Subgroups — #11790344

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592634	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×#63573	C₂	1	2	yes	maximal
5	#10589164	C₂	1	2	yes	maximal
6	#70454	—	3	1	no	maximal
7	#69467	—	3	1	no	maximal
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
10	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
11	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₃	—	2	1	no	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
16	C₃×C₃⋊#95	—	2	1	no	—
17	C₃×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
18	#63573	—	2	4	no	—
19	C₂×C₃×C₄⋊C₈	—	3	1	no	—
20	C₃×C₄×C₄⋊C₄	—	3	1	no	—
21	C₂×#817	—	3	2	no	—
22	C₂×#808	—	3	2	no	—
23	#4935	—	3	1	no	—
24	#4935	—	3	1	no	—
25	#4935	—	6	1	no	—
26	C₄×C₄⋊Dic₃	D₃	1	1	yes	characteristic
27	C₂×C₄⋊(C₃⋊C₈)	D₃	1	1	yes	characteristic
28	#4551	—	3	2	no	—
29	#4529	—	3	2	no	—
30	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃⋊Dic₃	—	2	2	no	—
34	C₂²×C₃×Dic₃	—	2	1	no	—
35	C₂²×C₃×Dic₃	—	2	1	no	—
36	C₃²×C₄²	C₂×C₄	1	2	yes	—
37	C₃²×C₄²	Q₈	1	2	yes	—
38	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
39	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
40	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
41	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
42	C₃×C₄⋊Dic₃	—	2	1	no	—
43	C₃×C₄⋊Dic₃	—	2	1	no	—
44	C₃×C₄⋊Dic₃	D₄	1	2	yes	—
45	C₃×C₄⋊Dic₃	Q₈	1	2	yes	—
46	C₃×C₄×Dic₃	—	4	2	no	—
47	C₂×C₃×C₃⋊C₈	—	2	2	no	—
48	C₂×C₃×C₃⋊C₈	—	2	2	no	—
49	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
50	#1948	—	9	1	no	Sylow
51	C₂²×C₃×C₈	—	3	2	no	—
52	C₂×C₃×C₄⋊C₄	—	3	1	no	—
53	C₂×C₃×C₄⋊C₄	—	3	1	no	—
54	C₂×C₃×C₄²	—	2	1	no	—
55	C₂×C₃×C₄²	—	6	1	no	—
56	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
58	C₂×C₄⋊Dic₃	—	3	2	no	—
59	C₂×C₄⋊Dic₃	—	3	2	no	—
60	C₂×C₄⋊Dic₃	—	6	2	no	—
61	C₂×C₄⋊Dic₃	—	6	2	no	—
62	C₂×C₄⋊Dic₃	—	6	2	no	—
63	C₂×C₄⋊Dic₃	—	6	1	no	—
64	C₂×C₄⋊Dic₃	—	6	1	no	—
65	C₂×C₄⋊Dic₃	—	6	1	no	—
66	C₂×C₄⋊Dic₃	—	6	1	no	—
67	C₂×C₄⋊Dic₃	C₂×D₃	1	1	yes	characteristic
68	C₂×C₄⋊Dic₃	C₂×D₃	1	1	yes	characteristic
69	C₂×C₄×Dic₃	—	2	1	no	—
70	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
71	C₃×C₄⋊C₈	—	3	4	no	—
72	C₃×#95	—	6	1	no	—
73	C₃⋊#95	—	2	1	no	—
74	#817	—	6	4	no	—
75	#808	—	6	4	no	—
76	C₄⋊(C₃⋊C₈)	Dic₃	1	4	yes	complemented
77	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
78	C₂×C₃²×C₄	—	2	1	no	—
79	C₂×C₃²×C₄	—	2	1	no	—
80	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
81	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
82	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
83	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
84	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃²×C₄	#41	1	1	yes	characteristic
89	C₂×C₃²×C₄	#41	1	1	yes	characteristic
90	C₂×C₃⋊Dic₃	—	4	2	no	—
91	C₂×C₃⋊Dic₃	—	4	2	no	—
92	C₂×C₃⋊Dic₃	—	4	2	no	—
93	C₂×C₃×Dic₃	—	2	2	no	—
94	C₂×C₃×Dic₃	—	2	2	no	—
95	C₂×C₃×Dic₃	—	4	1	no	—
96	C₂×C₃×Dic₃	—	4	1	no	—
97	C₂×C₃×Dic₃	—	4	1	no	—
98	C₂×C₃×Dic₃	—	4	1	no	—
99	C₃×C₃⋊C₈	—	2	4	no	—
100	C₂×#106	—	9	2	no	—
101	C₂×C₄⋊C₈	—	3	1	no	—
102	#384	—	9	1	no	—
103	C₄×C₄⋊C₄	—	3	1	no	—
104	#340	—	9	2	no	—
105	C₂²×C₃×C₄	—	2	1	no	—
106	C₂²×C₃×C₄	—	2	1	no	—
107	C₂²×C₃×C₄	—	2	1	no	—
108	C₂²×C₃×C₄	—	6	1	no	—
109	C₂²×C₃×C₄	—	6	1	no	—
110	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
111	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
112	C₂²×C₃×C₄	#67	1	1	yes	characteristic
113	C₂²×C₃×C₄	#67	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
115	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
116	C₂²×Dic₃	—	2	1	no	—
117	C₂²×Dic₃	—	2	1	no	—
118	C₂²×Dic₃	—	6	4	no	—
119	C₂²×Dic₃	—	6	2	no	—
120	C₂²×Dic₃	—	6	2	no	—
121	C₂×C₃×C₈	—	3	4	no	—
122	C₂×C₃×C₈	—	6	2	no	—
123	C₂×C₃×C₈	—	6	2	no	—
124	C₃×C₄⋊C₄	—	3	2	no	—
125	C₃×C₄⋊C₄	—	3	2	no	—
126	C₃×C₄⋊C₄	—	6	1	no	—
127	C₃×C₄⋊C₄	—	6	1	no	—
128	C₃×C₄²	—	2	2	no	—
129	C₃×C₄²	—	2	2	no	—
130	C₃×C₄²	—	12	2	no	—
131	C₃×C₄²	Dic₆	1	2	yes	—
132	C₃×C₄²	Dic₆	1	2	yes	—
133	C₃×C₄²	C₄×D₃	1	2	yes	—
134	C₃×C₄²	C₂×Dic₃	1	2	yes	—
135	C₄⋊Dic₃	—	2	1	no	—
136	C₄⋊Dic₃	—	2	1	no	—
137	C₄⋊Dic₃	—	6	2	no	—
138	C₄⋊Dic₃	—	6	2	no	—
139	C₄⋊Dic₃	—	6	2	no	—
140	C₄⋊Dic₃	—	6	2	no	—
141	C₄⋊Dic₃	—	12	2	no	—
142	C₄⋊Dic₃	—	12	2	no	—
143	C₄⋊Dic₃	—	12	4	no	—
144	C₄⋊Dic₃	—	12	2	no	—
145	C₄⋊Dic₃	—	12	2	no	—
146	C₄⋊Dic₃	—	12	4	no	—
147	C₄⋊Dic₃	—	12	2	no	—
148	C₄⋊Dic₃	—	12	2	no	—
149	C₄⋊Dic₃	Dic₆	1	2	yes	—
150	C₄⋊Dic₃	D₁₂	1	2	yes	—
151	C₄×Dic₃	—	4	2	no	—
152	C₂×C₃⋊C₈	—	2	2	no	—
153	C₂×C₃⋊C₈	—	2	2	no	—
154	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	—
155	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₃²	#121	1	1	yes	characteristic
157	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
159	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
160	C₂²×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂²×C₃²	#137	1	1	yes	characteristic
162	C₃²×C₄	—	2	2	no	—
163	C₃²×C₄	#106	1	4	yes	complemented
164	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
165	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
166	C₃²×C₄	#125	1	1	yes	characteristic
167	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
168	C₃⋊Dic₃	—	8	2	no	—
169	C₃×Dic₃	—	4	2	no	—
170	C₃×Dic₃	—	4	2	no	—
171	C₂²×C₈	—	3	2	no	—
172	C₂×C₄⋊C₄	—	3	1	no	—
173	C₂×C₄⋊C₄	—	3	1	no	—
174	C₂×C₄⋊C₄	—	9	2	no	—
175	C₂×C₄⋊C₄	—	18	1	no	—
176	C₂×C₄⋊C₄	—	18	1	no	—
177	C₂×C₄²	—	6	1	no	—
178	C₂×C₄²	D₃²	1	1	yes	characteristic
179	#106	—	18	4	no	—
180	C₄⋊C₈	—	3	4	no	—
181	#95	—	6	1	no	—
182	C₂³×C₃	—	2	1	no	—
183	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
184	C₂³×C₃	C₂×#67	1	1	yes	characteristic
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	1	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	2	no	—
192	C₂×C₃×C₄	—	2	2	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	1	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	1	no	—
199	C₂×C₃×C₄	—	2	1	no	—
200	C₂×C₃×C₄	—	2	1	no	—
201	C₂×C₃×C₄	—	6	2	no	—
202	C₂×C₃×C₄	—	6	2	no	—
203	C₂×C₃×C₄	—	12	1	no	—
204	C₂×C₃×C₄	—	12	1	no	—
205	C₂×C₃×C₄	—	12	1	no	—
206	C₂×C₃×C₄	—	12	1	no	—
207	C₂×C₃×C₄	#204	1	2	yes	—
208	C₂×C₃×C₄	#204	1	2	yes	—
209	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
210	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
211	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
212	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
213	C₂×C₃×C₄	#214	1	2	yes	—
214	C₂×C₃×C₄	#215	1	2	yes	—
215	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
220	C₂×C₃×C₄	#235	1	1	yes	characteristic
221	C₂×C₃×C₄	#235	1	1	yes	characteristic
222	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄	#237	1	1	yes	characteristic
224	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
225	C₂×C₃×C₄	#239	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
227	C₂×Dic₃	—	2	2	no	—
228	C₂×Dic₃	—	2	2	no	—
229	C₂×Dic₃	—	4	1	no	—
230	C₂×Dic₃	—	4	1	no	—
231	C₂×Dic₃	—	4	1	no	—
232	C₂×Dic₃	—	4	1	no	—
233	C₂×Dic₃	—	12	4	no	—
234	C₂×Dic₃	—	12	4	no	—
235	C₂×Dic₃	—	12	4	no	—
236	C₂×Dic₃	—	12	2	no	—
237	C₂×Dic₃	—	12	2	no	—
238	C₂×Dic₃	—	12	2	no	—
239	C₂×Dic₃	—	12	2	no	—
240	C₂×Dic₃	—	12	2	no	—
241	C₂×Dic₃	—	12	2	no	—
242	C₃×C₈	—	6	4	no	—
243	C₃⋊C₈	—	2	4	no	—
244	C₂×C₃²	#389	1	1	yes	characteristic
245	C₂×C₃²	C₂×#106	1	1	yes	characteristic
246	C₂×C₃²	#428	1	1	yes	characteristic
247	C₂×C₃²	#460	1	1	yes	characteristic
248	C₂×C₃²	#461	1	1	yes	characteristic
249	C₂×C₃²	#475	1	1	yes	characteristic
250	C₂×C₃²	#476	1	1	yes	characteristic
251	C₂²×C₄	—	6	1	no	—
252	C₂²×C₄	—	6	1	no	—
253	C₂²×C₄	—	18	2	no	—
254	C₂²×C₄	#626	1	1	yes	characteristic
255	C₂²×C₄	#626	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
257	C₂×C₈	—	3	4	no	—
258	C₂×C₈	—	6	2	no	—
259	C₂×C₈	—	6	2	no	—
260	C₄⋊C₄	—	3	2	no	—
261	C₄⋊C₄	—	3	2	no	—
262	C₄⋊C₄	—	6	1	no	—
263	C₄⋊C₄	—	6	1	no	—
264	C₄⋊C₄	—	18	2	no	—
265	C₄⋊C₄	—	18	2	no	—
266	C₄⋊C₄	—	36	2	no	—
267	C₄⋊C₄	—	36	2	no	—
268	C₄²	—	12	2	no	—
269	C₄²	D₃×Dic₃	1	2	yes	—
270	C₄²	#627	1	2	yes	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	#895	1	1	yes	characteristic
279	C₂²×C₃	#897	1	1	yes	characteristic
280	C₂²×C₃	C₂×#204	1	1	yes	characteristic
281	C₂²×C₃	C₂×#204	1	1	yes	characteristic
282	C₂²×C₃	#908	1	1	yes	characteristic
283	C₂²×C₃	#909	1	1	yes	characteristic
284	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
285	C₂²×C₃	#924	1	1	yes	characteristic
286	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
287	C₂²×C₃	#930	1	1	yes	characteristic
288	C₂²×C₃	C₂×#214	1	1	yes	characteristic
289	C₂²×C₃	C₂×#215	1	1	yes	characteristic
290	C₂²×C₃	#949	1	1	yes	characteristic
291	C₂²×C₃	#951	1	1	yes	characteristic
292	C₃×C₄	—	2	4	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	12	2	no	—
301	C₃×C₄	—	12	2	no	—
302	C₃×C₄	#808	1	4	yes	complemented
303	C₃×C₄	#817	1	4	yes	complemented
304	C₃×C₄	C₄×Dic₆	1	1	yes	characteristic
305	C₃×C₄	#869	1	1	yes	characteristic
306	C₃×C₄	#870	1	1	yes	characteristic
307	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
308	C₃×C₄	#888	1	1	yes	characteristic
309	C₃×C₄	#890	1	1	yes	characteristic
310	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
311	C₃×C₄	Q₈×Dic₃	1	1	yes	characteristic
312	Dic₃	—	4	2	no	—
313	Dic₃	—	4	2	no	—
314	Dic₃	—	24	4	no	—
315	Dic₃	—	24	2	no	—
316	Dic₃	—	24	2	no	—
317	C₃²	#1948	1	1	yes	characteristic, complemented, Sylow
318	C₂³	C₂×#626	1	1	yes	characteristic
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	6	2	no	—
322	C₂×C₄	—	6	2	no	—
323	C₂×C₄	—	12	1	no	—
324	C₂×C₄	—	12	1	no	—
325	C₂×C₄	—	12	1	no	—
326	C₂×C₄	—	12	1	no	—
327	C₂×C₄	—	36	2	no	—
328	C₂×C₄	—	36	2	no	—
329	C₂×C₄	—	36	2	no	—
330	C₂×C₄	#3716	1	2	yes	—
331	C₂×C₄	#3717	1	2	yes	—
332	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
333	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
334	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
335	C₂×C₄	#3795	1	1	yes	characteristic
336	C₂×C₄	#3799	1	1	yes	characteristic
337	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
338	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
339	C₂×C₄	C₂×#627	1	1	yes	characteristic
340	C₈	—	6	4	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	#4841	1	1	yes	characteristic
349	C₂×C₃	#4842	1	1	yes	characteristic
350	C₂×C₃	#4848	1	1	yes	characteristic
351	C₂×C₃	#4851	1	1	yes	characteristic
352	C₂×C₃	#4928	1	1	yes	characteristic
353	C₂×C₃	C₂×#808	1	1	yes	characteristic
354	C₂×C₃	#4984	1	1	yes	characteristic
355	C₂×C₃	#4995	1	1	yes	characteristic
356	C₂×C₃	#5008	1	1	yes	characteristic
357	C₂×C₃	#5019	1	1	yes	characteristic
358	C₂×C₃	#5020	1	1	yes	characteristic
359	C₂×C₃	#5027	1	1	yes	characteristic
360	C₂×C₃	C₂×#817	1	1	yes	characteristic
361	C₂×C₃	#5121	1	1	yes	characteristic
362	C₂²	#63825	1	1	yes	characteristic
363	C₂²	C₂×#3716	1	1	yes	characteristic
364	C₂²	#63831	1	1	yes	characteristic
365	C₂²	C₂×#3717	1	1	yes	characteristic
366	C₂²	#63857	1	1	yes	characteristic
367	C₂²	#63909	1	1	yes	characteristic
368	C₂²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	12	2	no	—
371	C₄	—	12	2	no	—
372	C₄	—	72	2	no	—
373	C₄	#63573	1	4	yes	complemented
374	C₄	Dic₃×Dic₆	1	1	yes	characteristic
375	C₄	#63869	1	1	yes	characteristic
376	C₄	Dic₃×D₁₂	1	1	yes	characteristic
377	C₄	#63918	1	1	yes	characteristic
378	C₃	—	2	1	no	—
379	C₃	#69467	1	1	yes	characteristic, complemented
380	C₃	#70454	1	1	yes	characteristic, complemented
381	C₂	#10590268	1	1	yes	characteristic
382	C₂	#10590301	1	1	yes	characteristic
383	C₂	#10590365	1	1	yes	characteristic
384	C₂	#10590367	1	1	yes	characteristic
385	C₂	C₂×#63573	1	1	yes	characteristic
386	C₂	#10591131	1	1	yes	characteristic
387	C₂	#10591352	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#626
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1948
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
17. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
76. C₄⋊(C₃⋊C₈)	Dic₃	semidirect
163. C₃²×C₄	#106	semidirect
302. C₃×C₄	#808	semidirect
303. C₃×C₄	#817	semidirect
317. C₃²	#1948	semidirect
373. C₄	#63573	semidirect
379. C₃	#69467	semidirect
380. C₃	#70454	semidirect

Maximal subgroups

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

subgroup	index
#10592634	2
C₃×C₄×C₄⋊Dic₃	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×#63573	2
#10589164	2
#70454	3
#69467	3