇	1	2	yes	—
334	D₈	—	67	2	no	—
335	D₈	—	67	1	no	—
336	D₈	C₈×D₆₇	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	67	2	no	—
339	M₁₆	—	134	2	no	—
340	M₁₆	—	134	2	no	—
341	M₁₆	—	134	2	no	—
342	M₁₆	—	134	2	no	—
343	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	1	no	—
347	C₂×C₈	—	67	1	no	—
348	C₂×C₈	—	67	1	no	—
349	C₂×C₈	—	67	1	no	—
350	C₂×C₈	—	67	1	no	—
351	C₂×C₈	—	67	1	no	—
352	C₂×C₈	—	67	1	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	134	2	no	—
356	C₂×C₈	—	134	2	no	—
357	C₂×C₈	—	134	2	no	—
358	C₂×C₈	—	134	2	no	—
359	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
361	C₄²	—	67	1	no	—
362	C₄²	—	134	1	no	—
363	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	67	1	no	—
367	C₁₆	—	67	1	no	—
368	C₁₆	—	134	2	no	—
369	C₁₆	—	134	1	no	—
370	C₁₆	D₄×D₆₇	1	1	yes	characteristic
371	C₁₆	D₄×D₆₇	1	1	yes	characteristic
372	C₂³	—	67	1	no	—
373	C₂³	—	134	2	no	—
374	Q₈	—	67	2	no	—
375	Q₈	—	134	2	no	—
376	Q₈	C₂×C₈×D₆₇	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	67	2	no	—
379	D₄	—	134	2	no	—
380	D₄	—	134	2	no	—
381	D₄	—	134	2	no	—
382	D₄	—	134	2	no	—
383	D₄	C₂×C₈×D₆₇	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	268	2	no	—
387	C₂×C₄	—	67	1	no	—
388	C₂×C₄	—	67	1	no	—
389	C₂×C₄	—	67	1	no	—
390	C₂×C₄	—	67	1	no	—
391	C₂×C₄	—	67	1	no	—
392	C₂×C₄	—	134	2	no	—
393	C₂×C₄	—	134	2	no	—
394	C₂×C₄	—	134	1	no	—
395	C₂×C₄	—	134	2	no	—
396	C₂×C₄	—	134	2	no	—
397	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	67	1	no	—
400	C₈	—	67	1	no	—
401	C₈	—	67	1	no	—
402	C₈	—	67	1	no	—
403	C₈	—	134	2	no	—
404	C₈	C₂×C₈×D₆₇	1	1	yes	characteristic
405	C₈	C₂×C₈×D₆₇	1	1	yes	characteristic
406	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
407	C₈	#41×D₆₇	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	268	1	no	—
410	C₂²	—	536	2	no	—
411	C₂²	—	67	1	no	—
412	C₂²	—	67	1	no	—
413	C₂²	—	134	2	no	—
414	C₂²	#131×D₆₇	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	268	1	no	—
418	C₄	—	67	1	no	—
419	C₄	—	67	1	no	—
420	C₄	—	134	2	no	—
421	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₆₇	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	268	2	no	—
426	C₂	—	134	1	no	—
427	C₂	—	134	1	no	—
428	C₂	C₈×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2170	C₂
socle	C₂×C₆₇	C₂×C₈×D₄
prime radical	#135×D₆₇	C₄
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2170	D₆₇
hypocenter	C₆₇	#33443
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #22573310	C₂	semidirect
3. #22562049	C₂	semidirect
4. #22562048	C₂	semidirect
5. #22562047	C₂	semidirect
6. #22562046	C₂	semidirect
7. #22562045	C₂	semidirect
8. #364×D₆₇	C₂	semidirect
9. #22561835	C₂	semidirect
10. C₄×#14523982	C₂	semidirect
11. C₆₇×#2170	C₂	semidirect
15. #16863814	C₂²	semidirect
16. #16863813	C₂²	semidirect
18. #16863812	C₂²	semidirect
32. #16863217	C₂²	semidirect
33. #16863216	C₂²	semidirect
34. #16863181	C₂²	semidirect
35. #16863180	C₂²	semidirect
36. #16863179	C₂²	semidirect
37. #16863171	C₂²	semidirect
38. #16863171	C₂²	semidirect
39. C₄×C₆₇⋊C₁₆	C₂²	semidirect
40. #504×C₆₇	C₂²	semidirect
42. #364×C₆₇	C₂²	semidirect
43. #350×C₆₇	C₂²	semidirect
44. C₄×C₁₆×C₆₇	C₂²	semidirect
222. #2170	D₆₇	semidirect
226. C₆₇	#33443	semidirect
234. #504	C₂×D₆₇	semidirect
251. #364	C₂×D₆₇	semidirect
255. #350	C₂×D₆₇	semidirect
259. C₄×C₁₆	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573310	2
#443×D₆₇	2
#22562049	2
#22562048	2
#22562047	2
#22562046	2
#22562045	2
#364×D₆₇	2
#22561835	2
C₄×#14523982	2
C₆₇×#2170	2
#33443	67