Subgroups — #184568

Order 512.

667 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21430	C₂	1	1	yes	maximal, characteristic
2	#21430	C₂	1	1	yes	maximal, characteristic
3	#20809	C₂	1	1	yes	maximal, characteristic
4	#8265	C₂	1	1	yes	maximal, characteristic, complemented
5	#8265	C₂	1	1	yes	maximal, characteristic, complemented
6	#8264	C₂	1	1	yes	maximal, characteristic, complemented
7	#8264	C₂	1	1	yes	maximal, characteristic, complemented
8	#8261	C₂	1	1	yes	maximal, characteristic, complemented
9	#8260	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#8149	C₂	1	1	yes	maximal, characteristic
13	#8148	C₂	1	1	yes	maximal, characteristic
14	#8148	C₂	1	1	yes	maximal, characteristic
15	#8148	C₂	1	1	yes	maximal, characteristic
16	C₂×#431	C₂²	1	1	yes	characteristic
17	C₂×#431	C₂²	1	1	yes	characteristic
18	C₄×#117	C₂²	1	1	yes	characteristic
19	#1923	C₄	1	2	yes	—
20	#1923	C₄	1	2	yes	—
21	#1923	C₄	1	2	yes	—
22	#1923	C₄	1	2	yes	—
23	#1916	C₄	1	2	yes	—
24	#1916	C₄	1	2	yes	—
25	#1916	C₄	1	2	yes	—
26	#1916	C₄	1	2	yes	—
27	#1843	C₄	1	2	yes	—
28	#1832	C₄	1	2	yes	—
29	#1798	C₄	1	2	yes	—
30	#1798	C₄	1	2	yes	—
31	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	#1744	C₂²	1	1	yes	characteristic
44	#1744	C₂²	1	1	yes	characteristic
45	C₄²×C₈	C₂²	1	1	yes	characteristic
46	C₄²×C₈	C₂²	1	1	yes	characteristic
47	C₂×#322	C₂²	1	1	yes	characteristic
48	C₂×#322	C₂²	1	1	yes	characteristic
49	C₂×#322	C₂²	1	1	yes	characteristic
50	C₂×#322	C₂²	1	1	yes	characteristic
51	C₂×#322	C₂²	1	1	yes	characteristic
52	C₂×C₈²	C₂²	1	1	yes	characteristic
53	C₂×C₈²	C₂²	1	1	yes	characteristic
54	C₂×C₈²	C₂²	1	1	yes	characteristic
55	#1273	C₂²	1	1	yes	characteristic
56	#1273	C₂²	1	1	yes	characteristic
57	#1273	C₂²	1	1	yes	characteristic
58	#1273	C₂²	1	1	yes	characteristic
59	#1273	C₂²	1	1	yes	characteristic
60	#1273	C₂²	1	1	yes	characteristic
61	#1273	C₂²	1	1	yes	characteristic
62	#1273	C₂²	1	1	yes	characteristic
63	C₂×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×#117	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄²	C₂³	1	1	yes	characteristic
66	#431	—	4	1	no	—
67	#431	—	4	1	no	—
68	#431	—	4	1	no	—
69	#431	—	4	1	no	—
70	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
87	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
88	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
89	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
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	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	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂³	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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₄×C₂²⋊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	#376	C₂×C₄	1	1	yes	characteristic
111	#376	C₂×C₄	1	1	yes	characteristic
112	C₄³	C₂³	1	1	yes	characteristic
113	C₄³	C₂³	1	1	yes	characteristic
114	#336	C₂×C₄	1	2	yes	—
115	#336	C₂×C₄	1	2	yes	—
116	#336	C₂×C₄	1	2	yes	—
117	#336	C₂×C₄	1	2	yes	—
118	#336	C₂×C₄	1	2	yes	—
119	#336	C₂×C₄	1	2	yes	—
120	#336	C₂×C₄	1	2	yes	—
121	#336	C₂×C₄	1	2	yes	—
122	#336	C₂×C₄	1	2	yes	—
123	#336	C₂×C₄	1	2	yes	—
124	#336	C₂×C₄	1	2	yes	—
125	#336	C₂×C₄	1	2	yes	—
126	#336	C₂×C₄	1	2	yes	—
127	#336	C₂×C₄	1	2	yes	—
128	#336	C₂×C₄	1	2	yes	—
129	#336	C₂×C₄	1	2	yes	—
130	#322	—	4	1	no	—
131	#322	—	4	1	no	—
132	#322	—	4	1	no	—
133	#322	—	4	1	no	—
134	#322	—	4	1	no	—
135	C₈²	—	4	1	no	—
136	C₈²	—	4	1	no	—
137	C₈²	—	4	1	no	—
138	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₈	C₂²×C₄	1	2	yes	—
142	C₂²×C₈	C₂²×C₄	1	2	yes	—
143	C₂²×C₈	C₂²×C₄	1	2	yes	—
144	C₂²×C₈	C₂²×C₄	1	2	yes	—
145	C₂²×C₈	C₂²×C₄	1	2	yes	—
146	C₂²×C₈	C₂²×C₄	1	2	yes	—
147	C₂²×C₈	C₂²×C₄	1	2	yes	—
148	C₂²×C₈	C₂²×C₄	1	2	yes	—
149	C₂²×C₈	C₂²×C₄	1	2	yes	—
150	C₂²×C₈	C₂²×C₄	1	2	yes	—
151	C₂²×C₈	C₂²×C₄	1	2	yes	—
152	C₂²×C₈	C₂²×C₄	1	2	yes	—
153	#117	—	2	4	no	—
154	#117	—	2	4	no	—
155	C₂×C₄⋊C₄	C₄²	1	1	yes	characteristic
156	C₂×C₄⋊C₄	C₄²	1	1	yes	characteristic
157	C₂×C₄⋊C₄	C₄²	1	1	yes	characteristic
158	C₂×C₄⋊C₄	C₄²	1	1	yes	characteristic
159	C₂×C₂²⋊C₄	C₄²	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	C₄²	1	1	yes	characteristic
161	C₂×C₂²⋊C₄	C₄²	1	1	yes	characteristic
162	C₂×C₂²⋊C₄	C₄²	1	1	yes	characteristic
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	—	2	1	no	—
165	C₂×C₄²	—	2	1	no	—
166	C₂×C₄²	—	2	1	no	—
167	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄²	C₂²×C₄	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×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	C₂⁴	1	1	yes	characteristic
183	C₄⋊C₈	—	2	4	no	—
184	C₄⋊C₈	—	2	4	no	—
185	C₄⋊C₈	—	2	4	no	—
186	C₄⋊C₈	—	2	4	no	—
187	C₄⋊C₈	—	2	4	no	—
188	C₄⋊C₈	—	2	4	no	—
189	C₄⋊C₈	—	2	4	no	—
190	C₄⋊C₈	—	4	2	no	—
191	C₄⋊C₈	—	4	2	no	—
192	C₄⋊C₈	—	4	2	no	—
193	C₂²⋊C₈	—	2	4	no	—
194	C₂²⋊C₈	—	2	4	no	—
195	C₂²⋊C₈	—	2	4	no	—
196	C₂²⋊C₈	—	4	2	no	—
197	C₂²⋊C₈	—	4	2	no	—
198	C₂²⋊C₈	—	4	2	no	—
199	C₄×C₈	—	2	4	no	—
200	C₄×C₈	—	2	4	no	—
201	C₄×C₈	—	2	4	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₄×C₈	—	2	1	no	—
207	C₄×C₈	—	2	1	no	—
208	C₄×C₈	—	2	1	no	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	2	1	no	—
211	C₄×C₈	—	2	1	no	—
212	C₄×C₈	—	2	1	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	—	2	1	no	—
226	C₄×C₈	—	4	2	no	—
227	#95	C₄²	1	1	yes	characteristic
228	#95	C₄²	1	1	yes	characteristic
229	#95	C₄²	1	1	yes	characteristic
230	#95	C₄²	1	1	yes	characteristic
231	#95	C₄²	1	1	yes	characteristic
232	#95	C₄²	1	1	yes	characteristic
233	#95	C₄²	1	1	yes	characteristic
234	#95	C₄²	1	1	yes	characteristic
235	C₂⁴	C₂×C₄²	1	1	yes	characteristic
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	1	no	—
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
253	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	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	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	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	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	#131	1	4	yes	—
296	C₂×C₈	#131	1	4	yes	—
297	C₂×C₈	#131	1	4	yes	—
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	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	#131	1	4	yes	—
323	C₄²	#131	1	4	yes	—
324	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
325	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
326	C₄²	2₋¹⁺⁴	1	1	yes	characteristic
327	C₄²	2₋¹⁺⁴	1	1	yes	characteristic
328	C₂³	—	2	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	C₂²×C₄²	1	1	yes	characteristic
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	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	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	#405	1	2	yes	—
372	C₂×C₄	#405	1	2	yes	—
373	C₂×C₄	#405	1	2	yes	—
374	C₂×C₄	#405	1	2	yes	—
375	C₂×C₄	#518	1	1	yes	characteristic
376	C₂×C₄	#519	1	1	yes	characteristic
377	C₂×C₄	#520	1	1	yes	characteristic
378	C₂×C₄	#520	1	1	yes	characteristic
379	C₂×C₄	#520	1	1	yes	characteristic
380	C₂×C₄	#520	1	1	yes	characteristic
381	C₂×C₄	C₂×#131	1	2	yes	—
382	C₂×C₄	C₂×#131	1	2	yes	—
383	C₂×C₄	C₂×#131	1	2	yes	—
384	C₂×C₄	C₂×#131	1	2	yes	—
385	C₂×C₄	C₂×#131	1	2	yes	—
386	C₂×C₄	#568	1	2	yes	—
387	C₈	—	2	4	no	—
388	C₈	—	2	4	no	—
389	C₈	—	2	4	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	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	—	4	1	no	—
406	C₂²	#2274	1	1	yes	characteristic
407	C₂²	C₂×#405	1	1	yes	characteristic
408	C₂²	C₂×#405	1	1	yes	characteristic
409	C₂²	C₄×#131	1	1	yes	characteristic
410	C₂²	C₄×#131	1	1	yes	characteristic
411	C₂²	C₄×#131	1	1	yes	characteristic
412	C₂²	#2875	1	1	yes	characteristic
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	#2979	1	2	yes	—
425	C₄	#2986	1	2	yes	—
426	C₄	#2992	1	2	yes	—
427	C₄	#2993	1	2	yes	—
428	C₄	#2994	1	2	yes	—
429	C₄	#2994	1	2	yes	—
430	C₂	—	8	1	no	—
431	C₂	#17328	1	1	yes	characteristic
432	C₂	#17328	1	1	yes	characteristic
433	C₂	#17330	1	1	yes	characteristic
434	C₂	#17331	1	1	yes	characteristic
435	C₂	#20538	1	1	yes	characteristic
436	C₂	#20552	1	1	yes	characteristic
437	C₂	#20553	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄²	C₂⁴
commutator, socle	C₂³	C₂²×C₄²
prime radical	C₂⁴	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #8265	C₂	semidirect
5. #8265	C₂	semidirect
6. #8264	C₂	semidirect
7. #8264	C₂	semidirect
8. #8261	C₂	semidirect
9. #8260	C₂	semidirect
10. C₈×C₄⋊C₈	C₂	semidirect
11. C₈×C₄⋊C₈	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21430	2
#20809	2
#8265	2
#8264	2
#8261	2
#8260	2
C₈×C₄⋊C₈	2
#8149	2
#8148	2