Subgroups — #7622667

Order 512.

1395 conjugacy classes of subgroups.

The subgroup lattice has 535 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	#33485	C₂	1	2	yes	maximal, complemented
3	#33484	C₂	1	4	yes	maximal, complemented
4	#33484	C₂	1	2	yes	maximal, complemented
5	#33481	C₂	1	4	yes	maximal, complemented
6	#33480	C₂	1	4	yes	maximal, complemented
7	#33476	C₂	1	2	yes	maximal, complemented
8	#33438	C₂	1	2	yes	maximal, complemented
9	#33436	C₂	1	4	yes	maximal, complemented
10	#33421	C₂	1	2	yes	maximal, complemented
11	C₂×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	#33326	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
14	#3444	C₄	1	1	yes	characteristic
15	C₂×#504	C₂²	1	4	yes	—
16	C₂²×M₃₂	C₂²	1	2	yes	—
17	#2966	C₄	1	2	yes	—
18	#2966	C₄	1	2	yes	—
19	#2966	C₂²	1	2	yes	—
20	#2966	C₂²	1	2	yes	—
21	#2965	C₄	1	2	yes	—
22	#2965	C₄	1	2	yes	—
23	C₈×#41	C₂²	1	2	yes	—
24	C₈×#41	C₂²	1	2	yes	—
25	#2960	C₄	1	1	yes	characteristic
26	#2960	C₂²	1	1	yes	characteristic
27	#2931	C₄	1	1	yes	characteristic
28	#2931	C₂²	1	1	yes	characteristic
29	#2929	C₄	1	2	yes	—
30	#2929	C₂²	1	2	yes	—
31	#2922	C₄	1	2	yes	—
32	#2920	C₄	1	1	yes	characteristic
33	C₄×#131	C₂²	1	2	yes	—
34	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
35	#2183	C₂²	1	4	yes	complemented
36	#2183	C₂²	1	8	yes	complemented
37	Q₈×C₁₆	C₂²	1	4	yes	complemented
38	#2169	C₂²	1	8	yes	—
39	#2169	C₂²	1	4	yes	complemented
40	#2168	C₂²	1	8	yes	—
41	#2168	C₂²	1	8	yes	—
42	#2168	C₂²	1	8	yes	complemented
43	D₄×C₁₆	C₂²	1	8	yes	—
44	D₄×C₁₆	C₂²	1	4	yes	complemented
45	#2164	C₂²	1	8	yes	complemented
46	#2163	C₂²	1	2	yes	—
47	#2163	C₂²	1	2	yes	—
48	#2163	C₂²	1	1	yes	characteristic
49	#2163	C₂²	1	2	yes	—
50	#2163	C₂²	1	1	yes	characteristic
51	#2163	C₂²	1	4	yes	complemented
52	#2163	C₂²	1	4	yes	complemented
53	#2151	C₂²	1	4	yes	—
54	C₂×C₄⋊C₁₆	C₂²	1	2	yes	—
55	#2113	C₂²	1	4	yes	—
56	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	—
57	#2108	C₂²	1	4	yes	—
58	#2108	C₂²	1	8	yes	complemented
59	C₄×M₃₂	C₂²	1	1	yes	characteristic
60	C₄×M₃₂	C₂²	1	1	yes	characteristic
61	C₄×M₃₂	C₂²	1	2	yes	—
62	C₄×M₃₂	C₂²	1	2	yes	—
63	C₄×M₃₂	C₂²	1	2	yes	—
64	C₄×M₃₂	C₂²	1	4	yes	complemented
65	C₂×#346	C₂²	1	2	yes	—
66	C₂×#346	C₂²	1	2	yes	—
67	C₂×#346	C₂²	1	4	yes	complemented
68	C₂×C₄×C₁₆	C₂²	1	2	yes	—
69	C₂×#131	C₂×C₄	1	2	yes	—
70	C₂×#131	C₂³	1	2	yes	—
71	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₈	C₂³	1	1	yes	characteristic
73	#533	C₈	1	1	yes	characteristic
74	#533	C₈	1	1	yes	characteristic
75	#533	C₂×C₄	1	1	yes	characteristic
76	#532	C₈	1	1	yes	characteristic
77	#532	C₈	1	1	yes	characteristic
78	#532	C₂×C₄	1	1	yes	characteristic
79	#529	C₈	1	2	yes	—
80	#529	C₈	1	2	yes	—
81	#529	C₈	1	2	yes	—
82	#529	C₈	1	2	yes	—
83	#529	C₂×C₄	1	2	yes	—
84	#529	C₂×C₄	1	2	yes	—
85	#525	C₈	1	2	yes	—
86	#525	C₈	1	2	yes	—
87	#525	C₂×C₄	1	2	yes	—
88	C₄×#41	C₂×C₄	1	2	yes	—
89	C₄×#41	C₂×C₄	1	2	yes	—
90	C₄×#41	C₂×C₄	1	2	yes	—
91	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
92	#504	—	2	16	no	—
93	C₂×M₃₂	—	2	8	no	—
94	C₂×M₃₂	C₂³	1	2	yes	—
95	C₂×M₃₂	C₂³	1	4	yes	—
96	C₂×M₃₂	C₂³	1	8	yes	—
97	C₂×M₃₂	C₂³	1	2	yes	—
98	C₂²×C₁₆	C₂³	1	4	yes	—
99	C₂²×C₁₆	C₂³	1	4	yes	—
100	C₂²×C₁₆	C₂³	1	8	yes	—
101	#446	C₂×C₄	1	2	yes	—
102	#446	C₂×C₄	1	2	yes	—
103	#446	C₂×C₄	1	2	yes	—
104	#446	C₂×C₄	1	2	yes	—
105	C₈×Q₈	C₂×C₄	1	2	yes	—
106	C₈×Q₈	C₂×C₄	1	2	yes	—
107	C₈×Q₈	C₂³	1	2	yes	—
108	C₈×Q₈	C₂³	1	2	yes	—
109	#436	C₂×C₄	1	2	yes	—
110	#436	C₂×C₄	1	2	yes	—
111	#436	C₂×C₄	1	2	yes	—
112	#436	C₂×C₄	1	2	yes	—
113	#435	C₂×C₄	1	4	yes	—
114	#435	C₂×C₄	1	4	yes	—
115	#435	C₂×C₄	1	4	yes	—
116	#435	C₂×C₄	1	4	yes	—
117	C₈×D₄	C₂×C₄	1	4	yes	—
118	C₈×D₄	C₂×C₄	1	4	yes	—
119	C₈×D₄	C₂×C₄	1	2	yes	—
120	C₈×D₄	C₂×C₄	1	2	yes	—
121	C₈×D₄	C₂³	1	4	yes	—
122	C₈×D₄	C₂³	1	4	yes	—
123	C₈×D₄	C₂³	1	2	yes	—
124	C₈×D₄	C₂³	1	2	yes	—
125	#433	C₂×C₄	1	4	yes	—
126	#433	C₂×C₄	1	4	yes	—
127	#432	C₂×C₄	1	2	yes	—
128	#432	C₂×C₄	1	2	yes	—
129	#431	C₂×C₄	1	2	yes	—
130	#431	C₂×C₄	1	2	yes	—
131	#431	C₂×C₄	1	4	yes	—
132	#431	C₂×C₄	1	4	yes	—
133	#424	C₂×C₄	1	2	yes	—
134	#424	C₂×C₄	1	2	yes	—
135	#423	C₂×C₄	1	1	yes	characteristic
136	#423	C₂×C₄	1	1	yes	characteristic
137	#408	C₂×C₄	1	2	yes	—
138	#408	C₂×C₄	1	2	yes	—
139	#407	C₂×C₄	1	2	yes	—
140	#405	C₂×C₄	1	2	yes	—
141	#405	C₂×C₄	1	4	yes	—
142	#405	C₂³	1	2	yes	—
143	#405	C₂³	1	4	yes	—
144	C₄×M₁₆	C₂×C₄	1	2	yes	—
145	C₄×M₁₆	C₂×C₄	1	4	yes	—
146	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
147	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
148	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
149	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
150	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
153	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
154	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂³	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	4	yes	—
159	C₄⋊C₁₆	C₂³	1	2	yes	—
160	C₄⋊C₁₆	C₂³	1	4	yes	—
161	C₄⋊C₁₆	C₂³	1	2	yes	—
162	C₄⋊C₁₆	C₂³	1	8	yes	—
163	C₄⋊C₁₆	C₂³	1	8	yes	—
164	C₂²⋊C₁₆	C₂³	1	4	yes	—
165	C₂²⋊C₁₆	C₂³	1	2	yes	—
166	C₂²⋊C₁₆	C₂³	1	2	yes	—
167	C₂²⋊C₁₆	C₂³	1	8	yes	—
168	C₂²⋊C₁₆	C₂³	1	8	yes	—
169	#346	C₂³	1	2	yes	—
170	#346	C₂³	1	2	yes	—
171	#346	C₂³	1	2	yes	—
172	#346	C₂³	1	4	yes	—
173	#346	C₂³	1	2	yes	—
174	#346	C₂³	1	4	yes	—
175	#346	C₂³	1	8	yes	—
176	C₄×C₁₆	C₂³	1	2	yes	—
177	C₄×C₁₆	C₂³	1	2	yes	—
178	C₄×C₁₆	C₂³	1	4	yes	—
179	C₄×C₁₆	C₂³	1	8	yes	—
180	C₂×#41	C₂×C₈	1	2	yes	—
181	C₂×#41	C₂×C₈	1	2	yes	—
182	C₂×#41	C₂²×C₄	1	2	yes	—
183	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
184	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
185	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
186	#131	—	2	8	no	—
187	#131	—	2	8	no	—
188	C₂×M₁₆	C₂²×C₄	1	2	yes	—
189	C₂×M₁₆	C₂²×C₄	1	4	yes	—
190	C₂×M₁₆	C₂²×C₄	1	2	yes	—
191	C₂×M₁₆	C₂²×C₄	1	4	yes	—
192	C₂²×C₈	—	2	4	no	—
193	C₂²×C₈	—	2	4	no	—
194	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₈	C₂²×C₄	1	4	yes	—
203	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₈	C₂⁴	1	1	yes	characteristic
205	C₂²×C₈	C₂⁴	1	1	yes	characteristic
206	C₂²×C₈	C₂⁴	1	4	yes	—
207	C₂²×C₈	C₂⁴	1	1	yes	characteristic
208	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
209	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
210	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
211	#127	C₂×C₈	1	1	yes	characteristic
212	#126	C₂×C₈	1	4	yes	—
213	#126	C₂×C₈	1	4	yes	—
214	#125	C₂×C₈	1	2	yes	—
215	#125	C₂×C₈	1	2	yes	—
216	#125	C₂×C₈	1	2	yes	—
217	#124	C₂×C₈	1	2	yes	—
218	#124	C₂×C₈	1	2	yes	—
219	#124	C₂×C₈	1	2	yes	—
220	#123	C₂×C₈	1	4	yes	—
221	#123	C₂×C₈	1	4	yes	—
222	#123	C₂×C₈	1	4	yes	—
223	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
224	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
225	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
226	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
227	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
228	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
229	#121	C₂×C₈	1	2	yes	—
230	#121	C₂×C₈	1	2	yes	—
231	#121	C₂×C₈	1	2	yes	—
232	#121	C₂×C₈	1	2	yes	—
233	#121	C₂×C₈	1	2	yes	—
234	#121	C₂×C₈	1	2	yes	—
235	#120	C₂×C₈	1	4	yes	—
236	C₄×Q₈	C₂×C₈	1	2	yes	—
237	C₄×Q₈	C₂×C₈	1	2	yes	—
238	C₄×Q₈	C₂×C₈	1	2	yes	—
239	C₄×Q₈	C₂×C₈	1	2	yes	—
240	C₄×Q₈	C₂²×C₄	1	2	yes	—
241	C₄×Q₈	C₂²×C₄	1	2	yes	—
242	C₄×D₄	C₂×C₈	1	4	yes	—
243	C₄×D₄	C₂×C₈	1	4	yes	—
244	C₄×D₄	C₂×C₈	1	4	yes	—
245	C₄×D₄	C₂×C₈	1	4	yes	—
246	C₄×D₄	C₂×C₈	1	2	yes	—
247	C₄×D₄	C₂×C₈	1	2	yes	—
248	C₄×D₄	C₂×C₈	1	2	yes	—
249	C₄×D₄	C₂×C₈	1	2	yes	—
250	C₄×D₄	C₂²×C₄	1	4	yes	—
251	C₄×D₄	C₂²×C₄	1	4	yes	—
252	C₄×D₄	C₂²×C₄	1	2	yes	—
253	C₄×D₄	C₂²×C₄	1	2	yes	—
254	#117	C₂×C₈	1	2	yes	—
255	#117	C₂×C₈	1	2	yes	—
256	#117	C₂×C₈	1	4	yes	—
257	#117	C₂×C₈	1	4	yes	—
258	#117	C₂²×C₄	1	2	yes	—
259	#117	C₂²×C₄	1	4	yes	—
260	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
266	C₂×C₄²	C₂²×C₄	1	4	yes	—
267	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
268	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
269	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
270	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
271	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
272	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
273	M₃₂	—	2	4	no	—
274	M₃₂	—	2	8	no	—
275	M₃₂	—	2	16	no	—
276	M₃₂	#41	1	8	yes	complemented
277	C₂×C₁₆	—	2	8	no	—
278	C₂×C₁₆	—	2	8	no	—
279	C₂×C₁₆	—	2	16	no	—
280	C₂×C₁₆	C₂⁴	1	4	yes	—
281	C₂×C₁₆	C₂⁴	1	4	yes	—
282	C₂×C₁₆	C₂⁴	1	4	yes	—
283	C₂×C₁₆	C₂⁴	1	4	yes	—
284	C₄⋊C₈	C₂²×C₄	1	2	yes	—
285	C₄⋊C₈	C₂²×C₄	1	2	yes	—
286	C₄⋊C₈	C₂²×C₄	1	2	yes	—
287	C₄⋊C₈	C₂²×C₄	1	2	yes	—
288	C₄⋊C₈	C₂²×C₄	1	4	yes	—
289	C₄⋊C₈	C₂²×C₄	1	4	yes	—
290	C₄⋊C₈	C₂²×C₄	1	4	yes	—
291	C₄⋊C₈	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
293	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
294	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
295	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
296	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
297	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
298	#97	C₂²×C₄	1	4	yes	—
299	#97	C₂²×C₄	1	4	yes	—
300	#97	C₂²×C₄	1	4	yes	—
301	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
302	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
303	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
304	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
305	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
306	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
307	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
308	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
309	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
310	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
311	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
312	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
313	C₄×C₈	C₂²×C₄	1	4	yes	—
314	C₄×C₈	C₂²×C₄	1	4	yes	—
315	C₄×C₈	C₂⁴	1	1	yes	characteristic
316	C₄×C₈	C₂⁴	1	1	yes	characteristic
317	C₄×C₈	C₂⁴	1	4	yes	—
318	C₄×C₈	C₂⁴	1	1	yes	characteristic
319	C₄×C₈	C₂⁴	1	1	yes	characteristic
320	C₂⁴	C₂²×C₈	1	1	yes	characteristic
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	C₂×Q₈	C₂²×C₈	1	2	yes	—
326	C₂×Q₈	C₂²×C₈	1	2	yes	—
327	C₂×Q₈	C₂²×C₈	1	2	yes	—
328	C₂×D₄	C₂²×C₈	1	4	yes	—
329	C₂×D₄	C₂²×C₈	1	2	yes	—
330	C₂×D₄	C₂²×C₈	1	4	yes	—
331	C₂×D₄	C₂²×C₈	1	2	yes	—
332	C₂×D₄	C₂²×C₈	1	4	yes	—
333	C₂×D₄	C₂²×C₈	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	4	yes	—
354	C₂²×C₄	C₂²×C₈	1	4	yes	—
355	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
356	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
357	C₂²×C₄	C₂³×C₄	1	4	yes	—
358	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	8	no	—
362	M₁₆	—	2	8	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	#131	1	4	yes	—
376	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
378	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
379	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
380	C₂×C₈	C₂³×C₄	1	4	yes	—
381	C₂×C₈	C₂³×C₄	1	4	yes	—
382	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
383	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
384	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
385	C₂×C₈	C₂×#41	1	4	yes	—
386	C₂×C₈	C₂⁵	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×C₈	1	2	yes	—
388	C₄⋊C₄	C₂²×C₈	1	2	yes	—
389	C₄⋊C₄	C₂²×C₈	1	4	yes	—
390	C₄⋊C₄	C₂²×C₈	1	4	yes	—
391	C₄⋊C₄	C₂²×C₈	1	2	yes	—
392	C₄⋊C₄	C₂²×C₈	1	2	yes	—
393	C₄⋊C₄	C₂²×C₈	1	4	yes	—
394	C₄⋊C₄	C₂²×C₈	1	4	yes	—
395	C₄⋊C₄	C₂²×C₈	1	2	yes	—
396	C₄⋊C₄	C₂²×C₈	1	2	yes	—
397	C₄⋊C₄	C₂²×C₈	1	4	yes	—
398	C₄⋊C₄	C₂²×C₈	1	4	yes	—
399	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
400	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
401	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
402	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
403	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
404	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
405	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
406	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
407	C₂²⋊C₄	C₂²×C₈	1	4	yes	—
408	C₄²	C₂²×C₈	1	1	yes	characteristic
409	C₄²	C₂²×C₈	1	1	yes	characteristic
410	C₄²	C₂²×C₈	1	1	yes	characteristic
411	C₄²	C₂²×C₈	1	1	yes	characteristic
412	C₄²	C₂²×C₈	1	1	yes	characteristic
413	C₄²	C₂²×C₈	1	1	yes	characteristic
414	C₄²	C₂²×C₈	1	1	yes	characteristic
415	C₄²	C₂²×C₈	1	1	yes	characteristic
416	C₄²	C₂²×C₈	1	1	yes	characteristic
417	C₄²	C₂²×C₈	1	1	yes	characteristic
418	C₄²	C₂²×C₈	1	1	yes	characteristic
419	C₄²	C₂²×C₈	1	1	yes	characteristic
420	C₄²	C₂²×C₈	1	4	yes	—
421	C₄²	C₂²×C₈	1	4	yes	—
422	C₄²	C₂³×C₄	1	1	yes	characteristic
423	C₄²	C₂³×C₄	1	1	yes	characteristic
424	C₄²	C₂³×C₄	1	1	yes	characteristic
425	C₄²	C₂³×C₄	1	1	yes	characteristic
426	C₄²	C₂³×C₄	1	4	yes	—
427	C₁₆	—	2	4	no	—
428	C₁₆	—	2	4	no	—
429	C₁₆	—	2	4	no	—
430	C₁₆	C₂×#41	1	8	yes	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	C₂³×C₈	1	4	yes	—
435	C₂³	C₂³×C₈	1	1	yes	characteristic
436	C₂³	C₂³×C₈	1	1	yes	characteristic
437	C₂³	C₂³×C₈	1	1	yes	characteristic
438	Q₈	—	2	4	no	—
439	Q₈	—	2	4	no	—
440	Q₈	—	4	2	no	—
441	D₄	—	2	8	no	—
442	D₄	—	2	8	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	C₄×#41	1	2	yes	—
471	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
472	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
473	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
474	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
475	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
476	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
477	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
478	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
479	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
480	C₂×C₄	C₂³×C₈	1	4	yes	—
481	C₂×C₄	C₂³×C₈	1	4	yes	—
482	C₂×C₄	C₂³×C₈	1	4	yes	—
483	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
484	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
485	C₂×C₄	C₂×#131	1	2	yes	—
486	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	4	no	—
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	4	no	—
493	C₈	C₄×#41	1	2	yes	—
494	C₈	C₂×#131	1	2	yes	—
495	C₈	C₂×#131	1	2	yes	—
496	C₈	C₂²×#41	1	2	yes	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	C₈×#41	1	2	yes	—
509	C₂²	#3407	1	2	yes	—
510	C₂²	C₂⁴×C₈	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	4	no	—
523	C₄	C₈×#41	1	2	yes	—
524	C₄	#3407	1	2	yes	—
525	C₄	C₂×C₄×#41	1	1	yes	characteristic
526	C₄	C₂²×#131	1	1	yes	characteristic
527	C₂	—	2	2	no	—
528	C₂	—	2	2	no	—
529	C₂	—	4	4	no	—
530	C₂	—	4	1	no	—
531	C₂	C₂×C₈×#41	1	1	yes	characteristic
532	C₂	C₂×#3407	1	1	yes	characteristic
533	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. #33485	C₂	semidirect
3. #33484	C₂	semidirect
4. #33484	C₂	semidirect
5. #33481	C₂	semidirect
6. #33480	C₂	semidirect
7. #33476	C₂	semidirect
8. #33438	C₂	semidirect
9. #33436	C₂	semidirect
10. #33421	C₂	semidirect
11. C₂×#2163	C₂	semidirect
12. #33326	C₂	semidirect
13. C₂×C₄×M₃₂	C₂	semidirect
35. #2183	C₂²	semidirect
36. #2183	C₂²	semidirect
37. Q₈×C₁₆	C₂²	semidirect
39. #2169	C₂²	semidirect
42. #2168	C₂²	semidirect
44. D₄×C₁₆	C₂²	semidirect
45. #2164	C₂²	semidirect
51. #2163	C₂²	semidirect
52. #2163	C₂²	semidirect
58. #2108	C₂²	semidirect
64. C₄×M₃₂	C₂²	semidirect
67. C₂×#346	C₂²	semidirect
276. M₃₂	#41	semidirect

Maximal subgroups

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

subgroup	index
#60204	2
#33485	2
#33484	2
#33481	2
#33480	2
#33476	2
#33438	2
#33436	2
#33421	2
C₂×#2163	2
#33326	2
C₂×C₄×M₃₂	2