Subgroups — #10948778

Order 768.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#71963	C₂	1	1	yes	maximal, characteristic, complemented
4	#71407	C₂	1	2	yes	maximal, complemented
5	C₁₆×#67	C₂	1	2	yes	maximal, complemented
6	#69106	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#69104	C₂	1	2	yes	maximal, complemented
9	#69103	C₂	1	2	yes	maximal, complemented
10	#69093	C₂	1	1	yes	maximal, characteristic, complemented
11	#69092	C₂	1	1	yes	maximal, characteristic, complemented
12	#33488	—	3	1	no	maximal, Sylow
13	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×#67	C₄	1	1	yes	characteristic
15	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₁₆	C₂²	1	2	yes	complemented
17	C₂×#830	C₄	1	1	yes	characteristic
18	C₈×#67	C₄	1	1	yes	characteristic
19	C₈×#67	C₄	1	1	yes	characteristic
20	C₈×#67	C₄	1	1	yes	characteristic
21	C₈×#67	C₄	1	1	yes	characteristic
22	C₈×#67	C₂²	1	1	yes	characteristic
23	C₈×#67	C₂²	1	1	yes	characteristic
24	C₈×#67	C₂²	1	1	yes	characteristic
25	C₈×#67	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₃)⋊C₈	C₄	1	1	yes	characteristic
27	C₂×Dic₃⋊C₈	C₄	1	1	yes	characteristic
28	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×#812	C₂²	1	2	yes	complemented
30	C₂×#798	C₂²	1	2	yes	complemented
31	C₂×D₃×C₁₆	C₂²	1	2	yes	complemented
32	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	#4549	C₂²	1	1	yes	characteristic
36	#4549	C₂²	1	1	yes	characteristic
37	#4549	C₂²	1	2	yes	complemented
38	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	complemented
39	(C₂×D₃)⋊C₁₆	C₂²	1	2	yes	complemented
40	#4502	C₂²	1	2	yes	complemented
41	Dic₃⋊C₁₆	C₂²	1	2	yes	complemented
42	Dic₃⋊C₁₆	C₂²	1	2	yes	complemented
43	Dic₃×C₁₆	C₂²	1	2	yes	complemented
44	C₂×C₈×D₄	—	3	1	no	—
45	#2169	—	3	2	no	—
46	#2168	—	3	2	no	—
47	#2168	—	3	2	no	—
48	D₄×C₁₆	—	3	2	no	—
49	#2163	—	3	1	no	—
50	#2162	—	3	1	no	—
51	#2112	—	3	1	no	—
52	#2112	—	3	1	no	—
53	C₂×C₂²⋊C₁₆	—	3	1	no	—
54	C₂×C₂²⋊C₁₆	D₃	1	1	yes	characteristic, complemented
55	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×#67	C₈	1	1	yes	characteristic
57	C₂²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₈	—	4	2	no	—
59	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
65	C₂×#217	C₈	1	1	yes	characteristic
66	C₄×#67	C₈	1	1	yes	characteristic
67	C₄×#67	C₈	1	1	yes	characteristic
68	C₄×#67	C₈	1	1	yes	characteristic
69	C₄×#67	C₈	1	1	yes	characteristic
70	C₄×#67	C₂×C₄	1	1	yes	characteristic
71	C₄×#67	C₂×C₄	1	1	yes	characteristic
72	C₄×#67	C₂×C₄	1	1	yes	characteristic
73	C₄×#67	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₃)⋊C₄	C₈	1	1	yes	characteristic
75	C₂×Dic₃⋊C₄	C₈	1	1	yes	characteristic
76	C₂×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂×D₃×C₈	—	4	2	no	—
80	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
81	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
82	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
83	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₁₆	—	4	2	no	—
85	C₂×C₃×C₁₆	C₂³	1	2	yes	—
86	C₂×C₃×C₁₆	C₂³	1	2	yes	—
87	#830	C₂×C₄	1	1	yes	characteristic
88	#830	C₂×C₄	1	1	yes	characteristic
89	#830	C₂×C₄	1	1	yes	characteristic
90	#830	C₂×C₄	1	1	yes	characteristic
91	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
95	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
96	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
97	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
98	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₃	C₂³	1	1	yes	characteristic
102	C₈×Dic₃	C₂³	1	1	yes	characteristic
103	#812	—	4	2	no	—
104	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
105	C₂×C₃⋊C₁₆	C₂³	1	2	yes	—
106	#798	—	4	2	no	—
107	D₃×C₁₆	—	4	2	no	—
108	C₂³×C₈	—	3	1	no	—
109	C₂³×C₈	C₂×D₃	1	1	yes	characteristic
110	C₂×C₄×D₄	—	3	1	no	—
111	C₂×M₃₂	—	3	2	no	—
112	C₂×M₃₂	—	3	2	no	—
113	C₂²×C₁₆	—	3	2	no	—
114	C₂²×C₁₆	C₂×D₃	1	2	yes	complemented
115	C₈×D₄	—	3	1	no	—
116	C₈×D₄	—	3	1	no	—
117	C₈×D₄	—	3	1	no	—
118	C₈×D₄	—	3	1	no	—
119	C₈×D₄	—	3	1	no	—
120	C₈×D₄	—	3	1	no	—
121	C₈×D₄	—	3	1	no	—
122	C₈×D₄	—	3	1	no	—
123	C₂×C₄⋊C₈	—	3	1	no	—
124	C₂×C₂²⋊C₈	—	3	1	no	—
125	C₂×C₂²⋊C₈	—	3	1	no	—
126	C₂×C₄×C₈	—	3	1	no	—
127	C₄⋊C₁₆	—	3	2	no	—
128	C₄⋊C₁₆	—	3	2	no	—
129	C₂²⋊C₁₆	—	3	1	no	—
130	C₂²⋊C₁₆	—	3	1	no	—
131	C₂²⋊C₁₆	—	3	2	no	—
132	C₂²⋊C₁₆	—	3	2	no	—
133	C₂²⋊C₁₆	—	3	2	no	—
134	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
135	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
136	C₂²⋊C₁₆	C₂×D₃	1	2	yes	complemented
137	#346	—	3	2	no	—
138	C₄×C₁₆	—	3	2	no	—
139	C₂⁴×C₃	C₂×C₈	1	1	yes	characteristic
140	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	4	1	no	—
142	C₂²×C₃×C₄	—	4	1	no	—
143	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂×C₈	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
149	C₂×#67	—	2	4	no	—
150	C₂×#67	C₂×C₈	1	1	yes	characteristic
151	C₂×#67	C₂×C₈	1	1	yes	characteristic
152	C₂×#67	C₂×C₈	1	1	yes	characteristic
153	C₂×#67	C₂×C₈	1	1	yes	characteristic
154	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
155	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
156	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
157	C₂×C₄×D₃	—	4	1	no	—
158	C₂×C₄×D₃	—	4	1	no	—
159	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
161	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	4	1	no	—
168	C₂×C₃×C₈	—	4	1	no	—
169	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
173	#217	C₂×C₈	1	1	yes	characteristic
174	#217	C₂×C₈	1	1	yes	characteristic
175	#217	C₂×C₈	1	1	yes	characteristic
176	#217	C₂×C₈	1	1	yes	characteristic
177	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
178	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
179	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
180	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
181	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
182	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
183	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
184	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
185	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
186	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
187	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃⋊C₈	—	4	1	no	—
190	C₂×C₃⋊C₈	—	4	1	no	—
191	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
195	D₃×C₈	—	2	2	no	—
196	D₃×C₈	—	2	2	no	—
197	D₃×C₈	—	4	1	no	—
198	D₃×C₈	—	4	1	no	—
199	C₃×C₁₆	—	2	2	no	—
200	C₃×C₁₆	—	2	2	no	—
201	C₃⋊C₁₆	—	2	2	no	—
202	C₃⋊C₁₆	—	2	2	no	—
203	C₂²×D₄	—	3	1	no	—
204	C₂³×C₄	—	3	1	no	—
205	C₂³×C₄	C₄×D₃	1	1	yes	characteristic
206	C₂²×C₈	—	3	1	no	—
207	C₂²×C₈	—	3	1	no	—
208	C₂²×C₈	—	3	1	no	—
209	C₂²×C₈	—	3	1	no	—
210	C₂²×C₈	—	3	1	no	—
211	C₂²×C₈	—	3	1	no	—
212	C₂²×C₈	—	4	2	no	—
213	C₂²×C₈	—	12	2	no	—
214	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
215	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
216	C₂²×C₈	C₄×D₃	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
220	C₄×D₄	—	3	1	no	—
221	C₄×D₄	—	3	1	no	—
222	C₄×D₄	—	3	1	no	—
223	C₄×D₄	—	3	1	no	—
224	C₄×D₄	—	3	1	no	—
225	C₄×D₄	—	3	1	no	—
226	C₄×D₄	—	3	1	no	—
227	C₄×D₄	—	3	1	no	—
228	C₂×C₄⋊C₄	—	3	1	no	—
229	C₂×C₂²⋊C₄	—	3	1	no	—
230	C₂×C₂²⋊C₄	—	3	1	no	—
231	C₂×C₄²	—	3	1	no	—
232	M₃₂	—	12	2	no	—
233	M₃₂	—	12	2	no	—
234	C₂×C₁₆	—	3	2	no	—
235	C₂×C₁₆	—	3	2	no	—
236	C₂×C₁₆	—	4	2	no	—
237	C₂×C₁₆	—	12	2	no	—
238	C₂×C₁₆	C₂²×D₃	1	2	yes	—
239	C₂×C₁₆	C₂²×D₃	1	2	yes	—
240	C₄⋊C₈	—	3	1	no	—
241	C₄⋊C₈	—	3	1	no	—
242	C₄⋊C₈	—	3	1	no	—
243	C₄⋊C₈	—	3	1	no	—
244	C₂²⋊C₈	—	3	1	no	—
245	C₂²⋊C₈	—	3	1	no	—
246	C₂²⋊C₈	—	3	1	no	—
247	C₂²⋊C₈	—	3	1	no	—
248	C₂²⋊C₈	—	3	1	no	—
249	C₂²⋊C₈	—	3	1	no	—
250	C₂²⋊C₈	—	3	1	no	—
251	C₂²⋊C₈	—	3	1	no	—
252	C₄×C₈	—	3	1	no	—
253	C₄×C₈	—	3	1	no	—
254	C₄×C₈	—	3	1	no	—
255	C₄×C₈	—	3	1	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	4	1	no	—
259	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
260	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
261	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
262	C₂²×D₃	—	2	2	no	—
263	C₂²×D₃	—	2	2	no	—
264	C₂²×D₃	—	4	1	no	—
265	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
266	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	—	4	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
280	#67	—	2	2	no	—
281	#67	—	2	2	no	—
282	#67	—	2	2	no	—
283	#67	M₃₂	1	4	yes	complemented
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	—	4	1	no	—
287	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
288	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
289	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
290	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
291	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
292	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
293	C₄×D₃	—	2	1	no	—
294	C₄×D₃	—	2	1	no	—
295	C₄×D₃	—	2	1	no	—
296	C₄×D₃	—	2	1	no	—
297	C₄×D₃	—	4	1	no	—
298	C₄×D₃	—	4	1	no	—
299	C₃×C₈	—	2	1	no	—
300	C₃×C₈	—	2	1	no	—
301	C₃×C₈	—	2	1	no	—
302	C₃×C₈	H(5,𝔽₂)	1	2	yes	—
303	C₃⋊C₈	—	2	1	no	—
304	C₃⋊C₈	—	2	1	no	—
305	C₃⋊C₈	—	2	1	no	—
306	C₃⋊C₈	—	2	1	no	—
307	C₂⁴	—	3	1	no	—
308	C₂⁴	D₃×C₈	1	1	yes	characteristic
309	C₂×D₄	—	3	1	no	—
310	C₂×D₄	—	3	1	no	—
311	C₂×D₄	—	3	1	no	—
312	C₂×D₄	—	3	1	no	—
313	C₂×D₄	—	6	4	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	3	1	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	12	1	no	—
324	C₂²×C₄	—	12	1	no	—
325	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
326	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
327	C₂²×C₄	D₃×C₈	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	3	1	no	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	—	3	1	no	—
337	C₂×C₈	—	3	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	6	2	no	—
342	C₂×C₈	—	6	2	no	—
343	C₂×C₈	—	12	1	no	—
344	C₂×C₈	—	12	1	no	—
345	C₂×C₈	—	12	1	no	—
346	C₂×C₈	—	12	1	no	—
347	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
351	C₄⋊C₄	—	3	1	no	—
352	C₄⋊C₄	—	3	1	no	—
353	C₄⋊C₄	—	3	1	no	—
354	C₄⋊C₄	—	3	1	no	—
355	C₂²⋊C₄	—	3	1	no	—
356	C₂²⋊C₄	—	3	1	no	—
357	C₂²⋊C₄	—	3	1	no	—
358	C₂²⋊C₄	—	3	1	no	—
359	C₂²⋊C₄	—	3	1	no	—
360	C₂²⋊C₄	—	3	1	no	—
361	C₂²⋊C₄	—	3	1	no	—
362	C₂²⋊C₄	—	3	1	no	—
363	C₄²	—	3	1	no	—
364	C₄²	—	3	1	no	—
365	C₄²	—	3	1	no	—
366	C₄²	—	3	1	no	—
367	C₁₆	—	2	2	no	—
368	C₁₆	—	2	2	no	—
369	C₁₆	—	6	2	no	—
370	C₁₆	—	6	2	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	4	4	no	—
379	C₂²×C₃	C₂×M₃₂	1	2	yes	—
380	C₂²×C₃	#504	1	2	yes	—
381	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
382	C₂×D₃	—	2	1	no	—
383	C₂×D₃	—	2	1	no	—
384	C₂×D₃	—	2	1	no	—
385	C₂×D₃	—	2	1	no	—
386	C₂×D₃	—	2	1	no	—
387	C₂×D₃	—	4	4	no	—
388	C₂×D₃	C₂×M₃₂	1	2	yes	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	#518	1	1	yes	characteristic
393	C₃×C₄	#568	1	1	yes	characteristic
394	Dic₃	—	2	1	no	—
395	Dic₃	—	2	1	no	—
396	Dic₃	—	2	1	no	—
397	Dic₃	—	2	1	no	—
398	Dic₃	—	2	1	no	—
399	Dic₃	C₂×M₃₂	1	2	yes	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	3	1	no	—
403	C₂³	—	3	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	6	2	no	—
406	C₂³	—	6	2	no	—
407	C₂³	—	12	1	no	—
408	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
409	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
410	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
411	D₄	—	3	4	no	—
412	D₄	—	6	2	no	—
413	D₄	—	6	2	no	—
414	D₄	—	6	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	6	1	no	—
433	C₂×C₄	—	6	1	no	—
434	C₂×C₄	—	6	1	no	—
435	C₂×C₄	—	6	1	no	—
436	C₂×C₄	—	12	1	no	—
437	C₂×C₄	—	12	1	no	—
438	C₂×C₄	—	12	1	no	—
439	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
440	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
441	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	6	1	no	—
447	C₈	—	6	1	no	—
448	C₈	—	6	1	no	—
449	C₈	—	6	1	no	—
450	C₈	#1004	1	2	yes	—
451	C₂×C₃	—	2	2	no	—
452	C₂×C₃	—	2	2	no	—
453	C₂×C₃	—	4	1	no	—
454	C₂×C₃	#2972	1	1	yes	characteristic
455	C₂×C₃	C₂²×M₃₂	1	1	yes	characteristic
456	C₂×C₃	C₂×#504	1	1	yes	characteristic
457	D₃	—	2	2	no	—
458	D₃	—	4	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	3	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	6	1	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	6	1	no	—
472	C₂²	—	6	1	no	—
473	C₂²	—	12	4	no	—
474	C₂²	#4901	1	2	yes	—
475	C₂²	D₃×M₃₂	1	2	yes	—
476	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	3	2	no	—
481	C₄	—	6	1	no	—
482	C₄	—	6	1	no	—
483	C₄	—	6	1	no	—
484	C₄	—	6	1	no	—
485	C₄	—	6	1	no	—
486	C₄	#5486	1	1	yes	characteristic
487	C₄	#5745	1	1	yes	characteristic
488	C₃	#33488	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	4	1	no	—
492	C₂	—	6	2	no	—
493	C₂	—	12	1	no	—
494	C₂	#78601	1	1	yes	characteristic
495	C₂	C₂×#4901	1	1	yes	characteristic
496	C₂	C₂×D₃×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₂×C₃×C₂²⋊C₁₆	C₂
prime radical	C₂²×#67	C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₃
hypocenter	C₃	#33488
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₂²⋊C₁₆	C₂	semidirect
3. #71963	C₂	semidirect
4. #71407	C₂	semidirect
5. C₁₆×#67	C₂	semidirect
6. #69106	C₂	semidirect
7. D₃×C₂²⋊C₁₆	C₂	semidirect
8. #69104	C₂	semidirect
9. #69103	C₂	semidirect
10. #69093	C₂	semidirect
11. #69092	C₂	semidirect
16. C₂²×C₃×C₁₆	C₂²	semidirect
29. C₂×#812	C₂²	semidirect
30. C₂×#798	C₂²	semidirect
31. C₂×D₃×C₁₆	C₂²	semidirect
34. C₃×C₂²⋊C₁₆	C₂²	semidirect
37. #4549	C₂²	semidirect
38. (C₂×D₃)⋊C₁₆	C₂²	semidirect
39. (C₂×D₃)⋊C₁₆	C₂²	semidirect
40. #4502	C₂²	semidirect
41. Dic₃⋊C₁₆	C₂²	semidirect
42. Dic₃⋊C₁₆	C₂²	semidirect
43. Dic₃×C₁₆	C₂²	semidirect
54. C₂×C₂²⋊C₁₆	D₃	semidirect
114. C₂²×C₁₆	C₂×D₃	semidirect
136. C₂²⋊C₁₆	C₂×D₃	semidirect
283. #67	M₃₂	semidirect
488. C₃	#33488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×#67	2
C₂×C₃×C₂²⋊C₁₆	2
#71963	2
#71407	2
C₁₆×#67	2
#69106	2
D₃×C₂²⋊C₁₆	2
#69104	2
#69103	2
#69093	2
#69092	2
#33488	3