Subgroups — #30826419

Order 17152.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570804	C₂	1	1	yes	maximal, characteristic
2	#22569184	C₂	1	1	yes	maximal, characteristic, complemented
3	#22568922	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559124	C₂	1	2	yes	maximal, complemented
5	#22559113	C₂	1	2	yes	maximal, complemented
6	C₈×#11761617	C₂	1	2	yes	maximal, complemented
7	C₈×D₅₃₆	C₂	1	2	yes	maximal, complemented
8	#22558976	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558679	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	—	2	1	no	—
13	#16863946	C₂²	1	1	yes	characteristic
14	#16863930	C₂²	1	1	yes	characteristic
15	#16863805	C₄	1	1	yes	characteristic
16	#16863785	C₄	1	1	yes	characteristic
17	#16863761	C₄	1	1	yes	characteristic
18	#16863756	C₄	1	1	yes	characteristic
19	#16863649	C₄	1	2	yes	—
20	#16863642	C₄	1	2	yes	—
21	#16863526	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
23	C₄×#11761617	C₂²	1	2	yes	—
24	C₄×D₅₃₆	C₂²	1	2	yes	—
25	#16863475	—	2	1	no	—
26	#16863475	C₂²	1	2	yes	—
27	#16863475	C₂²	1	1	yes	characteristic
28	#16863467	—	2	1	no	—
29	C₈×D₂₆₈	—	2	1	no	—
30	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
31	C₈×D₂₆₈	C₂²	1	2	yes	—
32	C₈×C₂²⋊D₆₇	—	2	1	no	—
33	#16863455	—	2	1	no	—
34	#16863453	C₂²	1	1	yes	characteristic
35	#16863420	C₂²	1	1	yes	characteristic
36	#16863362	—	2	1	no	—
37	#16863350	—	2	1	no	—
38	#16863149	C₂²	1	2	yes	—
39	#16863147	C₂²	1	2	yes	—
40	#16863128	C₂²	1	2	yes	—
41	#16863125	C₂²	1	2	yes	—
42	#16863125	C₂²	1	2	yes	—
43	#16863125	C₂²	1	2	yes	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	#322×C₆₇	C₂²	1	2	yes	—
48	C₈²×C₆₇	C₂²	1	2	yes	—
49	C₂×#11761628	—	2	1	no	—
50	C₂×#11761617	C₂×C₄	1	2	yes	—
51	C₂×D₅₃₆	C₂×C₄	1	2	yes	—
52	#14524049	—	4	4	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761611	—	2	1	no	—
55	C₂×#11761611	—	2	2	no	—
56	C₂×C₈×D₆₇	—	2	1	no	—
57	C₂×C₈×D₆₇	—	2	2	no	—
58	#14524043	C₂×C₄	1	1	yes	characteristic
59	#14524040	C₂×C₄	1	1	yes	characteristic
60	#14524037	—	2	1	no	—
61	#14524035	C₂×C₄	1	1	yes	characteristic
62	#14524031	—	2	1	no	—
63	#14524031	C₂×C₄	1	1	yes	characteristic
64	#14524026	—	2	1	no	—
65	#14524022	C₂×C₄	1	1	yes	characteristic
66	#14524017	—	2	1	no	—
67	#14524017	C₂×C₄	1	2	yes	—
68	#14524017	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
70	C₄×D₂₆₈	—	2	1	no	—
71	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
72	C₄×D₂₆₈	C₂³	1	2	yes	—
73	C₄×C₂²⋊D₆₇	—	2	1	no	—
74	#14524000	—	2	1	no	—
75	#14523977	C₂×C₄	1	2	yes	—
76	#14523975	C₂×C₄	1	2	yes	—
77	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
78	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
81	Dic₆₇⋊C₈	—	2	1	no	—
82	Dic₆₇⋊C₈	—	2	1	no	—
83	#14523968	C₂×C₄	1	2	yes	—
84	#14523965	C₂×C₄	1	2	yes	—
85	#14523965	C₂×C₄	1	2	yes	—
86	#14523965	C₂×C₄	1	2	yes	—
87	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
88	(C₂×D₆₇)⋊C₈	—	2	2	no	—
89	(C₂×D₆₇)⋊C₈	—	2	2	no	—
90	(C₂×D₆₇)⋊C₈	—	2	1	no	—
91	(C₂×D₆₇)⋊C₈	—	2	1	no	—
92	#14523954	—	2	1	no	—
93	#14523953	—	2	1	no	—
94	C₈×Dic₆₇	—	2	1	no	—
95	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
96	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₆₇	—	2	1	no	—
100	C₂²⋊C₈×C₆₇	—	2	1	no	—
101	#97×C₆₇	C₂×C₄	1	1	yes	characteristic
102	#97×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₆₇	C₂³	1	2	yes	—
106	C₄×C₈×C₆₇	C₂³	1	2	yes	—
107	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	#11761628	—	4	2	no	—
110	#11761628	—	4	2	no	—
111	C₂×Dic₁₃₄	—	2	1	no	—
112	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₂₆₈	—	2	1	no	—
114	C₂×D₂₆₈	—	2	1	no	—
115	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
117	C₂×C₂²⋊D₆₇	—	2	1	no	—
118	C₂×C₂²⋊D₆₇	—	2	2	no	—
119	C₂×C₄×D₆₇	—	2	1	no	—
120	C₂×C₄×D₆₇	—	2	2	no	—
121	#11761617	—	2	4	no	—
122	D₅₃₆	—	2	4	no	—
123	#11761612	—	4	2	no	—
124	#11761611	—	4	2	no	—
125	#11761611	—	4	4	no	—
126	C₂×C₆₇⋊C₈	—	2	1	no	—
127	C₂×C₆₇⋊C₈	—	2	1	no	—
128	C₂×C₆₇⋊C₈	—	2	2	no	—
129	C₈×D₆₇	—	4	2	no	—
130	C₈×D₆₇	—	4	4	no	—
131	C₄⋊Dic₆₇	—	2	1	no	—
132	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
135	Dic₆₇⋊C₄	—	2	1	no	—
136	Dic₆₇⋊C₄	—	2	1	no	—
137	Dic₆₇⋊C₄	—	2	1	no	—
138	Dic₆₇⋊C₄	—	2	1	no	—
139	C₂²⋊Dic₆₇	—	2	1	no	—
140	(C₂×D₆₇)⋊C₄	—	2	1	no	—
141	(C₂×D₆₇)⋊C₄	—	2	1	no	—
142	(C₂×D₆₇)⋊C₄	—	2	1	no	—
143	(C₂×D₆₇)⋊C₄	—	2	2	no	—
144	(C₂×D₆₇)⋊C₄	—	2	2	no	—
145	(C₂×D₆₇)⋊C₄	—	2	1	no	—
146	C₄×Dic₆₇	—	2	1	no	—
147	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
150	M₁₆×C₆₇	—	2	4	no	—
151	C₂×C₈×C₆₇	—	2	2	no	—
152	C₂×C₈×C₆₇	—	2	2	no	—
153	C₂×C₈×C₆₇	—	4	1	no	—
154	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
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	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₇	#41	1	1	yes	characteristic
163	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₆₇	—	2	1	no	—
166	C₂²×D₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	1	no	—
170	C₂×C₄×C₆₇	—	4	1	no	—
171	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₆₇	—	4	2	no	—
178	C₂²⋊D₆₇	—	4	4	no	—
179	C₂×Dic₆₇	—	2	1	no	—
180	C₂×Dic₆₇	—	2	1	no	—
181	C₂×Dic₆₇	—	2	2	no	—
182	C₂×Dic₆₇	—	2	1	no	—
183	D₂₆₈	—	2	2	no	—
184	D₂₆₈	—	2	2	no	—
185	D₂₆₈	—	2	2	no	—
186	D₂₆₈	—	4	2	no	—
187	D₂₆₈	—	4	2	no	—
188	C₄×D₆₇	—	4	2	no	—
189	C₄×D₆₇	—	4	1	no	—
190	C₄×D₆₇	—	4	1	no	—
191	C₄×D₆₇	—	4	2	no	—
192	Dic₁₃₄	—	2	2	no	—
193	Dic₁₃₄	—	4	2	no	—
194	C₈×C₆₇	—	2	2	no	—
195	C₈×C₆₇	—	2	1	no	—
196	C₈×C₆₇	—	2	1	no	—
197	C₈×C₆₇	—	2	1	no	—
198	C₈×C₆₇	—	4	2	no	—
199	C₈×C₆₇	#131	1	4	yes	complemented
200	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
201	C₆₇⋊C₈	—	4	1	no	—
202	C₆₇⋊C₈	—	4	2	no	—
203	C₆₇⋊C₈	—	4	1	no	—
204	C₂²×C₆₇	—	2	1	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂×D₆₇	—	4	1	no	—
209	C₂×D₆₇	—	4	2	no	—
210	C₂×D₆₇	—	4	2	no	—
211	C₂×D₆₇	—	4	1	no	—
212	C₂×D₆₇	—	4	2	no	—
213	C₂×D₆₇	—	4	1	no	—
214	C₄×C₆₇	—	2	1	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	1	no	—
218	C₄×C₆₇	C₂×#131	1	2	yes	—
219	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₄×C₆₇	#575	1	1	yes	characteristic
221	Dic₆₇	—	4	1	no	—
222	Dic₆₇	—	4	2	no	—
223	Dic₆₇	—	4	1	no	—
224	Dic₆₇	—	4	1	no	—
225	#17964	—	67	1	no	maximal, Sylow
226	C₂×C₆₇	—	4	1	no	—
227	C₂×C₆₇	#2931	1	1	yes	characteristic
228	C₂×C₆₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×C₆₇	#2955	1	1	yes	characteristic
230	D₆₇	—	8	2	no	—
231	D₆₇	—	8	1	no	—
232	#3171	—	67	1	no	—
233	#2966	—	67	1	no	—
234	#2931	—	67	1	no	—
235	#1594	—	67	2	no	—
236	#1592	—	67	2	no	—
237	C₈×SD₁₆	—	67	2	no	—
238	C₈×D₈	—	67	2	no	—
239	#1569	—	67	1	no	—
240	#1496	—	67	1	no	—
241	#1495	—	67	1	no	—
242	C₈×M₁₆	D₆₇	1	1	yes	characteristic, complemented
243	C₆₇	#17964	1	1	yes	characteristic, complemented, Sylow
244	C₂×#131	—	134	1	no	—
245	#532	—	67	1	no	—
246	#529	—	67	1	no	—
247	#501	—	67	1	no	—
248	#496	—	67	1	no	—
249	#490	—	67	1	no	—
250	#489	—	67	1	no	—
251	#469	—	67	2	no	—
252	#468	—	67	2	no	—
253	#446	—	67	1	no	—
254	C₈×Q₈	—	67	1	no	—
255	C₄×SD₁₆	—	67	2	no	—
256	C₄×D₈	—	67	2	no	—
257	#436	—	67	2	no	—
258	#436	—	67	1	no	—
259	#436	—	134	1	no	—
260	#435	—	134	1	no	—
261	C₈×D₄	—	67	1	no	—
262	C₈×D₄	—	67	2	no	—
263	C₈×D₄	—	134	1	no	—
264	C₈×D₄	—	134	1	no	—
265	#433	—	134	1	no	—
266	#432	—	67	1	no	—
267	#431	C₂×D₆₇	1	1	yes	characteristic
268	#423	—	67	1	no	—
269	#408	—	134	1	no	—
270	#405	—	134	1	no	—
271	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
273	#335	—	67	2	no	—
274	#334	—	67	2	no	—
275	Q₈⋊C₈	—	67	2	no	—
276	D₄⋊C₈	—	67	2	no	—
277	D₄⋊C₈	—	67	2	no	—
278	D₄⋊C₈	—	67	2	no	—
279	#322	C₂×D₆₇	1	2	yes	—
280	C₈²	C₂×D₆₇	1	2	yes	—
281	C₂×#41	—	134	1	no	—
282	C₂×SD₁₆	—	67	2	no	—
283	C₂×D₈	—	67	2	no	—
284	#131	—	268	4	no	—
285	C₂×M₁₆	—	134	1	no	—
286	C₂×M₁₆	—	134	2	no	—
287	C₂×M₁₆	—	134	1	no	—
288	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
289	C₂²×C₈	—	134	2	no	—
290	C₂²×C₈	—	134	1	no	—
291	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
292	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
293	C₄⋊Q₈	—	67	1	no	—
294	#127	—	67	1	no	—
295	#126	—	134	1	no	—
296	#125	—	67	1	no	—
297	#124	—	67	1	no	—
298	#124	—	134	1	no	—
299	#123	—	134	1	no	—
300	C₂²⋊Q₈	—	67	1	no	—
301	#121	—	67	1	no	—
302	#121	—	67	2	no	—
303	#121	—	134	1	no	—
304	C₄×Q₈	—	67	1	no	—
305	C₄×D₄	—	67	1	no	—
306	C₄×D₄	—	67	2	no	—
307	C₄×D₄	—	134	1	no	—
308	C₄×D₄	—	134	1	no	—
309	#117	—	134	1	no	—
310	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
311	#107	—	67	2	no	—
312	#106	—	67	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	67	1	no	—
315	C₄⋊C₈	—	67	1	no	—
316	C₄⋊C₈	—	67	2	no	—
317	C₄⋊C₈	—	134	1	no	—
318	C₄⋊C₈	—	134	1	no	—
319	C₄⋊C₈	—	134	1	no	—
320	#103	—	67	2	no	—
321	#102	—	67	2	no	—
322	#102	—	67	2	no	—
323	#102	—	67	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	134	1	no	—
326	C₂²⋊C₈	—	134	2	no	—
327	C₂²⋊C₈	—	134	2	no	—
328	C₂²⋊C₈	—	134	1	no	—
329	C₂²⋊C₈	—	134	1	no	—
330	#97	—	134	1	no	—
331	#97	—	134	1	no	—
332	#97	C₄×D₆₇	1	1	yes	characteristic
333	#97	C₄×D₆₇	1	1	yes	characteristic
334	C₄×C₈	—	134	1	no	—
335	C₄×C₈	D₂₆₈	1	1	yes	characteristic
336	C₄×C₈	D₂₆₈	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₆₇	1	2	yes	—
338	C₄×C₈	C₂²×D₆₇	1	2	yes	—
339	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
341	#41	—	268	2	no	—
342	#41	—	268	2	no	—
343	C₂×Q₈	—	67	1	no	—
344	C₂×Q₈	—	134	1	no	—
345	C₂×D₄	—	67	1	no	—
346	C₂×D₄	—	67	2	no	—
347	C₂×D₄	—	134	1	no	—
348	C₂×D₄	—	134	2	no	—
349	C₂×D₄	—	134	1	no	—
350	C₂×D₄	—	134	1	no	—
351	C₂²×C₄	—	134	1	no	—
352	C₂²×C₄	—	134	2	no	—
353	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
355	C₂²×C₄	#11761628	1	1	yes	characteristic
356	SD₁₆	—	134	4	no	—
357	D₈	—	134	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	268	4	no	—
360	M₁₆	—	268	2	no	—
361	M₁₆	—	268	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	268	4	no	—
366	C₂×C₈	—	268	2	no	—
367	C₂×C₈	—	134	1	no	—
368	C₂×C₈	—	134	1	no	—
369	C₂×C₈	—	134	2	no	—
370	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
371	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
372	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
373	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
374	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
375	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
376	C₄⋊C₄	—	67	1	no	—
377	C₄⋊C₄	—	67	1	no	—
378	C₄⋊C₄	—	67	2	no	—
379	C₄⋊C₄	—	134	1	no	—
380	C₄⋊C₄	—	134	1	no	—
381	C₄⋊C₄	—	134	1	no	—
382	C₄⋊C₄	—	134	1	no	—
383	C₄⋊C₄	—	134	1	no	—
384	C₂²⋊C₄	—	134	1	no	—
385	C₂²⋊C₄	—	134	1	no	—
386	C₂²⋊C₄	—	134	1	no	—
387	C₂²⋊C₄	—	134	2	no	—
388	C₂²⋊C₄	—	134	1	no	—
389	C₂²⋊C₄	—	134	2	no	—
390	C₂²⋊C₄	—	134	1	no	—
391	C₄²	—	134	1	no	—
392	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
393	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
394	C₄²	#11761628	1	1	yes	characteristic
395	C₄²	C₂³×D₆₇	1	1	yes	characteristic
396	C₂³	—	134	1	no	—
397	C₂³	—	134	2	no	—
398	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
399	Q₈	—	268	2	no	—
400	Q₈	—	134	2	no	—
401	D₄	—	268	2	no	—
402	D₄	—	268	2	no	—
403	D₄	—	268	4	no	—
404	D₄	—	268	2	no	—
405	D₄	—	134	2	no	—
406	D₄	—	134	2	no	—
407	D₄	—	134	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	268	2	no	—
413	C₂×C₄	—	268	1	no	—
414	C₂×C₄	—	268	1	no	—
415	C₂×C₄	—	268	2	no	—
416	C₂×C₄	—	134	1	no	—
417	C₂×C₄	—	134	1	no	—
418	C₂×C₄	—	134	1	no	—
419	C₂×C₄	—	134	2	no	—
420	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
421	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
422	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
425	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	268	2	no	—
432	C₈	—	268	1	no	—
433	C₈	—	268	1	no	—
434	C₈	#14524049	1	4	yes	complemented
435	C₈	#14524071	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	268	2	no	—
440	C₂²	—	268	1	no	—
441	C₂²	—	268	2	no	—
442	C₂²	—	268	1	no	—
443	C₂²	—	268	1	no	—
444	C₂²	—	268	2	no	—
445	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	268	2	no	—
451	C₄	—	268	1	no	—
452	C₄	—	268	1	no	—
453	C₄	—	268	1	no	—
454	C₄	C₂×#14524049	1	2	yes	—
455	C₄	C₂×#14524071	1	1	yes	characteristic
456	C₄	#16864196	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	536	2	no	—
459	C₂	—	536	1	no	—
460	C₂	#22568922	1	1	yes	characteristic
461	C₂	C₄×#14524071	1	1	yes	characteristic
462	C₂	#22569113	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×M₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22570804	C₂
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×M₁₆	D₆₇
hypocenter	C₆₇	#17964
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #22569184	C₂	semidirect
3. #22568922	C₂	semidirect
4. #22559124	C₂	semidirect
5. #22559113	C₂	semidirect
6. C₈×#11761617	C₂	semidirect
7. C₈×D₅₃₆	C₂	semidirect
8. #22558976	C₂	semidirect
9. #22558679	C₂	semidirect
10. #22558675	C₂	semidirect
11. C₈×M₁₆×C₆₇	C₂	semidirect
199. C₈×C₆₇	#131	semidirect
242. C₈×M₁₆	D₆₇	semidirect
243. C₆₇	#17964	semidirect
434. C₈	#14524049	semidirect

Maximal subgroups

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

subgroup	index
#22570804	2
#22569184	2
#22568922	2
#22559124	2
#22559113	2
C₈×#11761617	2
C₈×D₅₃₆	2
#22558976	2
#22558679	2
#22558675	2
C₈×M₁₆×C₆₇	2
#17964	67