Subgroups — #191548

Order 512.

722 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21976	C₂	1	1	yes	maximal, characteristic
2	#21974	C₂	1	1	yes	maximal, characteristic
3	#20472	C₂	1	1	yes	maximal, characteristic
4	C₂×#1572	C₂	1	1	yes	maximal, characteristic
5	C₂×#1570	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	#8811	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	#8807	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×#423	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
22	C₄×#117	C₂²	1	1	yes	characteristic
23	#1940	—	2	2	no	—
24	#1939	—	2	2	no	—
25	#1851	—	2	2	no	—
26	#1850	—	2	2	no	—
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	#1831	C₂²	1	1	yes	characteristic
34	#1831	C₂²	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	#1771	C₄	1	1	yes	characteristic
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	#1572	—	2	4	no	—
48	#1570	—	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×#334	C₂²	1	1	yes	characteristic
58	C₂×#334	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	Q₈	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	#423	—	2	2	no	—
80	#423	—	2	2	no	—
81	C₂×C₄⋊C₈	—	2	2	no	—
82	C₂×C₄⋊C₈	—	2	2	no	—
83	C₂×C₄⋊C₈	—	2	1	no	—
84	C₂×C₄⋊C₈	—	2	1	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	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₈	C₂×C₄	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×C₂²⋊C₈	—	2	1	no	—
100	C₂×C₂²⋊C₈	—	2	1	no	—
101	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₄×M₁₆	D₄	1	4	yes	—
104	C₄×M₁₆	Q₈	1	4	yes	—
105	C₂×#97	—	2	1	no	—
106	C₂×#97	C₂×C₄	1	1	yes	characteristic
107	C₂×#97	C₂×C₄	1	1	yes	characteristic
108	C₂×#97	C₂×C₄	1	1	yes	characteristic
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×C₄×C₈	—	2	1	no	—
113	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
121	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₄×C₄⋊C₄	D₄	1	2	yes	—
124	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₄×C₂²⋊C₄	D₄	1	2	yes	—
127	#376	Q₈	1	2	yes	—
128	C₄³	C₂³	1	1	yes	characteristic
129	C₄³	C₂³	1	1	yes	characteristic
130	#336	—	2	2	no	—
131	#336	—	2	2	no	—
132	#336	—	2	2	no	—
133	#336	—	2	2	no	—
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	#336	C₂×C₄	1	1	yes	characteristic
140	#336	C₂×C₄	1	1	yes	characteristic
141	#336	C₂×C₄	1	1	yes	characteristic
142	#335	—	2	2	no	—
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	#334	—	2	2	no	—
149	#334	—	2	2	no	—
150	#334	—	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	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
159	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	4	1	no	—
164	C₂×M₁₆	—	4	1	no	—
165	C₂×M₁₆	—	4	2	no	—
166	C₂×M₁₆	—	8	2	no	—
167	C₂×M₁₆	C₄⋊C₄	1	4	yes	—
168	C₂×M₁₆	C₄⋊C₄	1	4	yes	—
169	C₂²×C₈	—	2	1	no	—
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	—	4	2	no	—
178	C₂²×C₈	—	8	2	no	—
179	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
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	#117	—	4	4	no	—
188	C₂×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
189	C₂×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
190	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
191	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
192	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
198	C₂×C₄²	C₂×D₄	1	2	yes	—
199	C₂×C₄²	C₂×D₄	1	2	yes	—
200	C₂×C₄²	C₂×D₄	1	2	yes	—
201	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
202	C₂×C₄²	C₂×Q₈	1	2	yes	—
203	C₂×C₄²	C₂×Q₈	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	1	yes	characteristic
207	C₂×C₄²	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
225	C₄⋊C₈	—	4	2	no	—
226	C₄⋊C₈	—	8	2	no	—
227	C₄⋊C₈	—	8	2	no	—
228	C₄⋊C₈	—	8	2	no	—
229	C₄⋊C₈	—	8	2	no	—
230	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
231	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
232	C₂²⋊C₈	—	4	2	no	—
233	C₂²⋊C₈	—	4	2	no	—
234	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
235	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
236	#97	—	2	2	no	—
237	#97	—	2	2	no	—
238	#97	—	4	1	no	—
239	#97	—	4	1	no	—
240	#97	—	4	2	no	—
241	#97	C₄⋊C₄	1	4	yes	—
242	#97	C₄⋊C₄	1	4	yes	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	—	4	1	no	—
246	C₄×C₈	—	4	1	no	—
247	C₄×C₈	—	4	2	no	—
248	C₄×C₈	C₂×D₄	1	2	yes	—
249	C₄×C₈	C₂×D₄	1	2	yes	—
250	C₄×C₈	C₂×D₄	1	2	yes	—
251	C₄×C₈	C₂×D₄	1	2	yes	—
252	C₄×C₈	C₂×Q₈	1	2	yes	—
253	C₄×C₈	C₂×Q₈	1	2	yes	—
254	C₄×C₈	C₂×Q₈	1	2	yes	—
255	C₄×C₈	C₂×Q₈	1	2	yes	—
256	#95	C₄⋊C₄	1	2	yes	—
257	#95	C₄⋊C₄	1	2	yes	—
258	#95	C₄⋊C₄	1	2	yes	—
259	#95	C₄⋊C₄	1	2	yes	—
260	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
269	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
270	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
271	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
272	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
273	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
277	C₂²×C₄	#127	1	2	yes	—
278	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
279	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
280	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
281	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
284	M₁₆	—	2	8	no	—
285	M₁₆	—	4	4	no	—
286	M₁₆	—	8	4	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	—	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	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	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	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	2	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	—	8	4	no	—
318	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
319	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
320	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
321	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
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	#131	1	2	yes	—
327	C₂×C₈	#131	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	4	2	no	—
346	C₄²	C₂×C₄⋊C₄	1	2	yes	—
347	C₄²	C₂×C₄⋊C₄	1	2	yes	—
348	C₄²	#127	1	2	yes	—
349	C₄²	C₄⋊Q₈	1	2	yes	—
350	C₄²	C₄⋊Q₈	1	2	yes	—
351	C₄²	C₄⋊Q₈	1	2	yes	—
352	C₄²	C₂²×D₄	1	1	yes	characteristic
353	C₄²	C₂²×D₄	1	1	yes	characteristic
354	C₄²	C₂²×Q₈	1	1	yes	characteristic
355	C₄²	C₂²×Q₈	1	1	yes	characteristic
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	#384	1	2	yes	—
361	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	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	4	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	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	#384	1	2	yes	—
388	C₂×C₄	#384	1	2	yes	—
389	C₂×C₄	#384	1	2	yes	—
390	C₂×C₄	#430	1	4	yes	—
391	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
393	C₂×C₄	C₂×#127	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
396	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
397	C₂×C₄	C₂×#131	1	1	yes	characteristic
398	C₂×C₄	C₂×#131	1	1	yes	characteristic
399	C₂×C₄	#568	1	1	yes	characteristic
400	C₂×C₄	#568	1	1	yes	characteristic
401	C₂×C₄	#577	1	2	yes	—
402	C₂×C₄	#577	1	2	yes	—
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	8	1	no	—
411	C₈	—	8	1	no	—
412	C₈	—	8	1	no	—
413	C₈	—	8	1	no	—
414	C₈	—	8	1	no	—
415	C₈	—	8	1	no	—
416	C₈	—	8	1	no	—
417	C₈	—	8	1	no	—
418	C₈	#424	1	4	yes	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	C₂×#384	1	1	yes	characteristic
425	C₂²	#2906	1	1	yes	characteristic
426	C₂²	#2906	1	1	yes	characteristic
427	C₂²	#2912	1	2	yes	—
428	C₂²	C₂×#430	1	2	yes	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	C₂×#424	1	1	yes	characteristic
439	C₄	#2905	1	1	yes	characteristic
440	C₄	#2906	1	1	yes	characteristic
441	C₄	#2906	1	1	yes	characteristic
442	C₄	#3154	1	1	yes	characteristic
443	C₄	#3154	1	1	yes	characteristic
444	C₄	#3163	1	2	yes	—
445	C₂	—	4	2	no	—
446	C₂	#17838	1	2	yes	—
447	C₂	#17841	1	2	yes	—
448	C₂	#20793	1	1	yes	characteristic
449	C₂	#20802	1	1	yes	characteristic
450	C₂	#20806	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. #8811	C₂	semidirect
11. #8809	C₂	semidirect
12. #8808	C₂	semidirect
13. #8808	C₂	semidirect
14. #8807	C₂	semidirect
15. #8805	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21976	2
#21974	2
#20472	2
C₂×#1572	2
C₂×#1570	2
C₂×#1569	2
C₂×#1565	2
#8812	2
#8811	2
#8809	2
#8808	2
#8807	2
#8805	2