Subgroups — #483683

Order 512.

461 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#33505	C₂	1	1	yes	maximal, characteristic, complemented
2	#33488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	#12064	C₂	1	1	yes	maximal, characteristic, complemented
5	#12063	C₂	1	1	yes	maximal, characteristic, complemented
6	#12056	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#12050	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#12039	C₂	1	1	yes	maximal, characteristic, complemented
11	#12038	C₂	1	1	yes	maximal, characteristic, complemented
12	#12017	C₂	1	1	yes	maximal, characteristic, complemented
13	#11615	C₂	1	1	yes	maximal, characteristic, complemented
14	#11583	C₂	1	1	yes	maximal, characteristic, complemented
15	#11409	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈×#41	C₂²	1	1	yes	characteristic
17	C₄×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
18	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
19	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
20	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	#2169	—	2	1	no	—
22	#2169	—	2	1	no	—
23	#2169	C₂²	1	1	yes	characteristic
24	#2169	C₂²	1	1	yes	characteristic
25	#2169	C₂²	1	1	yes	characteristic, complemented
26	#2169	C₂²	1	1	yes	characteristic, complemented
27	#2168	—	2	1	no	—
28	#2168	—	2	1	no	—
29	D₄×C₁₆	C₂²	1	1	yes	characteristic
30	D₄×C₁₆	C₂²	1	1	yes	characteristic
31	#2163	C₂²	1	1	yes	characteristic
32	#2162	—	2	1	no	—
33	#2162	C₂²	1	1	yes	characteristic
34	#2150	—	2	1	no	—
35	#2150	C₂²	1	1	yes	characteristic
36	#2112	—	2	1	no	—
37	C₂×C₂²⋊C₁₆	—	2	1	no	—
38	C₄×M₃₂	C₂²	1	1	yes	characteristic
39	#1580	C₄	1	1	yes	characteristic
40	#1580	C₄	1	1	yes	characteristic
41	SD₁₆⋊C₈	C₄	1	1	yes	characteristic
42	SD₁₆⋊C₈	C₄	1	1	yes	characteristic
43	C₈×SD₁₆	C₂²	1	1	yes	characteristic
44	C₈×SD₁₆	C₂²	1	1	yes	characteristic
45	C₈×D₈	C₂²	1	1	yes	characteristic
46	C₈×D₈	C₂²	1	1	yes	characteristic
47	#1565	C₄	1	1	yes	characteristic
48	#1478	C₄	1	1	yes	characteristic
49	#1477	C₄	1	1	yes	characteristic
50	C₈×M₁₆	C₂²	1	1	yes	characteristic
51	#1370	C₂²	1	1	yes	characteristic, complemented
52	#1370	C₂²	1	1	yes	characteristic, complemented
53	#1367	C₂²	1	1	yes	characteristic, complemented
54	#1367	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
58	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
59	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
60	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
61	D₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
62	D₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
63	#1312	C₂²	1	1	yes	characteristic, complemented
64	#1312	C₂²	1	1	yes	characteristic, complemented
65	#1311	C₂²	1	1	yes	characteristic, complemented
66	C₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
67	C₂×AGL(1,ℤ/8)	C₈	1	1	yes	characteristic
68	C₂³×C₈	—	2	1	no	—
69	C₄×#41	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
71	C₂×M₃₂	—	2	1	no	—
72	C₂×M₃₂	—	2	1	no	—
73	C₂×M₃₂	—	2	1	no	—
74	C₂×M₃₂	—	2	1	no	—
75	C₂×M₃₂	—	2	1	no	—
76	C₂×M₃₂	—	2	1	no	—
77	C₂²×C₁₆	—	2	1	no	—
78	C₂²×C₁₆	—	2	1	no	—
79	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₈×Q₈	C₂³	1	1	yes	characteristic
81	#442	C₈	1	1	yes	characteristic
82	#442	C₈	1	1	yes	characteristic
83	#440	C₈	1	1	yes	characteristic
84	#440	C₈	1	1	yes	characteristic
85	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
86	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
87	C₄×D₈	C₂×C₄	1	1	yes	characteristic
88	C₄×D₈	C₂×C₄	1	1	yes	characteristic
89	C₈×D₄	—	2	1	no	—
90	C₈×D₄	—	2	1	no	—
91	C₈×D₄	—	2	1	no	—
92	C₈×D₄	—	2	1	no	—
93	C₈×D₄	C₂×C₄	1	1	yes	characteristic
94	C₈×D₄	C₂×C₄	1	1	yes	characteristic
95	C₈×D₄	C₂×C₄	1	1	yes	characteristic
96	C₈×D₄	C₂³	1	1	yes	characteristic
97	C₈×D₄	C₂³	1	1	yes	characteristic
98	C₈×D₄	C₂³	1	1	yes	characteristic
99	#431	—	2	1	no	—
100	#431	C₂×C₄	1	1	yes	characteristic
101	#431	C₂×C₄	1	1	yes	characteristic
102	#428	C₈	1	1	yes	characteristic
103	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
104	#418	C₈	1	1	yes	characteristic
105	#417	C₈	1	1	yes	characteristic
106	C₂×C₂²⋊C₈	—	2	1	no	—
107	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×C₈	—	2	1	no	—
109	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
110	C₄⋊C₁₆	—	2	1	no	—
111	C₄⋊C₁₆	—	2	1	no	—
112	C₄⋊C₁₆	—	2	1	no	—
113	C₄⋊C₁₆	D₄	1	1	yes	characteristic
114	C₄⋊C₁₆	D₄	1	1	yes	characteristic
115	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
116	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
117	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
118	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
119	C₂²⋊C₁₆	—	2	1	no	—
120	C₂²⋊C₁₆	—	2	1	no	—
121	C₂²⋊C₁₆	—	2	1	no	—
122	C₂²⋊C₁₆	—	2	1	no	—
123	C₂²⋊C₁₆	—	2	1	no	—
124	C₂²⋊C₁₆	—	2	1	no	—
125	C₂²⋊C₁₆	—	2	1	no	—
126	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
127	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
128	#346	—	2	1	no	—
129	#346	—	2	1	no	—
130	C₄×C₁₆	—	2	1	no	—
131	C₄×C₁₆	—	2	1	no	—
132	C₄×C₁₆	C₂³	1	1	yes	characteristic
133	C₄×C₁₆	C₂³	1	1	yes	characteristic
134	C₄×C₁₆	C₂³	1	1	yes	characteristic
135	C₄×C₁₆	C₂³	1	1	yes	characteristic
136	#335	C₂×C₄	1	1	yes	characteristic
137	#335	C₂×C₄	1	1	yes	characteristic
138	#334	C₂×C₄	1	1	yes	characteristic
139	#334	C₂×C₄	1	1	yes	characteristic
140	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
141	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
142	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
143	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
144	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
145	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
146	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
147	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
148	#322	C₂×C₄	1	1	yes	characteristic
149	#322	C₂×C₄	1	1	yes	characteristic
150	C₈²	C₂³	1	1	yes	characteristic
151	C₈²	C₂³	1	1	yes	characteristic
152	C₂×#41	C₂×C₈	1	1	yes	characteristic
153	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
154	C₂³×C₄	—	2	1	no	—
155	AGL(1,ℤ/8)	—	2	4	no	—
156	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
157	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
158	C₂×D₈	C₂×C₈	1	1	yes	characteristic
159	C₂×D₈	C₂×C₈	1	1	yes	characteristic
160	C₂×M₁₆	C₂×C₈	1	1	yes	characteristic
161	C₂×M₁₆	C₂×C₈	1	1	yes	characteristic
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	2	1	no	—
169	C₂²×C₈	—	8	1	no	—
170	C₂²×C₈	—	8	1	no	—
171	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₈	#41	1	1	yes	characteristic
173	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
174	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
175	C₄×D₄	—	2	1	no	—
176	C₄×D₄	—	2	1	no	—
177	C₄×D₄	—	2	1	no	—
178	C₄×D₄	—	2	1	no	—
179	C₄×D₄	C₂×C₈	1	1	yes	characteristic
180	C₄×D₄	C₂×C₈	1	1	yes	characteristic
181	C₄×D₄	C₂×C₈	1	1	yes	characteristic
182	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
183	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
184	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
185	#117	—	2	1	no	—
186	#117	C₂×C₈	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₄²	—	2	1	no	—
190	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
191	M₃₂	—	4	2	no	—
192	M₃₂	—	8	1	no	—
193	M₃₂	—	8	1	no	—
194	M₃₂	—	8	1	no	—
195	M₃₂	—	8	1	no	—
196	M₃₂	—	8	1	no	—
197	C₂×C₁₆	—	2	1	no	—
198	C₂×C₁₆	—	2	1	no	—
199	C₂×C₁₆	—	2	1	no	—
200	C₂×C₁₆	—	2	1	no	—
201	C₂×C₁₆	—	2	1	no	—
202	C₂×C₁₆	—	2	1	no	—
203	C₂×C₁₆	—	8	1	no	—
204	C₂×C₁₆	—	8	1	no	—
205	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
206	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
207	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
208	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
209	#107	C₂×C₈	1	1	yes	characteristic
210	#107	C₂×C₈	1	1	yes	characteristic
211	#106	C₂×C₈	1	1	yes	characteristic
212	#106	C₂×C₈	1	1	yes	characteristic
213	C₄⋊C₈	—	2	1	no	—
214	C₄⋊C₈	—	2	1	no	—
215	C₄⋊C₈	—	2	1	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
220	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
221	#103	C₂×C₈	1	1	yes	characteristic
222	#103	C₂×C₈	1	1	yes	characteristic
223	#102	C₂×C₈	1	1	yes	characteristic
224	#102	C₂×C₈	1	1	yes	characteristic
225	#102	C₂×C₈	1	1	yes	characteristic
226	#102	C₂×C₈	1	1	yes	characteristic
227	#102	C₂×C₈	1	1	yes	characteristic
228	#102	C₂×C₈	1	1	yes	characteristic
229	C₂²⋊C₈	—	2	1	no	—
230	C₂²⋊C₈	—	2	1	no	—
231	C₂²⋊C₈	—	2	1	no	—
232	C₂²⋊C₈	—	2	1	no	—
233	C₂²⋊C₈	—	2	1	no	—
234	C₂²⋊C₈	—	2	1	no	—
235	C₂²⋊C₈	—	2	1	no	—
236	C₂²⋊C₈	—	2	1	no	—
237	#97	C₂×C₈	1	1	yes	characteristic
238	#97	C₂×C₈	1	1	yes	characteristic
239	C₄×C₈	—	2	1	no	—
240	C₄×C₈	—	2	1	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
243	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
244	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
245	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
246	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
247	C₄×C₈	C₂×D₄	1	1	yes	characteristic
248	C₄×C₈	#41	1	1	yes	characteristic
249	C₄×C₈	C₂⁴	1	1	yes	characteristic
250	C₂⁴	—	2	1	no	—
251	#41	—	2	2	no	—
252	#41	—	4	1	no	—
253	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	4	1	no	—
258	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
259	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
260	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	8	1	no	—
270	C₂²×C₄	—	8	1	no	—
271	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
273	C₂²×C₄	#131	1	1	yes	characteristic
274	SD₁₆	—	2	2	no	—
275	SD₁₆	M₃₂	1	4	yes	complemented
276	D₈	—	2	2	no	—
277	D₈	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	4	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	8	1	no	—
296	C₂×C₈	—	8	1	no	—
297	C₂×C₈	—	8	1	no	—
298	C₂×C₈	—	8	1	no	—
299	C₂×C₈	C₄×D₄	1	1	yes	characteristic
300	C₂×C₈	C₄×D₄	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₈	C₂×#41	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
311	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
312	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
313	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	C₄×D₄	1	1	yes	characteristic
325	C₄²	C₂²×C₈	1	1	yes	characteristic
326	C₄²	#131	1	1	yes	characteristic
327	C₄²	C₂³×C₄	1	1	yes	characteristic
328	C₁₆	—	2	2	no	—
329	C₁₆	—	2	1	no	—
330	C₁₆	—	2	1	no	—
331	C₁₆	—	2	1	no	—
332	C₁₆	—	2	1	no	—
333	C₁₆	—	4	1	no	—
334	C₁₆	—	4	1	no	—
335	C₁₆	—	4	1	no	—
336	C₁₆	—	4	1	no	—
337	C₁₆	—	4	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	1	no	—
344	C₂³	C₈×D₄	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	C₂×M₃₂	1	2	yes	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	C₂×M₃₂	1	2	yes	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	C₈×D₄	1	1	yes	characteristic
377	C₂×C₄	C₈×D₄	1	1	yes	characteristic
378	C₂×C₄	C₈×D₄	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
380	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
381	C₂×C₄	C₂×#131	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	C₂×M₃₂	1	2	yes	—
395	C₈	#576	1	1	yes	characteristic
396	C₈	#577	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	#2946	1	1	yes	characteristic
421	C₄	#2956	1	1	yes	characteristic
422	C₄	C₂²×M₃₂	1	1	yes	characteristic
423	C₄	#3407	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	—	8	1	no	—
428	C₂	#17852	1	1	yes	characteristic
429	C₂	D₄×M₃₂	1	1	yes	characteristic
430	C₂	#33441	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₄
commutator	C₂×C₄	C₂³×C₈
Frattini, cosocle	C₄×C₈	C₂⁴
socle	C₂²	C₂×C₈×D₄
prime radical	C₂×AGL(1,ℤ/8)	C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ #2162 ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #33505	C₂	semidirect
2. #33488	C₂	semidirect
4. #12064	C₂	semidirect
5. #12063	C₂	semidirect
6. #12056	C₂	semidirect
7. SD₁₆⋊C₁₆	C₂	semidirect
8. #12050	C₂	semidirect
9. C₁₆×SD₁₆	C₂	semidirect
10. #12039	C₂	semidirect
11. #12038	C₂	semidirect
12. #12017	C₂	semidirect
13. #11615	C₂	semidirect
14. #11583	C₂	semidirect
15. #11409	C₂	semidirect
19. Q₈×C₁₆	C₂²	semidirect
20. Q₈×C₁₆	C₂²	semidirect
25. #2169	C₂²	semidirect
26. #2169	C₂²	semidirect
51. #1370	C₂²	semidirect
52. #1370	C₂²	semidirect
53. #1367	C₂²	semidirect
54. #1367	C₂²	semidirect
55. Q₈⋊C₁₆	C₂²	semidirect
56. Q₈⋊C₁₆	C₂²	semidirect
61. D₄⋊C₁₆	C₂²	semidirect
62. D₄⋊C₁₆	C₂²	semidirect
63. #1312	C₂²	semidirect
64. #1312	C₂²	semidirect
65. #1311	C₂²	semidirect
66. C₈×C₁₆	C₂²	semidirect
275. SD₁₆	M₃₂	semidirect

Maximal subgroups

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

subgroup	index
#33505	2
#33488	2
C₈×AGL(1,ℤ/8)	2
#12064	2
#12063	2
#12056	2
SD₁₆⋊C₁₆	2
#12050	2
C₁₆×SD₁₆	2
#12039	2
#12038	2
#12017	2
#11615	2
#11583	2
#11409	2