Subgroups — #495963

Order 512.

616 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2183	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#346	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	#13264	C₂	1	1	yes	maximal, characteristic, complemented
5	#13160	C₂	1	1	yes	maximal, characteristic, complemented
6	#13105	C₂	1	1	yes	maximal, characteristic, complemented
7	#13105	C₂	1	1	yes	maximal, characteristic, complemented
8	#12912	C₂	1	1	yes	maximal, characteristic
9	#12912	C₂	1	1	yes	maximal, characteristic
10	#12783	C₂	1	1	yes	maximal, characteristic
11	#12663	C₂	1	1	yes	maximal, characteristic, complemented
12	#12663	C₂	1	1	yes	maximal, characteristic, complemented
13	#12662	C₂	1	1	yes	maximal, characteristic, complemented
14	#12611	C₂	1	1	yes	maximal, characteristic
15	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	#2183	—	2	4	no	—
22	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×#346	—	2	4	no	—
31	C₂×#346	C₂²	1	1	yes	characteristic
32	C₂×#346	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×#346	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
39	#1984	C₄	1	1	yes	characteristic
40	#1939	C₄	1	1	yes	characteristic
41	#1916	C₄	1	1	yes	characteristic
42	#1916	C₄	1	1	yes	characteristic
43	#1850	C₄	1	1	yes	characteristic
44	#1850	C₄	1	1	yes	characteristic
45	#1797	C₄	1	1	yes	characteristic
46	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₈×C₂²⋊C₄	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	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊Q₈	C₈	1	1	yes	characteristic
64	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₁₆	—	2	2	no	—
67	C₂²×C₁₆	—	2	2	no	—
68	C₂²×C₁₆	—	2	2	no	—
69	C₂²×C₁₆	—	2	2	no	—
70	C₂²×C₁₆	—	2	2	no	—
71	C₂²×C₁₆	Q₈	1	4	yes	complemented
72	C₂²×C₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₁₆	C₂³	1	1	yes	characteristic
74	C₂²×C₁₆	C₂³	1	1	yes	characteristic
75	C₂²×C₁₆	C₂³	1	1	yes	characteristic
76	C₂²×C₁₆	C₂³	1	1	yes	characteristic
77	C₂²×C₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₁₆	C₂³	1	1	yes	characteristic
79	C₂²×C₁₆	C₂³	1	1	yes	characteristic
80	C₈×Q₈	—	2	2	no	—
81	C₈×Q₈	—	2	2	no	—
82	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×C₈	—	2	2	no	—
91	C₂×C₄×C₈	—	2	2	no	—
92	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
100	#391	C₈	1	1	yes	characteristic
101	#389	C₈	1	1	yes	characteristic
102	#387	C₈	1	1	yes	characteristic
103	#387	C₈	1	1	yes	characteristic
104	#385	C₈	1	1	yes	characteristic
105	#385	C₈	1	1	yes	characteristic
106	#380	C₈	1	1	yes	characteristic
107	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₄⋊C₁₆	—	2	2	no	—
113	C₄⋊C₁₆	—	2	2	no	—
114	C₄⋊C₁₆	—	2	2	no	—
115	C₄⋊C₁₆	—	2	2	no	—
116	C₄⋊C₁₆	—	2	2	no	—
117	C₄⋊C₁₆	—	2	2	no	—
118	C₂²⋊C₁₆	—	2	2	no	—
119	C₂²⋊C₁₆	—	2	2	no	—
120	#346	—	2	2	no	—
121	#346	—	2	2	no	—
122	#346	—	2	2	no	—
123	#346	—	2	2	no	—
124	#346	—	2	2	no	—
125	#346	D₄	1	4	yes	—
126	C₄×C₁₆	—	2	2	no	—
127	C₄×C₁₆	—	2	2	no	—
128	#336	C₂×C₄	1	1	yes	characteristic
129	#336	C₂×C₄	1	1	yes	characteristic
130	#336	C₂×C₄	1	1	yes	characteristic
131	#336	C₂×C₄	1	1	yes	characteristic
132	#336	C₂×C₄	1	1	yes	characteristic
133	#336	C₂×C₄	1	1	yes	characteristic
134	#336	C₂×C₄	1	1	yes	characteristic
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	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
139	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
140	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
141	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	2	1	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₈	C₂×Q₈	1	2	yes	—
157	C₂²×C₈	#41	1	2	yes	—
158	C₂²×C₈	C₂⁴	1	1	yes	characteristic
159	C₂²⋊Q₈	—	2	4	no	—
160	C₄×Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
166	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
168	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₂×C₄²	—	2	2	no	—
176	C₂×C₄²	—	2	2	no	—
177	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
178	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
179	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₁₆	—	2	8	no	—
186	C₂×C₁₆	—	2	1	no	—
187	C₂×C₁₆	—	2	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₂×C₁₆	—	2	1	no	—
192	C₂×C₁₆	—	2	8	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	C₂×D₄	1	2	yes	—
206	C₂×C₁₆	C₂×D₄	1	2	yes	—
207	C₂×C₁₆	C₂×Q₈	1	2	yes	—
208	C₂×C₁₆	C₂×Q₈	1	2	yes	—
209	C₂×C₁₆	#41	1	2	yes	—
210	C₂×C₁₆	#41	1	2	yes	—
211	C₄⋊C₈	—	2	2	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	—	2	2	no	—
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	2	2	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	C₂²⋊C₈	—	2	2	no	—
219	C₄×C₈	—	2	2	no	—
220	C₄×C₈	—	2	1	no	—
221	C₄×C₈	—	2	1	no	—
222	C₄×C₈	—	2	1	no	—
223	C₄×C₈	—	2	1	no	—
224	C₄×C₈	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	2	no	—
231	C₄×C₈	C₂×D₄	1	2	yes	—
232	C₄×C₈	#41	1	2	yes	—
233	#95	C₂×C₈	1	1	yes	characteristic
234	#95	C₂×C₈	1	1	yes	characteristic
235	#95	C₂×C₈	1	1	yes	characteristic
236	#95	C₂×C₈	1	1	yes	characteristic
237	#95	C₂×C₈	1	1	yes	characteristic
238	#95	C₂×C₈	1	1	yes	characteristic
239	#95	C₂×C₈	1	1	yes	characteristic
240	#95	C₂×C₈	1	1	yes	characteristic
241	#95	C₂×C₈	1	1	yes	characteristic
242	#95	C₂×C₈	1	1	yes	characteristic
243	C₂⁴	C₂²×C₈	1	1	yes	characteristic
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	4	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	C₄×Q₈	1	2	yes	—
258	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
271	C₂²×C₄	#131	1	2	yes	—
272	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₈	—	2	8	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	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	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	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	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	C₄×D₄	1	2	yes	—
297	C₂×C₈	C₄×Q₈	1	2	yes	—
298	C₂×C₈	#131	1	2	yes	—
299	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
301	C₂×C₈	C₂×#41	1	1	yes	characteristic
302	C₂×C₈	C₂×#41	1	1	yes	characteristic
303	C₂×C₈	C₂×#41	1	1	yes	characteristic
304	C₂×C₈	C₂×#41	1	1	yes	characteristic
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	M₃₂	1	4	yes	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
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	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	C₄×D₄	1	2	yes	—
331	C₄²	#131	1	2	yes	—
332	C₁₆	—	2	2	no	—
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₁₆	—	4	1	no	—
336	C₁₆	—	4	1	no	—
337	C₁₆	—	4	1	no	—
338	C₁₆	—	4	1	no	—
339	C₁₆	C₂²⋊Q₈	1	4	yes	complemented
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	C₈×Q₈	1	2	yes	—
345	C₂³	C₂×M₃₂	1	2	yes	—
346	C₂³	#504	1	2	yes	—
347	C₂³	C₂³×C₈	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	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	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	C₈×D₄	1	2	yes	—
390	C₂×C₄	C₈×D₄	1	2	yes	—
391	C₂×C₄	C₈×Q₈	1	2	yes	—
392	C₂×C₄	C₂×M₃₂	1	2	yes	—
393	C₂×C₄	C₂×M₃₂	1	2	yes	—
394	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
396	C₂×C₄	C₄×#41	1	1	yes	characteristic
397	C₂×C₄	C₂×#131	1	1	yes	characteristic
398	C₂×C₄	C₂×#131	1	1	yes	characteristic
399	C₂×C₄	C₂×#131	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	C₂×C₂²⋊Q₈	1	1	yes	characteristic
408	C₈	#525	1	1	yes	characteristic
409	C₈	#529	1	1	yes	characteristic
410	C₈	#533	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	#2183	1	4	yes	complemented
418	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
419	C₂²	C₂×C₈×Q₈	1	1	yes	characteristic
420	C₂²	C₈×#41	1	1	yes	characteristic
421	C₂²	C₂²×M₃₂	1	1	yes	characteristic
422	C₂²	C₂×#504	1	1	yes	characteristic
423	C₂²	#3407	1	1	yes	characteristic
424	C₂²	#3407	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	C₄×C₂²⋊Q₈	1	1	yes	characteristic
439	C₄	#2929	1	1	yes	characteristic
440	C₄	#2960	1	1	yes	characteristic
441	C₄	#2966	1	1	yes	characteristic
442	C₂	—	2	4	no	—
443	C₂	C₈×C₂²⋊Q₈	1	1	yes	characteristic
444	C₂	#33436	1	1	yes	characteristic
445	C₂	D₄×M₃₂	1	1	yes	characteristic
446	C₂	C₂×#2183	1	1	yes	characteristic
447	C₂	#33475	1	1	yes	characteristic
448	C₂	#33482	1	1	yes	characteristic
449	C₂	#33484	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂⁴	C₂²×C₈
LCS	G ▷ C₂³ ▷ 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
1. C₂×#2183	C₂	semidirect
4. #13264	C₂	semidirect
5. #13160	C₂	semidirect
6. #13105	C₂	semidirect
7. #13105	C₂	semidirect
11. #12663	C₂	semidirect
12. #12663	C₂	semidirect
13. #12662	C₂	semidirect
71. C₂²×C₁₆	Q₈	semidirect
339. C₁₆	C₂²⋊Q₈	semidirect
417. C₂²	#2183	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2183	2
C₂²×#346	2
C₈×C₂²⋊Q₈	2
#13264	2
#13160	2
#13105	2
#12912	2
#12783	2
#12663	2
#12662	2
#12611	2
C₁₆×C₂²⋊C₄	2