Subgroups — C₃×C₄×#824 #11783803

Order 1152.

663 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#824	C₂	1	2	yes	maximal
4	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic
5	C₃×#4554	C₂	1	2	yes	maximal
6	C₃×C₄×#101	—	3	1	no	maximal
7	C₄×#824	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
9	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
13	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
14	C₂×C₃×#208	C₂²	1	2	yes	—
15	C₃×C₄×Dic₆	—	2	1	no	—
16	C₃×C₄×Dic₆	—	2	1	no	—
17	C₃×C₄×Dic₆	—	2	1	no	—
18	C₃×C₄×Dic₆	—	2	1	no	—
19	C₃²×#97	—	2	1	no	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×#824	C₄	1	8	yes	direct product factor
22	C₃×#803	—	2	1	no	—
23	C₃×C₄×C₃⋊C₈	—	2	1	no	—
24	C₂×C₃×C₄×Q₈	—	3	1	no	—
25	C₂×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#101	—	3	2	no	—
27	C₃×C₄×M₁₆	—	2	1	no	—
28	C₃×C₄×M₁₆	—	3	1	no	—
29	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic
30	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
31	C₂×#824	C₂×C₃	1	2	yes	—
32	C₄×#208	C₂×C₃	1	1	yes	characteristic
33	C₃×#343	—	3	2	no	—
34	#4554	C₂×C₃	1	2	yes	—
35	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
38	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
39	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
40	C₂×C₃×Dic₆	—	2	1	no	—
41	C₂×C₃×Dic₆	—	2	1	no	—
42	C₂×C₃×Dic₆	—	2	2	no	—
43	C₂×C₃×Dic₆	C₂×C₄	1	4	yes	—
44	C₃²×M₁₆	—	2	2	no	—
45	C₃²×M₁₆	C₂×C₄	1	4	yes	—
46	C₂×C₃²×C₈	—	2	2	no	—
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃²×C₄²	D₄	1	1	yes	characteristic
50	C₃²×C₄²	D₄	1	1	yes	characteristic
51	C₃×C₄⋊Dic₃	—	2	1	no	—
52	C₃×C₄⋊Dic₃	—	2	1	no	—
53	C₃×Dic₃⋊C₄	—	2	2	no	—
54	C₃×Dic₃⋊C₄	—	2	2	no	—
55	C₃×C₄×Dic₃	—	2	2	no	—
56	C₃×C₄×Dic₃	—	2	2	no	—
57	C₃×#208	—	2	2	no	—
58	C₃×#208	C₂×C₄	1	4	yes	—
59	C₂×C₃×C₃⋊C₈	—	2	2	no	—
60	C₄×#101	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	3	1	no	—
62	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×M₁₆	—	2	2	no	—
64	C₂×C₃×M₁₆	—	3	2	no	—
65	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
66	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
67	C₃×C₄×Q₈	—	6	1	no	—
68	C₃×C₄×Q₈	—	6	1	no	—
69	C₃×C₄×Q₈	—	6	1	no	—
70	C₃×C₄×Q₈	—	6	1	no	—
71	C₂×C₃×C₄⋊C₄	—	3	2	no	—
72	C₂×C₃×C₄⋊C₄	—	3	1	no	—
73	C₂×C₃×C₄²	—	2	1	no	—
74	C₂×C₃×C₄²	—	3	2	no	—
75	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
78	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
79	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
80	C₂×#208	C₂²×C₃	1	2	yes	—
81	C₄×Dic₆	—	2	1	no	—
82	C₄×Dic₆	—	2	1	no	—
83	C₄×Dic₆	—	2	1	no	—
84	C₄×Dic₆	—	2	1	no	—
85	C₃×#101	—	3	8	no	—
86	C₃×#97	—	2	2	no	—
87	C₃×#97	—	2	1	no	—
88	C₃×#97	—	2	1	no	—
89	C₃×#97	—	6	1	no	—
90	C₃×C₄×C₈	—	2	2	no	—
91	C₃×C₄×C₈	—	2	1	no	—
92	C₃×C₄×C₈	—	2	1	no	—
93	C₃×C₄×C₈	—	6	1	no	—
94	#824	C₃×C₄	1	8	yes	direct product factor
95	#803	—	2	1	no	—
96	C₄×C₃⋊C₈	—	2	1	no	—
97	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	4	1	no	—
100	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	#41	1	2	yes	—
108	C₂×C₃×Dic₃	—	2	2	no	—
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	2	2	no	—
111	C₂×C₃×Dic₃	—	4	2	no	—
112	C₂×C₃×Dic₃	C₄²	1	4	yes	—
113	C₃×Dic₆	—	2	4	no	—
114	C₃×Dic₆	—	2	4	no	—
115	C₃²×C₈	—	2	4	no	—
116	C₃×C₃⋊C₈	—	2	4	no	—
117	C₂×C₄×Q₈	—	3	1	no	—
118	C₂×#101	—	3	2	no	—
119	C₄×M₁₆	—	3	1	no	—
120	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic
121	#343	—	3	2	no	—
122	C₂×C₃×Q₈	—	3	4	no	—
123	C₂×C₃×Q₈	—	6	1	no	—
124	C₂×C₃×Q₈	—	6	2	no	—
125	C₂×C₃×Q₈	—	6	1	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	3	2	no	—
130	C₂²×C₃×C₄	—	3	2	no	—
131	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
138	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
139	C₂×Dic₆	—	2	1	no	—
140	C₂×Dic₆	—	2	1	no	—
141	C₂×Dic₆	—	2	2	no	—
142	C₂×Dic₆	C₂×C₃×C₄	1	4	yes	—
143	C₃×M₁₆	—	2	4	no	—
144	C₃×M₁₆	—	2	2	no	—
145	C₃×M₁₆	—	2	2	no	—
146	C₃×M₁₆	—	2	4	no	—
147	C₃×M₁₆	—	3	4	no	—
148	C₃×M₁₆	—	6	2	no	—
149	C₃×M₁₆	C₄×D₃	1	4	yes	—
150	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	—
151	C₂×C₃×C₈	—	2	4	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	6	2	no	—
155	C₃×C₄⋊C₄	—	6	2	no	—
156	C₃×C₄⋊C₄	—	6	2	no	—
157	C₃×C₄⋊C₄	—	6	1	no	—
158	C₃×C₄⋊C₄	—	6	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	1	no	—
161	C₃×C₄²	—	2	1	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₃×C₄²	—	6	2	no	—
164	C₃×C₄²	—	6	2	no	—
165	C₃×C₄²	D₁₂	1	1	yes	characteristic
166	C₃×C₄²	D₁₂	1	1	yes	characteristic
167	C₃×C₄²	#67	1	1	yes	characteristic
168	C₃×C₄²	#67	1	1	yes	characteristic
169	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
170	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
171	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
172	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
173	C₄⋊Dic₃	—	2	1	no	—
174	C₄⋊Dic₃	—	2	1	no	—
175	Dic₃⋊C₄	—	2	2	no	—
176	Dic₃⋊C₄	—	2	2	no	—
177	C₄×Dic₃	—	2	2	no	—
178	C₄×Dic₃	—	2	2	no	—
179	#208	—	2	2	no	—
180	#208	C₂×C₃×C₄	1	4	yes	—
181	C₂×C₃⋊C₈	—	2	2	no	—
182	C₂²×C₃²	—	2	1	no	—
183	C₂²×C₃²	—	2	1	no	—
184	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
185	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₃²	#117	1	1	yes	characteristic
187	C₃²×C₄	—	2	1	no	—
188	C₃²×C₄	—	2	1	no	—
189	C₃²×C₄	—	2	1	no	—
190	C₃²×C₄	#101	1	2	yes	complemented
191	C₃²×C₄	C₄×D₄	1	2	yes	—
192	C₃²×C₄	C₄×D₄	1	2	yes	—
193	C₃×Dic₃	—	2	4	no	—
194	C₃×Dic₃	—	4	2	no	—
195	C₂²×Q₈	—	3	1	no	—
196	C₂×M₁₆	—	3	2	no	—
197	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
198	C₄×Q₈	—	6	1	no	—
199	C₄×Q₈	—	6	1	no	—
200	C₄×Q₈	—	6	1	no	—
201	C₄×Q₈	—	6	1	no	—
202	C₂×C₄⋊C₄	—	3	2	no	—
203	C₂×C₄⋊C₄	—	3	1	no	—
204	C₂×C₄²	—	3	2	no	—
205	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
206	#101	—	3	8	no	—
207	#97	—	2	1	no	—
208	#97	—	6	1	no	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	6	1	no	—
211	C₂³×C₃	—	2	1	no	—
212	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
213	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₃×Q₈	—	6	4	no	—
215	C₃×Q₈	—	6	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	1	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	—	6	2	no	—
232	C₂×C₃×C₄	—	6	2	no	—
233	C₂×C₃×C₄	—	6	2	no	—
234	C₂×C₃×C₄	—	12	2	no	—
235	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
244	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
245	C₂×C₃×C₄	#235	1	2	yes	—
246	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₃×#41	1	2	yes	—
251	C₂×Dic₃	—	2	2	no	—
252	C₂×Dic₃	—	2	2	no	—
253	C₂×Dic₃	—	2	2	no	—
254	C₂×Dic₃	—	4	2	no	—
255	C₂×Dic₃	C₃×C₄²	1	4	yes	—
256	Dic₆	—	2	4	no	—
257	Dic₆	—	2	4	no	—
258	C₃×C₈	—	2	8	no	—
259	C₃×C₈	—	2	4	no	—
260	C₃×C₈	—	2	4	no	—
261	C₃×C₈	—	6	4	no	—
262	C₃⋊C₈	—	2	4	no	—
263	C₂×C₃²	—	2	1	no	—
264	C₂×C₃²	—	2	1	no	—
265	C₂×C₃²	C₄×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₃²	C₂×#101	1	1	yes	characteristic
267	C₂×C₃²	#413	1	1	yes	characteristic
268	C₂×Q₈	—	3	4	no	—
269	C₂×Q₈	—	6	1	no	—
270	C₂×Q₈	—	6	2	no	—
271	C₂×Q₈	—	6	1	no	—
272	C₂²×C₄	—	3	2	no	—
273	C₂²×C₄	—	3	2	no	—
274	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
275	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	M₁₆	—	2	2	no	—
278	M₁₆	—	3	4	no	—
279	M₁₆	—	6	2	no	—
280	M₁₆	C₃×C₄×D₃	1	4	yes	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	6	2	no	—
283	C₄⋊C₄	—	6	2	no	—
284	C₄⋊C₄	—	6	2	no	—
285	C₄⋊C₄	—	6	1	no	—
286	C₄⋊C₄	—	6	1	no	—
287	C₄²	—	6	2	no	—
288	C₄²	—	6	2	no	—
289	C₄²	C₃×D₁₂	1	1	yes	characteristic
290	C₄²	C₃×D₁₂	1	1	yes	characteristic
291	C₄²	C₃×#67	1	1	yes	characteristic
292	C₄²	C₃×#67	1	1	yes	characteristic
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
303	C₂²×C₃	#872	1	1	yes	characteristic
304	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₃	C₃×#117	1	1	yes	characteristic
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	6	4	no	—
321	C₃×C₄	—	12	2	no	—
322	C₃×C₄	#824	1	2	yes	direct product factor
323	C₃×C₄	C₃×#101	1	2	yes	complemented
324	C₃×C₄	C₄×D₁₂	1	2	yes	—
325	C₃×C₄	C₄×#67	1	2	yes	—
326	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
327	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
328	Dic₃	—	2	4	no	—
329	Dic₃	—	4	2	no	—
330	C₃²	C₄×#101	1	1	yes	characteristic, complemented, Sylow
331	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
332	Q₈	—	6	4	no	—
333	Q₈	—	6	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	3	4	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	—	12	2	no	—
341	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
346	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
347	C₂×C₄	C₃×#235	1	2	yes	—
348	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	6	4	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	4	1	no	—
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
361	C₂×C₃	#5132	1	1	yes	characteristic
362	C₂×C₃	C₂×#824	1	1	yes	characteristic
363	C₂×C₃	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₃	C₂×C₃×#101	1	1	yes	characteristic
365	C₂×C₃	C₃×#413	1	1	yes	characteristic
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
369	C₂²	C₃×#872	1	1	yes	characteristic
370	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	6	4	no	—
375	C₄	—	12	2	no	—
376	C₄	C₃×#824	1	2	yes	direct product factor
377	C₄	C₃×C₄×D₁₂	1	2	yes	—
378	C₄	C₃×C₄×#67	1	2	yes	—
379	C₃	—	2	1	no	—
380	C₃	C₄×#824	1	1	yes	characteristic, direct product factor
381	C₃	C₃×C₄×#101	1	1	yes	characteristic, complemented
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	C₃×C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
385	C₂	C₃×#5132	1	1	yes	characteristic
386	C₂	C₂×C₃×#824	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×C₄×#101
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
7. C₄×#824	C₃	direct (N × H)
21. C₃×#824	C₄	direct (N × H)
94. #824	C₃×C₄	direct (N × H)
190. C₃²×C₄	#101	semidirect
322. C₃×C₄	#824	direct (N × H)
323. C₃×C₄	C₃×#101	semidirect
330. C₃²	C₄×#101	semidirect
376. C₄	C₃×#824	direct (N × H)
380. C₃	C₄×#824	direct (N × H)
381. C₃	C₃×C₄×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×Dic₆	2
C₃²×C₄×M₁₆	2
C₂×C₃×#824	2
C₃×C₄×#208	2
C₃×#4554	2
C₃×C₄×#101	3
C₄×#824	3

Subgroups — C3×C4×#824 #11783803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#824 #11783803