Subgroups — #493221

Order 512.

818 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2169	C₂	1	1	yes	maximal, characteristic
2	C₂×#2168	C₂	1	1	yes	maximal, characteristic
3	C₂×#2108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#20484	C₂	1	1	yes	maximal, characteristic
6	#12663	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#12654	C₂	1	1	yes	maximal, characteristic, complemented
9	#12612	C₂	1	1	yes	maximal, characteristic, complemented
10	#12612	C₂	1	1	yes	maximal, characteristic, complemented
11	#12612	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	#12600	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	#12539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×M₃₂	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	#2169	C₄	1	8	yes	complemented
26	#2168	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	#2108	—	2	4	no	—
34	C₄×M₃₂	—	2	4	no	—
35	C₂×#346	C₂²	1	1	yes	characteristic
36	C₂×#346	C₂²	1	1	yes	characteristic
37	C₂×#346	C₂²	1	1	yes	characteristic
38	C₂×#346	C₂²	1	1	yes	characteristic
39	C₂×#346	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
47	#1771	C₄	1	1	yes	characteristic
48	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	#1768	C₄	1	1	yes	characteristic
50	#1753	C₄	1	1	yes	characteristic
51	#1752	C₄	1	1	yes	characteristic
52	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	#1750	C₄	1	1	yes	characteristic
55	#1749	C₄	1	1	yes	characteristic
56	#1726	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	#1374	C₂²	1	1	yes	characteristic
62	#1374	C₂²	1	1	yes	characteristic
63	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₈	C₂³	1	1	yes	characteristic
66	C₂³×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂×#117	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₂×M₃₂	—	2	2	no	—
71	C₂×M₃₂	—	2	2	no	—
72	C₂×M₃₂	—	2	2	no	—
73	C₂×M₃₂	—	2	2	no	—
74	C₂×M₃₂	—	2	2	no	—
75	C₂×M₃₂	—	2	2	no	—
76	C₂×M₃₂	C₂×C₄	1	4	yes	—
77	C₂×M₃₂	C₂×C₄	1	4	yes	—
78	C₂×M₃₂	C₂×C₄	1	4	yes	complemented
79	C₂²×C₁₆	—	2	2	no	—
80	C₂²×C₁₆	—	2	2	no	—
81	C₂²×C₁₆	C₂×C₄	1	4	yes	complemented
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	C₂²×C₁₆	C₂³	1	1	yes	characteristic
89	C₂²×C₁₆	C₂³	1	1	yes	characteristic
90	#435	C₈	1	8	yes	—
91	C₈×D₄	C₂×C₄	1	4	yes	—
92	C₈×D₄	C₂×C₄	1	4	yes	—
93	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊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	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	#405	—	2	2	no	—
100	#405	—	2	2	no	—
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×#97	C₂×C₄	1	1	yes	characteristic
105	C₂×#97	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄×C₈	—	2	2	no	—
107	C₂×C₄×C₈	—	2	2	no	—
108	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂×C₄	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	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
115	#388	C₈	1	2	yes	—
116	#387	C₈	1	2	yes	—
117	#386	C₈	1	2	yes	—
118	#385	C₈	1	2	yes	—
119	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
122	#376	C₂×C₄	1	1	yes	characteristic
123	C₄⋊C₁₆	C₂×C₄	1	4	yes	complemented
124	C₄⋊C₁₆	C₂×C₄	1	4	yes	complemented
125	C₂²⋊C₁₆	C₂×C₄	1	4	yes	—
126	C₂²⋊C₁₆	C₂×C₄	1	4	yes	—
127	C₂²⋊C₁₆	C₂×C₄	1	4	yes	complemented
128	C₂²⋊C₁₆	C₂×C₄	1	4	yes	complemented
129	#346	—	2	2	no	—
130	#346	—	2	2	no	—
131	#346	—	2	2	no	—
132	#346	C₂×C₄	1	4	yes	complemented
133	#346	D₄	1	4	yes	complemented
134	C₄×C₁₆	—	2	2	no	—
135	C₄×C₁₆	—	2	2	no	—
136	C₄×C₁₆	—	2	2	no	—
137	C₄×C₁₆	—	2	2	no	—
138	C₄×C₁₆	—	2	2	no	—
139	C₄×C₁₆	—	2	2	no	—
140	C₄×C₁₆	C₂×C₄	1	4	yes	complemented
141	#336	C₂×C₄	1	1	yes	characteristic
142	#336	C₂×C₄	1	1	yes	characteristic
143	#336	C₂×C₄	1	1	yes	characteristic
144	#336	C₂×C₄	1	1	yes	characteristic
145	#336	C₂×C₄	1	1	yes	characteristic
146	#336	C₂×C₄	1	1	yes	characteristic
147	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
148	C₂³×C₄	C₂×C₈	1	2	yes	—
149	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
150	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	C₂×C₈	1	4	yes	—
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	C₂×C₈	1	4	yes	—
165	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂²×C₄	1	2	yes	—
169	C₂²×C₈	C₂²×C₄	1	2	yes	—
170	C₂²×C₈	C₂²×C₄	1	2	yes	—
171	C₂²×C₈	C₂²×C₄	1	2	yes	—
172	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₈	C₂⁴	1	1	yes	characteristic
177	C₄×D₄	C₄²	1	4	yes	—
178	C₄×D₄	C₂×C₈	1	4	yes	—
179	#117	—	2	2	no	—
180	#117	—	2	2	no	—
181	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
182	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
183	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
186	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
189	C₂×C₄²	—	2	2	no	—
190	C₂×C₄²	—	2	2	no	—
191	C₂×C₄²	C₂×C₈	1	2	yes	—
192	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
197	M₃₂	—	2	8	no	—
198	M₃₂	—	2	8	no	—
199	M₃₂	—	2	8	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	—	2	1	no	—
209	C₂×C₁₆	—	2	1	no	—
210	C₂×C₁₆	—	2	1	no	—
211	C₂×C₁₆	—	2	1	no	—
212	C₂×C₁₆	—	2	8	no	—
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	C₂×C₁₆	C₂²×C₄	1	2	yes	—
220	C₂×C₁₆	C₂²×C₄	1	2	yes	—
221	C₂×C₁₆	C₂×D₄	1	2	yes	—
222	C₂×C₁₆	C₂×D₄	1	2	yes	—
223	C₂×C₁₆	#41	1	2	yes	—
224	C₂×C₁₆	#41	1	2	yes	—
225	C₄⋊C₈	C₄²	1	4	yes	—
226	C₄⋊C₈	C₂×C₈	1	4	yes	—
227	C₂²⋊C₈	C₄²	1	4	yes	—
228	C₂²⋊C₈	C₄²	1	4	yes	—
229	C₂²⋊C₈	C₂×C₈	1	4	yes	—
230	C₂²⋊C₈	C₂×C₈	1	4	yes	—
231	#97	—	2	2	no	—
232	#97	—	2	2	no	—
233	#97	—	2	2	no	—
234	#97	—	2	2	no	—
235	#97	C₂×C₈	1	4	yes	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	—	2	1	no	—
239	C₄×C₈	—	2	1	no	—
240	C₄×C₈	—	2	1	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	C₂²×C₄	1	2	yes	—
245	C₄×C₈	C₂²×C₄	1	2	yes	—
246	C₄×C₈	C₂×D₄	1	2	yes	—
247	C₄×C₈	#41	1	2	yes	—
248	#95	C₂×C₈	1	2	yes	—
249	#95	C₂×C₈	1	2	yes	—
250	#95	C₂×C₈	1	2	yes	—
251	#95	C₂×C₈	1	2	yes	—
252	#95	C₂×C₈	1	2	yes	—
253	C₂⁴	C₂²×C₈	1	1	yes	characteristic
254	C₂⁴	C₂²×C₈	1	1	yes	characteristic
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	C₄×C₈	1	4	yes	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
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	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	C₂×C₄²	1	2	yes	—
269	C₂²×C₄	C₂×C₄²	1	2	yes	—
270	C₂²×C₄	C₂²×C₈	1	2	yes	—
271	C₂²×C₄	C₂²×C₈	1	2	yes	—
272	C₂²×C₄	C₂²×C₈	1	2	yes	—
273	C₂²×C₄	C₂²×C₈	1	2	yes	—
274	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₈	1	2	yes	—
279	C₂²×C₄	C₂²×C₈	1	2	yes	—
280	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
281	M₁₆	—	2	8	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	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	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	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	8	no	—
303	C₂×C₈	C₂×C₄²	1	2	yes	—
304	C₂×C₈	C₂×C₄²	1	2	yes	—
305	C₂×C₈	C₂×C₄²	1	2	yes	—
306	C₂×C₈	C₄×D₄	1	2	yes	—
307	C₂×C₈	C₂²×C₈	1	2	yes	—
308	C₂×C₈	C₂²×C₈	1	2	yes	—
309	C₂×C₈	C₂²×C₈	1	2	yes	—
310	C₂×C₈	C₂²×C₈	1	2	yes	—
311	C₂×C₈	#131	1	2	yes	—
312	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
313	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₈	C₂×#41	1	1	yes	characteristic
316	C₂×C₈	C₂×#41	1	1	yes	characteristic
317	C₂×C₈	C₂×#41	1	1	yes	characteristic
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	C₄×C₈	1	4	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	C₄×C₈	1	4	yes	—
325	C₂²⋊C₄	C₄×C₈	1	4	yes	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	4	no	—
333	C₄²	C₂×C₄²	1	2	yes	—
334	C₄²	C₄×D₄	1	2	yes	—
335	C₄²	C₂²×C₈	1	2	yes	—
336	C₄²	#131	1	2	yes	—
337	C₁₆	—	2	2	no	—
338	C₁₆	—	2	2	no	—
339	C₁₆	—	2	2	no	—
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₁₆	C₄×D₄	1	4	yes	—
344	C₁₆	C₄×D₄	1	4	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	C₂×C₄×C₈	1	2	yes	—
354	C₂³	C₂×C₄×C₈	1	2	yes	—
355	C₂³	C₂³×C₈	1	1	yes	characteristic
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	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	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
383	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
384	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
385	C₂×C₄	C₂×C₄×C₈	1	2	yes	—
386	C₂×C₄	C₈×D₄	1	4	yes	—
387	C₂×C₄	#504	1	4	yes	—
388	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
390	C₂×C₄	C₄×#41	1	1	yes	characteristic
391	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
392	C₂×C₄	C₂×#131	1	1	yes	characteristic
393	C₂×C₄	C₂×#131	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	C₈×D₄	1	4	yes	—
401	C₈	C₂×C₄×D₄	1	1	yes	characteristic
402	C₈	C₂×C₄×D₄	1	1	yes	characteristic
403	C₈	C₄×#41	1	1	yes	characteristic
404	C₈	C₄×#41	1	1	yes	characteristic
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂²×C₄×C₈	1	1	yes	characteristic
416	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
417	C₂²	C₈×#41	1	1	yes	characteristic
418	C₂²	C₂×#504	1	2	yes	—
419	C₂²	#3407	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	C₄²×D₄	1	1	yes	characteristic
429	C₄	C₄×#131	1	1	yes	characteristic
430	C₄	C₂×C₈×D₄	1	1	yes	characteristic
431	C₄	C₈×#41	1	1	yes	characteristic
432	C₂	—	4	2	no	—
433	C₂	—	4	2	no	—
434	C₂	C₄×C₈×D₄	1	1	yes	characteristic
435	C₂	#33324	1	1	yes	characteristic
436	C₂	C₄×#504	1	1	yes	characteristic
437	C₂	#33436	1	2	yes	—
438	C₂	#33483	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
3. C₂×#2108	C₂	semidirect
4. C₂×C₄×M₃₂	C₂	semidirect
6. #12663	C₂	semidirect
7. C₁₆×C₄⋊C₄	C₂	semidirect
8. #12654	C₂	semidirect
9. #12612	C₂	semidirect
10. #12612	C₂	semidirect
11. #12612	C₂	semidirect
12. C₁₆×C₂²⋊C₄	C₂	semidirect
13. #12600	C₂	semidirect
14. C₄×C₂²⋊C₁₆	C₂	semidirect
15. #12539	C₂	semidirect
25. #2169	C₄	semidirect
26. #2168	C₄	semidirect
78. C₂×M₃₂	C₂×C₄	semidirect
81. C₂²×C₁₆	C₂×C₄	semidirect
123. C₄⋊C₁₆	C₂×C₄	semidirect
124. C₄⋊C₁₆	C₂×C₄	semidirect
127. C₂²⋊C₁₆	C₂×C₄	semidirect
128. C₂²⋊C₁₆	C₂×C₄	semidirect
132. #346	C₂×C₄	semidirect
133. #346	D₄	semidirect
140. 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×#2169	2
C₂×#2168	2
C₂×#2108	2
C₂×C₄×M₃₂	2
#20484	2
#12663	2
C₁₆×C₄⋊C₄	2
#12654	2
#12612	2
C₁₆×C₂²⋊C₄	2
#12600	2
C₄×C₂²⋊C₁₆	2
#12539	2