Subgroups — #203991

Order 512.

605 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21993	C₂	1	1	yes	maximal, characteristic
2	#20535	C₂	1	1	yes	maximal, characteristic
3	#17822	C₂	1	1	yes	maximal, characteristic
4	#17816	C₂	1	1	yes	maximal, characteristic
5	#17806	C₂	1	1	yes	maximal, characteristic
6	#9632	C₂	1	1	yes	maximal, characteristic, complemented
7	#9632	C₂	1	1	yes	maximal, characteristic, complemented
8	#9631	C₂	1	1	yes	maximal, characteristic, complemented
9	#9630	C₂	1	1	yes	maximal, characteristic, complemented
10	#9629	C₂	1	1	yes	maximal, characteristic, complemented
11	#9629	C₂	1	1	yes	maximal, characteristic, complemented
12	#9628	C₂	1	1	yes	maximal, characteristic, complemented
13	#9627	C₂	1	1	yes	maximal, characteristic, complemented
14	#8098	C₂	1	1	yes	maximal, characteristic
15	C₂×#1303	C₂	1	1	yes	maximal, characteristic
16	#2920	C₂²	1	1	yes	characteristic
17	#2920	C₂²	1	1	yes	characteristic
18	C₂×#432	C₂²	1	1	yes	characteristic
19	C₂×#431	C₂²	1	1	yes	characteristic
20	C₂×#431	C₂²	1	1	yes	characteristic
21	C₂×#423	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	#1950	—	2	1	no	—
24	#1950	—	2	1	no	—
25	#1855	—	2	1	no	—
26	#1855	—	2	1	no	—
27	#1848	C₂²	1	1	yes	characteristic
28	#1848	C₂²	1	1	yes	characteristic
29	#1837	C₂²	1	1	yes	characteristic
30	#1837	C₂²	1	1	yes	characteristic
31	#1771	—	2	1	no	—
32	#1771	—	2	1	no	—
33	#1770	C₂²	1	1	yes	characteristic
34	#1770	C₂²	1	1	yes	characteristic
35	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	#1749	—	2	1	no	—
38	C₄×C₂²⋊C₈	—	2	1	no	—
39	#1574	C₄	1	2	yes	complemented
40	#1574	C₄	1	2	yes	complemented
41	#1573	—	2	2	no	—
42	#1573	C₄	1	2	yes	complemented
43	#1573	C₄	1	2	yes	complemented
44	#1572	—	2	2	no	—
45	#1571	C₂²	1	1	yes	characteristic
46	#1571	C₂²	1	1	yes	characteristic
47	#1571	C₂²	1	1	yes	characteristic
48	#1571	C₂²	1	1	yes	characteristic
49	#1570	C₂²	1	1	yes	characteristic
50	#1570	C₂²	1	1	yes	characteristic
51	#1570	C₂²	1	1	yes	characteristic
52	#1570	C₂²	1	1	yes	characteristic
53	#1569	—	2	2	no	—
54	#1568	—	2	2	no	—
55	#1564	C₂²	1	1	yes	characteristic
56	#1564	C₂²	1	1	yes	characteristic
57	#1564	C₂²	1	1	yes	characteristic
58	#1564	C₂²	1	1	yes	characteristic
59	#1303	C₂²	1	1	yes	characteristic
60	#1303	C₂²	1	1	yes	characteristic
61	#1303	C₂²	1	1	yes	characteristic
62	#1303	C₂²	1	1	yes	characteristic
63	#1303	C₂²	1	1	yes	characteristic
64	#1303	C₂²	1	1	yes	characteristic
65	#1303	C₂²	1	1	yes	characteristic
66	#1303	C₂²	1	1	yes	characteristic
67	C₂²×M₁₆	—	2	1	no	—
68	C₂²×C₄⋊C₄	—	2	1	no	—
69	C₂²×C₄²	—	2	1	no	—
70	C₂²×C₄²	C₂³	1	1	yes	characteristic
71	#432	—	2	1	no	—
72	#432	—	2	1	no	—
73	#432	—	2	1	no	—
74	#432	—	2	1	no	—
75	#432	—	2	1	no	—
76	#432	C₂×C₄	1	2	yes	—
77	#432	D₄	1	2	yes	—
78	#432	D₄	1	2	yes	—
79	#431	—	2	1	no	—
80	#431	—	2	1	no	—
81	#431	—	2	1	no	—
82	#431	—	2	1	no	—
83	#431	—	2	1	no	—
84	#431	C₂×C₄	1	2	yes	—
85	#431	C₂×C₄	1	1	yes	characteristic
86	#431	C₂×C₄	1	1	yes	characteristic
87	#431	C₂×C₄	1	1	yes	characteristic
88	#431	C₂×C₄	1	1	yes	characteristic
89	#431	Q₈	1	1	yes	characteristic
90	#431	Q₈	1	1	yes	characteristic
91	#431	Q₈	1	1	yes	characteristic
92	#431	Q₈	1	1	yes	characteristic
93	#431	C₂³	1	1	yes	characteristic
94	#431	C₂³	1	1	yes	characteristic
95	#431	C₂³	1	1	yes	characteristic
96	#431	C₂³	1	1	yes	characteristic
97	C₂×#108	—	2	1	no	—
98	C₂×#108	—	2	1	no	—
99	C₂×#108	—	2	1	no	—
100	C₂×#108	—	2	1	no	—
101	#423	—	2	1	no	—
102	#423	—	2	1	no	—
103	#423	—	2	1	no	—
104	#423	C₂×C₄	1	2	yes	—
105	#423	C₂³	1	1	yes	characteristic
106	#423	C₂³	1	1	yes	characteristic
107	#423	C₂³	1	1	yes	characteristic
108	#423	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₈	—	2	1	no	—
110	C₂×C₄⋊C₈	—	2	1	no	—
111	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
112	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	#407	—	2	1	no	—
117	#407	—	2	1	no	—
118	C₂×C₂²⋊C₈	—	2	1	no	—
119	C₂×C₂²⋊C₈	—	2	1	no	—
120	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
122	C₄×M₁₆	—	2	1	no	—
123	C₄×M₁₆	—	2	1	no	—
124	C₂×#97	—	2	1	no	—
125	C₂×#97	—	2	1	no	—
126	C₂×#97	—	2	1	no	—
127	C₂×C₄×C₈	—	2	1	no	—
128	C₂×C₄×C₈	—	2	1	no	—
129	C₂×C₄×C₈	—	2	1	no	—
130	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
132	C₄×C₄⋊C₄	—	2	1	no	—
133	C₄×C₄⋊C₄	—	2	1	no	—
134	C₄×C₄⋊C₄	Q₈	1	2	yes	—
135	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×#95	Q₈	1	2	yes	—
138	#341	—	2	1	no	—
139	#341	—	2	1	no	—
140	#341	—	2	1	no	—
141	#341	—	2	1	no	—
142	#336	—	2	1	no	—
143	#336	—	2	1	no	—
144	#336	—	2	1	no	—
145	#336	—	2	1	no	—
146	#335	—	2	2	no	—
147	#335	—	2	2	no	—
148	#335	—	2	2	no	—
149	#335	—	2	2	no	—
150	#335	C₂×C₄	1	2	yes	complemented
151	#335	C₂×C₄	1	2	yes	complemented
152	#335	C₂×C₄	1	2	yes	complemented
153	#335	C₂×C₄	1	2	yes	complemented
154	#334	—	2	2	no	—
155	#334	—	2	2	no	—
156	#334	—	2	2	no	—
157	#334	—	2	2	no	—
158	#334	C₂×C₄	1	2	yes	complemented
159	#334	C₂×C₄	1	2	yes	complemented
160	#334	C₂×C₄	1	2	yes	complemented
161	#334	C₂×C₄	1	2	yes	complemented
162	C₂³×C₄	—	2	2	no	—
163	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
165	C₂³×C₄	#41	1	1	yes	characteristic
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	—	2	1	no	—
169	C₂×M₁₆	—	2	1	no	—
170	C₂×M₁₆	—	2	1	no	—
171	C₂×M₁₆	—	4	1	no	—
172	C₂×M₁₆	—	8	1	no	—
173	C₂×M₁₆	—	8	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	—	2	1	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	4	1	no	—
178	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	2	1	no	—
185	C₂×C₄⋊C₄	—	4	4	no	—
186	C₂×C₄²	—	2	1	no	—
187	C₂×C₄²	—	2	1	no	—
188	C₂×C₄²	—	2	2	no	—
189	C₂×C₄²	—	8	1	no	—
190	C₂×C₄²	—	8	1	no	—
191	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
197	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
198	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
199	C₂×C₄²	#41	1	1	yes	characteristic
200	C₂×C₄²	#41	1	1	yes	characteristic
201	C₂×C₄²	#41	1	1	yes	characteristic
202	C₂×C₄²	C₂⁴	1	1	yes	characteristic
203	#108	—	8	1	no	—
204	#108	—	8	1	no	—
205	#108	—	8	1	no	—
206	#108	—	8	1	no	—
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	—	2	2	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	—	4	1	no	—
220	C₄⋊C₈	—	4	1	no	—
221	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
222	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
223	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
224	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
225	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
226	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
227	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
228	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
229	C₄⋊C₈	C₂²×C₄	1	2	yes	—
230	C₄⋊C₈	C₂²×C₄	1	2	yes	—
231	C₄⋊C₈	C₂²×C₄	1	2	yes	—
232	C₄⋊C₈	C₂²×C₄	1	2	yes	—
233	C₄⋊C₈	C₂×D₄	1	2	yes	—
234	C₄⋊C₈	C₂×D₄	1	2	yes	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	1	no	—
240	C₂²⋊C₈	—	2	1	no	—
241	C₂²⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	4	1	no	—
244	C₂²⋊C₈	—	4	1	no	—
245	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
246	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
247	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
248	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
249	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
250	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
251	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
252	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
253	#97	—	2	2	no	—
254	#97	—	2	2	no	—
255	#97	—	2	2	no	—
256	#97	—	4	1	no	—
257	#97	—	8	1	no	—
258	#97	—	8	1	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	4	1	no	—
265	C₄×C₈	—	8	1	no	—
266	C₄×C₈	—	8	1	no	—
267	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
268	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
269	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
270	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
271	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
272	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
273	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
274	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
275	#95	—	2	2	no	—
276	#95	C₂×Q₈	1	2	yes	—
277	#95	C₂×Q₈	1	2	yes	—
278	C₂⁴	C₂²⋊Q₈	1	1	yes	characteristic
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	8	2	no	—
290	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
293	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
294	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
295	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
296	C₂²×C₄	#121	1	1	yes	characteristic
297	C₂²×C₄	#121	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
301	C₂²×C₄	#125	1	1	yes	characteristic
302	C₂²×C₄	#125	1	1	yes	characteristic
303	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
304	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
307	C₂²×C₄	C₂×#41	1	1	yes	characteristic
308	M₁₆	—	4	1	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	8	2	no	—
317	M₁₆	—	8	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	8	2	no	—
341	C₂×C₈	—	8	2	no	—
342	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	8	2	no	—
358	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
359	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
360	C₄²	C₄×D₄	1	1	yes	characteristic
361	C₄²	C₄×D₄	1	1	yes	characteristic
362	C₄²	C₄×Q₈	1	1	yes	characteristic
363	C₄²	C₄×Q₈	1	1	yes	characteristic
364	C₄²	#121	1	1	yes	characteristic
365	C₄²	#121	1	1	yes	characteristic
366	C₄²	#125	1	1	yes	characteristic
367	C₄²	#125	1	1	yes	characteristic
368	C₄²	C₄⋊Q₈	1	1	yes	characteristic
369	C₄²	C₄⋊Q₈	1	1	yes	characteristic
370	C₄²	C₂³×C₄	1	1	yes	characteristic
371	C₄²	C₂²×D₄	1	1	yes	characteristic
372	C₄²	C₂²×Q₈	1	1	yes	characteristic
373	C₄²	C₂×#41	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	#389	1	1	yes	characteristic
379	C₂³	#389	1	1	yes	characteristic
380	C₂³	C₂×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	8	no	—
410	C₂×C₄	#389	1	1	yes	characteristic
411	C₂×C₄	#389	1	1	yes	characteristic
412	C₂×C₄	#389	1	1	yes	characteristic
413	C₂×C₄	#389	1	1	yes	characteristic
414	C₂×C₄	#389	1	1	yes	characteristic
415	C₂×C₄	#389	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
419	C₂×C₄	C₂×#121	1	1	yes	characteristic
420	C₂×C₄	C₂×#125	1	1	yes	characteristic
421	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
422	C₂×C₄	#576	1	1	yes	characteristic
423	C₂×C₄	#577	1	1	yes	characteristic
424	C₂×C₄	#577	1	1	yes	characteristic
425	C₂×C₄	#578	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₈	—	8	1	no	—
441	C₈	—	8	1	no	—
442	C₈	—	8	1	no	—
443	C₈	—	8	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	#1953	1	2	yes	—
454	C₂²	C₂×#389	1	1	yes	characteristic
455	C₂²	#3081	1	1	yes	characteristic
456	C₂²	#3082	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	4	no	—
467	C₄	—	8	2	no	—
468	C₄	#2912	1	1	yes	characteristic
469	C₄	#2913	1	1	yes	characteristic
470	C₄	#2956	1	2	yes	—
471	C₄	#3045	1	1	yes	characteristic
472	C₄	#3046	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	2	no	—
476	C₂	—	4	1	no	—
477	C₂	#21165	1	1	yes	characteristic
478	C₂	#21175	1	1	yes	characteristic
479	C₂	C₂×#1953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#121
commutator	C₄²	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	C₂×#389
prime radical	C₂⁴	C₂²⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
6. #9632	C₂	semidirect
7. #9632	C₂	semidirect
8. #9631	C₂	semidirect
9. #9630	C₂	semidirect
10. #9629	C₂	semidirect
11. #9629	C₂	semidirect
12. #9628	C₂	semidirect
13. #9627	C₂	semidirect
39. #1574	C₄	semidirect
40. #1574	C₄	semidirect
42. #1573	C₄	semidirect
43. #1573	C₄	semidirect
150. #335	C₂×C₄	semidirect
151. #335	C₂×C₄	semidirect
152. #335	C₂×C₄	semidirect
153. #335	C₂×C₄	semidirect
158. #334	C₂×C₄	semidirect
159. #334	C₂×C₄	semidirect
160. #334	C₂×C₄	semidirect
161. #334	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#21993	2
#20535	2
#17822	2
#17816	2
#17806	2
#9632	2
#9631	2
#9630	2
#9629	2
#9628	2
#9627	2
#8098	2
C₂×#1303	2