Subgroups — #30878732

Order 17152.

896 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863666	C₂	1	1	yes	maximal, characteristic
2	#22569062	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569044	C₂	1	2	yes	maximal, complemented
4	#22568809	C₂	1	1	yes	maximal, characteristic, complemented
5	#22561075	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560994	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560872	C₂	1	2	yes	maximal, complemented
8	#22560583	C₂	1	2	yes	maximal, complemented
9	#22560420	C₂	1	2	yes	maximal, complemented
10	#22560088	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524068	C₂²	1	2	yes	—
13	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
14	#16863879	C₂²	1	2	yes	—
15	#16863870	C₂²	1	2	yes	—
16	#16863666	C₄	1	8	yes	complemented
17	#16863509	—	2	2	no	—
18	#16863505	—	2	2	no	—
19	#16863499	—	2	2	no	—
20	#16863481	—	2	2	no	—
21	C₄×D₅₃₆	—	2	1	no	—
22	C₄×D₅₃₆	—	2	1	no	—
23	#16863476	—	2	2	no	—
24	C₂×#14523979	C₂²	1	1	yes	characteristic
25	#16863439	C₂²	1	2	yes	—
26	#16863438	—	2	2	no	—
27	#16863438	C₂²	1	2	yes	—
28	#16863434	—	2	1	no	—
29	#16863434	C₂²	1	1	yes	characteristic
30	C₂×#14523977	—	2	1	no	—
31	C₂×#14523977	C₂²	1	1	yes	characteristic
32	#16863402	C₂²	1	2	yes	—
33	C₂×#14523965	C₂²	1	2	yes	—
34	C₂×#14523959	C₂²	1	2	yes	—
35	#16863351	C₂²	1	2	yes	—
36	#16863298	C₂²	1	2	yes	—
37	#16863164	C₂²	1	2	yes	—
38	#16863156	C₂²	1	2	yes	—
39	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
41	#416×C₆₇	C₂²	1	1	yes	characteristic
42	#405×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#341×C₆₇	C₂²	1	1	yes	characteristic
45	#339×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×D₂₆₈	C₂³	1	2	yes	—
47	#14524068	—	2	4	no	—
48	#14524068	C₂×C₄	1	8	yes	complemented
49	C₂×#11761615	—	2	2	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×D₅₃₆	—	2	1	no	—
52	C₂×D₅₃₆	—	2	2	no	—
53	C₂×D₅₃₆	C₂×C₄	1	4	yes	complemented
54	C₂×#11761613	—	2	2	no	—
55	C₂×#11761612	C₂³	1	2	yes	—
56	Q₈×Dic₆₇	—	2	2	no	—
57	C₄×D₂₆₈	—	2	2	no	—
58	C₄×D₂₆₈	—	2	2	no	—
59	D₄×Dic₆₇	—	2	2	no	—
60	D₄×Dic₆₇	—	4	2	no	—
61	#14524005	—	2	2	no	—
62	#14524005	—	2	2	no	—
63	#14524002	—	2	2	no	—
64	#14524002	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₆₇	—	2	2	no	—
66	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
67	C₂×(C₂×D₆₇)⋊C₄	—	4	2	no	—
68	C₂²⋊C₄×D₆₇	—	4	2	no	—
69	#14523979	C₂×C₄	1	4	yes	complemented
70	#14523977	—	2	2	no	—
71	#14523977	—	2	1	no	—
72	#14523977	—	2	1	no	—
73	#14523977	D₄	1	1	yes	characteristic
74	#14523977	D₄	1	1	yes	characteristic
75	#14523976	—	2	2	no	—
76	#14523975	—	2	2	no	—
77	#14523975	D₄	1	2	yes	—
78	#14523974	—	2	2	no	—
79	#14523965	—	2	2	no	—
80	#14523965	—	2	2	no	—
81	#14523965	—	2	2	no	—
82	#14523965	—	2	2	no	—
83	#14523959	C₂×C₄	1	8	yes	complemented
84	#14523953	—	2	2	no	—
85	C₈×Dic₆₇	—	2	2	no	—
86	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
87	#131×C₆₇	—	2	2	no	—
88	#131×C₆₇	C₂×C₄	1	4	yes	complemented
89	C₂×M₁₆×C₆₇	—	2	1	no	—
90	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₆₇	—	2	1	no	—
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#117×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
97	#104×C₆₇	—	2	2	no	—
98	#103×C₆₇	D₄	1	1	yes	characteristic
99	#103×C₆₇	D₄	1	1	yes	characteristic
100	#102×C₆₇	D₄	1	1	yes	characteristic
101	#102×C₆₇	D₄	1	1	yes	characteristic
102	#97×C₆₇	—	2	1	no	—
103	C₄×C₈×C₆₇	—	2	1	no	—
104	C₄×C₈×C₆₇	—	2	2	no	—
105	C₂³×D₆₇	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	2	2	no	—
110	C₂×D₂₆₈	—	2	2	no	—
111	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
112	C₂²×Dic₆₇	—	2	2	no	—
113	C₂²×Dic₆₇	—	4	2	no	—
114	C₂×C₄×D₆₇	—	4	2	no	—
115	C₂×C₄×D₆₇	—	4	2	no	—
116	#11761615	—	2	8	no	—
117	D₅₃₆	—	2	4	no	—
118	D₅₃₆	—	2	4	no	—
119	#11761613	—	2	8	no	—
120	#11761612	—	2	2	no	—
121	#11761612	C₂²×C₄	1	4	yes	—
122	C₂×C₆₇⋊C₈	—	2	2	no	—
123	C₄⋊Dic₆₇	—	2	2	no	—
124	C₄⋊Dic₆₇	—	2	2	no	—
125	C₄⋊Dic₆₇	—	4	2	no	—
126	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
127	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
128	C₂²⋊Dic₆₇	—	2	2	no	—
129	C₂²⋊Dic₆₇	—	4	2	no	—
130	(C₂×D₆₇)⋊C₄	—	4	2	no	—
131	(C₂×D₆₇)⋊C₄	—	4	2	no	—
132	(C₂×D₆₇)⋊C₄	—	8	4	no	—
133	C₄×Dic₆₇	—	2	2	no	—
134	C₄×Dic₆₇	—	4	2	no	—
135	#41×C₆₇	—	2	1	no	—
136	#41×C₆₇	—	2	1	no	—
137	#41×C₆₇	C₂²×C₄	1	2	yes	—
138	#41×C₆₇	#41	1	2	yes	—
139	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₆₇	—	2	1	no	—
141	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	—	2	1	no	—
143	C₂²×C₄×C₆₇	—	2	1	no	—
144	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₆₇	—	2	1	no	—
146	M₁₆×C₆₇	—	2	4	no	—
147	M₁₆×C₆₇	—	2	1	no	—
148	M₁₆×C₆₇	—	2	1	no	—
149	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₆₇	—	2	1	no	—
151	C₂×C₈×C₆₇	—	2	1	no	—
152	C₂×C₈×C₆₇	—	2	1	no	—
153	C₂×C₈×C₆₇	—	2	4	no	—
154	C₂×C₈×C₆₇	—	2	1	no	—
155	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₆₇	#41	1	2	yes	—
161	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₆₇	—	2	1	no	—
164	C₄²×C₆₇	—	2	1	no	—
165	C₄²×C₆₇	—	2	1	no	—
166	C₄²×C₆₇	—	2	1	no	—
167	C₂³×C₆₇	—	2	1	no	—
168	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²×D₆₇	—	2	4	no	—
170	C₂²×D₆₇	—	4	2	no	—
171	C₂²×D₆₇	—	4	2	no	—
172	C₂²×D₆₇	—	8	2	no	—
173	C₂²×D₆₇	—	8	2	no	—
174	Q₈×C₆₇	—	2	1	no	—
175	Q₈×C₆₇	C₄×D₄	1	2	yes	—
176	D₄×C₆₇	—	2	2	no	—
177	D₄×C₆₇	—	2	2	no	—
178	D₄×C₆₇	—	2	1	no	—
179	D₄×C₆₇	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₆₇	—	2	1	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	2	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	1	no	—
185	C₂×C₄×C₆₇	—	2	1	no	—
186	C₂×C₄×C₆₇	—	4	1	no	—
187	C₂×C₄×C₆₇	—	4	1	no	—
188	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×Dic₆₇	—	2	2	no	—
195	C₂×Dic₆₇	—	2	2	no	—
196	C₂×Dic₆₇	—	4	2	no	—
197	C₂×Dic₆₇	—	8	2	no	—
198	C₂×Dic₆₇	—	16	2	no	—
199	D₂₆₈	—	2	4	no	—
200	D₂₆₈	—	2	4	no	—
201	D₂₆₈	—	4	2	no	—
202	D₂₆₈	—	4	2	no	—
203	C₄×D₆₇	—	16	2	no	—
204	C₄×D₆₇	—	16	2	no	—
205	C₈×C₆₇	—	2	2	no	—
206	C₈×C₆₇	—	2	1	no	—
207	C₈×C₆₇	—	2	1	no	—
208	C₈×C₆₇	—	4	1	no	—
209	C₈×C₆₇	C₄×D₄	1	2	yes	—
210	C₈×C₆₇	C₄×D₄	1	2	yes	—
211	C₆₇⋊C₈	—	2	4	no	—
212	C₂²×C₆₇	—	2	1	no	—
213	C₂²×C₆₇	—	2	1	no	—
214	C₂²×C₆₇	—	2	2	no	—
215	C₂²×C₆₇	—	4	1	no	—
216	C₂²×C₆₇	—	4	1	no	—
217	C₂²×C₆₇	#520	1	1	yes	characteristic
218	C₂²×C₆₇	D₄²	1	1	yes	characteristic
219	C₂²×C₆₇	#553	1	1	yes	characteristic
220	C₂×D₆₇	—	4	4	no	—
221	C₂×D₆₇	—	8	2	no	—
222	C₂×D₆₇	—	8	2	no	—
223	C₂×D₆₇	—	8	4	no	—
224	C₂×D₆₇	—	16	2	no	—
225	C₄×C₆₇	—	2	2	no	—
226	C₄×C₆₇	—	4	2	no	—
227	C₄×C₆₇	—	4	1	no	—
228	C₄×C₆₇	—	4	1	no	—
229	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₆₇	#547	1	1	yes	characteristic
232	C₄×C₆₇	#548	1	1	yes	characteristic
233	Dic₆₇	—	4	2	no	—
234	Dic₆₇	—	4	2	no	—
235	Dic₆₇	—	8	2	no	—
236	#23046	—	67	1	no	maximal, Sylow
237	C₂×C₆₇	—	2	1	no	—
238	C₂×C₆₇	—	2	1	no	—
239	C₂×C₆₇	—	4	2	no	—
240	C₂×C₆₇	#2361	1	1	yes	characteristic
241	C₂×C₆₇	#3290	1	1	yes	characteristic
242	C₂×C₆₇	#3292	1	1	yes	characteristic
243	D₆₇	—	8	4	no	—
244	C₂×#472	—	67	1	no	—
245	#2948	—	67	1	no	—
246	#2946	—	67	2	no	—
247	#2913	—	67	1	no	—
248	#1970	—	67	1	no	—
249	#1952	—	67	1	no	—
250	#1931	—	67	2	no	—
251	#1883	—	67	2	no	—
252	#1856	—	67	2	no	—
253	#1772	—	67	1	no	—
254	#1764	D₆₇	1	1	yes	characteristic, complemented
255	C₆₇	#23046	1	1	yes	characteristic, complemented, Sylow
256	C₂×AGL(1,ℤ/8)	—	67	2	no	—
257	C₂²×D₈	—	67	1	no	—
258	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
259	#520	—	67	2	no	—
260	#518	—	67	2	no	—
261	#472	—	67	8	no	—
262	#442	—	134	2	no	—
263	#442	—	134	2	no	—
264	#440	—	134	2	no	—
265	C₄×SD₁₆	—	134	2	no	—
266	C₄×D₈	—	134	1	no	—
267	C₄×D₈	—	134	1	no	—
268	C₄×D₈	—	134	2	no	—
269	C₂×#108	—	67	1	no	—
270	#428	—	67	2	no	—
271	#428	—	67	2	no	—
272	#428	—	134	2	no	—
273	#427	—	67	1	no	—
274	#427	—	134	1	no	—
275	C₂×#107	—	67	1	no	—
276	C₂×#107	—	134	1	no	—
277	C₂×#104	C₂×D₆₇	1	1	yes	characteristic
278	#418	—	67	2	no	—
279	#416	C₂×D₆₇	1	1	yes	characteristic
280	C₂×#102	—	67	2	no	—
281	C₂×#100	—	67	2	no	—
282	#405	—	67	2	no	—
283	#405	C₂×D₆₇	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
285	#390	—	67	2	no	—
286	#343	—	67	2	no	—
287	#341	C₂×D₆₇	1	1	yes	characteristic
288	#339	—	67	2	no	—
289	#339	C₂×D₆₇	1	1	yes	characteristic
290	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
291	C₂²×D₄	—	67	2	no	—
292	AGL(1,ℤ/8)	—	67	8	no	—
293	AGL(1,ℤ/8)	—	134	4	no	—
294	C₂×SD₁₆	—	134	2	no	—
295	C₂×D₈	—	67	4	no	—
296	C₂×D₈	—	134	2	no	—
297	C₂×D₈	—	134	1	no	—
298	C₂×D₈	—	134	1	no	—
299	C₂×D₈	—	134	2	no	—
300	#131	—	2	2	no	—
301	#131	C₄×D₆₇	1	4	yes	complemented
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	67	2	no	—
304	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
305	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
308	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
309	C₄×Q₈	—	134	2	no	—
310	C₄×D₄	—	268	2	no	—
311	C₄×D₄	—	134	2	no	—
312	C₄×D₄	—	134	2	no	—
313	C₄×D₄	—	134	2	no	—
314	C₄×D₄	—	134	2	no	—
315	C₄×D₄	—	134	2	no	—
316	#117	—	67	2	no	—
317	#117	—	134	2	no	—
318	#117	C₂²×D₆₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	—	67	2	no	—
320	C₂×C₄⋊C₄	—	134	2	no	—
321	C₂×C₂²⋊C₄	—	268	2	no	—
322	C₂×C₂²⋊C₄	—	268	2	no	—
323	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
324	#108	—	67	4	no	—
325	#107	—	67	1	no	—
326	#107	—	67	1	no	—
327	#107	—	134	2	no	—
328	#107	—	134	1	no	—
329	#107	—	134	1	no	—
330	#107	—	134	2	no	—
331	#106	—	67	2	no	—
332	#106	—	134	2	no	—
333	#106	—	134	2	no	—
334	#104	—	2	2	no	—
335	#103	D₂₆₈	1	1	yes	characteristic
336	#103	D₂₆₈	1	1	yes	characteristic
337	#102	—	134	2	no	—
338	#102	—	134	2	no	—
339	#102	—	134	2	no	—
340	#102	—	134	2	no	—
341	#102	D₂₆₈	1	1	yes	characteristic
342	#102	D₂₆₈	1	1	yes	characteristic
343	#100	—	67	8	no	—
344	#97	—	2	1	no	—
345	#97	—	134	2	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	2	2	no	—
348	C₄×C₈	—	134	2	no	—
349	C₂⁴	—	134	2	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	C₂×C₄×D₆₇	1	2	yes	—
353	#41	#11761628	1	2	yes	—
354	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	67	4	no	—
357	C₂×D₄	—	134	2	no	—
358	C₂×D₄	—	134	2	no	—
359	C₂×D₄	—	134	2	no	—
360	C₂×D₄	—	134	2	no	—
361	C₂×D₄	—	134	2	no	—
362	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	268	2	no	—
366	C₂²×C₄	—	268	2	no	—
367	C₂²×C₄	—	268	2	no	—
368	C₂²×C₄	—	134	2	no	—
369	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
370	SD₁₆	—	134	8	no	—
371	D₈	—	134	8	no	—
372	D₈	—	134	4	no	—
373	D₈	—	134	4	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	67	4	no	—
379	M₁₆	—	134	2	no	—
380	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	134	2	no	—
387	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
388	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
389	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
390	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
391	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
392	C₂×C₈	#11761627	1	2	yes	—
393	C₄⋊C₄	—	268	2	no	—
394	C₄⋊C₄	—	67	2	no	—
395	C₄⋊C₄	—	67	2	no	—
396	C₄⋊C₄	—	134	2	no	—
397	C₄⋊C₄	—	134	2	no	—
398	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	268	2	no	—
402	C₂²⋊C₄	—	268	2	no	—
403	C₂²⋊C₄	—	268	2	no	—
404	C₂²⋊C₄	—	536	4	no	—
405	C₂²⋊C₄	—	134	2	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	268	2	no	—
410	C₄²	—	134	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	268	2	no	—
413	C₂³	—	268	2	no	—
414	C₂³	—	536	2	no	—
415	C₂³	—	536	2	no	—
416	C₂³	—	134	4	no	—
417	C₂³	#14524089	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	C₄×D₂₆₈	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	268	2	no	—
424	D₄	—	268	2	no	—
425	D₄	—	134	4	no	—
426	D₄	—	134	4	no	—
427	D₄	C₄×D₂₆₈	1	2	yes	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	268	2	no	—
437	C₂×C₄	—	536	2	no	—
438	C₂×C₄	—	1072	2	no	—
439	C₂×C₄	—	1072	2	no	—
440	C₂×C₄	—	1072	2	no	—
441	C₂×C₄	—	134	2	no	—
442	C₂×C₄	—	134	2	no	—
443	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
446	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
447	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
448	C₂×C₄	#14524090	1	1	yes	characteristic
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	134	4	no	—
454	C₈	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
455	C₈	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	268	4	no	—
462	C₂²	—	536	4	no	—
463	C₂²	—	536	2	no	—
464	C₂²	—	536	2	no	—
465	C₂²	—	1072	2	no	—
466	C₂²	#16863876	1	1	yes	characteristic
467	C₂²	D₄×D₂₆₈	1	1	yes	characteristic
468	C₂²	#16864092	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	268	2	no	—
474	C₄	—	268	2	no	—
475	C₄	—	536	2	no	—
476	C₄	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
477	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
478	C₄	#16864050	1	1	yes	characteristic
479	C₄	#16864055	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	536	4	no	—
484	C₂	#22563223	1	1	yes	characteristic
485	C₂	#22571996	1	1	yes	characteristic
486	C₂	#22572009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1764	C₂
socle	C₂²×C₆₇	D₄²
prime radical	C₂×#16863666	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1764	D₆₇
hypocenter	C₆₇	#23046
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #22569062	C₂	semidirect
3. #22569044	C₂	semidirect
4. #22568809	C₂	semidirect
5. #22561075	C₂	semidirect
6. #22560994	C₂	semidirect
7. #22560872	C₂	semidirect
8. #22560583	C₂	semidirect
9. #22560420	C₂	semidirect
10. #22560088	C₂	semidirect
11. C₆₇×#1764	C₂	semidirect
16. #16863666	C₄	semidirect
48. #14524068	C₂×C₄	semidirect
53. C₂×D₅₃₆	C₂×C₄	semidirect
69. #14523979	C₂×C₄	semidirect
83. #14523959	C₂×C₄	semidirect
88. #131×C₆₇	C₂×C₄	semidirect
254. #1764	D₆₇	semidirect
255. C₆₇	#23046	semidirect
301. #131	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863666	2
#22569062	2
#22569044	2
#22568809	2
#22561075	2
#22560994	2
#22560872	2
#22560583	2
#22560420	2
#22560088	2
C₆₇×#1764	2
#23046	67