Subgroups — C₃×#81789 #11885731

Order 1152.

1321 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×#5717	C₂	1	2	yes	maximal, complemented
3	C₃²×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5157	C₂	1	2	yes	maximal, complemented
5	C₃×#5156	C₂	1	4	yes	maximal, complemented
6	C₃×#5072	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×D₈	—	3	1	no	maximal
10	#81789	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×D₃×D₄	—	2	2	no	—
12	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
13	C₂×C₃²×D₈	C₂²	1	2	yes	complemented
14	C₂×C₃²×D₈	C₂²	1	2	yes	complemented
15	C₃²×#127	C₂²	1	2	yes	complemented
16	C₃×#938	—	2	2	no	—
17	C₃×#938	C₂²	1	4	yes	complemented
18	C₃×#937	—	2	4	no	—
19	C₂×C₃×#213	C₂²	1	4	yes	complemented
20	C₃×D₃×D₈	—	2	8	no	—
21	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
23	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
24	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
25	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×#832	C₂²	1	4	yes	complemented
27	C₃×#821	C₂²	1	2	yes	complemented
28	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
29	C₃×#818	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×D₈	—	3	2	no	—
32	C₃×D₄²	—	3	2	no	—
33	C₂×D₃×D₈	C₂×C₃	1	2	yes	complemented
34	#5717	C₂×C₃	1	2	yes	complemented
35	C₃×#493	—	2	1	no	—
36	C₃×#493	D₃	1	1	yes	characteristic, complemented
37	C₃×#493	C₂×C₃	1	1	yes	characteristic, complemented
38	C₃×#466	—	3	2	no	—
39	C₃×#459	—	3	2	no	—
40	C₃×#447	—	3	4	no	—
41	C₃×C₄×D₈	—	3	1	no	—
42	C₃×C₈×D₄	—	3	1	no	—
43	#5157	C₂×C₃	1	2	yes	complemented
44	#5156	C₂×C₃	1	4	yes	complemented
45	#5072	C₂×C₃	1	2	yes	complemented
46	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×D₃	—	2	4	no	—
49	C₂×C₃²×D₄	—	2	2	no	—
50	C₂×C₃²×D₄	—	2	2	no	—
51	C₂×C₃²×D₄	C₂³	1	4	yes	—
52	C₂×C₃×#67	—	2	4	no	—
53	C₂×C₃×#67	—	2	4	no	—
54	C₃×D₃×D₄	—	2	8	no	—
55	C₃×D₃×D₄	—	4	4	no	—
56	C₃×D₃×D₄	—	4	8	no	—
57	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
58	C₂×C₃×D₁₂	C₂³	1	2	yes	—
59	C₂×C₃×C₄×D₃	—	2	2	no	—
60	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
61	C₃²×D₈	—	2	4	no	—
62	C₃²×D₈	—	4	2	no	—
63	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
65	C₃²×C₄²	C₂³	1	1	yes	characteristic
66	C₃×#217	—	2	4	no	—
67	C₃×#213	—	2	8	no	—
68	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
69	C₃×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
70	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
72	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
73	C₃×D₂₄	D₄	1	4	yes	complemented
74	C₃×D₃×C₈	—	2	4	no	—
75	D₄×D₈	—	3	1	no	Sylow
76	C₂²×C₃×D₄	—	3	4	no	—
77	C₂²×C₃×D₄	—	6	2	no	—
78	C₂×D₃×D₄	—	2	2	no	—
79	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
80	C₂×C₃×D₈	—	2	2	no	—
81	C₂×C₃×D₈	—	2	2	no	—
82	C₂×C₃×D₈	—	3	4	no	—
83	C₂×C₃×D₈	—	3	1	no	—
84	C₂×C₃×D₈	—	6	8	no	—
85	C₂×C₃×D₈	C₂×D₃	1	2	yes	complemented
86	C₂×C₃×D₈	C₂×D₃	1	2	yes	complemented
87	C₂×C₃×D₈	C₂²×C₃	1	2	yes	complemented
88	C₂×C₃×D₈	C₂²×C₃	1	2	yes	complemented
89	C₂²×C₃×C₈	—	3	2	no	—
90	C₃×#127	—	2	2	no	—
91	C₃×#127	C₂×D₃	1	2	yes	complemented
92	C₃×#127	C₂²×C₃	1	2	yes	complemented
93	C₃×#121	—	3	4	no	—
94	C₃×#121	—	6	2	no	—
95	C₃×#120	—	6	4	no	—
96	C₃×C₄×D₄	—	3	1	no	—
97	C₃×C₄×D₄	—	3	2	no	—
98	#938	—	2	2	no	—
99	#938	C₂²×C₃	1	4	yes	complemented
100	#937	—	2	4	no	—
101	C₂×#213	C₂²×C₃	1	4	yes	complemented
102	D₃×D₈	—	2	8	no	—
103	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
105	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
106	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
107	C₃×#107	—	3	1	no	—
108	C₃×C₄⋊C₈	—	3	1	no	—
109	C₃×#102	—	3	4	no	—
110	C₃×#102	—	3	2	no	—
111	C₃×C₂²⋊C₈	—	3	2	no	—
112	C₃×C₄×C₈	—	2	1	no	—
113	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
114	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	#832	C₂²×C₃	1	4	yes	complemented
116	#821	C₂²×C₃	1	2	yes	complemented
117	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
118	#818	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₂³×C₃²	—	2	4	no	—
121	C₂²×C₃×D₃	—	2	2	no	—
122	C₂²×C₃×D₃	—	4	8	no	—
123	C₂²×C₃×D₃	—	4	8	no	—
124	C₂²×C₃×D₃	—	8	4	no	—
125	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
126	C₃²×D₄	—	2	4	no	—
127	C₃²×D₄	—	2	4	no	—
128	C₃²×D₄	—	4	4	no	—
129	C₃²×D₄	—	8	2	no	—
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
133	C₃×#67	—	4	8	no	—
134	C₃×#67	—	4	8	no	—
135	C₂×C₃×Dic₃	—	2	2	no	—
136	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
137	C₃×D₁₂	—	2	2	no	—
138	C₃×D₁₂	D₈	1	4	yes	complemented
139	C₃×D₁₂	C₂×D₄	1	4	yes	complemented
140	C₃×C₄×D₃	—	2	2	no	—
141	C₃×C₄×D₃	—	2	2	no	—
142	C₃×C₄×D₃	—	4	4	no	—
143	C₃²×C₈	—	2	1	no	—
144	C₃²×C₈	C₂×D₄	1	2	yes	complemented
145	C₃×C₃⋊C₈	—	2	2	no	—
146	C₂²×D₈	—	3	2	no	—
147	D₄²	—	3	2	no	—
148	#493	C₃×D₃	1	1	yes	characteristic, complemented
149	#466	—	3	2	no	—
150	#459	—	3	2	no	—
151	#447	—	3	4	no	—
152	C₄×D₈	—	3	1	no	—
153	C₈×D₄	—	3	1	no	—
154	C₂⁴×C₃	—	6	4	no	—
155	C₂³×D₃	—	2	4	no	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	2	4	no	—
161	C₂×C₃×D₄	—	3	1	no	—
162	C₂×C₃×D₄	—	3	2	no	—
163	C₂×C₃×D₄	—	4	2	no	—
164	C₂×C₃×D₄	—	4	2	no	—
165	C₂×C₃×D₄	—	6	4	no	—
166	C₂×C₃×D₄	—	6	8	no	—
167	C₂×C₃×D₄	—	6	4	no	—
168	C₂×C₃×D₄	—	12	4	no	—
169	C₂×C₃×D₄	—	12	8	no	—
170	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
171	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
172	C₂²×C₃×C₄	—	3	2	no	—
173	C₂²×C₃×C₄	—	6	2	no	—
174	C₂×#67	—	2	4	no	—
175	C₂×#67	—	2	4	no	—
176	D₃×D₄	—	2	8	no	—
177	D₃×D₄	—	4	4	no	—
178	D₃×D₄	—	4	8	no	—
179	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
180	C₂×D₁₂	C₂³×C₃	1	2	yes	—
181	C₂×C₄×D₃	—	2	2	no	—
182	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
183	C₃×D₈	—	2	4	no	—
184	C₃×D₈	—	2	4	no	—
185	C₃×D₈	—	3	4	no	—
186	C₃×D₈	—	4	4	no	—
187	C₃×D₈	—	4	2	no	—
188	C₃×D₈	—	4	2	no	—
189	C₃×D₈	—	4	4	no	—
190	C₃×D₈	—	6	8	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	3	2	no	—
194	C₂×C₃×C₈	—	6	4	no	—
195	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₃×C₄⋊C₄	—	3	1	no	—
200	C₃×C₄⋊C₄	—	3	2	no	—
201	C₃×C₂²⋊C₄	—	3	2	no	—
202	C₃×C₂²⋊C₄	—	6	4	no	—
203	C₃×C₂²⋊C₄	—	6	2	no	—
204	C₃×C₄²	—	2	1	no	—
205	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
206	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
207	#217	—	2	4	no	—
208	#213	—	2	8	no	—
209	(C₂×D₃)⋊C₄	—	2	2	no	—
210	(C₂×D₃)⋊C₄	C₃×D₄	1	2	yes	—
211	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
212	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
213	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
214	D₂₄	C₃×D₄	1	4	yes	complemented
215	D₃×C₈	—	2	4	no	—
216	C₂²×C₃²	—	4	4	no	—
217	C₂²×C₃²	—	4	4	no	—
218	C₂²×C₃²	—	4	4	no	—
219	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₃×D₃	—	2	2	no	—
221	C₂×C₃×D₃	—	2	2	no	—
222	C₂×C₃×D₃	—	2	4	no	—
223	C₂×C₃×D₃	—	4	2	no	—
224	C₂×C₃×D₃	—	4	2	no	—
225	C₂×C₃×D₃	—	8	16	no	—
226	C₂×C₃×D₃	C₂×D₈	1	4	yes	complemented
227	C₃²×C₄	—	2	1	no	—
228	C₃²×C₄	C₂×D₈	1	2	yes	complemented
229	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
230	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
231	C₃×Dic₃	—	2	2	no	—
232	C₃×Dic₃	—	4	2	no	—
233	C₂²×D₄	—	3	4	no	—
234	C₂²×D₄	—	6	2	no	—
235	C₂×D₈	—	3	4	no	—
236	C₂×D₈	—	3	1	no	—
237	C₂×D₈	—	6	8	no	—
238	C₂×D₈	C₂×C₃×D₃	1	2	yes	complemented
239	C₂×D₈	C₂×C₃×D₃	1	2	yes	complemented
240	C₂²×C₈	—	3	2	no	—
241	#127	C₂×C₃×D₃	1	2	yes	complemented
242	#121	—	3	4	no	—
243	#121	—	6	2	no	—
244	#120	—	6	4	no	—
245	C₄×D₄	—	3	1	no	—
246	C₄×D₄	—	3	2	no	—
247	#107	—	3	1	no	—
248	C₄⋊C₈	—	3	1	no	—
249	#102	—	3	4	no	—
250	#102	—	3	2	no	—
251	C₂²⋊C₈	—	3	2	no	—
252	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	4	no	—
255	C₂³×C₃	—	3	2	no	—
256	C₂³×C₃	—	4	4	no	—
257	C₂³×C₃	—	6	2	no	—
258	C₂³×C₃	—	12	8	no	—
259	C₂³×C₃	—	12	8	no	—
260	C₂³×C₃	—	24	4	no	—
261	C₂²×D₃	—	2	2	no	—
262	C₂²×D₃	—	4	8	no	—
263	C₂²×D₃	—	4	8	no	—
264	C₂²×D₃	—	8	4	no	—
265	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
266	C₃×D₄	—	2	4	no	—
267	C₃×D₄	—	2	4	no	—
268	C₃×D₄	—	2	4	no	—
269	C₃×D₄	—	2	4	no	—
270	C₃×D₄	—	3	4	no	—
271	C₃×D₄	—	3	4	no	—
272	C₃×D₄	—	4	4	no	—
273	C₃×D₄	—	4	4	no	—
274	C₃×D₄	—	4	4	no	—
275	C₃×D₄	—	4	4	no	—
276	C₃×D₄	—	6	2	no	—
277	C₃×D₄	—	8	4	no	—
278	C₃×D₄	—	8	2	no	—
279	C₃×D₄	—	8	2	no	—
280	C₃×D₄	—	8	4	no	—
281	C₃×D₄	—	12	8	no	—
282	C₃×D₄	—	12	8	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	3	2	no	—
287	C₂×C₃×C₄	—	6	2	no	—
288	C₂×C₃×C₄	—	6	2	no	—
289	C₂×C₃×C₄	—	6	2	no	—
290	C₂×C₃×C₄	—	12	4	no	—
291	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
297	#67	—	4	8	no	—
298	#67	—	4	8	no	—
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
301	D₁₂	—	2	2	no	—
302	D₁₂	C₃×D₈	1	4	yes	complemented
303	D₁₂	C₂×C₃×D₄	1	4	yes	complemented
304	C₄×D₃	—	2	2	no	—
305	C₄×D₃	—	2	2	no	—
306	C₄×D₃	—	4	4	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	2	1	no	—
309	C₃×C₈	—	2	1	no	—
310	C₃×C₈	—	2	2	no	—
311	C₃×C₈	—	6	2	no	—
312	C₃×C₈	D₃×D₄	1	2	yes	complemented
313	C₃×C₈	C₂×C₃×D₄	1	2	yes	complemented
314	C₃⋊C₈	—	2	2	no	—
315	C₂×C₃²	—	8	4	no	—
316	C₂×C₃²	D₄²	1	1	yes	characteristic
317	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
318	C₂×C₃²	#576	1	1	yes	characteristic
319	C₃×D₃	—	2	4	no	—
320	C₃×D₃	—	4	4	no	—
321	C₂⁴	—	6	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	3	2	no	—
325	C₂×D₄	—	3	1	no	—
326	C₂×D₄	—	6	4	no	—
327	C₂×D₄	—	6	8	no	—
328	C₂×D₄	—	6	4	no	—
329	C₂×D₄	—	12	4	no	—
330	C₂×D₄	—	12	8	no	—
331	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	6	2	no	—
334	D₈	—	2	4	no	—
335	D₈	—	3	4	no	—
336	D₈	—	4	2	no	—
337	D₈	—	6	8	no	—
338	C₂×C₈	—	3	2	no	—
339	C₂×C₈	—	6	4	no	—
340	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
341	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
342	C₄⋊C₄	—	3	1	no	—
343	C₄⋊C₄	—	3	2	no	—
344	C₂²⋊C₄	—	3	2	no	—
345	C₂²⋊C₄	—	6	4	no	—
346	C₂²⋊C₄	—	6	2	no	—
347	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	3	4	no	—
350	C₂²×C₃	—	4	4	no	—
351	C₂²×C₃	—	4	4	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	—	4	4	no	—
356	C₂²×C₃	—	6	2	no	—
357	C₂²×C₃	—	6	2	no	—
358	C₂²×C₃	—	6	4	no	—
359	C₂²×C₃	—	8	4	no	—
360	C₂²×C₃	—	8	4	no	—
361	C₂²×C₃	—	8	4	no	—
362	C₂²×C₃	—	12	2	no	—
363	C₂²×C₃	—	12	2	no	—
364	C₂²×C₃	—	24	16	no	—
365	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
367	C₂×D₃	—	2	2	no	—
368	C₂×D₃	—	2	2	no	—
369	C₂×D₃	—	2	4	no	—
370	C₂×D₃	—	4	2	no	—
371	C₂×D₃	—	4	2	no	—
372	C₂×D₃	—	8	16	no	—
373	C₂×D₃	C₂×C₃×D₈	1	4	yes	complemented
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	6	2	no	—
381	C₃×C₄	—	12	2	no	—
382	C₃×C₄	D₃×D₈	1	2	yes	complemented
383	C₃×C₄	C₂×C₃×D₈	1	2	yes	complemented
384	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
385	C₃×C₄	#1004	1	1	yes	characteristic
386	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
387	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
388	Dic₃	—	2	2	no	—
389	Dic₃	—	4	2	no	—
390	C₃²	D₄×D₈	1	1	yes	characteristic, complemented, Sylow
391	C₂³	—	2	4	no	—
392	C₂³	—	3	2	no	—
393	C₂³	—	6	2	no	—
394	C₂³	—	12	8	no	—
395	C₂³	—	12	8	no	—
396	C₂³	—	24	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	3	4	no	—
400	D₄	—	3	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	6	2	no	—
403	D₄	—	8	2	no	—
404	D₄	—	12	8	no	—
405	D₄	—	12	8	no	—
406	C₂×C₄	—	3	2	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	12	4	no	—
411	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
412	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	6	2	no	—
416	C₈	C₃×D₃×D₄	1	2	yes	complemented
417	C₂×C₃	—	2	1	no	—
418	C₂×C₃	—	2	1	no	—
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	6	4	no	—
421	C₂×C₃	—	8	4	no	—
422	C₂×C₃	—	8	4	no	—
423	C₂×C₃	—	12	4	no	—
424	C₂×C₃	—	16	4	no	—
425	C₂×C₃	#5717	1	1	yes	characteristic
426	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
427	C₂×C₃	#5757	1	1	yes	characteristic
428	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
429	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
430	C₂×C₃	C₃×#576	1	1	yes	characteristic
431	D₃	—	2	4	no	—
432	D₃	—	4	4	no	—
433	C₂²	—	3	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	6	2	no	—
438	C₂²	—	6	2	no	—
439	C₂²	—	6	4	no	—
440	C₂²	—	12	2	no	—
441	C₂²	—	12	2	no	—
442	C₂²	—	24	16	no	—
443	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	6	2	no	—
446	C₄	—	12	2	no	—
447	C₄	C₃×D₃×D₈	1	2	yes	complemented
448	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
449	C₄	C₃×#1004	1	1	yes	characteristic
450	C₃	—	2	1	no	—
451	C₃	#81789	1	1	yes	characteristic, direct product factor
452	C₃	C₃×D₄×D₈	1	1	yes	characteristic, complemented
453	C₂	—	6	4	no	—
454	C₂	—	8	4	no	—
455	C₂	—	12	4	no	—
456	C₂	C₃×#5717	1	1	yes	characteristic
457	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic
458	C₂	C₃×#5757	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#493	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×#493	D₃
hypocenter	C₃	C₃×D₄×D₈
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#493

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×D₈	C₂	semidirect
2. C₃×#5717	C₂	semidirect
3. C₃²×#493	C₂	semidirect
4. C₃×#5157	C₂	semidirect
5. C₃×#5156	C₂	semidirect
6. C₃×#5072	C₂	semidirect
7. C₃×C₄×D₂₄	C₂	semidirect
8. C₃×C₈×D₁₂	C₂	semidirect
10. #81789	C₃	direct (N × H)
12. C₂×C₃×D₃×D₄	C₂²	semidirect
13. C₂×C₃²×D₈	C₂²	semidirect
14. C₂×C₃²×D₈	C₂²	semidirect
15. C₃²×#127	C₂²	semidirect
17. C₃×#938	C₂²	semidirect
19. C₂×C₃×#213	C₂²	semidirect
22. C₂×C₃×D₃×C₈	C₂²	semidirect
24. C₃×C₄×D₁₂	C₂²	semidirect
25. C₃²×C₄×C₈	C₂²	semidirect
26. C₃×#832	C₂²	semidirect
27. C₃×#821	C₂²	semidirect
28. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
29. C₃×#818	C₂²	semidirect
30. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
33. C₂×D₃×D₈	C₂×C₃	semidirect
34. #5717	C₂×C₃	semidirect
36. C₃×#493	D₃	semidirect
37. C₃×#493	C₂×C₃	semidirect
43. #5157	C₂×C₃	semidirect
44. #5156	C₂×C₃	semidirect
45. #5072	C₂×C₃	semidirect
46. C₄×D₂₄	C₂×C₃	semidirect
47. C₈×D₁₂	C₂×C₃	semidirect
73. C₃×D₂₄	D₄	semidirect
79. C₂×D₃×D₄	C₂²×C₃	semidirect
85. C₂×C₃×D₈	C₂×D₃	semidirect
86. C₂×C₃×D₈	C₂×D₃	semidirect
87. C₂×C₃×D₈	C₂²×C₃	semidirect
88. C₂×C₃×D₈	C₂²×C₃	semidirect
91. C₃×#127	C₂×D₃	semidirect
92. C₃×#127	C₂²×C₃	semidirect
99. #938	C₂²×C₃	semidirect
101. C₂×#213	C₂²×C₃	semidirect
104. C₂×D₃×C₈	C₂²×C₃	semidirect
106. C₄×D₁₂	C₂²×C₃	semidirect
113. C₃×C₄×C₈	C₂×D₃	semidirect
114. C₃×C₄×C₈	C₂²×C₃	semidirect
115. #832	C₂²×C₃	semidirect
116. #821	C₂²×C₃	semidirect
117. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
118. #818	C₂²×C₃	semidirect
119. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
138. C₃×D₁₂	D₈	semidirect
139. C₃×D₁₂	C₂×D₄	semidirect
144. C₃²×C₈	C₂×D₄	semidirect
148. #493	C₃×D₃	semidirect
214. D₂₄	C₃×D₄	semidirect
226. C₂×C₃×D₃	C₂×D₈	semidirect
228. C₃²×C₄	C₂×D₈	semidirect
238. C₂×D₈	C₂×C₃×D₃	semidirect
239. C₂×D₈	C₂×C₃×D₃	semidirect
241. #127	C₂×C₃×D₃	semidirect
252. C₄×C₈	C₂×C₃×D₃	semidirect
302. D₁₂	C₃×D₈	semidirect
303. D₁₂	C₂×C₃×D₄	semidirect
312. C₃×C₈	D₃×D₄	semidirect
313. C₃×C₈	C₂×C₃×D₄	semidirect
373. C₂×D₃	C₂×C₃×D₈	semidirect
382. C₃×C₄	D₃×D₈	semidirect
383. C₃×C₄	C₂×C₃×D₈	semidirect
390. C₃²	D₄×D₈	semidirect
416. C₈	C₃×D₃×D₄	semidirect
447. C₄	C₃×D₃×D₈	semidirect
451. C₃	#81789	direct (N × H)
452. C₃	C₃×D₄×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×D₈	2
C₃×#5717	2
C₃²×#493	2
C₃×#5157	2
C₃×#5156	2
C₃×#5072	2
C₃×C₄×D₂₄	2
C₃×C₈×D₁₂	2
C₃×D₄×D₈	3
#81789	3

Subgroups — C3×#81789 #11885731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#81789 #11885731