Subgroups — #191546

Order 512.

764 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20815	C₂	1	1	yes	maximal, characteristic
2	#20793	C₂	1	1	yes	maximal, characteristic
3	#20472	C₂	1	1	yes	maximal, characteristic
4	C₂×#1574	C₂	1	1	yes	maximal, characteristic
5	C₂×#1573	C₂	1	1	yes	maximal, characteristic
6	C₂×#1569	C₂	1	1	yes	maximal, characteristic
7	C₂×#1565	C₂	1	1	yes	maximal, characteristic
8	#8812	C₂	1	1	yes	maximal, characteristic, complemented
9	#8812	C₂	1	1	yes	maximal, characteristic, complemented
10	#8810	C₂	1	1	yes	maximal, characteristic, complemented
11	#8809	C₂	1	1	yes	maximal, characteristic, complemented
12	#8808	C₂	1	1	yes	maximal, characteristic, complemented
13	#8808	C₂	1	1	yes	maximal, characteristic, complemented
14	#8806	C₂	1	1	yes	maximal, characteristic, complemented
15	#8805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#432	C₂²	1	1	yes	characteristic
17	C₂×#431	C₂²	1	1	yes	characteristic
18	C₂×#431	C₂²	1	1	yes	characteristic
19	C₂×#424	—	2	2	no	—
20	C₂×#423	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
23	C₄×#117	C₂²	1	1	yes	characteristic
24	#1843	—	2	2	no	—
25	#1842	C₂²	1	1	yes	characteristic
26	#1842	C₂²	1	1	yes	characteristic
27	#1842	C₂²	1	1	yes	characteristic
28	#1842	C₂²	1	1	yes	characteristic
29	#1842	C₂²	1	1	yes	characteristic
30	#1842	C₂²	1	1	yes	characteristic
31	#1831	C₂²	1	1	yes	characteristic
32	#1831	C₂²	1	1	yes	characteristic
33	#1798	—	2	2	no	—
34	#1771	C₄	1	1	yes	characteristic
35	#1771	C₄	1	1	yes	characteristic
36	#1771	C₄	1	1	yes	characteristic
37	#1771	C₄	1	1	yes	characteristic
38	#1768	—	2	2	no	—
39	#1753	C₄	1	1	yes	characteristic
40	#1753	C₄	1	1	yes	characteristic
41	#1753	C₄	1	1	yes	characteristic
42	#1753	C₄	1	1	yes	characteristic
43	#1744	C₂²	1	1	yes	characteristic
44	#1744	C₂²	1	1	yes	characteristic
45	C₄×#97	C₂²	1	1	yes	characteristic
46	C₄²×C₈	C₂²	1	1	yes	characteristic
47	#1574	—	2	4	no	—
48	#1573	—	2	4	no	—
49	#1569	—	2	4	no	—
50	#1565	—	2	4	no	—
51	C₂×#335	C₂²	1	1	yes	characteristic
52	C₂×#335	C₂²	1	1	yes	characteristic
53	C₂×#335	C₂²	1	1	yes	characteristic
54	C₂×#335	C₂²	1	1	yes	characteristic
55	C₂×#335	C₂²	1	1	yes	characteristic
56	C₂×#335	C₂²	1	1	yes	characteristic
57	C₂×#335	C₂²	1	1	yes	characteristic
58	C₂×#335	C₂²	1	1	yes	characteristic
59	C₂×#334	C₂²	1	1	yes	characteristic
60	C₂×#334	C₂²	1	1	yes	characteristic
61	C₂×#334	C₂²	1	1	yes	characteristic
62	C₂×#334	C₂²	1	1	yes	characteristic
63	C₂×#334	C₂²	1	1	yes	characteristic
64	C₂×#334	C₂²	1	1	yes	characteristic
65	C₂×#334	C₂²	1	1	yes	characteristic
66	C₂×#334	C₂²	1	1	yes	characteristic
67	C₂²×M₁₆	—	2	1	no	—
68	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
69	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₈	—	2	1	no	—
71	C₂×#117	D₄	1	2	yes	—
72	C₂²×C₄²	C₂³	1	1	yes	characteristic
73	#432	—	2	2	no	—
74	#432	—	2	2	no	—
75	#431	—	2	2	no	—
76	#431	—	2	2	no	—
77	#431	D₄	1	4	yes	—
78	#431	Q₈	1	4	yes	—
79	#424	—	4	8	no	—
80	#423	—	2	2	no	—
81	#423	—	2	2	no	—
82	C₂×C₄⋊C₈	—	2	2	no	—
83	C₂×C₄⋊C₈	—	2	2	no	—
84	C₂×C₄⋊C₈	—	2	2	no	—
85	C₂×C₄⋊C₈	—	2	2	no	—
86	C₂×C₄⋊C₈	—	2	2	no	—
87	C₂×C₄⋊C₈	—	2	2	no	—
88	C₂×C₄⋊C₈	—	2	2	no	—
89	C₂×C₄⋊C₈	—	2	2	no	—
90	C₂×C₄⋊C₈	—	2	1	no	—
91	C₂×C₄⋊C₈	—	2	1	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	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₈	—	2	1	no	—
103	C₂×C₂²⋊C₈	—	2	1	no	—
104	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₄×M₁₆	D₄	1	4	yes	—
107	C₄×M₁₆	Q₈	1	4	yes	—
108	C₂×#97	—	2	1	no	—
109	C₂×#97	C₂×C₄	1	1	yes	characteristic
110	C₂×#97	C₂×C₄	1	1	yes	characteristic
111	C₂×#97	C₂×C₄	1	1	yes	characteristic
112	C₂×#97	C₂×C₄	1	1	yes	characteristic
113	C₂×#97	C₂×C₄	1	1	yes	characteristic
114	C₂×#97	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄×C₈	—	2	1	no	—
116	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
124	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₄×C₄⋊C₄	Q₈	1	2	yes	—
127	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
130	#376	D₄	1	2	yes	—
131	C₄³	C₂³	1	1	yes	characteristic
132	C₄³	C₂³	1	1	yes	characteristic
133	#336	—	2	2	no	—
134	#336	—	2	2	no	—
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	#336	C₂×C₄	1	1	yes	characteristic
140	#336	C₂×C₄	1	1	yes	characteristic
141	#336	C₂×C₄	1	1	yes	characteristic
142	#336	C₂×C₄	1	1	yes	characteristic
143	#335	—	2	2	no	—
144	#335	—	2	2	no	—
145	#335	—	2	2	no	—
146	#335	—	2	2	no	—
147	#335	—	2	2	no	—
148	#335	—	2	2	no	—
149	#335	—	2	2	no	—
150	#335	—	2	2	no	—
151	#334	—	2	2	no	—
152	#334	—	2	2	no	—
153	#334	—	2	2	no	—
154	#334	—	2	2	no	—
155	#334	—	2	2	no	—
156	#334	—	2	2	no	—
157	#334	—	2	2	no	—
158	#334	—	2	2	no	—
159	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
160	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	2	2	no	—
164	C₂×M₁₆	—	4	1	no	—
165	C₂×M₁₆	—	4	1	no	—
166	C₂×M₁₆	—	4	4	no	—
167	C₂×M₁₆	—	4	2	no	—
168	C₂×M₁₆	C₄⋊C₄	1	4	yes	—
169	C₂×M₁₆	C₄⋊C₄	1	4	yes	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	—	2	1	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	—	2	1	no	—
176	C₂²×C₈	—	2	1	no	—
177	C₂²×C₈	—	2	1	no	—
178	C₂²×C₈	—	4	4	no	—
179	C₂²×C₈	—	4	2	no	—
180	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
188	#117	—	2	4	no	—
189	#117	—	2	4	no	—
190	C₂×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
191	C₂×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
192	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
193	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
194	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄²	C₂×D₄	1	2	yes	—
200	C₂×C₄²	C₂×D₄	1	2	yes	—
201	C₂×C₄²	C₂×D₄	1	2	yes	—
202	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄²	C₂×D₄	1	2	yes	—
204	C₂×C₄²	C₂×Q₈	1	2	yes	—
205	C₂×C₄²	C₂×Q₈	1	2	yes	—
206	C₂×C₄²	C₂×Q₈	1	2	yes	—
207	C₂×C₄²	C₂×Q₈	1	2	yes	—
208	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
209	C₂×C₄²	C₂⁴	1	1	yes	characteristic
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	4	no	—
227	C₄⋊C₈	—	4	4	no	—
228	C₄⋊C₈	—	4	2	no	—
229	C₄⋊C₈	—	4	2	no	—
230	C₄⋊C₈	—	4	4	no	—
231	C₄⋊C₈	—	4	4	no	—
232	C₄⋊C₈	—	4	4	no	—
233	C₄⋊C₈	—	4	4	no	—
234	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
235	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
236	C₂²⋊C₈	—	4	2	no	—
237	C₂²⋊C₈	—	4	2	no	—
238	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
239	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
240	#97	—	2	2	no	—
241	#97	—	2	2	no	—
242	#97	—	4	1	no	—
243	#97	—	4	1	no	—
244	#97	—	4	2	no	—
245	#97	C₄⋊C₄	1	4	yes	—
246	#97	C₄⋊C₄	1	4	yes	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	4	1	no	—
250	C₄×C₈	—	4	1	no	—
251	C₄×C₈	—	4	2	no	—
252	C₄×C₈	C₂×D₄	1	2	yes	—
253	C₄×C₈	C₂×D₄	1	2	yes	—
254	C₄×C₈	C₂×D₄	1	2	yes	—
255	C₄×C₈	C₂×D₄	1	2	yes	—
256	C₄×C₈	C₂×Q₈	1	2	yes	—
257	C₄×C₈	C₂×Q₈	1	2	yes	—
258	C₄×C₈	C₂×Q₈	1	2	yes	—
259	C₄×C₈	C₂×Q₈	1	2	yes	—
260	#95	C₄⋊C₄	1	2	yes	—
261	#95	C₄⋊C₄	1	2	yes	—
262	#95	C₄⋊C₄	1	2	yes	—
263	#95	C₄⋊C₄	1	2	yes	—
264	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
273	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
274	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
275	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
276	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
280	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
281	C₂²×C₄	#127	1	2	yes	—
282	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
283	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
284	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
285	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
288	M₁₆	—	2	8	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	8	4	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	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	8	4	no	—
322	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
323	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
324	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
325	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
326	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
327	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
328	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
329	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
330	C₂×C₈	#131	1	2	yes	—
331	C₂×C₈	#131	1	2	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	C₂×C₄⋊C₄	1	2	yes	—
349	C₄²	C₂×C₄⋊C₄	1	2	yes	—
350	C₄²	#127	1	2	yes	—
351	C₄²	C₄⋊Q₈	1	2	yes	—
352	C₄²	C₄⋊Q₈	1	2	yes	—
353	C₄²	C₄⋊Q₈	1	2	yes	—
354	C₄²	AGL(1,ℤ/8)	1	4	yes	—
355	C₄²	#137	1	4	yes	—
356	C₄²	C₂²×D₄	1	1	yes	characteristic
357	C₄²	C₂²×D₄	1	1	yes	characteristic
358	C₄²	C₂²×Q₈	1	1	yes	characteristic
359	C₄²	C₂²×Q₈	1	1	yes	characteristic
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	#384	1	2	yes	—
365	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#384	1	2	yes	—
391	C₂×C₄	#384	1	2	yes	—
392	C₂×C₄	#384	1	2	yes	—
393	C₂×C₄	#428	1	4	yes	—
394	C₂×C₄	#428	1	4	yes	—
395	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
397	C₂×C₄	C₂×#127	1	1	yes	characteristic
398	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
401	C₂×C₄	C₂×#131	1	1	yes	characteristic
402	C₂×C₄	C₂×#131	1	1	yes	characteristic
403	C₂×C₄	#568	1	1	yes	characteristic
404	C₂×C₄	#568	1	1	yes	characteristic
405	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
406	C₂×C₄	C₂×#137	1	2	yes	—
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	8	1	no	—
415	C₈	—	8	1	no	—
416	C₈	—	8	1	no	—
417	C₈	—	8	1	no	—
418	C₈	—	8	1	no	—
419	C₈	—	8	1	no	—
420	C₈	—	8	1	no	—
421	C₈	—	8	1	no	—
422	C₈	#424	1	4	yes	complemented
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	C₂×#384	1	1	yes	characteristic
429	C₂²	#2906	1	1	yes	characteristic
430	C₂²	#2906	1	1	yes	characteristic
431	C₂²	C₂×#428	1	2	yes	—
432	C₂²	#2916	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	C₂×#424	1	1	yes	characteristic
443	C₄	#2905	1	1	yes	characteristic
444	C₄	#2906	1	1	yes	characteristic
445	C₄	#2906	1	1	yes	characteristic
446	C₄	#3151	1	1	yes	characteristic
447	C₄	#3152	1	1	yes	characteristic
448	C₄	#3165	1	2	yes	—
449	C₂	—	4	2	no	—
450	C₂	#17830	1	2	yes	—
451	C₂	#17832	1	2	yes	—
452	C₂	#20793	1	1	yes	characteristic
453	C₂	#20800	1	1	yes	characteristic
454	C₂	#20807	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator	C₂²×C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	C₂²×C₄⋊C₄
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
8. #8812	C₂	semidirect
9. #8812	C₂	semidirect
10. #8810	C₂	semidirect
11. #8809	C₂	semidirect
12. #8808	C₂	semidirect
13. #8808	C₂	semidirect
14. #8806	C₂	semidirect
15. #8805	C₂	semidirect
422. C₈	#424	semidirect

Maximal subgroups

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

subgroup	index
#20815	2
#20793	2
#20472	2
C₂×#1574	2
C₂×#1573	2
C₂×#1569	2
C₂×#1565	2
#8812	2
#8810	2
#8809	2
#8808	2
#8806	2
#8805	2