Subgroups — #497159

Order 512.

536 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#13264	C₂	1	1	yes	maximal, characteristic, complemented
3	#13263	C₂	1	1	yes	maximal, characteristic, complemented
4	#13160	C₂	1	1	yes	maximal, characteristic, complemented
5	#13159	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	#13104	C₂	1	1	yes	maximal, characteristic, complemented
9	#13104	C₂	1	1	yes	maximal, characteristic, complemented
10	#12912	C₂	1	1	yes	maximal, characteristic
11	#12912	C₂	1	1	yes	maximal, characteristic
12	#12783	C₂	1	1	yes	maximal, characteristic
13	#12611	C₂	1	1	yes	maximal, characteristic
14	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₂×#1374	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	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
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×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×#346	C₂²	1	1	yes	characteristic
30	C₂×#346	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
33	#1984	C₄	1	1	yes	characteristic
34	#1939	C₄	1	1	yes	characteristic
35	#1916	C₄	1	1	yes	characteristic
36	#1916	C₄	1	1	yes	characteristic
37	#1850	C₄	1	1	yes	characteristic
38	#1850	C₄	1	1	yes	characteristic
39	#1797	C₄	1	1	yes	characteristic
40	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	#1374	C₂²	1	1	yes	characteristic
46	#1374	C₂²	1	1	yes	characteristic
47	#1374	C₂²	1	1	yes	characteristic
48	#1374	C₂²	1	1	yes	characteristic
49	#1374	C₂²	1	1	yes	characteristic
50	#1374	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	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊Q₈	C₈	1	1	yes	characteristic
62	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₁₆	—	2	2	no	—
65	C₂²×C₁₆	—	4	1	no	—
66	C₂²×C₁₆	—	4	1	no	—
67	C₂²×C₁₆	—	4	1	no	—
68	C₂²×C₁₆	—	4	1	no	—
69	C₂²×C₁₆	Q₈	1	4	yes	complemented
70	C₂²×C₁₆	C₂³	1	1	yes	characteristic
71	C₂²×C₁₆	C₂³	1	1	yes	characteristic
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	C₈×Q₈	—	4	1	no	—
79	C₈×Q₈	—	4	1	no	—
80	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×C₈	—	4	1	no	—
89	C₂×C₄×C₈	—	4	1	no	—
90	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂³	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	#391	C₈	1	1	yes	characteristic
99	#389	C₈	1	1	yes	characteristic
100	#387	C₈	1	1	yes	characteristic
101	#387	C₈	1	1	yes	characteristic
102	#385	C₈	1	1	yes	characteristic
103	#385	C₈	1	1	yes	characteristic
104	#380	C₈	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₄⋊C₁₆	—	4	1	no	—
111	C₄⋊C₁₆	—	4	1	no	—
112	C₄⋊C₁₆	—	4	1	no	—
113	C₄⋊C₁₆	—	4	1	no	—
114	C₄⋊C₁₆	—	4	1	no	—
115	C₄⋊C₁₆	—	4	1	no	—
116	C₂²⋊C₁₆	—	2	2	no	—
117	C₂²⋊C₁₆	—	2	2	no	—
118	#346	—	4	1	no	—
119	#346	—	4	1	no	—
120	C₄×C₁₆	—	4	1	no	—
121	C₄×C₁₆	—	4	1	no	—
122	#336	C₂×C₄	1	1	yes	characteristic
123	#336	C₂×C₄	1	1	yes	characteristic
124	#336	C₂×C₄	1	1	yes	characteristic
125	#336	C₂×C₄	1	1	yes	characteristic
126	#336	C₂×C₄	1	1	yes	characteristic
127	#336	C₂×C₄	1	1	yes	characteristic
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	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
133	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
134	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
135	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	4	1	no	—
142	C₂²×C₈	—	4	1	no	—
143	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₈	C₂×Q₈	1	2	yes	—
151	C₂²×C₈	#41	1	2	yes	—
152	C₂²×C₈	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Q₈	—	2	4	no	—
154	C₄×Q₈	—	4	1	no	—
155	C₄×Q₈	—	4	1	no	—
156	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
158	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
161	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
166	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
167	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
168	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
169	C₂×C₄²	—	4	1	no	—
170	C₂×C₄²	—	4	1	no	—
171	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
172	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
173	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₁₆	—	2	1	no	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	2	1	no	—
184	C₂×C₁₆	—	2	1	no	—
185	C₂×C₁₆	—	2	1	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	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	—	4	4	no	—
202	C₂×C₁₆	—	4	4	no	—
203	C₂×C₁₆	C₂×Q₈	1	2	yes	—
204	C₂×C₁₆	C₂×Q₈	1	2	yes	—
205	C₄⋊C₈	—	4	1	no	—
206	C₄⋊C₈	—	4	1	no	—
207	C₄⋊C₈	—	4	1	no	—
208	C₄⋊C₈	—	4	1	no	—
209	C₄⋊C₈	—	4	1	no	—
210	C₄⋊C₈	—	4	1	no	—
211	C₂²⋊C₈	—	2	2	no	—
212	C₂²⋊C₈	—	2	2	no	—
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	—	2	1	no	—
218	C₄×C₈	—	2	1	no	—
219	C₄×C₈	—	2	1	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	—	4	1	no	—
226	C₄×C₈	—	4	1	no	—
227	#95	C₂×C₈	1	1	yes	characteristic
228	#95	C₂×C₈	1	1	yes	characteristic
229	#95	C₂×C₈	1	1	yes	characteristic
230	#95	C₂×C₈	1	1	yes	characteristic
231	#95	C₂×C₈	1	1	yes	characteristic
232	#95	C₂×C₈	1	1	yes	characteristic
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	C₂⁴	C₂²×C₈	1	1	yes	characteristic
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	4	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	4	1	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	C₄×Q₈	1	2	yes	—
252	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	#131	1	2	yes	—
266	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	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	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	1	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	C₄×Q₈	1	2	yes	—
293	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
294	C₂×C₈	C₂×#41	1	1	yes	characteristic
295	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	M₃₂	1	4	yes	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
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	—	4	1	no	—
325	C₄²	—	4	1	no	—
326	C₁₆	—	2	2	no	—
327	C₁₆	—	2	2	no	—
328	C₁₆	—	4	1	no	—
329	C₁₆	—	4	1	no	—
330	C₁₆	—	4	1	no	—
331	C₁₆	—	4	1	no	—
332	C₁₆	—	4	1	no	—
333	C₁₆	—	4	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₈×Q₈	1	2	yes	—
339	C₂³	C₂×M₃₂	1	2	yes	—
340	C₂³	#504	1	2	yes	—
341	C₂³	C₂³×C₈	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	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	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	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	—	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	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	C₈×Q₈	1	2	yes	—
384	C₂×C₄	C₂×M₃₂	1	2	yes	—
385	C₂×C₄	C₂×M₃₂	1	2	yes	—
386	C₂×C₄	#504	1	2	yes	—
387	C₂×C₄	#504	1	2	yes	—
388	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
389	C₂×C₄	#518	1	1	yes	characteristic
390	C₂×C₄	#520	1	1	yes	characteristic
391	C₂×C₄	C₂×#131	1	1	yes	characteristic
392	C₂×C₄	#568	1	1	yes	characteristic
393	C₂×C₄	#568	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	#538	1	1	yes	characteristic
402	C₈	#539	1	1	yes	characteristic
403	C₈	#543	1	1	yes	characteristic
404	C₈	#544	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	#2183	1	4	yes	—
412	C₂²	C₂×C₈×Q₈	1	1	yes	characteristic
413	C₂²	#2972	1	1	yes	characteristic
414	C₂²	#2988	1	1	yes	characteristic
415	C₂²	C₂²×M₃₂	1	1	yes	characteristic
416	C₂²	C₂×#504	1	1	yes	characteristic
417	C₂²	C₂×#504	1	1	yes	characteristic
418	C₂²	C₂×#504	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	#2329	1	1	yes	characteristic
433	C₄	#2961	1	1	yes	characteristic
434	C₄	#2976	1	1	yes	characteristic
435	C₄	#2992	1	1	yes	characteristic
436	C₂	—	2	4	no	—
437	C₂	#22287	1	1	yes	characteristic
438	C₂	C₂×#2183	1	1	yes	characteristic
439	C₂	#33474	1	1	yes	characteristic
440	C₂	#33488	1	1	yes	characteristic
441	C₂	#33491	1	1	yes	characteristic
442	C₂	#33504	1	1	yes	characteristic
443	C₂	#33508	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
2. #13264	C₂	semidirect
3. #13263	C₂	semidirect
4. #13160	C₂	semidirect
5. #13159	C₂	semidirect
6. #13105	C₂	semidirect
7. #13105	C₂	semidirect
8. #13104	C₂	semidirect
9. #13104	C₂	semidirect
69. C₂²×C₁₆	Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₈×C₂²⋊Q₈	2
#13264	2
#13263	2
#13160	2
#13159	2
#13105	2
#13104	2
#12912	2
#12783	2
#12611	2
C₁₆×C₂²⋊C₄	2
C₂×#1374	2