Subgroups — #7622720

Order 512.

1351 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60204	C₂	1	1	yes	maximal, characteristic
2	#33508	C₂	1	4	yes	maximal, complemented
3	#33507	C₂	1	4	yes	maximal, complemented
4	#33505	C₂	1	2	yes	maximal, complemented
5	#33504	C₂	1	2	yes	maximal, complemented
6	#33503	C₂	1	2	yes	maximal, complemented
7	#33502	C₂	1	2	yes	maximal, complemented
8	#33474	C₂	1	2	yes	maximal, complemented
9	#33436	C₂	1	4	yes	maximal, complemented
10	#33434	C₂	1	2	yes	maximal, complemented
11	#33423	C₂	1	2	yes	maximal, complemented
12	C₂×#2162	C₂	1	1	yes	maximal, characteristic, complemented
13	#33398	C₂	1	2	yes	maximal, complemented
14	C₂×#2150	C₂	1	1	yes	maximal, characteristic, complemented
15	#3444	C₄	1	1	yes	characteristic
16	C₂×#504	C₂²	1	4	yes	—
17	C₂²×M₃₂	C₂²	1	2	yes	—
18	#2966	C₄	1	2	yes	—
19	#2966	C₄	1	2	yes	—
20	#2966	C₂²	1	2	yes	—
21	#2966	C₂²	1	2	yes	—
22	#2965	C₄	1	2	yes	—
23	#2965	C₄	1	2	yes	—
24	C₈×#41	C₂²	1	2	yes	—
25	C₈×#41	C₂²	1	2	yes	—
26	#2960	C₄	1	1	yes	characteristic
27	#2960	C₂²	1	1	yes	characteristic
28	#2931	C₄	1	1	yes	characteristic
29	#2931	C₂²	1	1	yes	characteristic
30	#2929	C₄	1	2	yes	—
31	#2929	C₂²	1	2	yes	—
32	#2922	C₄	1	2	yes	—
33	#2920	C₄	1	1	yes	characteristic
34	C₄×#131	C₂²	1	2	yes	—
35	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
36	#2183	C₂²	1	4	yes	complemented
37	#2183	C₂²	1	4	yes	complemented
38	Q₈×C₁₆	C₂²	1	4	yes	complemented
39	Q₈×C₁₆	C₂²	1	4	yes	complemented
40	#2169	C₂²	1	8	yes	—
41	#2169	C₂²	1	4	yes	complemented
42	#2169	C₂²	1	4	yes	complemented
43	#2168	C₂²	1	8	yes	—
44	#2168	C₂²	1	8	yes	—
45	D₄×C₁₆	C₂²	1	8	yes	—
46	D₄×C₁₆	C₂²	1	4	yes	complemented
47	D₄×C₁₆	C₂²	1	4	yes	complemented
48	#2164	C₂²	1	8	yes	complemented
49	#2163	C₂²	1	4	yes	complemented
50	#2162	C₂²	1	1	yes	characteristic
51	#2162	C₂²	1	1	yes	characteristic
52	#2162	C₂²	1	1	yes	characteristic
53	#2162	C₂²	1	1	yes	characteristic
54	#2162	C₂²	1	2	yes	—
55	#2162	C₂²	1	2	yes	—
56	#2162	C₂²	1	4	yes	complemented
57	#2151	C₂²	1	4	yes	—
58	#2151	C₂²	1	8	yes	complemented
59	#2150	C₂²	1	2	yes	—
60	#2150	C₂²	1	2	yes	—
61	#2150	C₂²	1	2	yes	—
62	#2150	C₂²	1	2	yes	—
63	#2150	C₂²	1	4	yes	complemented
64	C₂×C₄⋊C₁₆	C₂²	1	2	yes	—
65	C₂×C₄⋊C₁₆	C₂²	1	2	yes	—
66	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊C₁₆	C₂²	1	4	yes	complemented
69	#2113	C₂²	1	4	yes	—
70	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	—
71	#2108	C₂²	1	4	yes	—
72	C₂×C₄×C₁₆	C₂²	1	2	yes	—
73	C₂×#131	C₂×C₄	1	2	yes	—
74	C₂×#131	C₂³	1	2	yes	—
75	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₈	C₂³	1	1	yes	characteristic
77	#533	C₈	1	1	yes	characteristic
78	#533	C₈	1	1	yes	characteristic
79	#533	C₂×C₄	1	1	yes	characteristic
80	#532	C₈	1	1	yes	characteristic
81	#532	C₈	1	1	yes	characteristic
82	#532	C₂×C₄	1	1	yes	characteristic
83	#529	C₈	1	2	yes	—
84	#529	C₈	1	2	yes	—
85	#529	C₈	1	2	yes	—
86	#529	C₈	1	2	yes	—
87	#529	C₂×C₄	1	2	yes	—
88	#529	C₂×C₄	1	2	yes	—
89	#525	C₈	1	2	yes	—
90	#525	C₈	1	2	yes	—
91	#525	C₂×C₄	1	2	yes	—
92	C₄×#41	C₂×C₄	1	2	yes	—
93	C₄×#41	C₂×C₄	1	2	yes	—
94	C₄×#41	C₂×C₄	1	2	yes	—
95	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
96	#504	—	4	8	no	—
97	C₂×M₃₂	—	4	4	no	—
98	C₂×M₃₂	C₂³	1	4	yes	—
99	C₂×M₃₂	C₂³	1	4	yes	—
100	C₂×M₃₂	C₂³	1	8	yes	—
101	C₂²×C₁₆	C₂³	1	2	yes	—
102	C₂²×C₁₆	C₂³	1	2	yes	—
103	C₂²×C₁₆	C₂³	1	4	yes	—
104	C₂²×C₁₆	C₂³	1	8	yes	—
105	#446	C₂×C₄	1	2	yes	—
106	#446	C₂×C₄	1	2	yes	—
107	#446	C₂×C₄	1	2	yes	—
108	#446	C₂×C₄	1	2	yes	—
109	C₈×Q₈	C₂×C₄	1	2	yes	—
110	C₈×Q₈	C₂×C₄	1	2	yes	—
111	C₈×Q₈	C₂³	1	2	yes	—
112	C₈×Q₈	C₂³	1	2	yes	—
113	#436	C₂×C₄	1	2	yes	—
114	#436	C₂×C₄	1	2	yes	—
115	#436	C₂×C₄	1	2	yes	—
116	#436	C₂×C₄	1	2	yes	—
117	#435	C₂×C₄	1	4	yes	—
118	#435	C₂×C₄	1	4	yes	—
119	#435	C₂×C₄	1	4	yes	—
120	#435	C₂×C₄	1	4	yes	—
121	C₈×D₄	C₂×C₄	1	4	yes	—
122	C₈×D₄	C₂×C₄	1	4	yes	—
123	C₈×D₄	C₂×C₄	1	2	yes	—
124	C₈×D₄	C₂×C₄	1	2	yes	—
125	C₈×D₄	C₂³	1	4	yes	—
126	C₈×D₄	C₂³	1	4	yes	—
127	C₈×D₄	C₂³	1	2	yes	—
128	C₈×D₄	C₂³	1	2	yes	—
129	#433	C₂×C₄	1	4	yes	—
130	#433	C₂×C₄	1	4	yes	—
131	#432	C₂×C₄	1	2	yes	—
132	#432	C₂×C₄	1	2	yes	—
133	#431	C₂×C₄	1	2	yes	—
134	#431	C₂×C₄	1	2	yes	—
135	#431	C₂×C₄	1	4	yes	—
136	#431	C₂×C₄	1	4	yes	—
137	#424	C₂×C₄	1	2	yes	—
138	#424	C₂×C₄	1	2	yes	—
139	#423	C₂×C₄	1	1	yes	characteristic
140	#423	C₂×C₄	1	1	yes	characteristic
141	#408	C₂×C₄	1	2	yes	—
142	#408	C₂×C₄	1	2	yes	—
143	#407	C₂×C₄	1	2	yes	—
144	#405	C₂×C₄	1	2	yes	—
145	#405	C₂×C₄	1	4	yes	—
146	#405	C₂³	1	2	yes	—
147	#405	C₂³	1	4	yes	—
148	C₄×M₁₆	C₂×C₄	1	2	yes	—
149	C₄×M₁₆	C₂×C₄	1	4	yes	—
150	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
153	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
156	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
161	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
162	C₂×C₄×C₈	C₂³	1	4	yes	—
163	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
164	C₄⋊C₁₆	C₂³	1	4	yes	—
165	C₄⋊C₁₆	C₂³	1	4	yes	—
166	C₄⋊C₁₆	C₂³	1	4	yes	—
167	C₄⋊C₁₆	C₂³	1	4	yes	—
168	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
169	C₄⋊C₁₆	C₂³	1	2	yes	—
170	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
171	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
172	C₄⋊C₁₆	C₂³	1	2	yes	—
173	C₄⋊C₁₆	C₂³	1	8	yes	—
174	C₄⋊C₁₆	C₂³	1	8	yes	—
175	C₂²⋊C₁₆	C₂³	1	2	yes	—
176	C₂²⋊C₁₆	C₂³	1	2	yes	—
177	C₂²⋊C₁₆	C₂³	1	2	yes	—
178	C₂²⋊C₁₆	C₂³	1	2	yes	—
179	C₂²⋊C₁₆	C₂³	1	8	yes	—
180	C₂²⋊C₁₆	C₂³	1	8	yes	—
181	#346	C₂³	1	8	yes	—
182	C₄×C₁₆	C₂³	1	2	yes	—
183	C₄×C₁₆	C₂³	1	2	yes	—
184	C₄×C₁₆	C₂³	1	2	yes	—
185	C₄×C₁₆	C₂³	1	2	yes	—
186	C₄×C₁₆	C₂³	1	8	yes	—
187	C₂×#41	C₂×C₈	1	2	yes	—
188	C₂×#41	C₂×C₈	1	2	yes	—
189	C₂×#41	C₂²×C₄	1	2	yes	—
190	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
191	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
192	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
193	#131	—	2	4	no	—
194	#131	—	2	4	no	—
195	#131	—	4	4	no	—
196	C₂×M₁₆	C₂²×C₄	1	2	yes	—
197	C₂×M₁₆	C₂²×C₄	1	2	yes	—
198	C₂×M₁₆	C₂²×C₄	1	4	yes	—
199	C₂×M₁₆	C₂²×C₄	1	4	yes	—
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	—	4	2	no	—
203	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₈	C₂²×C₄	1	4	yes	—
213	C₂²×C₈	C₂⁴	1	1	yes	characteristic
214	C₂²×C₈	C₂⁴	1	1	yes	characteristic
215	C₂²×C₈	C₂⁴	1	4	yes	—
216	C₂²×C₈	C₂⁴	1	1	yes	characteristic
217	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
218	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
219	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
220	#127	C₂×C₈	1	1	yes	characteristic
221	#126	C₂×C₈	1	4	yes	—
222	#126	C₂×C₈	1	4	yes	—
223	#125	C₂×C₈	1	2	yes	—
224	#125	C₂×C₈	1	2	yes	—
225	#125	C₂×C₈	1	2	yes	—
226	#124	C₂×C₈	1	2	yes	—
227	#124	C₂×C₈	1	2	yes	—
228	#124	C₂×C₈	1	2	yes	—
229	#123	C₂×C₈	1	4	yes	—
230	#123	C₂×C₈	1	4	yes	—
231	#123	C₂×C₈	1	4	yes	—
232	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
233	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
234	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
235	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
236	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
237	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
238	#121	C₂×C₈	1	2	yes	—
239	#121	C₂×C₈	1	2	yes	—
240	#121	C₂×C₈	1	2	yes	—
241	#121	C₂×C₈	1	2	yes	—
242	#121	C₂×C₈	1	2	yes	—
243	#121	C₂×C₈	1	2	yes	—
244	#120	C₂×C₈	1	4	yes	—
245	C₄×Q₈	C₂×C₈	1	2	yes	—
246	C₄×Q₈	C₂×C₈	1	2	yes	—
247	C₄×Q₈	C₂×C₈	1	2	yes	—
248	C₄×Q₈	C₂×C₈	1	2	yes	—
249	C₄×Q₈	C₂²×C₄	1	2	yes	—
250	C₄×Q₈	C₂²×C₄	1	2	yes	—
251	C₄×D₄	C₂×C₈	1	4	yes	—
252	C₄×D₄	C₂×C₈	1	4	yes	—
253	C₄×D₄	C₂×C₈	1	4	yes	—
254	C₄×D₄	C₂×C₈	1	4	yes	—
255	C₄×D₄	C₂×C₈	1	2	yes	—
256	C₄×D₄	C₂×C₈	1	2	yes	—
257	C₄×D₄	C₂×C₈	1	2	yes	—
258	C₄×D₄	C₂×C₈	1	2	yes	—
259	C₄×D₄	C₂²×C₄	1	4	yes	—
260	C₄×D₄	C₂²×C₄	1	4	yes	—
261	C₄×D₄	C₂²×C₄	1	2	yes	—
262	C₄×D₄	C₂²×C₄	1	2	yes	—
263	#117	C₂×C₈	1	2	yes	—
264	#117	C₂×C₈	1	2	yes	—
265	#117	C₂×C₈	1	4	yes	—
266	#117	C₂×C₈	1	4	yes	—
267	#117	C₂²×C₄	1	2	yes	—
268	#117	C₂²×C₄	1	4	yes	—
269	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
273	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
275	C₂×C₄²	C₂²×C₄	1	4	yes	—
276	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
277	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
278	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
279	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
280	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
281	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
282	M₃₂	—	2	8	no	—
283	M₃₂	—	4	4	no	—
284	M₃₂	—	4	8	no	—
285	C₂×C₁₆	—	2	4	no	—
286	C₂×C₁₆	—	2	4	no	—
287	C₂×C₁₆	—	4	4	no	—
288	C₂×C₁₆	—	4	8	no	—
289	C₂×C₁₆	C₂⁴	1	2	yes	—
290	C₂×C₁₆	C₂⁴	1	2	yes	—
291	C₂×C₁₆	C₂⁴	1	2	yes	—
292	C₂×C₁₆	C₂⁴	1	2	yes	—
293	C₂×C₁₆	C₂⁴	1	8	yes	—
294	C₄⋊C₈	C₂²×C₄	1	2	yes	—
295	C₄⋊C₈	C₂²×C₄	1	2	yes	—
296	C₄⋊C₈	C₂²×C₄	1	2	yes	—
297	C₄⋊C₈	C₂²×C₄	1	2	yes	—
298	C₄⋊C₈	C₂²×C₄	1	4	yes	—
299	C₄⋊C₈	C₂²×C₄	1	4	yes	—
300	C₄⋊C₈	C₂²×C₄	1	4	yes	—
301	C₄⋊C₈	C₂²×C₄	1	4	yes	—
302	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
303	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
304	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
305	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
306	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
307	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
308	#97	C₂²×C₄	1	4	yes	—
309	#97	C₂²×C₄	1	4	yes	—
310	#97	C₂²×C₄	1	4	yes	—
311	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
312	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
313	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
314	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
315	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
316	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
317	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
318	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
319	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
320	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
321	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
322	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
323	C₄×C₈	C₂²×C₄	1	4	yes	—
324	C₄×C₈	C₂²×C₄	1	4	yes	—
325	C₄×C₈	C₂⁴	1	1	yes	characteristic
326	C₄×C₈	C₂⁴	1	1	yes	characteristic
327	C₄×C₈	C₂⁴	1	4	yes	—
328	C₄×C₈	C₂⁴	1	1	yes	characteristic
329	C₄×C₈	C₂⁴	1	1	yes	characteristic
330	C₂⁴	C₂²×C₈	1	1	yes	characteristic
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	8	no	—
334	#41	—	4	4	no	—
335	C₂×Q₈	C₂²×C₈	1	2	yes	—
336	C₂×Q₈	C₂²×C₈	1	2	yes	—
337	C₂×Q₈	C₂²×C₈	1	2	yes	—
338	C₂×D₄	C₂²×C₈	1	4	yes	—
339	C₂×D₄	C₂²×C₈	1	2	yes	—
340	C₂×D₄	C₂²×C₈	1	4	yes	—
341	C₂×D₄	C₂²×C₈	1	2	yes	—
342	C₂×D₄	C₂²×C₈	1	2	yes	—
343	C₂×D₄	C₂²×C₈	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₈	1	4	yes	—
360	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₈	1	4	yes	—
364	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₄	1	4	yes	—
368	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	8	no	—
372	M₁₆	—	4	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	—	4	4	no	—
389	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
390	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
391	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
392	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
393	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
394	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
395	C₂×C₈	C₂³×C₄	1	4	yes	—
396	C₂×C₈	C₂³×C₄	1	4	yes	—
397	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
398	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
399	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
400	C₂×C₈	C₂⁵	1	1	yes	characteristic
401	C₄⋊C₄	C₂²×C₈	1	2	yes	—
402	C₄⋊C₄	C₂²×C₈	1	2	yes	—
403	C₄⋊C₄	C₂²×C₈	1	4	yes	—
404	C₄⋊C₄	C₂²×C₈	1	4	yes	—
405	C₄⋊C₄	C₂²×C₈	1	2	yes	—
406	C₄⋊C₄	C₂²×C₈	1	2	yes	—
407	C₄⋊C₄	C₂²×C₈	1	4	yes	—
408	C₄⋊C₄	C₂²×C₈	1	4	yes	—
409	C₄⋊C₄	C₂²×C₈	1	2	yes	—
410	C₄⋊C₄	C₂²×C₈	1	2	yes	—
411	C₄⋊C₄	C₂²×C₈	1	4	yes	—
412	C₄⋊C₄	C₂²×C₈	1	4	yes	—
413	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
414	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
415	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
416	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
417	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
418	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
419	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
420	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
421	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
422	C₄²	C₂²×C₈	1	1	yes	characteristic
423	C₄²	C₂²×C₈	1	1	yes	characteristic
424	C₄²	C₂²×C₈	1	1	yes	characteristic
425	C₄²	C₂²×C₈	1	1	yes	characteristic
426	C₄²	C₂²×C₈	1	1	yes	characteristic
427	C₄²	C₂²×C₈	1	1	yes	characteristic
428	C₄²	C₂²×C₈	1	1	yes	characteristic
429	C₄²	C₂²×C₈	1	1	yes	characteristic
430	C₄²	C₂²×C₈	1	1	yes	characteristic
431	C₄²	C₂²×C₈	1	1	yes	characteristic
432	C₄²	C₂²×C₈	1	1	yes	characteristic
433	C₄²	C₂²×C₈	1	1	yes	characteristic
434	C₄²	C₂²×C₈	1	4	yes	—
435	C₄²	C₂²×C₈	1	4	yes	—
436	C₄²	C₂³×C₄	1	1	yes	characteristic
437	C₄²	C₂³×C₄	1	1	yes	characteristic
438	C₄²	C₂³×C₄	1	1	yes	characteristic
439	C₄²	C₂³×C₄	1	1	yes	characteristic
440	C₄²	C₂³×C₄	1	4	yes	—
441	C₁₆	—	2	2	no	—
442	C₁₆	—	2	2	no	—
443	C₁₆	—	2	8	no	—
444	C₁₆	—	2	2	no	—
445	C₁₆	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	C₂³×C₈	1	4	yes	—
450	C₂³	C₂³×C₈	1	1	yes	characteristic
451	C₂³	C₂³×C₈	1	1	yes	characteristic
452	C₂³	C₂³×C₈	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	2	4	no	—
455	Q₈	—	2	4	no	—
456	D₄	—	2	8	no	—
457	D₄	—	2	8	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	4	no	—
461	D₄	—	4	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	#504	1	4	yes	complemented
485	C₂×C₄	#520	1	2	yes	—
486	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
487	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
488	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
489	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
491	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
492	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
493	C₂×C₄	C₂³×C₈	1	4	yes	—
494	C₂×C₄	C₂³×C₈	1	4	yes	—
495	C₂×C₄	C₂³×C₈	1	4	yes	—
496	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
497	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
498	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
499	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
500	C₂×C₄	#568	1	2	yes	—
501	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	4	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	4	no	—
510	C₈	#520	1	2	yes	—
511	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	C₈	C₂×2₋¹⁺⁴	1	1	yes	characteristic
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	#2988	1	2	yes	—
525	C₂²	C₂×#504	1	2	yes	—
526	C₂²	C₂⁴×C₈	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	4	no	—
537	C₄	#2988	1	2	yes	—
538	C₄	C₂×#504	1	2	yes	—
539	C₄	C₂×#504	1	2	yes	—
540	C₄	#3407	1	2	yes	—
541	C₄	C₂×#520	1	1	yes	characteristic
542	C₄	C₂×#568	1	1	yes	characteristic
543	C₂	—	2	2	no	—
544	C₂	—	2	2	no	—
545	C₂	—	4	4	no	—
546	C₂	—	4	1	no	—
547	C₂	C₂×#2988	1	1	yes	characteristic
548	C₂	C₂²×#504	1	1	yes	characteristic
549	C₂	C₂×#3407	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₈	C₂⁵
commutator, socle	C₂²	C₂⁴×C₈
prime radical	#3444	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #33508	C₂	semidirect
3. #33507	C₂	semidirect
4. #33505	C₂	semidirect
5. #33504	C₂	semidirect
6. #33503	C₂	semidirect
7. #33502	C₂	semidirect
8. #33474	C₂	semidirect
9. #33436	C₂	semidirect
10. #33434	C₂	semidirect
11. #33423	C₂	semidirect
12. C₂×#2162	C₂	semidirect
13. #33398	C₂	semidirect
14. C₂×#2150	C₂	semidirect
36. #2183	C₂²	semidirect
37. #2183	C₂²	semidirect
38. Q₈×C₁₆	C₂²	semidirect
39. Q₈×C₁₆	C₂²	semidirect
41. #2169	C₂²	semidirect
42. #2169	C₂²	semidirect
46. D₄×C₁₆	C₂²	semidirect
47. D₄×C₁₆	C₂²	semidirect
48. #2164	C₂²	semidirect
49. #2163	C₂²	semidirect
56. #2162	C₂²	semidirect
58. #2151	C₂²	semidirect
63. #2150	C₂²	semidirect
68. C₂×C₄⋊C₁₆	C₂²	semidirect
484. C₂×C₄	#504	semidirect

Maximal subgroups

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

subgroup	index
#60204	2
#33508	2
#33507	2
#33505	2
#33504	2
#33503	2
#33502	2
#33474	2
#33436	2
#33434	2
#33423	2
C₂×#2162	2
#33398	2
C₂×#2150	2