Subgroups — C₃×C₄×#825 #11783870

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#825	C₂	1	2	yes	maximal
4	C₃×C₄²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4555	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#104	—	3	1	no	maximal
7	C₄×#825	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#235	C₂²	1	1	yes	characteristic
9	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₃×C₄×#67	—	2	2	no	—
12	C₃×#926	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₃	—	2	2	no	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
15	C₃×C₄×D₁₂	C₄	1	2	yes	complemented
16	C₃×#872	—	2	1	no	—
17	C₃×C₄²×D₃	—	2	1	no	—
18	C₃×C₄×Dic₆	C₄	1	2	yes	complemented
19	C₃²×#97	—	2	1	no	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×#825	C₄	1	8	yes	direct product factor
22	C₃×C₄×#41	—	3	1	no	—
23	C₄×#235	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#104	—	3	2	no	—
25	C₃×C₄×M₁₆	—	2	1	no	—
26	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
27	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
28	C₃×C₄³	—	3	1	no	—
29	C₂×#825	C₂×C₃	1	2	yes	—
30	C₄²×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#339	—	3	2	no	—
32	#4555	C₂×C₃	1	2	yes	complemented
33	C₂²×C₃²×C₄	D₄	1	2	yes	—
34	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
35	C₂×C₃×#67	—	2	1	no	—
36	C₂²×C₃×Dic₃	—	2	2	no	—
37	C₃×#235	—	2	2	no	—
38	C₃×#235	C₂×C₄	1	4	yes	—
39	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₃	—	2	1	no	—
41	C₂×C₃×C₄×D₃	—	2	2	no	—
42	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
43	C₃²×M₁₆	—	2	2	no	—
44	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
45	C₂×C₃²×C₈	—	2	2	no	—
46	C₃²×C₄²	C₂×C₄	1	2	yes	—
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃×#217	—	2	1	no	—
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
52	C₃×Dic₃⋊C₄	—	2	2	no	—
53	C₃×C₄×Dic₃	—	2	8	no	—
54	C₃×C₄×Dic₃	—	2	2	no	—
55	C₃×C₄×Dic₃	—	2	1	no	—
56	C₃×C₄×Dic₃	—	2	2	no	—
57	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	complemented
58	C₄×#104	—	3	1	no	Sylow
59	C₂×C₃×#41	—	3	1	no	—
60	C₂×#235	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×M₁₆	—	2	2	no	—
62	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
63	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
64	C₃×C₄×Q₈	—	3	2	no	—
65	C₃×C₄×D₄	—	3	2	no	—
66	C₃×C₄×D₄	—	6	2	no	—
67	C₃×#117	—	3	1	no	—
68	C₃×#117	—	6	1	no	—
69	C₂×C₃×C₄²	—	2	1	no	—
70	C₂×C₃×C₄²	—	3	2	no	—
71	C₂×C₃×C₄²	—	6	2	no	—
72	C₂×C₃×C₄²	—	6	1	no	—
73	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
75	C₄×#67	—	2	2	no	—
76	#926	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄×Dic₃	—	2	2	no	—
78	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
79	C₄×D₁₂	C₃×C₄	1	2	yes	complemented
80	#872	—	2	1	no	—
81	C₄²×D₃	—	2	1	no	—
82	C₄×Dic₆	C₃×C₄	1	2	yes	complemented
83	C₃×#104	—	3	8	no	—
84	C₃×#97	—	2	2	no	—
85	C₃×#97	—	2	1	no	—
86	C₃×#97	—	2	1	no	—
87	C₃×C₄×C₈	—	2	2	no	—
88	C₃×C₄×C₈	—	2	1	no	—
89	C₃×C₄×C₈	—	2	1	no	—
90	#825	C₃×C₄	1	8	yes	direct product factor
91	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	2	1	no	—
93	C₂×C₃²×C₄	—	2	4	no	—
94	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃²×C₄	C₂²⋊C₄	1	2	yes	—
96	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
98	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃²×C₄	#41	1	2	yes	—
100	C₃×#67	—	2	4	no	—
101	C₂×C₃×Dic₃	—	2	8	no	—
102	C₂×C₃×Dic₃	—	2	1	no	—
103	C₂×C₃×Dic₃	—	2	4	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₃×D₁₂	—	2	1	no	—
106	C₃×D₁₂	C₄²	1	2	yes	complemented
107	C₃×C₄×D₃	—	2	4	no	—
108	C₃×C₄×D₃	—	4	4	no	—
109	C₃×Dic₆	—	2	1	no	—
110	C₃×Dic₆	C₄²	1	2	yes	complemented
111	C₃²×C₈	—	2	4	no	—
112	C₄×#41	—	3	1	no	—
113	C₂×#104	—	3	2	no	—
114	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
115	C₄³	—	3	1	no	—
116	#339	—	3	2	no	—
117	C₃×#41	—	3	4	no	—
118	C₃×#41	—	6	2	no	—
119	C₂×C₃×Q₈	—	3	1	no	—
120	C₂×C₃×D₄	—	3	1	no	—
121	C₂×C₃×D₄	—	6	1	no	—
122	C₂²×C₃×C₄	—	2	2	no	—
123	C₂²×C₃×C₄	—	2	1	no	—
124	C₂²×C₃×C₄	—	6	2	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	2	no	—
127	C₂²×C₃×C₄	D₁₂	1	2	yes	—
128	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
129	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
131	C₂×#67	—	2	1	no	—
132	C₂²×Dic₃	—	2	2	no	—
133	#235	—	2	2	no	—
134	#235	C₂×C₃×C₄	1	4	yes	—
135	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₃	—	2	1	no	—
137	C₂×C₄×D₃	—	2	2	no	—
138	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
139	C₃×M₁₆	—	2	4	no	—
140	C₃×M₁₆	—	2	2	no	—
141	C₃×M₁₆	—	2	2	no	—
142	C₃×M₁₆	—	2	4	no	—
143	C₃×M₁₆	C₄×D₃	1	4	yes	complemented
144	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
145	C₂×C₃×C₈	—	2	4	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₂×C₃×C₈	—	2	2	no	—
148	C₃×C₄⋊C₄	—	3	2	no	—
149	C₃×C₄⋊C₄	—	6	2	no	—
150	C₃×C₂²⋊C₄	—	6	1	no	—
151	C₃×C₂²⋊C₄	—	6	2	no	—
152	C₃×C₄²	—	2	2	no	—
153	C₃×C₄²	—	2	1	no	—
154	C₃×C₄²	—	2	1	no	—
155	C₃×C₄²	—	3	4	no	—
156	C₃×C₄²	—	6	8	no	—
157	C₃×C₄²	—	6	2	no	—
158	C₃×C₄²	—	6	2	no	—
159	C₃×C₄²	—	6	1	no	—
160	C₃×C₄²	C₄×D₃	1	2	yes	—
161	C₃×C₄²	#67	1	1	yes	characteristic
162	C₃×C₄²	#67	1	1	yes	characteristic
163	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
164	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
165	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
166	#217	—	2	1	no	—
167	(C₂×D₃)⋊C₄	—	2	2	no	—
168	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
169	Dic₃⋊C₄	—	2	2	no	—
170	C₄×Dic₃	—	2	8	no	—
171	C₄×Dic₃	—	2	2	no	—
172	C₄×Dic₃	—	2	1	no	—
173	C₄×Dic₃	—	2	2	no	—
174	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	complemented
175	C₂²×C₃²	—	2	2	no	—
176	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃²	C₄×D₄	1	2	yes	—
178	C₂×C₃×D₃	—	2	2	no	—
179	C₂×C₃×D₃	—	4	2	no	—
180	C₃²×C₄	—	2	2	no	—
181	C₃²×C₄	#104	1	4	yes	complemented
182	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
183	C₃²×C₄	#117	1	1	yes	characteristic
184	C₃²×C₄	C₄×D₄	1	2	yes	—
185	C₃×Dic₃	—	2	8	no	—
186	C₃×Dic₃	—	2	2	no	—
187	C₃×Dic₃	—	4	2	no	—
188	C₂×#41	—	3	1	no	—
189	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
190	C₄×Q₈	—	3	2	no	—
191	C₄×D₄	—	3	2	no	—
192	C₄×D₄	—	6	2	no	—
193	#117	—	3	1	no	—
194	#117	—	6	1	no	—
195	C₂×C₄²	—	3	2	no	—
196	C₂×C₄²	—	6	2	no	—
197	C₂×C₄²	—	6	1	no	—
198	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
199	#104	—	3	8	no	—
200	#97	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₂³×C₃	—	2	1	no	—
203	C₂³×C₃	—	6	1	no	—
204	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
205	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂²×D₃	—	2	1	no	—
207	C₃×Q₈	—	3	2	no	—
208	C₃×Q₈	—	6	1	no	—
209	C₃×D₄	—	3	2	no	—
210	C₃×D₄	—	6	4	no	—
211	C₃×D₄	—	6	1	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	4	4	no	—
221	C₂×C₃×C₄	—	6	8	no	—
222	C₂×C₃×C₄	—	6	4	no	—
223	C₂×C₃×C₄	—	6	1	no	—
224	C₂×C₃×C₄	—	6	4	no	—
225	C₂×C₃×C₄	—	6	2	no	—
226	C₂×C₃×C₄	—	12	4	no	—
227	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
228	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
229	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
230	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
233	C₂×C₃×C₄	#235	1	2	yes	—
234	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
237	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₃×#41	1	2	yes	—
239	#67	—	2	4	no	—
240	C₂×Dic₃	—	2	8	no	—
241	C₂×Dic₃	—	2	1	no	—
242	C₂×Dic₃	—	2	4	no	—
243	C₂×Dic₃	—	2	2	no	—
244	D₁₂	—	2	1	no	—
245	D₁₂	C₃×C₄²	1	2	yes	complemented
246	C₄×D₃	—	2	4	no	—
247	C₄×D₃	—	4	4	no	—
248	Dic₆	—	2	1	no	—
249	Dic₆	C₃×C₄²	1	2	yes	complemented
250	C₃×C₈	—	2	8	no	—
251	C₃×C₈	—	2	4	no	—
252	C₃×C₈	—	2	4	no	—
253	C₂×C₃²	—	2	2	no	—
254	C₂×C₃²	C₄×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃²	C₂×#104	1	2	yes	—
256	C₃×D₃	—	4	2	no	—
257	#41	—	3	4	no	—
258	#41	—	6	2	no	—
259	C₂×Q₈	—	3	1	no	—
260	C₂×D₄	—	3	1	no	—
261	C₂×D₄	—	6	1	no	—
262	C₂²×C₄	—	6	2	no	—
263	C₂²×C₄	—	6	1	no	—
264	C₂²×C₄	—	6	2	no	—
265	C₂²×C₄	C₃×D₁₂	1	2	yes	—
266	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	M₁₆	—	2	2	no	—
268	M₁₆	C₃×C₄×D₃	1	4	yes	complemented
269	C₂×C₈	—	2	2	no	—
270	C₄⋊C₄	—	3	2	no	—
271	C₄⋊C₄	—	6	2	no	—
272	C₂²⋊C₄	—	6	1	no	—
273	C₂²⋊C₄	—	6	2	no	—
274	C₄²	—	3	4	no	—
275	C₄²	—	6	8	no	—
276	C₄²	—	6	2	no	—
277	C₄²	—	6	2	no	—
278	C₄²	—	6	1	no	—
279	C₄²	C₃×C₄×D₃	1	2	yes	—
280	C₄²	C₃×#67	1	1	yes	characteristic
281	C₄²	C₃×#67	1	1	yes	characteristic
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	2	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	4	2	no	—
287	C₂²×C₃	—	6	2	no	—
288	C₂²×C₃	—	12	2	no	—
289	C₂²×C₃	C₄×D₁₂	1	2	yes	—
290	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
293	C₂×D₃	—	2	2	no	—
294	C₂×D₃	—	4	2	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	2	2	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	4	2	no	—
302	C₃×C₄	—	6	8	no	—
303	C₃×C₄	—	6	2	no	—
304	C₃×C₄	—	12	2	no	—
305	C₃×C₄	#825	1	4	yes	direct product factor
306	C₃×C₄	C₃×#104	1	4	yes	complemented
307	C₃×C₄	C₄²×D₃	1	1	yes	characteristic
308	C₃×C₄	#872	1	1	yes	characteristic
309	C₃×C₄	C₄×#67	1	2	yes	—
310	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
311	C₃×C₄	C₃×#117	1	1	yes	characteristic
312	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
313	Dic₃	—	2	8	no	—
314	Dic₃	—	2	2	no	—
315	Dic₃	—	4	2	no	—
316	C₃²	C₄×#104	1	1	yes	characteristic, complemented, Sylow
317	C₂³	—	6	1	no	—
318	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
319	Q₈	—	3	2	no	—
320	Q₈	—	6	1	no	—
321	D₄	—	3	2	no	—
322	D₄	—	6	4	no	—
323	D₄	—	6	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	6	8	no	—
326	C₂×C₄	—	6	1	no	—
327	C₂×C₄	—	6	4	no	—
328	C₂×C₄	—	6	4	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	—	12	4	no	—
331	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
332	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
333	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
335	C₂×C₄	C₃×#235	1	2	yes	—
336	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	—	4	2	no	—
343	C₂×C₃	—	12	2	no	—
344	C₂×C₃	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₃	C₂×#825	1	2	yes	—
346	C₂×C₃	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₃	C₂×C₃×#104	1	2	yes	—
348	D₃	—	4	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	6	2	no	—
351	C₂²	—	12	2	no	—
352	C₂²	C₃×C₄×D₁₂	1	2	yes	—
353	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	6	8	no	—
356	C₄	—	6	2	no	—
357	C₄	—	12	2	no	—
358	C₄	C₃×#825	1	4	yes	direct product factor
359	C₄	C₃×C₄²×D₃	1	1	yes	characteristic
360	C₄	C₃×#872	1	1	yes	characteristic
361	C₄	C₃×C₄×#67	1	2	yes	—
362	C₃	—	2	1	no	—
363	C₃	C₄×#825	1	1	yes	characteristic, direct product factor
364	C₃	C₃×C₄×#104	1	1	yes	characteristic, complemented
365	C₂	—	2	2	no	—
366	C₂	—	12	2	no	—
367	C₂	C₃×C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
368	C₂	C₂×C₃×#825	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	#67
commutator	C₃×C₄	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×C₄×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×M₁₆	C₂	semidirect
4. C₃×C₄²×Dic₃	C₂	semidirect
5. C₃×#4555	C₂	semidirect
7. C₄×#825	C₃	direct (N × H)
15. C₃×C₄×D₁₂	C₄	semidirect
18. C₃×C₄×Dic₆	C₄	semidirect
21. C₃×#825	C₄	direct (N × H)
26. C₃×C₄×M₁₆	D₃	semidirect
27. C₃×C₄×M₁₆	C₂×C₃	semidirect
30. C₄²×Dic₃	C₂×C₃	semidirect
32. #4555	C₂×C₃	semidirect
44. C₃²×M₁₆	C₂×C₄	semidirect
57. C₃×C₄×Dic₃	C₂×C₄	semidirect
79. C₄×D₁₂	C₃×C₄	semidirect
82. C₄×Dic₆	C₃×C₄	semidirect
90. #825	C₃×C₄	direct (N × H)
106. C₃×D₁₂	C₄²	semidirect
110. C₃×Dic₆	C₄²	semidirect
114. C₄×M₁₆	C₃×D₃	semidirect
143. C₃×M₁₆	C₄×D₃	semidirect
144. C₃×M₁₆	C₂×C₃×C₄	semidirect
174. C₄×Dic₃	C₂×C₃×C₄	semidirect
181. C₃²×C₄	#104	semidirect
245. D₁₂	C₃×C₄²	semidirect
249. Dic₆	C₃×C₄²	semidirect
268. M₁₆	C₃×C₄×D₃	semidirect
305. C₃×C₄	#825	direct (N × H)
306. C₃×C₄	C₃×#104	semidirect
316. C₃²	C₄×#104	semidirect
358. C₄	C₃×#825	direct (N × H)
363. C₃	C₄×#825	direct (N × H)
364. C₃	C₃×C₄×#104	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
C₃²×C₄×M₁₆	2
C₂×C₃×#825	2
C₃×C₄²×Dic₃	2
C₃×#4555	2
C₃×C₄×#104	3
C₄×#825	3

Subgroups — C3×C4×#825 #11783870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#825 #11783870