Subgroups — #10819994

Order 768.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×#5024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#5011	C₂	1	1	yes	maximal, characteristic
4	#71635	C₂	1	1	yes	maximal, characteristic, complemented
5	#71615	C₂	1	1	yes	maximal, characteristic
6	#69452	C₂	1	1	yes	maximal, characteristic, complemented
7	#69451	C₂	1	1	yes	maximal, characteristic, complemented
8	#69451	C₂	1	1	yes	maximal, characteristic, complemented
9	#69451	C₂	1	1	yes	maximal, characteristic, complemented
10	#69450	C₂	1	1	yes	maximal, characteristic, complemented
11	#69449	C₂	1	1	yes	maximal, characteristic, complemented
12	#69448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#69391	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
16	#23206	—	3	1	no	maximal, Sylow
17	C₂×C₃×#124	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
20	C₂²×#208	C₂²	1	1	yes	characteristic
21	C₂³×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×#391	C₄	1	1	yes	characteristic
23	C₃×#390	C₄	1	1	yes	characteristic
24	C₃×#388	C₄	1	1	yes	characteristic
25	C₃×#388	C₄	1	1	yes	characteristic
26	C₃×#388	C₄	1	1	yes	characteristic
27	C₃×#388	C₄	1	1	yes	characteristic
28	C₃×#382	C₄	1	1	yes	characteristic
29	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₄³	C₂²	1	1	yes	characteristic
34	C₂×#830	C₂²	1	1	yes	characteristic
35	C₂×#830	C₂²	1	1	yes	characteristic
36	C₂×#830	C₂²	1	1	yes	characteristic
37	C₂×#830	C₂²	1	1	yes	characteristic
38	C₂×#830	C₂²	1	1	yes	characteristic
39	C₂×#830	C₂²	1	1	yes	characteristic
40	#5024	—	2	4	no	—
41	#5011	—	2	4	no	—
42	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
48	C₂×#803	C₂²	1	1	yes	characteristic
49	C₂×#803	C₂²	1	1	yes	characteristic
50	C₂×#803	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
54	#4524	C₂²	1	1	yes	characteristic
55	#4524	C₂²	1	1	yes	characteristic
56	#4524	C₂²	1	1	yes	characteristic
57	#4524	C₂²	1	1	yes	characteristic
58	#4524	C₂²	1	1	yes	characteristic
59	#4524	C₂²	1	1	yes	characteristic
60	#4524	C₂²	1	1	yes	characteristic
61	#4524	C₂²	1	1	yes	characteristic
62	C₂×#446	—	3	1	no	—
63	C₂×#435	—	3	1	no	—
64	C₄×#124	D₃	1	1	yes	characteristic
65	#1985	—	3	1	no	—
66	#1955	—	3	1	no	—
67	#1924	—	3	1	no	—
68	#1923	—	3	1	no	—
69	#1923	—	3	1	no	—
70	#1923	—	3	1	no	—
71	#1851	—	3	1	no	—
72	#1850	—	3	1	no	—
73	#1767	—	3	1	no	—
74	C₄×C₄⋊C₈	—	3	1	no	—
75	#1753	—	3	1	no	—
76	C₈×C₂²⋊C₄	—	3	1	no	—
77	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
81	C₃×#124	—	2	4	no	—
82	C₃×C₄×Q₈	—	2	2	no	—
83	C₃×C₄×Q₈	—	2	2	no	—
84	C₃×C₄×D₄	—	2	2	no	—
85	C₃×C₄×D₄	—	2	2	no	—
86	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
109	C₂×#208	—	2	2	no	—
110	C₂×#208	—	2	2	no	—
111	C₂×#208	—	4	1	no	—
112	C₂²×C₃⋊C₈	—	2	2	no	—
113	C₂²×C₃⋊C₈	—	2	2	no	—
114	C₂²×C₃⋊C₈	—	4	1	no	—
115	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
116	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₃×#95	C₂×C₄	1	1	yes	characteristic
124	C₃×#95	C₂×C₄	1	1	yes	characteristic
125	C₃×#95	C₂×C₄	1	1	yes	characteristic
126	C₃×#95	C₂×C₄	1	1	yes	characteristic
127	C₃×#95	C₂×C₄	1	1	yes	characteristic
128	C₃×#95	C₂×C₄	1	1	yes	characteristic
129	C₃×#95	C₂×C₄	1	1	yes	characteristic
130	C₃×#95	C₂×C₄	1	1	yes	characteristic
131	#830	—	2	2	no	—
132	#830	—	2	2	no	—
133	#830	—	2	2	no	—
134	#830	—	2	2	no	—
135	#830	—	4	1	no	—
136	#830	—	4	1	no	—
137	C₄⋊(C₃⋊C₈)	—	2	2	no	—
138	C₄⋊(C₃⋊C₈)	—	2	2	no	—
139	C₄⋊(C₃⋊C₈)	—	2	2	no	—
140	C₄⋊(C₃⋊C₈)	—	2	2	no	—
141	C₄⋊(C₃⋊C₈)	—	2	2	no	—
142	C₄⋊(C₃⋊C₈)	D₄	1	4	yes	—
143	#803	—	2	2	no	—
144	#803	—	2	2	no	—
145	#803	—	2	2	no	—
146	C₄×C₃⋊C₈	—	2	2	no	—
147	C₄×C₃⋊C₈	—	4	1	no	—
148	C₄×C₃⋊C₈	—	4	1	no	—
149	C₂²×M₁₆	—	3	1	no	—
150	C₂³×C₈	—	3	1	no	—
151	C₂×#124	Dic₃	1	1	yes	characteristic
152	C₂×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂×D₃	1	1	yes	characteristic
154	#446	—	6	4	no	—
155	#435	—	6	4	no	—
156	C₂×C₄⋊C₈	—	3	1	no	—
157	C₂×C₄⋊C₈	—	3	1	no	—
158	C₂×C₄⋊C₈	—	3	1	no	—
159	C₂×C₄⋊C₈	—	3	1	no	—
160	C₂×C₄⋊C₈	—	3	1	no	—
161	C₂×C₄⋊C₈	—	3	1	no	—
162	C₂×C₂²⋊C₈	—	3	1	no	—
163	C₂×C₂²⋊C₈	—	3	1	no	—
164	C₂×C₂²⋊C₈	—	3	1	no	—
165	C₂×C₂²⋊C₈	—	3	1	no	—
166	C₂×C₂²⋊C₈	—	3	1	no	—
167	C₂×C₂²⋊C₈	—	3	1	no	—
168	C₂×#97	—	3	1	no	—
169	C₂×#97	—	3	1	no	—
170	C₂×#97	—	3	1	no	—
171	C₂×C₄×C₈	—	3	1	no	—
172	C₂×C₄×C₈	—	3	1	no	—
173	C₂×C₄×C₈	—	3	1	no	—
174	#391	Dic₃	1	1	yes	characteristic
175	#390	Dic₃	1	1	yes	characteristic
176	#388	Dic₃	1	1	yes	characteristic
177	#388	Dic₃	1	1	yes	characteristic
178	#388	Dic₃	1	1	yes	characteristic
179	#388	Dic₃	1	1	yes	characteristic
180	#382	Dic₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
185	C₄³	C₂×D₃	1	1	yes	characteristic
186	#336	—	3	1	no	—
187	#336	—	3	1	no	—
188	#336	—	3	1	no	—
189	#336	—	3	1	no	—
190	#336	—	3	1	no	—
191	#336	—	3	1	no	—
192	#336	—	3	1	no	—
193	#336	—	3	1	no	—
194	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
195	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×Q₈	—	2	2	no	—
197	C₂×C₃×Q₈	—	2	2	no	—
198	C₂×C₃×Q₈	—	4	1	no	—
199	C₂×C₃×D₄	—	2	2	no	—
200	C₂×C₃×D₄	—	2	2	no	—
201	C₂×C₃×D₄	—	4	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	—	2	2	no	—
234	C₃×C₂²⋊C₄	—	2	2	no	—
235	C₃×C₂²⋊C₄	—	2	2	no	—
236	C₃×C₂²⋊C₄	—	2	2	no	—
237	C₃×C₂²⋊C₄	—	2	2	no	—
238	C₃×C₂²⋊C₄	—	2	2	no	—
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	M₁₆	1	4	yes	complemented
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	2	2	no	—
243	C₃×C₄²	—	2	2	no	—
244	C₃×C₄²	—	2	1	no	—
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	—	2	1	no	—
247	C₃×C₄²	—	2	1	no	—
248	C₃×C₄²	—	2	1	no	—
249	C₃×C₄²	—	2	1	no	—
250	C₃×C₄²	—	2	1	no	—
251	C₃×C₄²	—	2	1	no	—
252	C₃×C₄²	—	4	1	no	—
253	C₃×C₄²	C₂×D₄	1	2	yes	—
254	C₃×C₄²	#41	1	2	yes	—
255	#208	—	4	4	no	—
256	C₂×C₃⋊C₈	—	2	1	no	—
257	C₂×C₃⋊C₈	—	2	1	no	—
258	C₂×C₃⋊C₈	—	2	1	no	—
259	C₂×C₃⋊C₈	—	2	1	no	—
260	C₂×C₃⋊C₈	—	2	1	no	—
261	C₂×C₃⋊C₈	—	2	1	no	—
262	C₂×C₃⋊C₈	—	2	1	no	—
263	C₂×C₃⋊C₈	—	2	1	no	—
264	C₂×C₃⋊C₈	—	2	1	no	—
265	C₂×C₃⋊C₈	—	2	1	no	—
266	C₂×C₃⋊C₈	—	2	1	no	—
267	C₂×C₃⋊C₈	—	2	1	no	—
268	C₂×C₃⋊C₈	—	2	1	no	—
269	C₂×C₃⋊C₈	—	2	1	no	—
270	C₂×C₃⋊C₈	—	2	1	no	—
271	C₂×C₃⋊C₈	—	2	1	no	—
272	C₂×C₃⋊C₈	—	2	1	no	—
273	C₂×C₃⋊C₈	—	2	1	no	—
274	C₂×C₃⋊C₈	—	2	1	no	—
275	C₂×C₃⋊C₈	—	2	1	no	—
276	C₂×C₃⋊C₈	—	4	4	no	—
277	C₂×C₃⋊C₈	C₂×D₄	1	2	yes	—
278	C₂×C₃⋊C₈	C₂×D₄	1	2	yes	—
279	C₂×C₃⋊C₈	#41	1	2	yes	—
280	C₂×C₃⋊C₈	#41	1	2	yes	—
281	C₂²×Q₈	C₂×Dic₃	1	1	yes	characteristic
282	C₂²×D₄	C₂×Dic₃	1	1	yes	characteristic
283	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
285	C₂×M₁₆	—	6	2	no	—
286	C₂×M₁₆	—	6	2	no	—
287	C₂×M₁₆	—	12	1	no	—
288	C₂²×C₈	—	3	1	no	—
289	C₂²×C₈	—	3	1	no	—
290	C₂²×C₈	—	3	1	no	—
291	C₂²×C₈	—	3	1	no	—
292	C₂²×C₈	—	3	1	no	—
293	C₂²×C₈	—	3	1	no	—
294	C₂²×C₈	—	3	1	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	6	2	no	—
297	C₂²×C₈	—	6	2	no	—
298	C₂²×C₈	—	12	1	no	—
299	#124	—	2	4	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
318	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
319	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
320	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
321	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
327	C₄⋊C₈	—	3	4	no	—
328	C₄⋊C₈	—	6	2	no	—
329	C₄⋊C₈	—	6	2	no	—
330	C₄⋊C₈	—	6	2	no	—
331	C₄⋊C₈	—	6	2	no	—
332	C₄⋊C₈	—	6	2	no	—
333	C₂²⋊C₈	—	6	2	no	—
334	C₂²⋊C₈	—	6	2	no	—
335	C₂²⋊C₈	—	6	2	no	—
336	C₂²⋊C₈	—	6	2	no	—
337	C₂²⋊C₈	—	12	1	no	—
338	C₂²⋊C₈	—	12	1	no	—
339	#97	—	6	2	no	—
340	#97	—	6	2	no	—
341	#97	—	6	2	no	—
342	C₄×C₈	—	6	2	no	—
343	C₄×C₈	—	12	1	no	—
344	C₄×C₈	—	12	1	no	—
345	#95	C₂×Dic₃	1	1	yes	characteristic
346	#95	C₂×Dic₃	1	1	yes	characteristic
347	#95	C₂×Dic₃	1	1	yes	characteristic
348	#95	C₂×Dic₃	1	1	yes	characteristic
349	#95	C₂×Dic₃	1	1	yes	characteristic
350	#95	C₂×Dic₃	1	1	yes	characteristic
351	#95	C₂×Dic₃	1	1	yes	characteristic
352	#95	C₂×Dic₃	1	1	yes	characteristic
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	C₂×M₁₆	1	2	yes	—
367	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
368	C₃×Q₈	—	4	4	no	—
369	C₃×D₄	—	4	4	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	4	1	no	—
401	C₂×C₃×C₄	—	4	1	no	—
402	C₂×C₃×C₄	—	4	1	no	—
403	C₂×C₃×C₄	—	4	1	no	—
404	C₂×C₃×C₄	—	4	1	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
409	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
410	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
411	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
412	C₂×C₃×C₄	#131	1	2	yes	—
413	C₂×C₃×C₄	#131	1	2	yes	—
414	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
418	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
420	C₃⋊C₈	—	2	2	no	—
421	C₃⋊C₈	—	2	2	no	—
422	C₃⋊C₈	—	2	2	no	—
423	C₃⋊C₈	—	2	2	no	—
424	C₃⋊C₈	—	4	1	no	—
425	C₃⋊C₈	—	4	1	no	—
426	C₃⋊C₈	—	4	1	no	—
427	C₃⋊C₈	—	4	1	no	—
428	C₂⁴	C₂²×Dic₃	1	1	yes	characteristic
429	C₂⁴	C₂²×Dic₃	1	1	yes	characteristic
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
460	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
461	M₁₆	—	12	4	no	—
462	C₂×C₈	—	3	2	no	—
463	C₂×C₈	—	3	2	no	—
464	C₂×C₈	—	3	2	no	—
465	C₂×C₈	—	3	2	no	—
466	C₂×C₈	—	6	1	no	—
467	C₂×C₈	—	6	1	no	—
468	C₂×C₈	—	6	1	no	—
469	C₂×C₈	—	6	1	no	—
470	C₂×C₈	—	6	1	no	—
471	C₂×C₈	—	6	1	no	—
472	C₂×C₈	—	6	1	no	—
473	C₂×C₈	—	6	1	no	—
474	C₂×C₈	—	6	1	no	—
475	C₂×C₈	—	6	1	no	—
476	C₂×C₈	—	6	1	no	—
477	C₂×C₈	—	6	1	no	—
478	C₂×C₈	—	6	1	no	—
479	C₂×C₈	—	6	1	no	—
480	C₂×C₈	—	6	1	no	—
481	C₂×C₈	—	6	1	no	—
482	C₂×C₈	—	6	1	no	—
483	C₂×C₈	—	6	1	no	—
484	C₂×C₈	—	6	1	no	—
485	C₂×C₈	—	6	1	no	—
486	C₂×C₈	—	12	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	#208	1	4	yes	complemented
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	4	1	no	—
513	C₄²	D₃×D₄	1	2	yes	—
514	C₄²	#237	1	2	yes	—
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	4	1	no	—
519	C₂²×C₃	—	4	1	no	—
520	C₂²×C₃	—	4	1	no	—
521	C₂²×C₃	—	4	1	no	—
522	C₂²×C₃	—	4	1	no	—
523	C₂²×C₃	—	4	1	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	1	no	—
526	C₂²×C₃	—	4	1	no	—
527	C₂²×C₃	—	4	1	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
530	C₂²×C₃	C₄×#41	1	1	yes	characteristic
531	C₂²×C₃	#520	1	1	yes	characteristic
532	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
533	C₂²×C₃	C₂×#131	1	1	yes	characteristic
534	C₂²×C₃	C₂×#131	1	1	yes	characteristic
535	C₂²×C₃	#568	1	1	yes	characteristic
536	C₃×C₄	—	2	2	no	—
537	C₃×C₄	—	2	2	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	2	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	4	1	no	—
543	C₃×C₄	—	4	1	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	—	4	1	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	1	no	—
548	C₃×C₄	#546	1	1	yes	characteristic
549	C₃×C₄	#548	1	1	yes	characteristic
550	C₃×C₄	#556	1	1	yes	characteristic
551	C₃×C₄	#559	1	1	yes	characteristic
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	C₂×#208	1	2	yes	—
566	C₂³	C₂³×Dic₃	1	1	yes	characteristic
567	Q₈	—	4	4	no	—
568	D₄	—	4	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	C₂×#208	1	2	yes	—
608	C₂×C₄	C₂×#208	1	2	yes	—
609	C₂×C₄	D₄×Dic₃	1	2	yes	—
610	C₂×C₄	D₄×Dic₃	1	2	yes	—
611	C₂×C₄	#948	1	2	yes	—
612	C₂×C₄	#948	1	2	yes	—
613	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
614	C₂×C₄	C₂×#237	1	1	yes	characteristic
615	C₂×C₄	D₃×#41	1	1	yes	characteristic
616	C₂×C₄	D₃×#41	1	1	yes	characteristic
617	C₂×C₄	#1009	1	1	yes	characteristic
618	C₂×C₄	#1010	1	1	yes	characteristic
619	C₈	—	6	2	no	—
620	C₈	—	6	2	no	—
621	C₈	—	6	2	no	—
622	C₈	—	6	2	no	—
623	C₈	—	12	1	no	—
624	C₈	—	12	1	no	—
625	C₈	—	12	1	no	—
626	C₈	—	12	1	no	—
627	C₂×C₃	—	4	2	no	—
628	C₂×C₃	—	8	1	no	—
629	C₂×C₃	#2367	1	1	yes	characteristic
630	C₂×C₃	#2931	1	1	yes	characteristic
631	C₂×C₃	D₄×M₁₆	1	1	yes	characteristic
632	C₂×C₃	#2965	1	1	yes	characteristic
633	C₂×C₃	#2968	1	1	yes	characteristic
634	C₂×C₃	#2990	1	1	yes	characteristic
635	C₂×C₃	#2992	1	1	yes	characteristic
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	C₂²×#208	1	1	yes	characteristic
651	C₂²	C₂×D₄×Dic₃	1	1	yes	characteristic
652	C₂²	C₂×#948	1	1	yes	characteristic
653	C₂²	C₂×#948	1	1	yes	characteristic
654	C₂²	#5819	1	1	yes	characteristic
655	C₂²	Dic₃×#41	1	1	yes	characteristic
656	C₂²	#5827	1	1	yes	characteristic
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	#5671	1	1	yes	characteristic
670	C₄	#5676	1	1	yes	characteristic
671	C₄	#5677	1	1	yes	characteristic
672	C₄	#5681	1	1	yes	characteristic
673	C₃	#23206	1	1	yes	characteristic, complemented, Sylow
674	C₂	—	4	2	no	—
675	C₂	—	8	1	no	—
676	C₂	D₄×#208	1	1	yes	characteristic
677	C₂	#82517	1	1	yes	characteristic
678	C₂	#82522	1	1	yes	characteristic
679	C₂	#82955	1	1	yes	characteristic
680	C₂	#83128	1	1	yes	characteristic
681	C₂	#83130	1	1	yes	characteristic
682	C₂	#83275	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₃
commutator, socle	C₂³×C₃	C₂³×C₄
Fitting	C₃×C₄×#124	C₂
prime radical	C₂²×C₃×D₄	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	C₄×#124	D₃
hypocenter	C₃	#23206
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
2. C₂×#5024	C₂	semidirect
4. #71635	C₂	semidirect
6. #69452	C₂	semidirect
7. #69451	C₂	semidirect
8. #69451	C₂	semidirect
9. #69451	C₂	semidirect
10. #69450	C₂	semidirect
11. #69449	C₂	semidirect
12. #69448	C₂	semidirect
13. C₂²⋊C₄×C₃⋊C₈	C₂	semidirect
14. #69391	C₂	semidirect
15. C₄×C₄⋊(C₃⋊C₈)	C₂	semidirect
240. C₃×C₂²⋊C₄	M₁₆	semidirect
500. C₂²⋊C₄	#208	semidirect
673. C₃	#23206	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#124	2
C₂×#5024	2
C₂×#5011	2
#71635	2
#71615	2
#69452	2
#69451	2
#69450	2
#69449	2
#69448	2
C₂²⋊C₄×C₃⋊C₈	2
#69391	2
C₄×C₄⋊(C₃⋊C₈)	2
#23206	3