Subgroups — #10948789

Order 768.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#79421	C₂	1	1	yes	maximal, characteristic
2	C₃×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#71409	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×D₃)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#71407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×#67	C₂	1	1	yes	maximal, characteristic, complemented
7	#70857	C₂	1	1	yes	maximal, characteristic, complemented
8	#69278	C₂	1	1	yes	maximal, characteristic, complemented
9	#69276	C₂	1	1	yes	maximal, characteristic, complemented
10	#69107	C₂	1	1	yes	maximal, characteristic, complemented
11	#69106	C₂	1	1	yes	maximal, characteristic, complemented
12	#69104	C₂	1	1	yes	maximal, characteristic, complemented
13	#69102	C₂	1	1	yes	maximal, characteristic, complemented
14	#69055	C₂	1	1	yes	maximal, characteristic, complemented
15	#69053	C₂	1	1	yes	maximal, characteristic, complemented
16	#33490	—	3	1	no	maximal, Sylow
17	C₂×#901	C₂²	1	1	yes	characteristic
18	C₂²×D₃×C₈	C₂²	1	1	yes	characteristic
19	#5547	C₄	1	1	yes	characteristic
20	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
23	C₈×#67	C₂²	1	1	yes	characteristic
24	C₈×#67	C₂²	1	1	yes	characteristic
25	C₂×#812	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
27	#5011	C₄	1	1	yes	characteristic
28	C₂×#798	C₂²	1	1	yes	characteristic
29	C₂×#798	C₂²	1	1	yes	characteristic
30	C₂×#798	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
32	#4839	C₄	1	1	yes	characteristic
33	#4836	C₄	1	1	yes	characteristic
34	#4730	C₄	1	1	yes	characteristic
35	#4728	C₄	1	1	yes	characteristic
36	#4727	C₄	1	1	yes	characteristic
37	#4726	C₄	1	1	yes	characteristic
38	#4689	C₂²	1	1	yes	characteristic
39	C₈×D₁₂	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
44	#4549	C₂²	1	1	yes	characteristic
45	#4549	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
48	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
49	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
50	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
51	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic
52	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₃)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
54	#4502	C₂²	1	1	yes	characteristic, complemented
55	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	Dic₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
59	#4461	C₂²	1	1	yes	characteristic, complemented
60	#2929	—	3	1	no	—
61	#2169	—	3	1	no	—
62	#2169	—	3	1	no	—
63	#2168	—	3	1	no	—
64	#2168	—	3	1	no	—
65	#2168	—	3	1	no	—
66	#2168	—	3	1	no	—
67	D₄×C₁₆	—	3	1	no	—
68	D₄×C₁₆	D₃	1	1	yes	characteristic, complemented
69	#2164	—	3	1	no	—
70	#2164	—	3	1	no	—
71	#2113	—	3	1	no	—
72	#2113	—	3	1	no	—
73	#2112	—	3	1	no	—
74	C₂×C₂²⋊C₁₆	—	3	1	no	—
75	C₂×#235	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
80	#939	C₈	1	1	yes	characteristic
81	#937	C₈	1	1	yes	characteristic
82	C₄×#67	C₂×C₄	1	1	yes	characteristic
83	C₄×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×#208	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	#901	—	4	1	no	—
87	#901	—	4	1	no	—
88	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
89	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
90	C₂×ΓL(1,𝔽₂₅)	C₂×C₄	1	1	yes	characteristic
91	C₂×D₃×C₈	—	4	1	no	—
92	C₂×D₃×C₈	—	4	1	no	—
93	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×D₃×C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
96	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
97	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
98	#896	C₈	1	1	yes	characteristic
99	#894	C₈	1	1	yes	characteristic
100	#884	C₈	1	1	yes	characteristic
101	#883	C₈	1	1	yes	characteristic
102	#882	C₈	1	1	yes	characteristic
103	#878	C₈	1	1	yes	characteristic
104	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
105	#872	C₂×C₄	1	1	yes	characteristic
106	C₂×C₃×C₁₆	—	4	1	no	—
107	C₂×C₃×C₁₆	—	4	1	no	—
108	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
112	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
116	#830	C₂×C₄	1	1	yes	characteristic
117	#830	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
119	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
120	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
122	#815	C₂×C₄	1	1	yes	characteristic
123	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
124	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₈×Dic₃	C₂³	1	1	yes	characteristic
126	#812	—	4	1	no	—
127	C₂×C₃⋊C₁₆	—	4	1	no	—
128	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
130	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
132	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
133	#803	C₂×C₄	1	1	yes	characteristic
134	#798	—	4	1	no	—
135	#798	—	4	1	no	—
136	#798	—	4	1	no	—
137	D₃×C₁₆	—	4	1	no	—
138	C₂×#131	—	3	1	no	—
139	C₂³×C₈	—	3	1	no	—
140	#525	—	3	1	no	—
141	C₂×M₃₂	—	3	1	no	—
142	C₂×M₃₂	—	3	1	no	—
143	C₂×M₃₂	—	3	1	no	—
144	C₂×M₃₂	—	3	1	no	—
145	C₂²×C₁₆	—	3	1	no	—
146	C₂²×C₁₆	—	3	1	no	—
147	C₂²×C₁₆	C₂×D₃	1	1	yes	characteristic
148	C₂²×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
149	#435	—	3	1	no	—
150	#435	—	3	1	no	—
151	#435	—	3	1	no	—
152	#435	—	3	1	no	—
153	C₈×D₄	—	3	1	no	—
154	C₈×D₄	—	3	1	no	—
155	C₈×D₄	—	3	1	no	—
156	C₈×D₄	C₂×D₃	1	1	yes	characteristic
157	#424	—	3	1	no	—
158	#408	—	3	1	no	—
159	#407	—	3	1	no	—
160	#405	—	3	1	no	—
161	C₄⋊C₁₆	—	3	1	no	—
162	C₄⋊C₁₆	—	3	1	no	—
163	C₄⋊C₁₆	—	3	1	no	—
164	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
165	C₂²⋊C₁₆	—	3	1	no	—
166	C₂²⋊C₁₆	—	3	1	no	—
167	C₂²⋊C₁₆	—	3	1	no	—
168	C₂²⋊C₁₆	—	3	1	no	—
169	C₂²⋊C₁₆	—	3	1	no	—
170	C₂²⋊C₁₆	—	3	1	no	—
171	C₂²⋊C₁₆	—	3	1	no	—
172	C₂²⋊C₁₆	—	3	1	no	—
173	C₂²⋊C₁₆	—	3	1	no	—
174	C₂²⋊C₁₆	—	3	1	no	—
175	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
176	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
177	#346	—	3	1	no	—
178	#346	—	3	1	no	—
179	C₄×C₁₆	—	3	1	no	—
180	C₄×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂³×D₃	C₂×C₈	1	1	yes	characteristic
182	C₂×C₃×D₄	C₂×C₈	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
185	C₂×#67	C₂×C₈	1	1	yes	characteristic
186	C₂×#67	C₂×C₈	1	1	yes	characteristic
187	C₂×#67	C₂×C₈	1	1	yes	characteristic
188	C₂×#67	C₂×C₈	1	1	yes	characteristic
189	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
190	#235	—	4	1	no	—
191	#235	—	4	1	no	—
192	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
193	C₂×D₁₂	C₂×C₈	1	1	yes	characteristic
194	C₂×C₄×D₃	—	4	1	no	—
195	C₂×C₄×D₃	—	4	1	no	—
196	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂×C₈	1	1	yes	characteristic
198	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₂×C₃×C₈	—	2	1	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
210	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
211	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
213	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
214	#217	C₂×C₈	1	1	yes	characteristic
215	#217	C₂×C₈	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
223	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
224	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
225	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
226	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
227	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
228	#208	—	4	1	no	—
229	C₂×C₃⋊C₈	—	4	1	no	—
230	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
234	ΓL(1,𝔽₂₅)	—	4	1	no	—
235	ΓL(1,𝔽₂₅)	—	4	1	no	—
236	ΓL(1,𝔽₂₅)	—	4	1	no	—
237	D₃×C₈	—	2	1	no	—
238	D₃×C₈	—	2	1	no	—
239	D₃×C₈	—	2	1	no	—
240	D₃×C₈	—	2	1	no	—
241	D₃×C₈	—	2	1	no	—
242	D₃×C₈	—	2	1	no	—
243	D₃×C₈	—	4	1	no	—
244	D₃×C₈	—	4	1	no	—
245	C₃×C₁₆	—	2	1	no	—
246	C₃×C₁₆	—	2	1	no	—
247	C₃×C₁₆	—	2	1	no	—
248	C₃×C₁₆	—	2	1	no	—
249	C₃⋊C₁₆	—	2	1	no	—
250	C₃⋊C₁₆	—	2	1	no	—
251	C₃⋊C₁₆	—	2	1	no	—
252	C₃⋊C₁₆	—	2	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂³×C₄	—	3	1	no	—
255	#131	—	12	1	no	—
256	#131	—	12	1	no	—
257	C₂×M₁₆	—	3	1	no	—
258	C₂×M₁₆	—	3	1	no	—
259	C₂×M₁₆	—	3	1	no	—
260	C₂×M₁₆	—	3	1	no	—
261	C₂²×C₈	—	3	1	no	—
262	C₂²×C₈	—	3	1	no	—
263	C₂²×C₈	—	3	1	no	—
264	C₂²×C₈	—	3	1	no	—
265	C₂²×C₈	—	3	1	no	—
266	C₂²×C₈	—	3	1	no	—
267	C₂²×C₈	—	12	1	no	—
268	C₂²×C₈	—	12	1	no	—
269	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
271	#123	—	3	1	no	—
272	#123	—	3	1	no	—
273	C₂²⋊Q₈	—	3	1	no	—
274	C₂²⋊Q₈	—	3	1	no	—
275	#121	—	3	1	no	—
276	#121	—	3	1	no	—
277	#120	—	3	1	no	—
278	#120	—	3	1	no	—
279	C₄×D₄	—	3	1	no	—
280	C₄×D₄	—	3	1	no	—
281	C₄×D₄	—	3	1	no	—
282	C₄×D₄	C₄×D₃	1	1	yes	characteristic
283	#117	—	3	1	no	—
284	M₃₂	—	12	1	no	—
285	M₃₂	—	12	1	no	—
286	M₃₂	—	12	1	no	—
287	M₃₂	—	12	1	no	—
288	C₂×C₁₆	—	3	1	no	—
289	C₂×C₁₆	—	3	1	no	—
290	C₂×C₁₆	—	3	1	no	—
291	C₂×C₁₆	—	3	1	no	—
292	C₂×C₁₆	—	4	1	no	—
293	C₂×C₁₆	—	4	1	no	—
294	C₂×C₁₆	—	12	1	no	—
295	C₂×C₁₆	—	12	1	no	—
296	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
298	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
299	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
300	C₄⋊C₈	—	3	1	no	—
301	C₄⋊C₈	—	3	1	no	—
302	C₄⋊C₈	—	3	1	no	—
303	C₄⋊C₈	C₄×D₃	1	1	yes	characteristic
304	C₂²⋊C₈	—	3	1	no	—
305	C₂²⋊C₈	—	3	1	no	—
306	C₂²⋊C₈	—	3	1	no	—
307	C₂²⋊C₈	—	3	1	no	—
308	C₂²⋊C₈	—	3	1	no	—
309	C₂²⋊C₈	—	3	1	no	—
310	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
311	C₂²⋊C₈	C₄×D₃	1	1	yes	characteristic
312	#97	—	3	1	no	—
313	#97	—	3	1	no	—
314	C₄×C₈	—	3	1	no	—
315	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
316	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
317	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
318	C₂²×D₃	—	2	2	no	—
319	C₂²×D₃	—	4	1	no	—
320	C₂²×D₃	—	4	1	no	—
321	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
322	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
323	C₂²×D₃	C₂²×C₈	1	1	yes	characteristic
324	C₃×D₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
334	#67	—	2	2	no	—
335	#67	—	4	1	no	—
336	#67	—	4	1	no	—
337	#67	—	4	1	no	—
338	C₂×Dic₃	—	4	1	no	—
339	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
340	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
341	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
342	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
343	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
344	D₁₂	—	4	1	no	—
345	D₁₂	—	4	1	no	—
346	C₄×D₃	—	2	1	no	—
347	C₄×D₃	—	2	1	no	—
348	C₄×D₃	—	2	1	no	—
349	C₄×D₃	—	2	1	no	—
350	C₄×D₃	—	2	1	no	—
351	C₄×D₃	—	2	1	no	—
352	C₄×D₃	—	4	1	no	—
353	C₄×D₃	—	4	1	no	—
354	Dic₆	—	4	1	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	—	2	1	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
359	C₃×C₈	H(5,𝔽₂)	1	1	yes	characteristic
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	—	2	1	no	—
362	C₃⋊C₈	—	2	1	no	—
363	C₃⋊C₈	—	2	1	no	—
364	C₂⁴	—	3	1	no	—
365	#41	—	12	1	no	—
366	#41	—	12	1	no	—
367	C₂×Q₈	—	3	1	no	—
368	C₂×D₄	—	3	1	no	—
369	C₂×D₄	—	3	1	no	—
370	C₂×D₄	—	3	1	no	—
371	C₂×D₄	—	3	1	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	3	1	no	—
374	C₂×D₄	D₃×C₈	1	1	yes	characteristic
375	C₂²×C₄	—	3	1	no	—
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	12	1	no	—
382	C₂²×C₄	—	12	1	no	—
383	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
385	M₁₆	—	12	1	no	—
386	M₁₆	—	12	1	no	—
387	M₁₆	—	12	1	no	—
388	M₁₆	—	12	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	—	3	1	no	—
395	C₂×C₈	—	3	1	no	—
396	C₂×C₈	—	3	1	no	—
397	C₂×C₈	—	6	1	no	—
398	C₂×C₈	—	6	1	no	—
399	C₂×C₈	—	6	1	no	—
400	C₂×C₈	—	6	1	no	—
401	C₂×C₈	—	6	1	no	—
402	C₂×C₈	—	6	1	no	—
403	C₂×C₈	—	12	1	no	—
404	C₂×C₈	—	12	1	no	—
405	C₂×C₈	—	12	1	no	—
406	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
407	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
408	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
409	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	—	3	1	no	—
412	C₄⋊C₄	—	3	1	no	—
413	C₄⋊C₄	—	3	1	no	—
414	C₄⋊C₄	—	3	1	no	—
415	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
416	C₂²⋊C₄	—	3	1	no	—
417	C₂²⋊C₄	—	3	1	no	—
418	C₂²⋊C₄	—	3	1	no	—
419	C₂²⋊C₄	—	3	1	no	—
420	C₂²⋊C₄	—	3	1	no	—
421	C₂²⋊C₄	—	3	1	no	—
422	C₂²⋊C₄	—	3	1	no	—
423	C₂²⋊C₄	—	3	1	no	—
424	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
425	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
426	C₄²	—	3	1	no	—
427	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
428	C₁₆	—	2	1	no	—
429	C₁₆	—	2	1	no	—
430	C₁₆	—	2	1	no	—
431	C₁₆	—	2	1	no	—
432	C₁₆	—	6	1	no	—
433	C₁₆	—	6	1	no	—
434	C₁₆	—	6	1	no	—
435	C₁₆	—	6	1	no	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	1	no	—
440	C₂²×C₃	—	2	1	no	—
441	C₂²×C₃	#504	1	2	yes	—
442	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
443	C₂×D₃	—	2	1	no	—
444	C₂×D₃	—	2	1	no	—
445	C₂×D₃	—	2	1	no	—
446	C₂×D₃	—	2	1	no	—
447	C₂×D₃	—	2	1	no	—
448	C₂×D₃	—	2	1	no	—
449	C₂×D₃	—	2	1	no	—
450	C₂×D₃	—	2	1	no	—
451	C₂×D₃	—	2	1	no	—
452	C₂×D₃	—	4	4	no	—
453	C₃×C₄	—	2	1	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	2	1	no	—
456	C₃×C₄	—	2	1	no	—
457	C₃×C₄	#518	1	1	yes	characteristic
458	C₃×C₄	#568	1	1	yes	characteristic
459	Dic₃	—	2	1	no	—
460	Dic₃	—	2	1	no	—
461	Dic₃	—	2	1	no	—
462	Dic₃	—	2	1	no	—
463	Dic₃	—	2	1	no	—
464	C₂³	—	3	1	no	—
465	C₂³	—	3	1	no	—
466	C₂³	—	3	1	no	—
467	C₂³	—	6	2	no	—
468	C₂³	—	12	1	no	—
469	C₂³	—	12	1	no	—
470	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
471	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
472	Q₈	—	12	1	no	—
473	D₄	—	2	2	no	—
474	D₄	—	6	2	no	—
475	D₄	—	12	1	no	—
476	D₄	—	12	1	no	—
477	D₄	—	12	1	no	—
478	D₄	—	12	1	no	—
479	D₄	—	12	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	1	no	—
486	C₂×C₄	—	3	1	no	—
487	C₂×C₄	—	3	1	no	—
488	C₂×C₄	—	3	1	no	—
489	C₂×C₄	—	6	1	no	—
490	C₂×C₄	—	6	1	no	—
491	C₂×C₄	—	6	1	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	1	no	—
494	C₂×C₄	—	6	1	no	—
495	C₂×C₄	—	12	1	no	—
496	C₂×C₄	—	12	1	no	—
497	C₂×C₄	—	12	1	no	—
498	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
499	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
500	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
501	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	6	1	no	—
507	C₈	—	6	1	no	—
508	C₈	—	6	1	no	—
509	C₈	—	6	1	no	—
510	C₈	#1004	1	1	yes	characteristic
511	C₈	#1009	1	1	yes	characteristic
512	C₂×C₃	—	2	2	no	—
513	C₂×C₃	—	4	1	no	—
514	C₂×C₃	#2972	1	1	yes	characteristic
515	C₂×C₃	C₂×#504	1	1	yes	characteristic
516	C₂×C₃	#3407	1	1	yes	characteristic
517	D₃	—	4	1	no	—
518	D₃	—	4	1	no	—
519	D₃	—	4	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	6	1	no	—
526	C₂²	—	6	1	no	—
527	C₂²	—	6	1	no	—
528	C₂²	—	6	1	no	—
529	C₂²	—	6	1	no	—
530	C₂²	—	6	1	no	—
531	C₂²	—	6	1	no	—
532	C₂²	—	6	1	no	—
533	C₂²	—	6	1	no	—
534	C₂²	—	12	4	no	—
535	C₂²	#4901	1	2	yes	—
536	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	6	1	no	—
542	C₄	—	6	1	no	—
543	C₄	—	6	1	no	—
544	C₄	—	6	1	no	—
545	C₄	—	6	1	no	—
546	C₄	#5545	1	1	yes	characteristic
547	C₄	#5750	1	1	yes	characteristic
548	C₃	#33490	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	1	no	—
551	C₂	—	12	1	no	—
552	C₂	—	12	1	no	—
553	C₂	—	12	1	no	—
554	C₂	#79426	1	1	yes	characteristic
555	C₂	C₂×#4901	1	1	yes	characteristic
556	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×D₄×C₁₆	C₂
prime radical	#5547	C₄
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	D₄×C₁₆	D₃
hypocenter	C₃	#33490
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×D₄×C₁₆	C₂	semidirect
3. #71409	C₂	semidirect
4. C₂×(C₂×D₃)⋊C₁₆	C₂	semidirect
5. #71407	C₂	semidirect
6. C₁₆×#67	C₂	semidirect
7. #70857	C₂	semidirect
8. #69278	C₂	semidirect
9. #69276	C₂	semidirect
10. #69107	C₂	semidirect
11. #69106	C₂	semidirect
12. #69104	C₂	semidirect
13. #69102	C₂	semidirect
14. #69055	C₂	semidirect
15. #69053	C₂	semidirect
21. C₂²×C₃×C₁₆	C₂²	semidirect
25. C₂×#812	C₂²	semidirect
30. C₂×#798	C₂²	semidirect
31. C₂×D₃×C₁₆	C₂²	semidirect
40. C₃×C₄⋊C₁₆	C₂²	semidirect
42. C₃×C₂²⋊C₁₆	C₂²	semidirect
43. C₃×C₄×C₁₆	C₂²	semidirect
45. #4549	C₂²	semidirect
52. (C₂×D₃)⋊C₁₆	C₂²	semidirect
53. (C₂×D₃)⋊C₁₆	C₂²	semidirect
54. #4502	C₂²	semidirect
55. Dic₃⋊C₁₆	C₂²	semidirect
56. Dic₃⋊C₁₆	C₂²	semidirect
57. Dic₃×C₁₆	C₂²	semidirect
58. C₄⋊(C₃⋊C₁₆)	C₂²	semidirect
59. #4461	C₂²	semidirect
68. D₄×C₁₆	D₃	semidirect
148. C₂²×C₁₆	C₂×D₃	semidirect
164. C₄⋊C₁₆	C₂×D₃	semidirect
176. C₂²⋊C₁₆	C₂×D₃	semidirect
180. C₄×C₁₆	C₂×D₃	semidirect
548. C₃	#33490	semidirect

Maximal subgroups

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

subgroup	index
#79421	2
C₃×D₄×C₁₆	2
#71409	2
C₂×(C₂×D₃)⋊C₁₆	2
#71407	2
C₁₆×#67	2
#70857	2
#69278	2
#69276	2
#69107	2
#69106	2
#69104	2
#69102	2
#69055	2
#69053	2
#33490	3