Subgroups — C₃×Dic₃×D₂₄ #13157747

Order 1728.

714 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₃×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₃×#63645	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63563	C₂	1	2	yes	maximal, complemented
6	C₃×Dic₃×D₈	—	3	1	no	maximal
7	C₃×C₄×D₂₄	—	3	1	no	maximal
8	Dic₃×D₂₄	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
10	C₂×C₃×D₃×Dic₃	—	2	2	no	—
11	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
13	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₃²×D₂₄	C₄	1	4	yes	complemented
16	C₃×(C₂×D₃)⋊Dic₃	—	2	2	no	—
17	C₂×C₃²×D₈	—	3	1	no	—
18	C₃×D₄×Dic₃	—	3	2	no	—
19	C₂×C₃×D₂₄	—	2	1	no	—
20	C₂×C₃×D₂₄	D₃	1	1	yes	characteristic
21	C₂×C₃×D₂₄	C₂×C₃	1	1	yes	characteristic
22	C₃×C₄×D₁₂	—	3	2	no	—
23	Dic₃×D₁₂	C₂×C₃	1	2	yes	complemented
24	C₃²×C₄×C₈	—	3	1	no	—
25	#63645	C₂×C₃	1	1	yes	characteristic, complemented
26	C₃×#832	—	3	2	no	—
27	C₃×#821	—	3	2	no	—
28	C₃×#818	—	3	1	no	—
29	C₃×#818	—	3	1	no	—
30	C₃×#818	—	6	1	no	—
31	C₃×C₈×Dic₃	—	2	1	no	—
32	C₃×C₈×Dic₃	D₃	1	1	yes	characteristic, complemented
33	C₃×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
34	#63563	C₂×C₃	1	2	yes	complemented
35	C₂²×C₃²×D₃	—	2	2	no	—
36	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
38	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
39	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
40	C₃²×D₁₂	—	2	2	no	—
41	C₃²×D₁₂	C₂×C₄	1	4	yes	complemented
42	C₃×D₃×Dic₃	—	4	4	no	—
43	C₃³×C₈	C₂×C₄	1	2	yes	complemented
44	C₃²×C₃⋊C₈	—	2	1	no	—
45	C₃×C₄×D₈	—	9	1	no	—
46	Dic₃×D₈	—	3	1	no	—
47	C₄×D₂₄	—	3	1	no	—
48	C₂×C₃²×D₄	—	3	2	no	—
49	C₂²×C₃×Dic₃	—	6	2	no	—
50	C₂×C₃×D₁₂	—	2	2	no	—
51	C₂×C₃×D₁₂	C₂×D₃	1	2	yes	—
52	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
53	C₂×C₃×C₄×D₃	—	6	2	no	—
54	C₂×D₃×Dic₃	—	2	2	no	—
55	C₃²×D₈	—	3	4	no	—
56	C₂×C₃²×C₈	—	2	1	no	—
57	C₂×C₃²×C₈	—	2	1	no	—
58	C₂×C₃²×C₈	—	2	1	no	—
59	C₂×C₃²×C₈	—	3	1	no	—
60	C₂×C₃²×C₈	—	4	1	no	—
61	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₃²×C₄²	—	3	1	no	—
65	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
66	C₃×#217	—	6	2	no	—
67	C₃×(C₂×D₃)⋊C₄	—	6	2	no	—
68	C₃×C₄⋊Dic₃	—	3	2	no	—
69	C₃×C₄⋊Dic₃	—	3	2	no	—
70	C₃×C₄⋊Dic₃	—	6	2	no	—
71	C₃×C₄×Dic₃	—	2	1	no	—
72	C₃×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
73	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₃⋊C₈	—	2	1	no	—
75	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
77	C₃×D₂₄	—	2	4	no	—
78	C₃×D₂₄	Dic₃	1	4	yes	direct product factor
79	C₃×D₂₄	C₃×C₄	1	4	yes	complemented
80	(C₂×D₃)⋊Dic₃	—	2	2	no	—
81	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃²×D₃	—	2	4	no	—
83	C₂×C₃²×D₃	—	4	2	no	—
84	C₂×C₃²×D₃	—	4	2	no	—
85	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
86	C₃³×C₄	#41	1	1	yes	characteristic
87	C₃×C₃⋊Dic₃	—	4	2	no	—
88	C₃²×Dic₃	—	2	1	no	—
89	C₃²×Dic₃	D₈	1	2	yes	complemented
90	C₂×C₃×D₈	—	3	1	no	—
91	C₂×C₃×D₈	—	3	1	no	—
92	C₂×C₃×D₈	—	6	1	no	—
93	C₃×C₄×D₄	—	9	2	no	—
94	D₄×Dic₃	—	3	2	no	—
95	C₂×D₂₄	C₃×D₃	1	1	yes	characteristic
96	C₄×D₁₂	—	3	2	no	—
97	C₃×#107	—	9	1	no	—
98	C₃×#102	—	9	2	no	—
99	C₃×C₄×C₈	—	3	1	no	—
100	C₃×C₄×C₈	—	3	1	no	—
101	C₃×C₄×C₈	—	6	1	no	—
102	#832	—	3	2	no	—
103	#821	—	3	2	no	—
104	#818	—	3	1	no	—
105	#818	—	3	1	no	—
106	#818	—	6	1	no	—
107	C₈×Dic₃	C₃×D₃	1	1	yes	characteristic, complemented
108	C₂³×C₃²	—	6	2	no	—
109	C₂²×C₃×D₃	—	2	2	no	—
110	C₂²×C₃×D₃	—	2	2	no	—
111	C₂²×C₃×D₃	—	4	2	no	—
112	C₃²×D₄	—	3	4	no	—
113	C₃²×D₄	—	6	2	no	—
114	C₂×C₃²×C₄	—	2	1	no	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	—	3	1	no	—
118	C₂×C₃²×C₄	—	3	1	no	—
119	C₂×C₃²×C₄	—	4	1	no	—
120	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₃⋊Dic₃	—	2	2	no	—
124	C₂×C₃×Dic₃	—	2	1	no	—
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	—	6	2	no	—
127	C₂×C₃×Dic₃	—	6	2	no	—
128	C₂×C₃×Dic₃	—	12	2	no	—
129	C₂×C₃×Dic₃	—	12	4	no	—
130	C₂×C₃×Dic₃	D₁₂	1	1	yes	characteristic
131	C₂×C₃×Dic₃	D₁₂	1	1	yes	characteristic
132	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
133	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
134	C₃×D₁₂	—	2	2	no	—
135	C₃×D₁₂	—	2	2	no	—
136	C₃×D₁₂	—	2	4	no	—
137	C₃×D₁₂	—	4	2	no	—
138	C₃×D₁₂	C₂×Dic₃	1	4	yes	complemented
139	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	complemented
140	C₃×C₄×D₃	—	12	4	no	—
141	D₃×Dic₃	—	4	4	no	—
142	C₃²×C₈	—	2	2	no	—
143	C₃²×C₈	—	2	2	no	—
144	C₃²×C₈	—	2	2	no	—
145	C₃²×C₈	—	4	2	no	—
146	C₃²×C₈	—	6	1	no	—
147	C₃²×C₈	C₄×D₃	1	2	yes	complemented
148	C₃²×C₈	C₂×Dic₃	1	2	yes	complemented
149	C₃²×C₈	C₂×C₃×C₄	1	2	yes	complemented
150	C₃×C₃⋊C₈	—	2	2	no	—
151	C₃×C₃⋊C₈	—	2	1	no	—
152	C₃×C₃⋊C₈	—	2	1	no	—
153	C₄×D₈	—	9	1	no	Sylow
154	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃³	C₂×D₈	1	1	yes	characteristic
156	C₂×C₃³	#135	1	1	yes	characteristic
157	C₃²×D₃	—	4	4	no	—
158	C₂×C₃×D₄	—	3	2	no	—
159	C₂×C₃×D₄	—	3	2	no	—
160	C₂×C₃×D₄	—	6	2	no	—
161	C₂²×C₃×C₄	—	18	2	no	—
162	C₂²×Dic₃	—	6	2	no	—
163	C₂×D₁₂	C₂×C₃×D₃	1	2	yes	—
164	C₂×C₄×D₃	—	6	2	no	—
165	C₃×D₈	—	3	4	no	—
166	C₃×D₈	—	3	4	no	—
167	C₃×D₈	—	6	4	no	—
168	C₂×C₃×C₈	—	2	1	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	3	1	no	—
172	C₂×C₃×C₈	—	3	1	no	—
173	C₂×C₃×C₈	—	4	1	no	—
174	C₂×C₃×C₈	—	6	1	no	—
175	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	9	2	no	—
179	C₃×C₂²⋊C₄	—	18	2	no	—
180	C₃×C₄²	—	3	1	no	—
181	C₃×C₄²	—	3	1	no	—
182	C₃×C₄²	—	6	1	no	—
183	#217	—	6	2	no	—
184	(C₂×D₃)⋊C₄	—	6	2	no	—
185	C₄⋊Dic₃	—	3	2	no	—
186	C₄⋊Dic₃	—	3	2	no	—
187	C₄⋊Dic₃	—	6	2	no	—
188	C₄×Dic₃	C₂×C₃×D₃	1	1	yes	characteristic
189	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
190	D₂₄	C₃×Dic₃	1	4	yes	direct product factor
191	C₂²×C₃²	—	2	1	no	—
192	C₂²×C₃²	—	2	1	no	—
193	C₂²×C₃²	—	2	1	no	—
194	C₂²×C₃²	—	4	1	no	—
195	C₂²×C₃²	—	6	4	no	—
196	C₂²×C₃²	—	12	2	no	—
197	C₂²×C₃²	—	12	2	no	—
198	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
199	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
200	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₃×D₃	—	2	4	no	—
202	C₂×C₃×D₃	—	2	4	no	—
203	C₂×C₃×D₃	—	4	4	no	—
204	C₂×C₃×D₃	—	4	2	no	—
205	C₂×C₃×D₃	—	4	2	no	—
206	C₂×C₃×D₃	—	4	2	no	—
207	C₂×C₃×D₃	—	4	2	no	—
208	C₂×C₃×D₃	—	8	2	no	—
209	C₂×C₃×D₃	—	8	2	no	—
210	C₃²×C₄	—	2	1	no	—
211	C₃²×C₄	—	2	1	no	—
212	C₃²×C₄	—	2	1	no	—
213	C₃²×C₄	—	2	1	no	—
214	C₃²×C₄	—	2	1	no	—
215	C₃²×C₄	—	2	1	no	—
216	C₃²×C₄	—	3	2	no	—
217	C₃²×C₄	—	4	1	no	—
218	C₃²×C₄	—	4	1	no	—
219	C₃²×C₄	—	6	1	no	—
220	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
221	C₃²×C₄	#235	1	1	yes	characteristic
222	C₃²×C₄	#237	1	1	yes	characteristic
223	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
224	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₃²×C₄	C₃×#41	1	1	yes	characteristic
226	C₃⋊Dic₃	—	4	2	no	—
227	C₃×Dic₃	—	2	2	no	—
228	C₃×Dic₃	—	2	1	no	—
229	C₃×Dic₃	—	2	1	no	—
230	C₃×Dic₃	—	2	2	no	—
231	C₃×Dic₃	—	12	2	no	—
232	C₃×Dic₃	—	12	2	no	—
233	C₃×Dic₃	—	24	2	no	—
234	C₃×Dic₃	D₂₄	1	2	yes	direct product factor
235	C₃×Dic₃	C₃×D₈	1	2	yes	complemented
236	C₂×D₈	—	3	1	no	—
237	C₄×D₄	—	9	2	no	—
238	#107	—	9	1	no	—
239	#102	—	9	2	no	—
240	C₄×C₈	—	3	1	no	—
241	C₃³	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₃	—	6	2	no	—
243	C₂³×C₃	—	6	2	no	—
244	C₂³×C₃	—	12	2	no	—
245	C₂²×D₃	—	2	2	no	—
246	C₃×D₄	—	3	4	no	—
247	C₃×D₄	—	3	4	no	—
248	C₃×D₄	—	6	4	no	—
249	C₃×D₄	—	6	2	no	—
250	C₃×D₄	—	6	2	no	—
251	C₃×D₄	—	12	2	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	3	1	no	—
256	C₂×C₃×C₄	—	3	1	no	—
257	C₂×C₃×C₄	—	3	1	no	—
258	C₂×C₃×C₄	—	3	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	6	1	no	—
261	C₂×C₃×C₄	—	6	1	no	—
262	C₂×C₃×C₄	—	18	2	no	—
263	C₂×C₃×C₄	—	36	4	no	—
264	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂×Dic₃	—	6	2	no	—
268	C₂×Dic₃	—	6	2	no	—
269	C₂×Dic₃	—	12	2	no	—
270	C₂×Dic₃	—	12	4	no	—
271	C₂×Dic₃	C₃×D₁₂	1	1	yes	characteristic
272	C₂×Dic₃	C₃×D₁₂	1	1	yes	characteristic
273	D₁₂	—	2	2	no	—
274	D₁₂	C₂×C₃×Dic₃	1	4	yes	complemented
275	C₄×D₃	—	12	4	no	—
276	C₃×C₈	—	2	2	no	—
277	C₃×C₈	—	2	2	no	—
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	—	4	2	no	—
280	C₃×C₈	—	6	2	no	—
281	C₃×C₈	—	6	1	no	—
282	C₃×C₈	—	6	1	no	—
283	C₃×C₈	D₃×Dic₃	1	2	yes	complemented
284	C₃×C₈	C₃×C₄×D₃	1	2	yes	complemented
285	C₃×C₈	C₂×C₃×Dic₃	1	2	yes	complemented
286	C₃⋊C₈	—	2	1	no	—
287	C₂×C₃²	—	2	1	no	—
288	C₂×C₃²	—	2	1	no	—
289	C₂×C₃²	—	2	1	no	—
290	C₂×C₃²	—	2	1	no	—
291	C₂×C₃²	—	2	1	no	—
292	C₂×C₃²	—	2	1	no	—
293	C₂×C₃²	—	2	1	no	—
294	C₂×C₃²	—	2	1	no	—
295	C₂×C₃²	—	2	1	no	—
296	C₂×C₃²	—	4	1	no	—
297	C₂×C₃²	—	4	1	no	—
298	C₂×C₃²	—	4	1	no	—
299	C₂×C₃²	—	12	4	no	—
300	C₂×C₃²	C₄×D₁₂	1	1	yes	characteristic
301	C₂×C₃²	C₂×D₂₄	1	1	yes	characteristic
302	C₂×C₃²	#904	1	1	yes	characteristic
303	C₂×C₃²	D₃×D₈	1	1	yes	characteristic
304	C₂×C₃²	#912	1	1	yes	characteristic
305	C₂×C₃²	D₄×Dic₃	1	1	yes	characteristic
306	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
307	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
308	C₂×C₃²	C₃×#135	1	1	yes	characteristic
309	C₃×D₃	—	4	4	no	—
310	C₃×D₃	—	4	4	no	—
311	C₃×D₃	—	8	4	no	—
312	C₂×D₄	—	3	2	no	—
313	C₂²×C₄	—	18	2	no	—
314	D₈	—	3	4	no	—
315	C₂×C₈	—	3	1	no	—
316	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
317	C₄⋊C₄	—	9	2	no	—
318	C₂²⋊C₄	—	18	2	no	—
319	C₄²	—	3	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	6	4	no	—
325	C₂²×C₃	—	6	4	no	—
326	C₂²×C₃	—	12	4	no	—
327	C₂²×C₃	—	12	2	no	—
328	C₂²×C₃	—	12	2	no	—
329	C₂²×C₃	—	12	2	no	—
330	C₂²×C₃	—	12	2	no	—
331	C₂²×C₃	—	24	2	no	—
332	C₂²×C₃	—	24	2	no	—
333	C₂²×C₃	D₃×D₁₂	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
335	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
336	C₂×D₃	—	2	4	no	—
337	C₂×D₃	—	4	2	no	—
338	C₂×D₃	—	4	2	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	3	2	no	—
346	C₃×C₄	—	3	2	no	—
347	C₃×C₄	—	4	1	no	—
348	C₃×C₄	—	4	1	no	—
349	C₃×C₄	—	6	2	no	—
350	C₃×C₄	—	6	2	no	—
351	C₃×C₄	—	6	1	no	—
352	C₃×C₄	—	6	1	no	—
353	C₃×C₄	—	36	2	no	—
354	C₃×C₄	#3795	1	1	yes	characteristic
355	C₃×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
356	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
357	C₃×C₄	C₃×#235	1	1	yes	characteristic
358	C₃×C₄	C₃×#237	1	1	yes	characteristic
359	C₃×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
360	Dic₃	—	2	1	no	—
361	Dic₃	—	12	2	no	—
362	Dic₃	—	12	2	no	—
363	Dic₃	—	24	2	no	—
364	Dic₃	C₃×D₂₄	1	2	yes	direct product factor
365	C₃²	—	2	1	no	—
366	C₃²	—	2	1	no	—
367	C₃²	—	2	1	no	—
368	C₃²	—	4	1	no	—
369	C₃²	C₄×D₂₄	1	1	yes	characteristic, complemented
370	C₃²	Dic₃×D₈	1	1	yes	characteristic, complemented
371	C₃²	C₃×C₄×D₈	1	1	yes	characteristic, complemented
372	C₂³	—	6	2	no	—
373	D₄	—	3	4	no	—
374	D₄	—	6	2	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	3	1	no	—
377	C₂×C₄	—	18	2	no	—
378	C₂×C₄	—	36	4	no	—
379	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic
380	C₈	—	6	1	no	—
381	C₈	C₃×D₃×Dic₃	1	2	yes	complemented
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	4	1	no	—
393	C₂×C₃	—	4	1	no	—
394	C₂×C₃	—	12	4	no	—
395	C₂×C₃	—	12	4	no	—
396	C₂×C₃	—	24	4	no	—
397	C₂×C₃	D₃×D₂₄	1	1	yes	characteristic
398	C₂×C₃	#63807	1	1	yes	characteristic
399	C₂×C₃	Dic₃×D₁₂	1	1	yes	characteristic
400	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
401	C₂×C₃	C₂×C₃×D₂₄	1	1	yes	characteristic
402	C₂×C₃	C₃×#904	1	1	yes	characteristic
403	C₂×C₃	C₃×D₃×D₈	1	1	yes	characteristic
404	C₂×C₃	C₃×#912	1	1	yes	characteristic
405	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
406	D₃	—	4	4	no	—
407	C₂²	—	6	4	no	—
408	C₂²	—	12	2	no	—
409	C₂²	—	12	2	no	—
410	C₂²	C₃×D₃×D₁₂	1	1	yes	characteristic
411	C₄	—	3	2	no	—
412	C₄	—	6	1	no	—
413	C₄	—	36	2	no	—
414	C₄	C₃×#3795	1	1	yes	characteristic
415	C₄	C₂×C₃×D₃×Dic₃	1	1	yes	characteristic
416	C₃	—	2	1	no	—
417	C₃	—	2	1	no	—
418	C₃	—	2	1	no	—
419	C₃	—	4	1	no	—
420	C₃	Dic₃×D₂₄	1	1	yes	characteristic, direct product factor
421	C₃	C₃×C₄×D₂₄	1	1	yes	characteristic, complemented
422	C₃	C₃×Dic₃×D₈	1	1	yes	characteristic, complemented
423	C₂	—	12	4	no	—
424	C₂	C₃×D₃×D₂₄	1	1	yes	characteristic
425	C₂	C₃×#63807	1	1	yes	characteristic
426	C₂	C₃×Dic₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₃×D₁₂
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃²
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃²×D₂₄	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₃²
hypocenter	C₃²	C₃×C₄×D₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₃×D₁₂	C₂	semidirect
3. C₃×#63645	C₂	semidirect
4. C₃²×C₈×Dic₃	C₂	semidirect
5. C₃×#63563	C₂	semidirect
8. Dic₃×D₂₄	C₃	direct (N × H)
15. C₃²×D₂₄	C₄	semidirect
23. Dic₃×D₁₂	C₂×C₃	semidirect
25. #63645	C₂×C₃	semidirect
32. C₃×C₈×Dic₃	D₃	semidirect
33. C₃×C₈×Dic₃	C₂×C₃	semidirect
34. #63563	C₂×C₃	semidirect
41. C₃²×D₁₂	C₂×C₄	semidirect
43. C₃³×C₈	C₂×C₄	semidirect
78. C₃×D₂₄	Dic₃	direct (N × H)
79. C₃×D₂₄	C₃×C₄	semidirect
89. C₃²×Dic₃	D₈	semidirect
107. C₈×Dic₃	C₃×D₃	semidirect
138. C₃×D₁₂	C₂×Dic₃	semidirect
139. C₃×D₁₂	C₂×C₃×C₄	semidirect
147. C₃²×C₈	C₄×D₃	semidirect
148. C₃²×C₈	C₂×Dic₃	semidirect
149. C₃²×C₈	C₂×C₃×C₄	semidirect
190. D₂₄	C₃×Dic₃	direct (N × H)
234. C₃×Dic₃	D₂₄	direct (N × H)
235. C₃×Dic₃	C₃×D₈	semidirect
241. C₃³	C₄×D₈	semidirect
274. D₁₂	C₂×C₃×Dic₃	semidirect
283. C₃×C₈	D₃×Dic₃	semidirect
284. C₃×C₈	C₃×C₄×D₃	semidirect
285. C₃×C₈	C₂×C₃×Dic₃	semidirect
364. Dic₃	C₃×D₂₄	direct (N × H)
369. C₃²	C₄×D₂₄	semidirect
370. C₃²	Dic₃×D₈	semidirect
371. C₃²	C₃×C₄×D₈	semidirect
381. C₈	C₃×D₃×Dic₃	semidirect
420. C₃	Dic₃×D₂₄	direct (N × H)
421. C₃	C₃×C₄×D₂₄	semidirect
422. C₃	C₃×Dic₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₂₄	2
C₃×Dic₃×D₁₂	2
C₃×#63645	2
C₃²×C₈×Dic₃	2
C₃×#63563	2
C₃×Dic₃×D₈	3
C₃×C₄×D₂₄	3
Dic₃×D₂₄	3

Subgroups — C3×Dic3×D24 #13157747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×D₂₄ #13157747