Subgroups — #496721

Order 512.

560 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×#2164	C₂	1	1	yes	maximal, characteristic
2	C₂×#2151	C₂	1	1	yes	maximal, characteristic
3	#20474	C₂	1	1	yes	maximal, characteristic
4	#13160	C₂	1	1	yes	maximal, characteristic, complemented
5	#13160	C₂	1	1	yes	maximal, characteristic, complemented
6	#13159	C₂	1	1	yes	maximal, characteristic, complemented
7	#13159	C₂	1	1	yes	maximal, characteristic, complemented
8	#12913	C₂	1	1	yes	maximal, characteristic
9	#12913	C₂	1	1	yes	maximal, characteristic
10	#12912	C₂	1	1	yes	maximal, characteristic
11	#12912	C₂	1	1	yes	maximal, characteristic
12	#12899	C₂	1	1	yes	maximal, characteristic, complemented
13	#12898	C₂	1	1	yes	maximal, characteristic, complemented
14	#12880	C₂	1	1	yes	maximal, characteristic, complemented
15	#12879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂×#433	C₄	1	1	yes	characteristic
19	C₂×#405	C₂²	1	1	yes	characteristic
20	#2298	C₄	1	1	yes	characteristic
21	#2164	—	2	4	no	—
22	#2151	—	2	4	no	—
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×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₂×#346	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	#1771	C₄	1	1	yes	characteristic
42	#1771	C₄	1	1	yes	characteristic
43	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	#1753	C₄	1	1	yes	characteristic
46	#1753	C₄	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	#1746	C₄	1	1	yes	characteristic
50	#1745	C₄	1	1	yes	characteristic
51	#1726	C₂²	1	1	yes	characteristic
52	C₄²×C₈	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	C₂³	1	1	yes	characteristic
63	C₂×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×M₃₂	—	2	2	no	—
65	C₂×M₃₂	—	4	1	no	—
66	C₂×M₃₂	—	4	1	no	—
67	C₂²×C₁₆	—	2	2	no	—
68	C₂²×C₁₆	—	4	1	no	—
69	C₂²×C₁₆	—	4	1	no	—
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	#433	—	2	4	no	—
79	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
83	#405	D₄	1	4	yes	—
84	#405	Q₈	1	4	yes	—
85	C₂×#97	C₂×C₄	1	1	yes	characteristic
86	C₂×#97	C₂×C₄	1	1	yes	characteristic
87	C₂×#97	C₂×C₄	1	1	yes	characteristic
88	C₂×#97	C₂×C₄	1	1	yes	characteristic
89	C₂×#97	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂×C₄	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	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
99	#388	C₈	1	1	yes	characteristic
100	#388	C₈	1	1	yes	characteristic
101	#388	C₈	1	1	yes	characteristic
102	#388	C₈	1	1	yes	characteristic
103	#387	C₈	1	1	yes	characteristic
104	#387	C₈	1	1	yes	characteristic
105	#387	C₈	1	1	yes	characteristic
106	#387	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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	#376	C₂×C₄	1	1	yes	characteristic
112	C₄³	C₂×C₄	1	1	yes	characteristic
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	C₄⋊C₁₆	—	2	2	no	—
119	C₄⋊C₁₆	—	4	1	no	—
120	C₄⋊C₁₆	—	4	1	no	—
121	C₄⋊C₁₆	—	4	1	no	—
122	C₄⋊C₁₆	—	4	1	no	—
123	C₄⋊C₁₆	—	4	1	no	—
124	C₄⋊C₁₆	—	4	1	no	—
125	C₄⋊C₁₆	—	4	1	no	—
126	C₄⋊C₁₆	—	4	1	no	—
127	C₂²⋊C₁₆	—	2	2	no	—
128	C₂²⋊C₁₆	—	2	2	no	—
129	#346	—	2	2	no	—
130	C₄×C₁₆	—	2	2	no	—
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	#336	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂×M₁₆	—	4	1	no	—
141	C₂×M₁₆	—	4	1	no	—
142	C₂×M₁₆	C₄⋊C₄	1	4	yes	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	2	1	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	1	no	—
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	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	C₂×D₄	1	2	yes	—
155	C₂²×C₈	C₂×Q₈	1	2	yes	—
156	C₂²×C₈	C₂⁴	1	1	yes	characteristic
157	#117	C₄⋊C₄	1	4	yes	—
158	#117	M₁₆	1	4	yes	—
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×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
171	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
172	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
173	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
174	C₂×C₄²	C₂×C₈	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×C₄²	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
181	M₃₂	—	4	4	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	—	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	—	4	4	no	—
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	—	2	2	no	—
209	C₂²⋊C₈	—	2	2	no	—
210	C₂²⋊C₈	—	2	2	no	—
211	#97	—	2	2	no	—
212	#97	—	4	1	no	—
213	#97	—	4	1	no	—
214	#97	C₄⋊C₄	1	4	yes	—
215	#97	C₄⋊C₄	1	4	yes	—
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	2	no	—
225	C₄×C₈	—	4	1	no	—
226	C₄×C₈	—	4	1	no	—
227	C₄×C₈	C₂×D₄	1	2	yes	—
228	C₄×C₈	C₂×D₄	1	2	yes	—
229	C₄×C₈	C₂×Q₈	1	2	yes	—
230	C₄×C₈	C₂×Q₈	1	2	yes	—
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	#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	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
249	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂×M₁₆	1	2	yes	—
263	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
264	M₁₆	—	4	4	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	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	C₂×C₄⋊C₄	1	2	yes	—
288	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
289	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
290	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
292	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
301	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
307	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	C₂×C₄⋊C₄	1	2	yes	—
321	C₄²	C₂×C₄⋊C₄	1	2	yes	—
322	C₄²	C₂×M₁₆	1	2	yes	—
323	C₄²	C₂×M₁₆	1	2	yes	—
324	C₁₆	—	4	1	no	—
325	C₁₆	—	4	1	no	—
326	C₁₆	—	4	1	no	—
327	C₁₆	—	4	1	no	—
328	C₁₆	—	4	1	no	—
329	C₁₆	—	4	1	no	—
330	C₁₆	—	4	1	no	—
331	C₁₆	—	4	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₂×C₄⋊C₈	1	2	yes	—
339	C₂³	C₂³×C₈	1	1	yes	characteristic
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	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	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	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	C₂×C₄⋊C₈	1	2	yes	—
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	2	yes	—
382	C₂×C₄	#504	1	2	yes	—
383	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
384	C₂×C₄	#520	1	1	yes	characteristic
385	C₂×C₄	#520	1	1	yes	characteristic
386	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
387	C₂×C₄	#568	1	1	yes	characteristic
388	C₂×C₄	#568	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	#535	1	1	yes	characteristic
397	C₈	#536	1	1	yes	characteristic
398	C₈	#544	1	1	yes	characteristic
399	C₈	#544	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂²×C₄⋊C₈	1	1	yes	characteristic
408	C₂²	#2988	1	1	yes	characteristic
409	C₂²	#2988	1	1	yes	characteristic
410	C₂²	C₂×#504	1	1	yes	characteristic
411	C₂²	C₂×#504	1	1	yes	characteristic
412	C₂²	#3407	1	1	yes	characteristic
413	C₂²	#3407	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	#2317	1	1	yes	characteristic
428	C₄	#2905	1	1	yes	characteristic
429	C₄	#2989	1	1	yes	characteristic
430	C₄	#2989	1	1	yes	characteristic
431	C₂	—	4	2	no	—
432	C₂	#21972	1	1	yes	characteristic
433	C₂	#33398	1	1	yes	characteristic
434	C₂	#33398	1	1	yes	characteristic
435	C₂	#33506	1	1	yes	characteristic
436	C₂	#33507	1	1	yes	characteristic
437	C₂	#33508	1	1	yes	characteristic
438	C₂	#33509	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
4. #13160	C₂	semidirect
5. #13160	C₂	semidirect
6. #13159	C₂	semidirect
7. #13159	C₂	semidirect
12. #12899	C₂	semidirect
13. #12898	C₂	semidirect
14. #12880	C₂	semidirect
15. #12879	C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2164	2
C₂×#2151	2
#20474	2
#13160	2
#13159	2
#12913	2
#12912	2
#12899	2
#12898	2
#12880	2
#12879	2