Subgroups — #30869758

Order 17152.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570695	C₂	1	1	yes	maximal, characteristic
2	#22569125	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569060	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561117	C₂	1	1	yes	maximal, characteristic, complemented
5	#22561105	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560740	C₂	1	2	yes	maximal, complemented
7	#22560735	C₂	1	2	yes	maximal, complemented
8	#22560695	C₂	1	2	yes	maximal, complemented
9	#22560688	C₂	1	2	yes	maximal, complemented
10	#22559964	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524071	C₂²	1	2	yes	—
13	C₂×#14524065	C₂²	1	1	yes	characteristic
14	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
15	#16864162	C₂²	1	2	yes	—
16	#16863965	C₂²	1	2	yes	—
17	#16863870	C₂²	1	2	yes	—
18	#16863785	C₄	1	4	yes	complemented
19	#16863780	C₄	1	2	yes	complemented
20	#16863773	C₄	1	2	yes	complemented
21	#16863517	—	2	2	no	—
22	#16863512	—	2	2	no	—
23	#16863507	—	2	2	no	—
24	#16863478	—	2	2	no	—
25	#16863414	C₂²	1	2	yes	—
26	#16863412	C₂²	1	2	yes	—
27	#16863402	C₂²	1	2	yes	—
28	#16863400	C₂²	1	2	yes	—
29	C₂×#14523959	C₂²	1	2	yes	—
30	#16863369	C₂²	1	2	yes	—
31	#16863351	C₂²	1	1	yes	characteristic
32	#16863351	C₂²	1	1	yes	characteristic
33	C₆₇⋊#338	C₂²	1	1	yes	characteristic
34	#16863153	C₂²	1	1	yes	characteristic
35	#16863152	C₂²	1	1	yes	characteristic
36	#16863152	C₂²	1	1	yes	characteristic
37	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
38	#427×C₆₇	C₂²	1	1	yes	characteristic
39	#405×C₆₇	C₂²	1	1	yes	characteristic
40	#344×C₆₇	C₂²	1	2	yes	—
41	H(3,ℤ/4)×C₆₇	C₂²	1	2	yes	—
42	C₂×#11761628	C₂³	1	2	yes	—
43	C₂²×D₂₆₈	C₂³	1	2	yes	—
44	#14524071	—	4	2	no	—
45	#14524071	—	4	2	no	—
46	#14524065	—	2	1	no	—
47	#14524065	—	2	1	no	—
48	#14524065	—	2	1	no	—
49	#14524065	—	2	1	no	—
50	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#11761617	C₂×C₄	1	2	yes	complemented
52	C₂×#11761617	C₂×C₄	1	4	yes	complemented
53	C₂×D₅₃₆	—	2	1	no	—
54	C₂×D₅₃₆	—	2	1	no	—
55	C₂×D₅₃₆	—	2	1	no	—
56	C₂×D₅₃₆	—	2	1	no	—
57	C₂×D₅₃₆	C₂×C₄	1	2	yes	—
58	C₂×D₅₃₆	C₂×C₄	1	2	yes	—
59	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×D₅₃₆	C₂×C₄	1	4	yes	complemented
61	#14524051	—	2	4	no	—
62	#14524049	—	4	2	no	—
63	C₂×#11761612	C₂³	1	1	yes	characteristic
64	C₂×#11761612	C₂³	1	1	yes	characteristic
65	M₁₆×D₆₇	—	4	2	no	—
66	#14524040	C₂×C₄	1	4	yes	complemented
67	#14524031	C₂×C₄	1	4	yes	complemented
68	#14524018	—	4	2	no	—
69	#14524013	—	4	2	no	—
70	C₄×D₂₆₈	—	4	2	no	—
71	#14524005	—	2	4	no	—
72	#14524002	C₂³	1	1	yes	characteristic
73	#14524002	C₂³	1	1	yes	characteristic
74	C₂²⋊C₄×D₆₇	—	4	2	no	—
75	#14523971	—	4	2	no	—
76	#14523969	—	2	4	no	—
77	#14523965	—	4	2	no	—
78	#14523963	—	2	4	no	—
79	#14523959	—	4	2	no	—
80	#14523957	—	4	2	no	—
81	#14523953	—	2	1	no	—
82	#14523953	D₄	1	2	yes	complemented
83	C₈×Dic₆₇	—	2	1	no	—
84	C₈×Dic₆₇	D₄	1	2	yes	complemented
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	C₂³	1	2	yes	—
89	#117×C₆₇	C₂³	1	1	yes	characteristic
90	#108×C₆₇	—	2	1	no	—
91	#108×C₆₇	—	2	1	no	—
92	#107×C₆₇	—	2	1	no	—
93	#106×C₆₇	—	2	1	no	—
94	#97×C₆₇	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	complemented
96	C₂³×D₆₇	—	2	2	no	—
97	#11761628	—	2	2	no	—
98	#11761628	—	2	2	no	—
99	#11761628	—	2	2	no	—
100	#11761628	—	2	2	no	—
101	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
102	C₂×D₂₆₈	—	2	2	no	—
103	C₂×D₂₆₈	—	2	2	no	—
104	C₂×D₂₆₈	—	2	2	no	—
105	C₂×D₂₆₈	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	4	4	no	—
108	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
109	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
110	C₂×C₂²⋊D₆₇	—	2	2	no	—
111	C₂×C₄×D₆₇	—	2	2	no	—
112	C₂×C₄×D₆₇	—	4	4	no	—
113	Dic₂₆₈	—	2	1	no	—
114	Dic₂₆₈	—	2	1	no	—
115	#11761617	—	2	2	no	—
116	#11761617	—	2	2	no	—
117	#11761617	—	4	4	no	—
118	D₅₃₆	—	2	2	no	—
119	D₅₃₆	—	2	2	no	—
120	D₅₃₆	—	2	2	no	—
121	D₅₃₆	—	2	2	no	—
122	D₅₃₆	—	2	1	no	—
123	D₅₃₆	—	2	1	no	—
124	D₅₃₆	—	4	4	no	—
125	#11761612	—	2	1	no	—
126	#11761612	—	2	1	no	—
127	#11761612	—	2	1	no	—
128	#11761612	—	2	1	no	—
129	#11761611	—	4	4	no	—
130	C₂×C₆₇⋊C₈	—	2	1	no	—
131	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
132	C₈×D₆₇	—	4	4	no	—
133	C₄⋊Dic₆₇	—	2	1	no	—
134	C₄⋊Dic₆₇	—	2	1	no	—
135	C₂²⋊Dic₆₇	—	2	1	no	—
136	C₂²⋊Dic₆₇	—	2	1	no	—
137	(C₂×D₆₇)⋊C₄	—	4	4	no	—
138	(C₂×D₆₇)⋊C₄	—	4	4	no	—
139	C₄×Dic₆₇	—	2	1	no	—
140	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₆₇	—	2	1	no	—
143	M₁₆×C₆₇	—	2	1	no	—
144	M₁₆×C₆₇	—	2	2	no	—
145	M₁₆×C₆₇	—	2	2	no	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
153	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
154	C₄⋊C₄×C₆₇	—	2	1	no	—
155	C₄⋊C₄×C₆₇	—	2	2	no	—
156	C₂²⋊C₄×C₆₇	—	2	1	no	—
157	C₂²⋊C₄×C₆₇	—	2	2	no	—
158	C₄²×C₆₇	—	2	2	no	—
159	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
160	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₆₇	—	2	4	no	—
162	C₂²×D₆₇	—	2	2	no	—
163	C₂²×D₆₇	—	4	2	no	—
164	C₂²×D₆₇	—	4	2	no	—
165	C₂²×D₆₇	—	16	2	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	4	2	no	—
168	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²⋊D₆₇	—	4	2	no	—
175	C₂²⋊D₆₇	—	4	2	no	—
176	C₂×Dic₆₇	—	2	2	no	—
177	C₂×Dic₆₇	—	2	2	no	—
178	C₂×Dic₆₇	—	4	1	no	—
179	D₂₆₈	—	2	4	no	—
180	D₂₆₈	—	2	2	no	—
181	D₂₆₈	—	2	2	no	—
182	D₂₆₈	—	2	4	no	—
183	D₂₆₈	—	4	2	no	—
184	D₂₆₈	—	4	2	no	—
185	D₂₆₈	—	16	4	no	—
186	C₄×D₆₇	—	4	2	no	—
187	C₄×D₆₇	—	4	2	no	—
188	C₄×D₆₇	—	16	4	no	—
189	Dic₁₃₄	—	2	2	no	—
190	Dic₁₃₄	—	2	2	no	—
191	C₈×C₆₇	—	2	2	no	—
192	C₈×C₆₇	—	4	2	no	—
193	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
194	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
195	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
196	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
197	C₆₇⋊C₈	—	2	2	no	—
198	C₆₇⋊C₈	—	4	1	no	—
199	C₂²×C₆₇	—	4	1	no	—
200	C₂²×C₆₇	#518	1	1	yes	characteristic
201	C₂²×C₆₇	#535	1	1	yes	characteristic
202	C₂²×C₆₇	#540	1	1	yes	characteristic
203	C₂×D₆₇	—	4	2	no	—
204	C₂×D₆₇	—	4	4	no	—
205	C₂×D₆₇	—	8	4	no	—
206	C₂×D₆₇	—	8	2	no	—
207	C₂×D₆₇	—	8	4	no	—
208	C₂×D₆₇	—	16	2	no	—
209	C₄×C₆₇	—	4	2	no	—
210	C₄×C₆₇	—	8	2	no	—
211	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₆₇	#518	1	1	yes	characteristic
213	C₄×C₆₇	#535	1	1	yes	characteristic
214	C₄×C₆₇	#540	1	1	yes	characteristic
215	Dic₆₇	—	4	2	no	—
216	Dic₆₇	—	4	2	no	—
217	Dic₆₇	—	8	1	no	—
218	#22286	—	67	1	no	maximal, Sylow
219	C₂×C₆₇	—	2	1	no	—
220	C₂×C₆₇	—	2	1	no	—
221	C₂×C₆₇	—	2	1	no	—
222	C₂×C₆₇	#2328	1	1	yes	characteristic
223	D₆₇	—	8	2	no	—
224	D₆₇	—	8	4	no	—
225	#3155	—	67	1	no	—
226	#2957	—	67	1	no	—
227	#2948	—	67	1	no	—
228	#1978	—	67	1	no	—
229	#1976	—	67	1	no	—
230	#1911	—	67	2	no	—
231	#1910	—	67	2	no	—
232	#1904	—	67	2	no	—
233	#1903	—	67	2	no	—
234	#1833	D₆₇	1	1	yes	characteristic, complemented
235	#1747	—	67	1	no	—
236	C₆₇	#22286	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	67	2	no	—
238	C₂×#135	—	67	1	no	—
239	C₂²×D₈	—	67	1	no	—
240	#568	—	67	2	no	—
241	#535	—	67	2	no	—
242	#518	—	67	2	no	—
243	#496	—	67	4	no	—
244	#495	—	67	2	no	—
245	#493	—	67	2	no	—
246	#444	—	134	2	no	—
247	#443	—	134	2	no	—
248	#442	—	134	2	no	—
249	C₄×D₈	—	134	2	no	—
250	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
251	#427	C₂×D₆₇	1	1	yes	characteristic
252	#421	—	67	2	no	—
253	#421	—	67	2	no	—
254	#418	—	67	2	no	—
255	#418	—	67	2	no	—
256	C₂×#100	—	67	2	no	—
257	#410	—	67	2	no	—
258	#405	—	67	1	no	—
259	#405	—	67	1	no	—
260	#405	C₂×D₆₇	1	1	yes	characteristic
261	#344	C₂×D₆₇	1	2	yes	—
262	#338	—	67	1	no	—
263	H(3,ℤ/4)	—	67	1	no	—
264	H(3,ℤ/4)	—	67	1	no	—
265	H(3,ℤ/4)	—	67	1	no	—
266	H(3,ℤ/4)	C₂×D₆₇	1	2	yes	—
267	C₂×#41	—	67	2	no	—
268	C₂²×D₄	—	67	2	no	—
269	AGL(1,ℤ/8)	—	268	2	no	—
270	AGL(1,ℤ/8)	—	268	2	no	—
271	#135	—	134	1	no	—
272	#135	—	134	1	no	—
273	#135	—	134	1	no	—
274	#135	—	134	1	no	—
275	C₂×Q₁₆	—	67	1	no	—
276	C₂×SD₁₆	—	67	4	no	—
277	C₂×SD₁₆	—	67	2	no	—
278	C₂×D₈	—	67	4	no	—
279	C₂×D₈	—	67	2	no	—
280	C₂×D₈	—	67	2	no	—
281	C₂×D₈	—	67	1	no	—
282	C₂×D₈	—	134	1	no	—
283	C₂×D₈	—	134	1	no	—
284	C₂×D₈	—	134	1	no	—
285	C₂×D₈	—	134	1	no	—
286	#131	—	268	2	no	—
287	#131	—	134	4	no	—
288	C₂×M₁₆	—	268	2	no	—
289	C₂×M₁₆	—	67	1	no	—
290	C₂×M₁₆	—	67	1	no	—
291	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
292	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
294	#127	—	67	4	no	—
295	#124	—	67	4	no	—
296	#121	—	268	2	no	—
297	#120	—	268	2	no	—
298	C₄×D₄	—	268	2	no	—
299	C₄×D₄	—	134	4	no	—
300	#117	—	67	1	no	—
301	#117	—	67	1	no	—
302	#117	C₂²×D₆₇	1	2	yes	—
303	#117	C₂²×D₆₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	268	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	2	1	no	—
308	#106	—	2	1	no	—
309	#104	—	268	2	no	—
310	#104	—	134	4	no	—
311	#102	—	268	2	no	—
312	#102	—	134	4	no	—
313	#100	—	268	2	no	—
314	#99	—	268	2	no	—
315	#97	—	67	2	no	—
316	#97	—	134	1	no	—
317	#97	C₄×D₆₇	1	2	yes	complemented
318	C₄×C₈	—	67	2	no	—
319	C₄×C₈	—	134	1	no	—
320	C₄×C₈	C₄×D₆₇	1	2	yes	complemented
321	C₂⁴	—	134	2	no	—
322	#41	—	134	2	no	—
323	#41	—	134	2	no	—
324	#41	—	134	2	no	—
325	#41	—	134	2	no	—
326	C₂×Q₈	—	67	2	no	—
327	C₂×D₄	—	268	4	no	—
328	C₂×D₄	—	67	4	no	—
329	C₂×D₄	—	67	2	no	—
330	C₂×D₄	—	134	2	no	—
331	C₂×D₄	—	134	2	no	—
332	C₂×D₄	—	134	2	no	—
333	C₂×D₄	—	134	2	no	—
334	C₂×D₄	—	134	2	no	—
335	C₂×D₄	—	134	2	no	—
336	C₂²×C₄	—	268	4	no	—
337	C₂²×C₄	—	134	2	no	—
338	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
339	Q₁₆	—	134	1	no	—
340	Q₁₆	—	134	1	no	—
341	SD₁₆	—	268	4	no	—
342	SD₁₆	—	134	2	no	—
343	SD₁₆	—	134	2	no	—
344	D₈	—	268	4	no	—
345	D₈	—	134	2	no	—
346	D₈	—	134	2	no	—
347	D₈	—	134	2	no	—
348	D₈	—	134	2	no	—
349	D₈	—	134	1	no	—
350	D₈	—	134	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	268	4	no	—
356	M₁₆	—	134	1	no	—
357	M₁₆	—	134	1	no	—
358	M₁₆	—	134	1	no	—
359	M₁₆	—	134	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	268	4	no	—
362	C₂×C₈	—	67	2	no	—
363	C₂×C₈	—	134	1	no	—
364	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
367	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
368	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
369	C₂×C₈	#11761629	1	1	yes	characteristic
370	C₂×C₈	#11761629	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	134	1	no	—
374	C₄⋊C₄	—	134	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	268	4	no	—
378	C₂²⋊C₄	—	268	4	no	—
379	C₂²⋊C₄	—	134	1	no	—
380	C₂²⋊C₄	—	134	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	67	2	no	—
383	C₄²	—	134	1	no	—
384	C₄²	C₂×C₄×D₆₇	1	2	yes	—
385	C₂³	—	268	2	no	—
386	C₂³	—	268	2	no	—
387	C₂³	—	1072	2	no	—
388	C₂³	—	134	4	no	—
389	C₂³	—	134	2	no	—
390	C₂³	#14524089	1	1	yes	characteristic
391	Q₈	—	134	2	no	—
392	Q₈	—	134	2	no	—
393	D₄	—	268	2	no	—
394	D₄	—	268	2	no	—
395	D₄	—	268	2	no	—
396	D₄	—	268	2	no	—
397	D₄	—	1072	4	no	—
398	D₄	—	134	4	no	—
399	D₄	—	134	2	no	—
400	D₄	—	134	2	no	—
401	D₄	—	134	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	268	2	no	—
405	C₂×C₄	—	268	2	no	—
406	C₂×C₄	—	268	1	no	—
407	C₂×C₄	—	1072	4	no	—
408	C₂×C₄	—	134	2	no	—
409	C₂×C₄	—	134	2	no	—
410	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
412	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
413	C₂×C₄	#14524089	1	1	yes	characteristic
414	C₂×C₄	#14524089	1	1	yes	characteristic
415	C₂×C₄	#14524089	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	268	1	no	—
419	C₈	—	134	2	no	—
420	C₈	#14524005	1	1	yes	characteristic
421	C₈	#14524005	1	1	yes	characteristic
422	C₈	#14524005	1	1	yes	characteristic
423	C₈	#14524005	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	268	2	no	—
426	C₂²	—	268	4	no	—
427	C₂²	—	536	2	no	—
428	C₂²	—	536	4	no	—
429	C₂²	—	536	4	no	—
430	C₂²	—	1072	2	no	—
431	C₂²	#16863870	1	1	yes	characteristic
432	C₂²	#16863964	1	1	yes	characteristic
433	C₂²	#16864002	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	268	2	no	—
437	C₄	—	268	2	no	—
438	C₄	—	536	1	no	—
439	C₄	C₂×#14524005	1	1	yes	characteristic
440	C₄	#16863870	1	1	yes	characteristic
441	C₄	#16863964	1	1	yes	characteristic
442	C₄	#16864002	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	536	4	no	—
447	C₂	—	536	2	no	—
448	C₂	#22562932	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22562932
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1833	C₂
socle	C₂×C₆₇	#2328
prime radical	#22570695	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1833	D₆₇
hypocenter	C₆₇	#22286
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1833

Complements

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

N	H ≅ G/N	type
2. #22569125	C₂	semidirect
3. #22569060	C₂	semidirect
4. #22561117	C₂	semidirect
5. #22561105	C₂	semidirect
6. #22560740	C₂	semidirect
7. #22560735	C₂	semidirect
8. #22560695	C₂	semidirect
9. #22560688	C₂	semidirect
10. #22559964	C₂	semidirect
11. C₆₇×#1833	C₂	semidirect
18. #16863785	C₄	semidirect
19. #16863780	C₄	semidirect
20. #16863773	C₄	semidirect
50. C₂×Dic₂₆₈	C₂×C₄	semidirect
51. C₂×#11761617	C₂×C₄	semidirect
52. C₂×#11761617	C₂×C₄	semidirect
59. C₂×D₅₃₆	C₂×C₄	semidirect
60. C₂×D₅₃₆	C₂×C₄	semidirect
66. #14524040	C₂×C₄	semidirect
67. #14524031	C₂×C₄	semidirect
82. #14523953	D₄	semidirect
84. C₈×Dic₆₇	D₄	semidirect
94. #97×C₆₇	C₂×C₄	semidirect
95. C₄×C₈×C₆₇	C₂×C₄	semidirect
234. #1833	D₆₇	semidirect
236. C₆₇	#22286	semidirect
317. #97	C₄×D₆₇	semidirect
320. C₄×C₈	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22570695	2
#22569125	2
#22569060	2
#22561117	2
#22561105	2
#22560740	2
#22560735	2
#22560695	2
#22560688	2
#22559964	2
C₆₇×#1833	2
#22286	67