Subgroups — #115935

Order 512.

834 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1990	C₂	1	1	yes	maximal, characteristic
2	C₂×#1987	C₂	1	1	yes	maximal, characteristic
3	C₂×#1939	C₂	1	1	yes	maximal, characteristic
4	C₂²×#333	C₂	1	1	yes	maximal, characteristic
5	#10849	C₂	1	1	yes	maximal, characteristic
6	C₂×#1296	C₂	1	1	yes	maximal, characteristic
7	C₂×#1277	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₈	—	2	1	no	—
10	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂×#384	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	#1990	—	2	2	no	—
17	#1990	—	2	2	no	—
18	#1987	—	2	2	no	—
19	#1987	C₄	1	4	yes	complemented
20	#1939	—	2	2	no	—
21	#1939	—	2	2	no	—
22	C₂×#340	—	2	1	no	—
23	C₂×#340	—	2	1	no	—
24	C₂×#340	—	2	1	no	—
25	C₂×#340	—	2	1	no	—
26	C₂×#340	—	2	1	no	—
27	C₂×#340	—	2	1	no	—
28	C₂×#336	—	2	1	no	—
29	C₂×#333	—	2	2	no	—
30	C₂×#333	—	2	2	no	—
31	C₂×#333	—	2	2	no	—
32	#1296	—	2	2	no	—
33	#1277	—	2	2	no	—
34	C₂³×Q₈	—	2	1	no	—
35	C₂³×C₈	—	2	1	no	—
36	C₂³×C₈	—	2	1	no	—
37	C₂³×C₈	—	2	1	no	—
38	C₂³×C₈	D₄	1	1	yes	characteristic
39	C₂³×C₈	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₄⋊Q₈	—	2	1	no	—
42	C₂×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₄⋊Q₈	—	2	1	no	—
44	C₂×C₄⋊Q₈	—	2	1	no	—
45	C₂×C₄⋊Q₈	—	2	1	no	—
46	C₂×C₄⋊Q₈	—	2	1	no	—
47	C₂×C₄⋊Q₈	—	2	1	no	—
48	C₂×C₄⋊Q₈	—	2	1	no	—
49	C₂×C₄⋊Q₈	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊Q₈	D₄	1	2	yes	—
51	C₂×C₄⋊Q₈	Q₈	1	2	yes	—
52	C₂²×C₄⋊C₄	—	2	1	no	—
53	C₂²×C₄⋊C₄	—	2	1	no	—
54	C₂²×C₄⋊C₄	—	2	1	no	—
55	C₂²×C₄⋊C₄	—	2	1	no	—
56	C₂²×C₄⋊C₄	—	2	1	no	—
57	C₂²×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂²×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂²×C₄²	—	2	1	no	—
60	C₂²×C₄²	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₈	—	2	1	no	—
62	C₂×C₄⋊C₈	—	2	1	no	—
63	C₂×C₄⋊C₈	—	2	1	no	—
64	C₂×C₄⋊C₈	—	2	1	no	—
65	C₂×C₄⋊C₈	—	2	1	no	—
66	C₂×C₄⋊C₈	—	2	1	no	—
67	C₂×C₄⋊C₈	—	2	1	no	—
68	C₂×C₄⋊C₈	—	2	1	no	—
69	C₂×C₄⋊C₈	—	2	1	no	—
70	C₂×C₄⋊C₈	—	2	1	no	—
71	C₂×C₄⋊C₈	—	2	1	no	—
72	C₂×C₄⋊C₈	—	2	1	no	—
73	C₂×C₄⋊C₈	—	2	4	no	—
74	C₂×C₄⋊C₈	—	2	1	no	—
75	C₂×C₄⋊C₈	—	2	1	no	—
76	C₂×C₄⋊C₈	—	2	1	no	—
77	C₂×C₄⋊C₈	—	4	2	no	—
78	C₂×C₄⋊C₈	—	4	2	no	—
79	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₈	D₄	1	2	yes	—
81	C₂×C₄⋊C₈	D₄	1	2	yes	—
82	C₂×C₄×C₈	—	2	1	no	—
83	C₂×C₄×C₈	—	2	1	no	—
84	C₂×C₄×C₈	—	2	1	no	—
85	C₂×C₄×C₈	—	2	1	no	—
86	C₂×C₄×C₈	—	2	1	no	—
87	C₂×C₄×C₈	—	2	1	no	—
88	#384	—	2	1	no	—
89	#384	—	2	1	no	—
90	#384	—	2	1	no	—
91	#384	D₄	1	2	yes	—
92	C₄×C₄⋊C₄	—	2	1	no	—
93	C₄×C₄⋊C₄	—	2	1	no	—
94	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
95	C₄×C₄⋊C₄	D₄	1	2	yes	—
96	C₂×#95	—	2	1	no	—
97	#340	—	2	4	no	—
98	#340	—	2	4	no	—
99	#340	—	2	4	no	—
100	#340	—	2	4	no	—
101	#340	—	4	2	no	—
102	#340	—	4	2	no	—
103	#336	—	2	4	no	—
104	#333	—	2	8	no	—
105	C₂²×Q₈	—	2	2	no	—
106	C₂²×Q₈	—	2	2	no	—
107	C₂²×Q₈	—	2	2	no	—
108	C₂²×Q₈	—	4	1	no	—
109	C₂²×Q₈	—	4	1	no	—
110	C₂²×Q₈	—	4	1	no	—
111	C₂²×Q₈	—	8	1	no	—
112	C₂²×Q₈	—	8	1	no	—
113	C₂²×Q₈	—	8	1	no	—
114	C₂²×Q₈	—	8	1	no	—
115	C₂³×C₄	—	2	1	no	—
116	C₂³×C₄	—	2	1	no	—
117	C₂³×C₄	—	4	1	no	—
118	C₂³×C₄	—	4	1	no	—
119	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂³×C₄	#41	1	1	yes	characteristic
122	C₂²×C₈	—	2	1	no	—
123	C₂²×C₈	—	2	1	no	—
124	C₂²×C₈	—	2	1	no	—
125	C₂²×C₈	—	2	1	no	—
126	C₂²×C₈	—	2	1	no	—
127	C₂²×C₈	—	2	1	no	—
128	C₂²×C₈	—	2	1	no	—
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	—	2	1	no	—
131	C₂²×C₈	—	2	1	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	4	1	no	—
138	C₂²×C₈	—	4	1	no	—
139	C₂²×C₈	—	4	1	no	—
140	C₂²×C₈	—	4	1	no	—
141	C₂²×C₈	—	4	1	no	—
142	C₂²×C₈	—	4	1	no	—
143	C₂²×C₈	—	4	1	no	—
144	C₂²×C₈	—	4	1	no	—
145	C₂²×C₈	—	4	1	no	—
146	C₂²×C₈	—	4	1	no	—
147	C₂²×C₈	—	4	1	no	—
148	C₂²×C₈	—	4	1	no	—
149	C₂²×C₈	—	4	1	no	—
150	C₂²×C₈	—	4	1	no	—
151	C₂²×C₈	—	4	1	no	—
152	C₂²×C₈	—	4	1	no	—
153	C₂²×C₈	—	4	1	no	—
154	C₂²×C₈	—	4	1	no	—
155	C₂²×C₈	SD₁₆	1	2	yes	—
156	C₂²×C₈	Q₁₆	1	2	yes	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	—	2	2	no	—
166	C₄⋊Q₈	—	4	1	no	—
167	C₄⋊Q₈	—	4	1	no	—
168	C₄⋊Q₈	—	4	1	no	—
169	C₄⋊Q₈	—	4	1	no	—
170	C₄⋊Q₈	—	4	1	no	—
171	C₄⋊Q₈	—	4	1	no	—
172	C₄⋊Q₈	C₄⋊C₄	1	4	yes	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	2	no	—
177	C₂×C₄⋊C₄	—	2	2	no	—
178	C₂×C₄⋊C₄	—	2	2	no	—
179	C₂×C₄⋊C₄	—	2	2	no	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₄⋊C₄	—	2	2	no	—
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄⋊C₄	—	2	1	no	—
185	C₂×C₄⋊C₄	—	2	1	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	4	1	no	—
191	C₂×C₄⋊C₄	—	4	1	no	—
192	C₂×C₄⋊C₄	—	4	1	no	—
193	C₂×C₄⋊C₄	—	4	1	no	—
194	C₂×C₄⋊C₄	—	4	1	no	—
195	C₂×C₄⋊C₄	—	4	1	no	—
196	C₂×C₄⋊C₄	—	4	1	no	—
197	C₂×C₄⋊C₄	—	4	1	no	—
198	C₂×C₄⋊C₄	—	4	1	no	—
199	C₂×C₄⋊C₄	—	4	1	no	—
200	C₂×C₄⋊C₄	—	4	1	no	—
201	C₂×C₄⋊C₄	—	4	1	no	—
202	C₂×C₄⋊C₄	—	4	1	no	—
203	C₂×C₄⋊C₄	—	4	1	no	—
204	C₂×C₄⋊C₄	—	4	1	no	—
205	C₂×C₄⋊C₄	—	4	1	no	—
206	C₂×C₄⋊C₄	—	4	1	no	—
207	C₂×C₄⋊C₄	—	8	1	no	—
208	C₂×C₄⋊C₄	—	8	1	no	—
209	C₂×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₂×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₂×C₄⋊C₄	SD₁₆	1	2	yes	—
212	C₂×C₄⋊C₄	Q₁₆	1	2	yes	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	—	4	1	no	—
216	C₂×C₄²	—	4	1	no	—
217	C₂×C₄²	—	4	1	no	—
218	C₂×C₄²	—	4	1	no	—
219	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
221	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
222	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
223	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
224	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
226	C₂×C₄²	#41	1	1	yes	characteristic
227	C₂×C₄²	#41	1	1	yes	characteristic
228	C₂×C₄²	#41	1	1	yes	characteristic
229	C₂×C₄²	#41	1	1	yes	characteristic
230	C₂×C₄²	#41	1	1	yes	characteristic
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	4	8	no	—
238	C₄⋊C₈	—	4	1	no	—
239	C₄⋊C₈	—	4	1	no	—
240	C₄⋊C₈	—	4	1	no	—
241	C₄⋊C₈	—	4	1	no	—
242	C₄⋊C₈	—	4	1	no	—
243	C₄⋊C₈	—	4	1	no	—
244	C₄×C₈	—	4	1	no	—
245	C₄×C₈	—	4	1	no	—
246	C₄×C₈	—	4	1	no	—
247	C₄×C₈	—	4	1	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	C₂⁴	#121	1	1	yes	characteristic
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	4	2	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×Q₈	—	4	2	no	—
255	C₂×Q₈	—	8	2	no	—
256	C₂×Q₈	—	8	2	no	—
257	C₂×Q₈	—	8	2	no	—
258	C₂×Q₈	—	8	2	no	—
259	C₂×Q₈	—	8	2	no	—
260	C₂×Q₈	—	8	2	no	—
261	C₂×Q₈	—	8	2	no	—
262	C₂×Q₈	—	8	2	no	—
263	C₂×Q₈	—	8	2	no	—
264	C₂×Q₈	—	8	2	no	—
265	C₂×Q₈	—	8	2	no	—
266	C₂×Q₈	—	8	2	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	8	1	no	—
290	C₂²×C₄	—	8	1	no	—
291	C₂²×C₄	—	8	1	no	—
292	C₂²×C₄	—	8	1	no	—
293	C₂²×C₄	—	8	1	no	—
294	C₂²×C₄	—	8	1	no	—
295	C₂²×C₄	—	8	1	no	—
296	C₂²×C₄	—	8	1	no	—
297	C₂²×C₄	—	8	1	no	—
298	C₂²×C₄	—	8	1	no	—
299	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
302	C₂²×C₄	#120	1	1	yes	characteristic
303	C₂²×C₄	#120	1	1	yes	characteristic
304	C₂²×C₄	#121	1	1	yes	characteristic
305	C₂²×C₄	#121	1	1	yes	characteristic
306	C₂²×C₄	#121	1	1	yes	characteristic
307	C₂²×C₄	#121	1	1	yes	characteristic
308	C₂²×C₄	#121	1	1	yes	characteristic
309	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
310	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
312	C₂²×C₄	#123	1	1	yes	characteristic
313	C₂²×C₄	#123	1	1	yes	characteristic
314	C₂²×C₄	#123	1	1	yes	characteristic
315	C₂²×C₄	#124	1	1	yes	characteristic
316	C₂²×C₄	#126	1	1	yes	characteristic
317	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
318	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
319	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
320	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
321	C₂²×C₄	#135	1	1	yes	characteristic
322	C₂²×C₄	#135	1	1	yes	characteristic
323	C₂²×C₄	#135	1	1	yes	characteristic
324	C₂²×C₄	#135	1	1	yes	characteristic
325	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₂²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₂²×C₄	#137	1	1	yes	characteristic
328	C₂²×C₄	#137	1	1	yes	characteristic
329	C₂²×C₄	#137	1	1	yes	characteristic
330	C₂²×C₄	#137	1	1	yes	characteristic
331	C₂²×C₄	#137	1	1	yes	characteristic
332	C₂²×C₄	#137	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	8	1	no	—
357	C₂×C₈	—	8	1	no	—
358	C₂×C₈	—	8	1	no	—
359	C₂×C₈	—	8	1	no	—
360	C₂×C₈	—	8	1	no	—
361	C₂×C₈	—	8	1	no	—
362	C₂×C₈	—	8	1	no	—
363	C₂×C₈	—	8	1	no	—
364	C₂×C₈	—	8	1	no	—
365	C₂×C₈	—	8	1	no	—
366	C₂×C₈	—	8	1	no	—
367	C₂×C₈	—	8	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	8	2	no	—
388	C₄⋊C₄	—	8	2	no	—
389	C₄⋊C₄	—	8	1	no	—
390	C₄⋊C₄	—	8	1	no	—
391	C₄⋊C₄	—	8	1	no	—
392	C₄⋊C₄	—	8	1	no	—
393	C₄⋊C₄	#103	1	4	yes	—
394	C₄²	—	4	2	no	—
395	C₄²	—	4	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
399	C₄²	#117	1	1	yes	characteristic
400	C₄²	C₄×D₄	1	1	yes	characteristic
401	C₄²	C₄×D₄	1	1	yes	characteristic
402	C₄²	#120	1	1	yes	characteristic
403	C₄²	#121	1	1	yes	characteristic
404	C₄²	#121	1	1	yes	characteristic
405	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
406	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
407	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
408	C₄²	#123	1	1	yes	characteristic
409	C₄²	#123	1	1	yes	characteristic
410	C₄²	#124	1	1	yes	characteristic
411	C₄²	#124	1	1	yes	characteristic
412	C₄²	#126	1	1	yes	characteristic
413	C₄²	#127	1	1	yes	characteristic
414	C₂³	#386	1	1	yes	characteristic
415	C₂³	#394	1	1	yes	characteristic
416	C₂³	#396	1	1	yes	characteristic
417	C₂³	#461	1	1	yes	characteristic
418	C₂³	#462	1	1	yes	characteristic
419	C₂³	#463	1	1	yes	characteristic
420	C₂³	#464	1	1	yes	characteristic
421	C₂³	#465	1	1	yes	characteristic
422	C₂³	#467	1	1	yes	characteristic
423	C₂³	#468	1	1	yes	characteristic
424	C₂³	#470	1	1	yes	characteristic
425	C₂³	#471	1	1	yes	characteristic
426	C₂³	#471	1	1	yes	characteristic
427	C₂³	#472	1	1	yes	characteristic
428	C₂³	#472	1	1	yes	characteristic
429	Q₈	—	8	4	no	—
430	Q₈	—	8	4	no	—
431	Q₈	—	8	4	no	—
432	Q₈	—	8	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	1	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	8	1	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	16	1	no	—
470	C₂×C₄	—	16	1	no	—
471	C₂×C₄	—	16	1	no	—
472	C₂×C₄	—	16	1	no	—
473	C₂×C₄	#380	1	1	yes	characteristic
474	C₂×C₄	#385	1	1	yes	characteristic
475	C₂×C₄	#385	1	1	yes	characteristic
476	C₂×C₄	#388	1	1	yes	characteristic
477	C₂×C₄	#388	1	1	yes	characteristic
478	C₂×C₄	#390	1	1	yes	characteristic
479	C₂×C₄	#392	1	1	yes	characteristic
480	C₂×C₄	#393	1	1	yes	characteristic
481	C₂×C₄	#394	1	1	yes	characteristic
482	C₂×C₄	#396	1	1	yes	characteristic
483	C₂×C₄	#397	1	1	yes	characteristic
484	C₂×C₄	#399	1	1	yes	characteristic
485	C₂×C₄	C₂×#103	1	1	yes	characteristic
486	C₂×C₄	#416	1	1	yes	characteristic
487	C₂×C₄	#417	1	1	yes	characteristic
488	C₂×C₄	#419	1	1	yes	characteristic
489	C₂×C₄	C₄×SD₁₆	1	1	yes	characteristic
490	C₂×C₄	C₄×Q₁₆	1	1	yes	characteristic
491	C₂×C₄	#440	1	1	yes	characteristic
492	C₂×C₄	#441	1	1	yes	characteristic
493	C₂×C₄	#448	1	1	yes	characteristic
494	C₂×C₄	#449	1	1	yes	characteristic
495	C₂×C₄	#450	1	1	yes	characteristic
496	C₂×C₄	#451	1	1	yes	characteristic
497	C₂×C₄	#451	1	1	yes	characteristic
498	C₂×C₄	#452	1	1	yes	characteristic
499	C₂×C₄	#452	1	1	yes	characteristic
500	C₂×C₄	#452	1	1	yes	characteristic
501	C₂×C₄	#460	1	1	yes	characteristic
502	C₂×C₄	#461	1	1	yes	characteristic
503	C₂×C₄	#461	1	1	yes	characteristic
504	C₂×C₄	#462	1	1	yes	characteristic
505	C₂×C₄	#462	1	1	yes	characteristic
506	C₂×C₄	#462	1	1	yes	characteristic
507	C₂×C₄	#463	1	1	yes	characteristic
508	C₂×C₄	#463	1	1	yes	characteristic
509	C₂×C₄	#464	1	1	yes	characteristic
510	C₂×C₄	#464	1	1	yes	characteristic
511	C₂×C₄	#464	1	1	yes	characteristic
512	C₂×C₄	#464	1	1	yes	characteristic
513	C₂×C₄	#465	1	1	yes	characteristic
514	C₂×C₄	#465	1	1	yes	characteristic
515	C₂×C₄	#467	1	1	yes	characteristic
516	C₂×C₄	#467	1	1	yes	characteristic
517	C₂×C₄	#468	1	1	yes	characteristic
518	C₂×C₄	#468	1	1	yes	characteristic
519	C₂×C₄	#470	1	1	yes	characteristic
520	C₂×C₄	#470	1	1	yes	characteristic
521	C₂×C₄	#475	1	1	yes	characteristic
522	C₂×C₄	#475	1	1	yes	characteristic
523	C₂×C₄	#477	1	1	yes	characteristic
524	C₂×C₄	#477	1	1	yes	characteristic
525	C₂×C₄	#479	1	1	yes	characteristic
526	C₂×C₄	#479	1	1	yes	characteristic
527	C₂×C₄	#479	1	1	yes	characteristic
528	C₂×C₄	#479	1	1	yes	characteristic
529	C₂×C₄	#487	1	1	yes	characteristic
530	C₂×C₄	#488	1	1	yes	characteristic
531	C₂×C₄	#489	1	1	yes	characteristic
532	C₂×C₄	#491	1	1	yes	characteristic
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₈	—	8	2	no	—
536	C₈	—	8	2	no	—
537	C₈	—	8	2	no	—
538	C₂²	#1439	1	1	yes	characteristic
539	C₂²	#1671	1	1	yes	characteristic
540	C₂²	#1672	1	1	yes	characteristic
541	C₂²	#1675	1	1	yes	characteristic
542	C₂²	#1676	1	1	yes	characteristic
543	C₂²	#1677	1	1	yes	characteristic
544	C₂²	#1678	1	1	yes	characteristic
545	C₂²	#1683	1	1	yes	characteristic
546	C₂²	#1684	1	1	yes	characteristic
547	C₂²	#1691	1	1	yes	characteristic
548	C₂²	#1692	1	1	yes	characteristic
549	C₂²	#1695	1	1	yes	characteristic
550	C₂²	#1696	1	1	yes	characteristic
551	C₂²	#1697	1	1	yes	characteristic
552	C₂²	#1698	1	1	yes	characteristic
553	C₂²	#1703	1	1	yes	characteristic
554	C₂²	#1704	1	1	yes	characteristic
555	C₂²	#1877	1	1	yes	characteristic
556	C₂²	#1878	1	1	yes	characteristic
557	C₂²	#1892	1	1	yes	characteristic
558	C₂²	#1894	1	1	yes	characteristic
559	C₂²	#1907	1	1	yes	characteristic
560	C₂²	#1907	1	1	yes	characteristic
561	C₂²	#2042	1	1	yes	characteristic
562	C₂²	#2043	1	1	yes	characteristic
563	C₂²	#2045	1	1	yes	characteristic
564	C₂²	#2046	1	1	yes	characteristic
565	C₂²	#2055	1	1	yes	characteristic
566	C₂²	#2056	1	1	yes	characteristic
567	C₂²	#2063	1	1	yes	characteristic
568	C₂²	#2063	1	1	yes	characteristic
569	C₂²	#2066	1	1	yes	characteristic
570	C₂²	#2066	1	1	yes	characteristic
571	C₂²	#2068	1	1	yes	characteristic
572	C₂²	#2068	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	4	4	no	—
578	C₄	—	8	2	no	—
579	C₄	—	8	4	no	—
580	C₄	—	16	2	no	—
581	C₄	#1803	1	1	yes	characteristic
582	C₄	#1805	1	1	yes	characteristic
583	C₄	#1863	1	1	yes	characteristic
584	C₄	#1865	1	1	yes	characteristic
585	C₄	#1933	1	1	yes	characteristic
586	C₄	#1935	1	1	yes	characteristic
587	C₄	#1981	1	1	yes	characteristic
588	C₄	#1983	1	1	yes	characteristic
589	C₄	#2000	1	1	yes	characteristic
590	C₄	#2001	1	1	yes	characteristic
591	C₄	#2024	1	1	yes	characteristic
592	C₄	#2026	1	1	yes	characteristic
593	C₄	#2055	1	1	yes	characteristic
594	C₄	#2056	1	1	yes	characteristic
595	C₄	#2066	1	1	yes	characteristic
596	C₄	#2068	1	1	yes	characteristic
597	C₂	#9215	1	1	yes	characteristic
598	C₂	#9216	1	1	yes	characteristic
599	C₂	#9223	1	1	yes	characteristic
600	C₂	#9224	1	1	yes	characteristic
601	C₂	#10539	1	1	yes	characteristic
602	C₂	#10541	1	1	yes	characteristic
603	C₂	#10543	1	1	yes	characteristic
604	C₂	#10544	1	1	yes	characteristic
605	C₂	#10589	1	1	yes	characteristic
606	C₂	#10593	1	1	yes	characteristic
607	C₂	#10597	1	1	yes	characteristic
608	C₂	#10601	1	1	yes	characteristic
609	C₂	#11061	1	1	yes	characteristic
610	C₂	#11067	1	1	yes	characteristic
611	C₂	#11077	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
19. #1987	C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1990	2
C₂×#1987	2
C₂×#1939	2
C₂²×#333	2
#10849	2
C₂×#1296	2
C₂×#1277	2