Subgroups — #493313

Order 512.

736 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2168	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#20484	C₂	1	1	yes	maximal, characteristic
4	#12663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#12654	C₂	1	1	yes	maximal, characteristic, complemented
7	#12612	C₂	1	1	yes	maximal, characteristic, complemented
8	#12611	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#12600	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#12592	C₂	1	1	yes	maximal, characteristic, complemented
14	#12545	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#1374	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₁₆	C₂²	1	1	yes	characteristic
20	C₂×#435	C₄	1	1	yes	characteristic
21	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₂×#405	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
24	#2290	C₄	1	1	yes	characteristic
25	#2168	C₄	1	8	yes	complemented
26	D₄×C₁₆	C₄	1	8	yes	complemented
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₂×#346	C₂²	1	1	yes	characteristic
34	C₂×#346	C₂²	1	1	yes	characteristic
35	C₂×#346	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	#1771	C₄	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	#1768	C₄	1	1	yes	characteristic
44	#1753	C₄	1	1	yes	characteristic
45	#1752	C₄	1	1	yes	characteristic
46	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	#1750	C₄	1	1	yes	characteristic
49	#1749	C₄	1	1	yes	characteristic
50	#1726	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	#1374	C₂²	1	1	yes	characteristic
60	#1374	C₂²	1	1	yes	characteristic
61	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₈	C₂³	1	1	yes	characteristic
64	C₂³×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂×#117	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂×M₃₂	—	4	1	no	—
69	C₂×M₃₂	—	4	1	no	—
70	C₂×M₃₂	C₂×C₄	1	4	yes	complemented
71	C₂²×C₁₆	—	4	1	no	—
72	C₂²×C₁₆	—	4	1	no	—
73	C₂²×C₁₆	—	4	1	no	—
74	C₂²×C₁₆	—	4	1	no	—
75	C₂²×C₁₆	—	4	1	no	—
76	C₂²×C₁₆	—	4	1	no	—
77	C₂²×C₁₆	C₂×C₄	1	4	yes	—
78	C₂²×C₁₆	C₂×C₄	1	4	yes	—
79	C₂²×C₁₆	C₂×C₄	1	4	yes	complemented
80	C₂²×C₁₆	C₂³	1	1	yes	characteristic
81	C₂²×C₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₁₆	C₂³	1	1	yes	characteristic
84	C₂²×C₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₁₆	C₂³	1	1	yes	characteristic
87	C₂²×C₁₆	C₂³	1	1	yes	characteristic
88	#435	C₈	1	8	yes	—
89	C₈×D₄	C₂×C₄	1	4	yes	—
90	C₈×D₄	C₂×C₄	1	4	yes	—
91	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	#405	—	4	1	no	—
98	#405	—	4	1	no	—
99	C₂×#97	C₂×C₄	1	1	yes	characteristic
100	C₂×#97	C₂×C₄	1	1	yes	characteristic
101	C₂×#97	C₂×C₄	1	1	yes	characteristic
102	C₂×#97	C₂×C₄	1	1	yes	characteristic
103	C₂×#97	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄×C₈	—	4	1	no	—
105	C₂×C₄×C₈	—	4	1	no	—
106	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
113	#388	C₈	1	2	yes	—
114	#387	C₈	1	2	yes	—
115	#386	C₈	1	2	yes	—
116	#385	C₈	1	2	yes	—
117	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	#376	C₂×C₄	1	1	yes	characteristic
121	C₄⋊C₁₆	C₂×C₄	1	4	yes	complemented
122	C₄⋊C₁₆	C₂×C₄	1	4	yes	complemented
123	C₂²⋊C₁₆	C₂×C₄	1	4	yes	—
124	C₂²⋊C₁₆	C₂×C₄	1	4	yes	—
125	C₂²⋊C₁₆	C₂×C₄	1	4	yes	complemented
126	C₂²⋊C₁₆	C₂×C₄	1	4	yes	complemented
127	#346	—	4	1	no	—
128	#346	—	4	1	no	—
129	#346	C₂×C₄	1	4	yes	complemented
130	C₄×C₁₆	—	4	1	no	—
131	C₄×C₁₆	—	4	1	no	—
132	C₄×C₁₆	—	4	1	no	—
133	C₄×C₁₆	—	4	1	no	—
134	C₄×C₁₆	C₂×C₄	1	4	yes	complemented
135	#336	C₂×C₄	1	1	yes	characteristic
136	#336	C₂×C₄	1	1	yes	characteristic
137	#336	C₂×C₄	1	1	yes	characteristic
138	#336	C₂×C₄	1	1	yes	characteristic
139	#336	C₂×C₄	1	1	yes	characteristic
140	#336	C₂×C₄	1	1	yes	characteristic
141	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
142	C₂³×C₄	C₂×C₈	1	2	yes	—
143	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
144	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
145	C₂×M₁₆	—	4	1	no	—
146	C₂×M₁₆	—	4	1	no	—
147	C₂×M₁₆	C₂×C₈	1	4	yes	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	2	1	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	—	2	1	no	—
153	C₂²×C₈	—	2	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	4	1	no	—
157	C₂²×C₈	—	4	1	no	—
158	C₂²×C₈	C₂×C₈	1	4	yes	—
159	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₈	C₂²×C₄	1	2	yes	—
163	C₂²×C₈	C₂²×C₄	1	2	yes	—
164	C₂²×C₈	C₂²×C₄	1	2	yes	—
165	C₂²×C₈	C₂²×C₄	1	2	yes	—
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₈	C₂⁴	1	1	yes	characteristic
171	C₄×D₄	C₄²	1	4	yes	—
172	C₄×D₄	C₂×C₈	1	4	yes	—
173	#117	—	4	1	no	—
174	#117	—	4	1	no	—
175	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
176	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
177	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
179	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
180	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
181	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
182	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
183	C₂×C₄²	—	4	1	no	—
184	C₂×C₄²	—	4	1	no	—
185	C₂×C₄²	C₂×C₈	1	2	yes	—
186	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
191	M₃₂	—	4	4	no	—
192	C₂×C₁₆	—	2	1	no	—
193	C₂×C₁₆	—	2	1	no	—
194	C₂×C₁₆	—	2	1	no	—
195	C₂×C₁₆	—	2	1	no	—
196	C₂×C₁₆	—	2	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	—	2	1	no	—
204	C₂×C₁₆	—	2	1	no	—
205	C₂×C₁₆	—	2	1	no	—
206	C₂×C₁₆	—	2	1	no	—
207	C₂×C₁₆	—	2	1	no	—
208	C₂×C₁₆	—	4	4	no	—
209	C₂×C₁₆	—	4	4	no	—
210	C₂×C₁₆	—	4	4	no	—
211	C₂×C₁₆	C₂²×C₄	1	2	yes	—
212	C₂×C₁₆	C₂²×C₄	1	2	yes	—
213	C₂×C₁₆	C₂²×C₄	1	2	yes	—
214	C₂×C₁₆	C₂²×C₄	1	2	yes	—
215	C₂×C₁₆	C₂²×C₄	1	2	yes	—
216	C₂×C₁₆	C₂²×C₄	1	2	yes	—
217	C₂×C₁₆	C₂²×C₄	1	2	yes	—
218	C₂×C₁₆	C₂²×C₄	1	2	yes	—
219	C₄⋊C₈	C₄²	1	4	yes	—
220	C₄⋊C₈	C₂×C₈	1	4	yes	—
221	C₂²⋊C₈	C₄²	1	4	yes	—
222	C₂²⋊C₈	C₄²	1	4	yes	—
223	C₂²⋊C₈	C₂×C₈	1	4	yes	—
224	C₂²⋊C₈	C₂×C₈	1	4	yes	—
225	#97	—	4	1	no	—
226	#97	—	4	1	no	—
227	#97	—	4	1	no	—
228	#97	—	4	1	no	—
229	#97	C₂×C₈	1	4	yes	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	2	1	no	—
234	C₄×C₈	—	2	1	no	—
235	C₄×C₈	—	2	1	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	—	4	1	no	—
239	C₄×C₈	—	4	1	no	—
240	C₄×C₈	C₂²×C₄	1	2	yes	—
241	C₄×C₈	C₂²×C₄	1	2	yes	—
242	#95	C₂×C₈	1	2	yes	—
243	#95	C₂×C₈	1	2	yes	—
244	#95	C₂×C₈	1	2	yes	—
245	#95	C₂×C₈	1	2	yes	—
246	#95	C₂×C₈	1	2	yes	—
247	C₂⁴	C₂²×C₈	1	1	yes	characteristic
248	C₂⁴	C₂²×C₈	1	1	yes	characteristic
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	C₄×C₈	1	4	yes	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₂×C₄²	1	2	yes	—
263	C₂²×C₄	C₂×C₄²	1	2	yes	—
264	C₂²×C₄	C₂²×C₈	1	2	yes	—
265	C₂²×C₄	C₂²×C₈	1	2	yes	—
266	C₂²×C₄	C₂²×C₈	1	2	yes	—
267	C₂²×C₄	C₂²×C₈	1	2	yes	—
268	C₂²×C₄	C₂²×C₈	1	2	yes	—
269	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₈	1	2	yes	—
274	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
275	M₁₆	—	4	4	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	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	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂×C₄²	1	2	yes	—
300	C₂×C₈	C₂×C₄²	1	2	yes	—
301	C₂×C₈	C₂×C₄²	1	2	yes	—
302	C₂×C₈	C₂²×C₈	1	2	yes	—
303	C₂×C₈	C₂²×C₈	1	2	yes	—
304	C₂×C₈	C₂²×C₈	1	2	yes	—
305	C₂×C₈	C₂²×C₈	1	2	yes	—
306	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₄×C₈	1	4	yes	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	C₄×C₈	1	4	yes	—
319	C₂²⋊C₄	C₄×C₈	1	4	yes	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂×C₄²	1	2	yes	—
330	C₄²	C₂²×C₈	1	2	yes	—
331	C₁₆	—	2	2	no	—
332	C₁₆	—	2	2	no	—
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₁₆	—	2	2	no	—
337	C₁₆	—	2	2	no	—
338	C₁₆	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	C₂×C₄×C₈	1	2	yes	—
347	C₂³	C₂×C₄×C₈	1	2	yes	—
348	C₂³	#504	1	4	yes	—
349	C₂³	C₂³×C₈	1	1	yes	characteristic
350	D₄	—	2	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
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	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
378	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
379	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
380	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
381	C₂×C₄	#504	1	4	yes	—
382	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
383	C₂×C₄	#518	1	1	yes	characteristic
384	C₂×C₄	#520	1	1	yes	characteristic
385	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
386	C₂×C₄	#568	1	1	yes	characteristic
387	C₂×C₄	#568	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	#518	1	1	yes	characteristic
396	C₈	#518	1	1	yes	characteristic
397	C₈	#520	1	1	yes	characteristic
398	C₈	#520	1	1	yes	characteristic
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	#2108	1	4	yes	—
409	C₂²	C₂²×C₄×C₈	1	1	yes	characteristic
410	C₂²	#2972	1	1	yes	characteristic
411	C₂²	#2988	1	1	yes	characteristic
412	C₂²	C₂×#504	1	2	yes	—
413	C₂²	C₂×#504	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	#2275	1	1	yes	characteristic
423	C₄	#2875	1	1	yes	characteristic
424	C₄	#2972	1	1	yes	characteristic
425	C₄	#2988	1	1	yes	characteristic
426	C₂	—	2	4	no	—
427	C₂	—	4	2	no	—
428	C₂	#20555	1	1	yes	characteristic
429	C₂	C₂×#2108	1	1	yes	characteristic
430	C₂	C₄×#504	1	1	yes	characteristic
431	C₂	#33491	1	2	yes	—
432	C₂	#33508	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator	C₂²	C₂²×C₄×C₈
socle	C₂³	C₂³×C₈
prime radical	C₂²×D₄	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #12663	C₂	semidirect
5. C₁₆×C₄⋊C₄	C₂	semidirect
6. #12654	C₂	semidirect
7. #12612	C₂	semidirect
8. #12611	C₂	semidirect
9. C₁₆×C₂²⋊C₄	C₂	semidirect
10. C₁₆×C₂²⋊C₄	C₂	semidirect
11. #12600	C₂	semidirect
12. C₄×C₂²⋊C₁₆	C₂	semidirect
13. #12592	C₂	semidirect
14. #12545	C₂	semidirect
15. C₂×#1374	C₂	semidirect
25. #2168	C₄	semidirect
26. D₄×C₁₆	C₄	semidirect
70. C₂×M₃₂	C₂×C₄	semidirect
79. C₂²×C₁₆	C₂×C₄	semidirect
121. C₄⋊C₁₆	C₂×C₄	semidirect
122. C₄⋊C₁₆	C₂×C₄	semidirect
125. C₂²⋊C₁₆	C₂×C₄	semidirect
126. C₂²⋊C₁₆	C₂×C₄	semidirect
129. #346	C₂×C₄	semidirect
134. C₄×C₁₆	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2168	2
C₂×D₄×C₁₆	2
#20484	2
#12663	2
C₁₆×C₄⋊C₄	2
#12654	2
#12612	2
#12611	2
C₁₆×C₂²⋊C₄	2
#12600	2
C₄×C₂²⋊C₁₆	2
#12592	2
#12545	2
C₂×#1374	2