Subgroups — #498390

Order 512.

531 conjugacy classes of subgroups.

The subgroup lattice has 438 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	C₂×#2164	C₂	1	1	yes	maximal, characteristic
3	#21601	C₂	1	1	yes	maximal, characteristic
4	#13263	C₂	1	1	yes	maximal, characteristic, complemented
5	#13160	C₂	1	1	yes	maximal, characteristic, complemented
6	#13121	C₂	1	1	yes	maximal, characteristic
7	#13120	C₂	1	1	yes	maximal, characteristic
8	#13120	C₂	1	1	yes	maximal, characteristic
9	#13120	C₂	1	1	yes	maximal, characteristic
10	#13105	C₂	1	1	yes	maximal, characteristic, complemented
11	#13104	C₂	1	1	yes	maximal, characteristic, complemented
12	#12662	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	#12600	C₂	1	1	yes	maximal, characteristic
16	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
17	C₂×#405	C₂²	1	1	yes	characteristic
18	#2396	C₄	1	1	yes	characteristic
19	#2183	—	2	4	no	—
20	#2164	—	2	4	no	—
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×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
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×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×C₄×C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
39	#1985	C₄	1	1	yes	characteristic
40	#1940	C₄	1	1	yes	characteristic
41	#1917	C₄	1	1	yes	characteristic
42	#1917	C₄	1	1	yes	characteristic
43	#1851	C₄	1	1	yes	characteristic
44	#1851	C₄	1	1	yes	characteristic
45	#1798	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	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
64	C₂×#117	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₁₆	C₂³	1	1	yes	characteristic
66	C₂²×C₁₆	C₂³	1	1	yes	characteristic
67	C₂²×C₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₁₆	C₂³	1	1	yes	characteristic
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	C₈×Q₈	—	2	2	no	—
74	C₈×Q₈	—	2	2	no	—
75	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
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	—	2	2	no	—
84	#405	—	2	2	no	—
85	C₂×#97	C₂×C₄	1	1	yes	characteristic
86	C₂×#97	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
93	#400	C₈	1	1	yes	characteristic
94	#399	C₈	1	1	yes	characteristic
95	#398	C₈	1	1	yes	characteristic
96	#398	C₈	1	1	yes	characteristic
97	#396	C₈	1	1	yes	characteristic
98	#396	C₈	1	1	yes	characteristic
99	#395	C₈	1	1	yes	characteristic
100	#393	C₈	1	1	yes	characteristic
101	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₁₆	—	2	2	no	—
107	C₄⋊C₁₆	—	2	2	no	—
108	C₄⋊C₁₆	—	2	2	no	—
109	C₄⋊C₁₆	—	2	2	no	—
110	C₄⋊C₁₆	—	2	2	no	—
111	C₄⋊C₁₆	D₄	1	4	yes	—
112	C₂²⋊C₁₆	—	2	2	no	—
113	C₂²⋊C₁₆	—	2	2	no	—
114	C₂²⋊C₁₆	—	2	2	no	—
115	C₂²⋊C₁₆	—	2	2	no	—
116	#346	—	2	2	no	—
117	#346	—	2	2	no	—
118	#346	—	2	2	no	—
119	C₄×C₁₆	—	2	2	no	—
120	C₄×C₁₆	—	2	2	no	—
121	C₄×C₁₆	—	2	2	no	—
122	C₄×C₁₆	—	2	2	no	—
123	C₄×C₁₆	—	2	2	no	—
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	#336	C₂×C₄	1	1	yes	characteristic
133	#336	C₂×C₄	1	1	yes	characteristic
134	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
135	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂×M₁₆	—	2	2	no	—
137	C₂×M₁₆	—	2	2	no	—
138	C₂×M₁₆	—	4	1	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₈	C₂⁴	1	1	yes	characteristic
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	#117	—	2	2	no	—
156	#117	—	2	2	no	—
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×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×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×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×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×C₄²	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
201	C₂×C₁₆	C₂×D₄	1	2	yes	—
202	C₂×C₁₆	#41	1	2	yes	—
203	C₂×C₁₆	#41	1	2	yes	—
204	C₄⋊C₈	—	2	2	no	—
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	—	2	2	no	—
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	—	2	2	no	—
209	C₄⋊C₈	—	2	2	no	—
210	C₂²⋊C₈	—	4	1	no	—
211	C₂²⋊C₈	—	4	1	no	—
212	#97	—	2	2	no	—
213	#97	—	2	2	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	C₂×D₄	1	2	yes	—
225	C₄×C₈	#41	1	2	yes	—
226	#95	C₂×C₈	1	1	yes	characteristic
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	C₂⁴	C₂²×C₈	1	1	yes	characteristic
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	4	1	no	—
240	C₂²×C₄	—	2	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	1	no	—
246	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
260	M₁₆	—	4	4	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	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	1	no	—
272	C₂×C₈	—	2	1	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	—	4	1	no	—
281	C₂×C₈	—	4	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	C₄×D₄	1	2	yes	—
285	C₂×C₈	#131	1	2	yes	—
286	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₈	C₂×#41	1	1	yes	characteristic
288	C₂×C₈	C₂×#41	1	1	yes	characteristic
289	C₂×C₈	C₂×#41	1	1	yes	characteristic
290	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
291	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	4	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	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	C₄×D₄	1	2	yes	—
320	C₄²	#131	1	2	yes	—
321	C₁₆	—	2	2	no	—
322	C₁₆	—	2	2	no	—
323	C₁₆	—	2	2	no	—
324	C₁₆	—	2	2	no	—
325	C₁₆	—	4	1	no	—
326	C₁₆	—	4	1	no	—
327	C₁₆	—	4	1	no	—
328	C₁₆	—	4	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	C₂³×C₈	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
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	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	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	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	C₈×D₄	1	2	yes	—
377	C₂×C₄	C₈×D₄	1	2	yes	—
378	C₂×C₄	#504	1	2	yes	—
379	C₂×C₄	#504	1	2	yes	—
380	C₂×C₄	#504	1	2	yes	—
381	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
382	C₂×C₄	C₄×#41	1	1	yes	characteristic
383	C₂×C₄	#519	1	1	yes	characteristic
384	C₂×C₄	C₂×#131	1	1	yes	characteristic
385	C₂×C₄	C₂×#131	1	1	yes	characteristic
386	C₂×C₄	#568	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	#547	1	1	yes	characteristic
395	C₈	#548	1	1	yes	characteristic
396	C₈	#552	1	1	yes	characteristic
397	C₈	#556	1	1	yes	characteristic
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
406	C₂²	C₈×#41	1	1	yes	characteristic
407	C₂²	#2982	1	1	yes	characteristic
408	C₂²	C₂×#504	1	1	yes	characteristic
409	C₂²	C₂×#504	1	1	yes	characteristic
410	C₂²	C₂×#504	1	1	yes	characteristic
411	C₂²	#3407	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	#2362	1	1	yes	characteristic
426	C₄	#2933	1	1	yes	characteristic
427	C₄	#2969	1	1	yes	characteristic
428	C₄	#2986	1	1	yes	characteristic
429	C₂	—	8	1	no	—
430	C₂	#23050	1	1	yes	characteristic
431	C₂	#33434	1	1	yes	characteristic
432	C₂	#33436	1	1	yes	characteristic
433	C₂	#33480	1	1	yes	characteristic
434	C₂	#33482	1	1	yes	characteristic
435	C₂	#33499	1	1	yes	characteristic
436	C₂	#33500	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. #13263	C₂	semidirect
5. #13160	C₂	semidirect
10. #13105	C₂	semidirect
11. #13104	C₂	semidirect
12. #12662	C₂	semidirect
13. C₁₆×C₄⋊C₄	C₂	semidirect
14. C₁₆×C₄⋊C₄	C₂	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
C₂×#2164	2
#21601	2
#13263	2
#13160	2
#13121	2
#13120	2
#13105	2
#13104	2
#12662	2
C₁₆×C₄⋊C₄	2
#12600	2