Subgroups — C₃×C₄×#912 #11859962

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#912	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#237	C₂	1	2	yes	maximal, complemented
3	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#214	C₂	1	2	yes	maximal, complemented
6	C₃×#4880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4772	C₂	1	2	yes	maximal, complemented
9	C₃×#4758	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×#135	—	3	1	no	maximal
13	C₄×#912	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#237	C₂²	1	2	yes	—
15	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
16	C₃²×C₄×D₄	C₂²	1	2	yes	—
17	C₃×D₄×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#214	C₂²	1	2	yes	—
19	C₃×C₄×#67	—	2	2	no	—
20	C₂×C₃×C₄×Dic₃	—	2	2	no	—
21	C₃×#912	C₄	1	8	yes	direct product factor
22	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₃×#892	C₂²	1	2	yes	—
26	C₃×#887	C₂²	1	2	yes	—
27	C₃×#67⋊C₄	—	2	2	no	—
28	C₃×#877	—	2	2	no	—
29	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₆	C₂²	1	2	yes	—
31	C₃²×#107	C₂²	1	1	yes	characteristic
32	C₃²×#102	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃×#832	C₂²	1	2	yes	—
35	C₃×#818	C₂²	1	1	yes	characteristic
36	C₃×#816	C₂²	1	2	yes	—
37	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×#810	C₂²	1	2	yes	—
40	C₃×#808	C₂²	1	2	yes	—
41	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×#135	—	3	1	no	—
43	C₃×C₄×#41	—	3	2	no	—
44	C₂×#912	C₂×C₃	1	1	yes	characteristic
45	C₄×#237	C₂×C₃	1	2	yes	complemented
46	C₃×C₄×Q₁₆	—	3	1	no	—
47	C₃×C₄×Q₁₆	—	3	1	no	—
48	C₃×C₄×SD₁₆	—	3	2	no	—
49	C₃×C₄×SD₁₆	—	3	2	no	—
50	C₃×C₄×D₈	—	2	1	no	—
51	C₃×C₄×D₈	—	3	1	no	—
52	C₃×C₄×D₈	D₃	1	1	yes	characteristic, complemented
53	C₃×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×#427	—	3	1	no	—
55	C₃×#416	—	3	2	no	—
56	C₂×C₃×C₄×C₈	—	3	1	no	—
57	Dic₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×#214	C₂×C₃	1	2	yes	complemented
59	#4880	C₂×C₃	1	1	yes	characteristic, complemented
60	#4873	C₂×C₃	1	1	yes	characteristic, complemented
61	#4772	C₂×C₃	1	2	yes	complemented
62	#4758	C₂×C₃	1	2	yes	complemented
63	C₄×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×C₃²×D₄	C₂³	1	2	yes	—
66	C₂²×C₃²×C₄	—	2	2	no	—
67	C₂×C₃×#67	—	2	2	no	—
68	C₂²×C₃×Dic₃	—	2	2	no	—
69	C₂²×C₃×Dic₃	—	2	2	no	—
70	C₃×#237	—	2	4	no	—
71	C₃×#237	C₂×C₄	1	8	yes	complemented
72	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×Dic₆	C₂³	1	2	yes	—
76	C₃²×D₈	C₂×C₄	1	4	yes	complemented
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₂²⋊C₄	—	2	2	no	—
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#217	—	2	2	no	—
83	C₃×#214	C₂×C₄	1	8	yes	complemented
84	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₃×Dic₃⋊C₄	—	2	2	no	—
87	C₃×Dic₃⋊C₄	—	2	2	no	—
88	C₃×C₄×Dic₃	—	2	2	no	—
89	C₃×C₄×Dic₃	—	2	2	no	—
90	C₃×C₄×Dic₃	—	2	2	no	—
91	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
93	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
97	C₃×D₃×C₈	—	2	2	no	—
98	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
99	C₄×#135	—	3	1	no	Sylow
100	C₂×C₃×#41	—	3	2	no	—
101	C₂×#237	C₂²×C₃	1	2	yes	—
102	C₃×#135	—	3	8	no	—
103	C₂×C₃×Q₁₆	—	3	1	no	—
104	C₂×C₃×SD₁₆	—	3	2	no	—
105	C₂×C₃×D₈	—	2	1	no	—
106	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	—	3	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₃×C₄×Q₈	—	3	2	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×D₄	—	2	2	no	—
113	C₃×C₄×D₄	—	3	2	no	—
114	C₃×C₄×D₄	—	6	2	no	—
115	C₃×C₄×D₄	—	6	2	no	—
116	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
117	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
118	C₃×#117	—	3	2	no	—
119	C₃×#117	—	6	2	no	—
120	C₂×C₃×C₄²	—	3	1	no	—
121	C₂×C₃×C₄²	—	6	2	no	—
122	D₄×Dic₃	C₂²×C₃	1	2	yes	—
123	C₂×#214	C₂²×C₃	1	2	yes	—
124	C₄×#67	—	2	2	no	—
125	C₂×C₄×Dic₃	—	2	2	no	—
126	#912	C₃×C₄	1	8	yes	direct product factor
127	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
128	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
130	#892	C₂²×C₃	1	2	yes	—
131	#887	C₂²×C₃	1	2	yes	—
132	#67⋊C₄	—	2	2	no	—
133	#877	—	2	2	no	—
134	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
135	C₄×Dic₆	C₂²×C₃	1	2	yes	—
136	C₃×#107	—	2	1	no	—
137	C₃×#107	—	3	1	no	—
138	C₃×#107	C₂×D₃	1	1	yes	characteristic
139	C₃×#107	C₂²×C₃	1	1	yes	characteristic
140	C₃×#106	—	3	2	no	—
141	C₃×#103	—	3	2	no	—
142	C₃×#103	—	3	2	no	—
143	C₃×#102	—	2	2	no	—
144	C₃×#102	—	3	2	no	—
145	C₃×#102	C₂×D₃	1	2	yes	—
146	C₃×#102	C₂²×C₃	1	2	yes	—
147	C₃×C₄×C₈	—	2	1	no	—
148	C₃×C₄×C₈	—	3	1	no	—
149	C₃×C₄×C₈	—	3	1	no	—
150	C₃×C₄×C₈	—	3	1	no	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
153	#832	C₂²×C₃	1	2	yes	—
154	#818	C₂²×C₃	1	1	yes	characteristic
155	#816	C₂²×C₃	1	2	yes	—
156	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
157	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
158	#810	C₂²×C₃	1	2	yes	—
159	#808	C₂²×C₃	1	2	yes	—
160	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
161	C₂³×C₃²	—	2	2	no	—
162	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
163	C₃²×D₄	—	2	2	no	—
164	C₃²×D₄	C₂²×C₄	1	4	yes	—
165	C₂×C₃²×C₄	—	2	2	no	—
166	C₂×C₃²×C₄	—	4	4	no	—
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
170	C₃×#67	—	2	8	no	—
171	C₂×C₃×Dic₃	—	2	2	no	—
172	C₂×C₃×Dic₃	—	2	8	no	—
173	C₂×C₃×Dic₃	—	2	2	no	—
174	C₂×C₃×Dic₃	—	4	4	no	—
175	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
178	C₃×C₄×D₃	—	2	2	no	—
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
181	C₃×C₄×D₃	#41	1	2	yes	—
182	C₃×Dic₆	—	2	2	no	—
183	C₃×Dic₆	C₂²×C₄	1	4	yes	—
184	C₃²×C₈	—	2	1	no	—
185	C₃²×C₈	C₂²×C₄	1	2	yes	—
186	C₃×C₃⋊C₈	—	2	1	no	—
187	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
188	C₂×#135	—	3	1	no	—
189	C₄×#41	—	3	2	no	—
190	C₄×Q₁₆	—	3	1	no	—
191	C₄×Q₁₆	—	3	1	no	—
192	C₄×SD₁₆	—	3	2	no	—
193	C₄×SD₁₆	—	3	2	no	—
194	C₄×D₈	—	3	1	no	—
195	C₄×D₈	C₃×D₃	1	1	yes	characteristic, complemented
196	#427	—	3	1	no	—
197	#416	—	3	2	no	—
198	C₂×C₄×C₈	—	3	1	no	—
199	C₃×#41	—	3	8	no	—
200	C₃×#41	—	6	4	no	—
201	C₂×C₃×Q₈	—	3	2	no	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	6	2	no	—
204	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
205	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	2	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	4	2	no	—
212	C₂²×C₃×C₄	—	6	2	no	—
213	C₂²×C₃×C₄	—	6	2	no	—
214	C₂×#67	—	2	2	no	—
215	C₂²×Dic₃	—	2	2	no	—
216	C₂²×Dic₃	—	2	2	no	—
217	#237	—	2	4	no	—
218	#237	C₂×C₃×C₄	1	8	yes	complemented
219	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
221	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
222	C₂×Dic₆	C₂³×C₃	1	2	yes	—
223	C₃×Q₁₆	—	3	4	no	—
224	C₃×SD₁₆	—	3	8	no	—
225	C₃×D₈	—	2	4	no	—
226	C₃×D₈	C₄×D₃	1	4	yes	complemented
227	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
228	C₂×C₃×C₈	—	2	1	no	—
229	C₂×C₃×C₈	—	2	1	no	—
230	C₂×C₃×C₈	—	3	1	no	—
231	C₂×C₃×C₈	—	3	4	no	—
232	C₂×C₃×C₈	—	3	1	no	—
233	C₂×C₃×C₈	—	6	2	no	—
234	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	6	2	no	—
241	C₃×C₄⋊C₄	—	6	2	no	—
242	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
243	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
244	C₃×C₂²⋊C₄	—	2	2	no	—
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₂²⋊C₄	—	4	2	no	—
247	C₃×C₂²⋊C₄	—	6	2	no	—
248	C₃×C₂²⋊C₄	—	6	2	no	—
249	C₃×C₄²	—	2	1	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	1	no	—
252	C₃×C₄²	—	3	1	no	—
253	C₃×C₄²	—	6	2	no	—
254	C₃×C₄²	—	6	2	no	—
255	C₃×C₄²	—	6	2	no	—
256	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
257	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
258	#217	—	2	2	no	—
259	#214	C₂×C₃×C₄	1	8	yes	complemented
260	(C₂×D₃)⋊C₄	—	2	2	no	—
261	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
262	Dic₃⋊C₄	—	2	2	no	—
263	Dic₃⋊C₄	—	2	2	no	—
264	C₄×Dic₃	—	2	2	no	—
265	C₄×Dic₃	—	2	2	no	—
266	C₄×Dic₃	—	2	2	no	—
267	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
268	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
269	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
272	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
273	D₃×C₈	—	2	2	no	—
274	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
275	C₂²×C₃²	—	2	4	no	—
276	C₂²×C₃²	—	4	2	no	—
277	C₂²×C₃²	—	4	2	no	—
278	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₃×D₃	—	2	1	no	—
280	C₂×C₃×D₃	—	2	1	no	—
281	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	—	4	2	no	—
284	C₃²×C₄	#135	1	2	yes	complemented
285	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
286	C₃²×C₄	C₂×#41	1	1	yes	characteristic
287	C₃×Dic₃	—	2	4	no	—
288	C₃×Dic₃	—	2	1	no	—
289	C₃×Dic₃	—	4	2	no	—
290	C₃×Dic₃	C₄×D₄	1	2	yes	—
291	C₃×Dic₃	#135	1	2	yes	complemented
292	C₂×#41	—	3	2	no	—
293	#135	—	3	8	no	—
294	C₂×Q₁₆	—	3	1	no	—
295	C₂×SD₁₆	—	3	2	no	—
296	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
297	C₂²×C₈	—	3	1	no	—
298	C₂²×C₈	—	3	1	no	—
299	C₄×Q₈	—	3	2	no	—
300	C₄×Q₈	—	3	2	no	—
301	C₄×D₄	—	3	2	no	—
302	C₄×D₄	—	6	2	no	—
303	C₄×D₄	—	6	2	no	—
304	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
305	#117	—	3	2	no	—
306	#117	—	6	2	no	—
307	C₂×C₄²	—	3	1	no	—
308	C₂×C₄²	—	6	2	no	—
309	#107	—	3	1	no	—
310	#107	C₂×C₃×D₃	1	1	yes	characteristic
311	#106	—	3	2	no	—
312	#103	—	3	2	no	—
313	#103	—	3	2	no	—
314	#102	—	3	2	no	—
315	#102	C₂×C₃×D₃	1	2	yes	—
316	C₄×C₈	—	3	1	no	—
317	C₄×C₈	—	3	1	no	—
318	C₄×C₈	—	3	1	no	—
319	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
320	C₂³×C₃	—	2	2	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	3	1	no	—
323	C₂³×C₃	—	4	2	no	—
324	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
325	C₃×Q₈	—	3	4	no	—
326	C₃×Q₈	—	6	2	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	4	no	—
330	C₃×D₄	—	4	2	no	—
331	C₃×D₄	—	6	8	no	—
332	C₃×D₄	C₂×C₄×D₃	1	4	yes	—
333	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	3	1	no	—
340	C₂×C₃×C₄	—	3	1	no	—
341	C₂×C₃×C₄	—	3	2	no	—
342	C₂×C₃×C₄	—	3	2	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	4	4	no	—
346	C₂×C₃×C₄	—	4	4	no	—
347	C₂×C₃×C₄	—	6	2	no	—
348	C₂×C₃×C₄	—	6	8	no	—
349	C₂×C₃×C₄	—	6	2	no	—
350	C₂×C₃×C₄	—	6	2	no	—
351	C₂×C₃×C₄	—	6	2	no	—
352	C₂×C₃×C₄	—	8	4	no	—
353	C₂×C₃×C₄	—	12	4	no	—
354	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
360	#67	—	2	8	no	—
361	C₂×Dic₃	—	2	2	no	—
362	C₂×Dic₃	—	2	8	no	—
363	C₂×Dic₃	—	2	2	no	—
364	C₂×Dic₃	—	4	4	no	—
365	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
366	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
368	C₄×D₃	—	2	2	no	—
369	C₄×D₃	—	2	2	no	—
370	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
371	C₄×D₃	C₃×#41	1	2	yes	—
372	Dic₆	—	2	2	no	—
373	Dic₆	C₂²×C₃×C₄	1	4	yes	—
374	C₃×C₈	—	2	1	no	—
375	C₃×C₈	—	2	1	no	—
376	C₃×C₈	—	2	2	no	—
377	C₃×C₈	—	3	2	no	—
378	C₃×C₈	—	4	1	no	—
379	C₃×C₈	—	6	1	no	—
380	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
381	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
382	C₃⋊C₈	—	2	1	no	—
383	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
384	C₂×C₃²	—	4	4	no	—
385	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
386	C₂×C₃²	C₂×#135	1	1	yes	characteristic
387	C₂×C₃²	C₂×#135	1	1	yes	characteristic
388	C₃×D₃	—	2	2	no	—
389	#41	—	3	8	no	—
390	#41	—	6	4	no	—
391	C₂×Q₈	—	3	2	no	—
392	C₂×D₄	—	6	2	no	—
393	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	3	1	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	6	2	no	—
399	C₂²×C₄	—	6	2	no	—
400	Q₁₆	—	3	4	no	—
401	SD₁₆	—	3	8	no	—
402	D₈	C₃×C₄×D₃	1	4	yes	complemented
403	C₂×C₈	—	3	1	no	—
404	C₂×C₈	—	3	4	no	—
405	C₂×C₈	—	3	1	no	—
406	C₂×C₈	—	6	2	no	—
407	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
408	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
409	C₄⋊C₄	—	3	2	no	—
410	C₄⋊C₄	—	6	2	no	—
411	C₄⋊C₄	—	6	2	no	—
412	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	6	2	no	—
415	C₂²⋊C₄	—	6	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	3	1	no	—
418	C₄²	—	3	1	no	—
419	C₄²	—	6	2	no	—
420	C₄²	—	6	2	no	—
421	C₄²	—	6	2	no	—
422	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
423	C₂²×C₃	—	2	4	no	—
424	C₂²×C₃	—	2	4	no	—
425	C₂²×C₃	—	2	1	no	—
426	C₂²×C₃	—	3	2	no	—
427	C₂²×C₃	—	4	4	no	—
428	C₂²×C₃	—	4	2	no	—
429	C₂²×C₃	—	4	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	6	1	no	—
433	C₂²×C₃	—	6	1	no	—
434	C₂²×C₃	—	8	2	no	—
435	C₂²×C₃	—	8	2	no	—
436	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
437	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
438	C₂×D₃	—	2	1	no	—
439	C₂×D₃	—	2	1	no	—
440	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	2	1	no	—
445	C₃×C₄	—	2	1	no	—
446	C₃×C₄	—	3	2	no	—
447	C₃×C₄	—	3	2	no	—
448	C₃×C₄	—	4	1	no	—
449	C₃×C₄	—	4	2	no	—
450	C₃×C₄	—	4	2	no	—
451	C₃×C₄	—	6	1	no	—
452	C₃×C₄	—	6	4	no	—
453	C₃×C₄	—	8	2	no	—
454	C₃×C₄	—	12	2	no	—
455	C₃×C₄	#912	1	2	yes	direct product factor
456	C₃×C₄	C₃×#135	1	2	yes	complemented
457	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
458	C₃×C₄	D₃×#41	1	1	yes	characteristic
459	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
460	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
461	Dic₃	—	2	1	no	—
462	Dic₃	—	2	4	no	—
463	Dic₃	—	4	2	no	—
464	Dic₃	C₃×C₄×D₄	1	2	yes	—
465	Dic₃	C₃×#135	1	2	yes	complemented
466	C₃²	C₄×#135	1	1	yes	characteristic, complemented, Sylow
467	C₂³	—	2	2	no	—
468	C₂³	—	3	1	no	—
469	Q₈	—	3	4	no	—
470	Q₈	—	6	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	6	8	no	—
473	D₄	C₂×C₃×C₄×D₃	1	4	yes	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	3	1	no	—
476	C₂×C₄	—	3	1	no	—
477	C₂×C₄	—	3	2	no	—
478	C₂×C₄	—	3	2	no	—
479	C₂×C₄	—	3	1	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	6	2	no	—
482	C₂×C₄	—	6	8	no	—
483	C₂×C₄	—	6	2	no	—
484	C₂×C₄	—	6	2	no	—
485	C₂×C₄	—	6	2	no	—
486	C₂×C₄	—	12	4	no	—
487	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
488	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	3	2	no	—
492	C₈	—	6	1	no	—
493	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
494	C₂×C₃	—	2	1	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	2	1	no	—
497	C₂×C₃	—	4	4	no	—
498	C₂×C₃	—	4	4	no	—
499	C₂×C₃	—	6	2	no	—
500	C₂×C₃	—	8	4	no	—
501	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
502	C₂×C₃	C₂×#912	1	1	yes	characteristic
503	C₂×C₃	D₃×#135	1	1	yes	characteristic
504	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
505	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
506	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
507	D₃	—	2	2	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	3	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	6	1	no	—
513	C₂²	—	6	1	no	—
514	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
515	C₄	—	2	1	no	—
516	C₄	—	3	2	no	—
517	C₄	—	3	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	6	1	no	—
520	C₄	—	6	4	no	—
521	C₄	—	12	2	no	—
522	C₄	C₃×#912	1	2	yes	direct product factor
523	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
524	C₄	C₃×D₃×#41	1	1	yes	characteristic
525	C₃	—	2	1	no	—
526	C₃	C₄×#912	1	1	yes	characteristic, direct product factor
527	C₃	C₃×C₄×#135	1	1	yes	characteristic, complemented
528	C₂	—	4	4	no	—
529	C₂	—	6	2	no	—
530	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
531	C₂	C₂×C₃×#912	1	1	yes	characteristic
532	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×D₈	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#912	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×D₈	D₃
hypocenter	C₃	C₃×C₄×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#237	C₂	semidirect
3. C₃²×C₄×D₈	C₂	semidirect
4. C₃×Dic₃×D₈	C₂	semidirect
5. C₃×C₄×#214	C₂	semidirect
6. C₃×#4880	C₂	semidirect
7. C₃×#4873	C₂	semidirect
8. C₃×#4772	C₂	semidirect
9. C₃×#4758	C₂	semidirect
10. C₃×C₄×Dic₁₂	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. C₄×#912	C₃	direct (N × H)
21. C₃×#912	C₄	direct (N × H)
45. C₄×#237	C₂×C₃	semidirect
52. C₃×C₄×D₈	D₃	semidirect
53. C₃×C₄×D₈	C₂×C₃	semidirect
57. Dic₃×D₈	C₂×C₃	semidirect
58. C₄×#214	C₂×C₃	semidirect
59. #4880	C₂×C₃	semidirect
60. #4873	C₂×C₃	semidirect
61. #4772	C₂×C₃	semidirect
62. #4758	C₂×C₃	semidirect
63. C₄×Dic₁₂	C₂×C₃	semidirect
64. C₄×D₃×C₈	C₂×C₃	semidirect
71. C₃×#237	C₂×C₄	semidirect
76. C₃²×D₈	C₂×C₄	semidirect
83. C₃×#214	C₂×C₄	semidirect
96. C₃×Dic₁₂	C₂×C₄	semidirect
98. C₃×D₃×C₈	C₂×C₄	semidirect
126. #912	C₃×C₄	direct (N × H)
195. C₄×D₈	C₃×D₃	semidirect
218. #237	C₂×C₃×C₄	semidirect
226. C₃×D₈	C₄×D₃	semidirect
227. C₃×D₈	C₂×C₃×C₄	semidirect
259. #214	C₂×C₃×C₄	semidirect
272. Dic₁₂	C₂×C₃×C₄	semidirect
274. D₃×C₈	C₂×C₃×C₄	semidirect
284. C₃²×C₄	#135	semidirect
291. C₃×Dic₃	#135	semidirect
402. D₈	C₃×C₄×D₃	semidirect
455. C₃×C₄	#912	direct (N × H)
456. C₃×C₄	C₃×#135	semidirect
465. Dic₃	C₃×#135	semidirect
466. C₃²	C₄×#135	semidirect
522. C₄	C₃×#912	direct (N × H)
526. C₃	C₄×#912	direct (N × H)
527. C₃	C₃×C₄×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#912	2
C₃×C₄×#237	2
C₃²×C₄×D₈	2
C₃×Dic₃×D₈	2
C₃×C₄×#214	2
C₃×#4880	2
C₃×#4873	2
C₃×#4772	2
C₃×#4758	2
C₃×C₄×Dic₁₂	2
C₃×C₄×D₃×C₈	2
C₃×C₄×#135	3
C₄×#912	3

Subgroups — C3×C4×#912 #11859962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#912 #11859962