Subgroups — C₃×#10596014 #13179296

Order 1728.

1744 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×D₄×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal, complemented
4	C₃×#64133	C₂	1	2	yes	maximal, complemented
5	C₃×#64099	C₂	1	2	yes	maximal, complemented
6	C₃×#64087	C₂	1	4	yes	maximal, complemented
7	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596014	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5543	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊Dic₃	C₂²	1	4	yes	—
14	C₂×C₃×#634	C₂²	1	1	yes	characteristic
15	C₂×C₃×#634	C₂²	1	2	yes	—
16	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄²	C₂²	1	1	yes	characteristic
19	C₃×#3757	C₂²	1	4	yes	—
20	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
21	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
24	C₃×#3750	C₂²	1	2	yes	—
25	C₃×#3750	C₂²	1	4	yes	—
26	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
27	C₃²×C₄×D₄	—	2	4	no	—
28	C₃²×C₄×D₄	D₃	1	4	yes	—
29	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
30	D₄×C₃⋊Dic₃	C₂×C₃	1	2	yes	—
31	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	2	yes	complemented
32	#64133	C₂×C₃	1	2	yes	complemented
33	#64099	C₂×C₃	1	2	yes	complemented
34	#64087	C₂×C₃	1	4	yes	complemented
35	#64078	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×D₄×Dic₃	—	3	8	no	—
38	C₂×C₃×C₄⋊Dic₃	—	3	8	no	—
39	C₃×#924	—	3	8	no	—
40	C₃×#890	—	3	8	no	—
41	C₃×#878	—	3	16	no	—
42	C₃×#869	—	3	4	no	—
43	C₃×C₄×Dic₆	—	3	4	no	—
44	C₂³×C₃³	C₂³	1	2	yes	—
45	C₃³×D₄	Q₈	1	4	yes	complemented
46	C₂×C₃³×C₄	—	2	4	no	—
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₃⋊Dic₃	—	4	4	no	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
55	C₃×#634	—	2	2	no	—
56	C₃×#634	—	4	2	no	—
57	C₃×#554	—	9	1	no	—
58	#5543	—	3	4	no	—
59	C₂×C₃²×D₄	—	2	4	no	—
60	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
61	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₃²×C₄	—	2	8	no	—
63	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
65	C₂²×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
66	C₂×#634	C₂²×C₃	1	1	yes	characteristic
67	C₂×#634	C₂²×C₃	1	2	yes	—
68	C₂²×C₃×Dic₃	—	3	16	no	—
69	C₂×C₃×Dic₆	—	3	4	no	—
70	C₂×C₃×Dic₆	—	3	8	no	—
71	C₃²×C₄⋊C₄	—	2	4	no	—
72	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
73	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
74	C₃²×C₂²⋊C₄	—	2	8	no	—
75	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
76	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
77	C₃²×C₄²	—	2	4	no	—
78	C₃²×C₄²	C₂×D₃	1	4	yes	—
79	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
80	#3757	C₂²×C₃	1	4	yes	—
81	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
82	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
83	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
84	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	—
85	#3750	C₂²×C₃	1	2	yes	—
86	#3750	C₂²×C₃	1	4	yes	—
87	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
88	C₃×#217	—	3	16	no	—
89	C₃×C₄⋊Dic₃	—	3	16	no	—
90	C₃×C₄⋊Dic₃	—	3	8	no	—
91	C₃×C₄⋊Dic₃	—	3	8	no	—
92	C₃×C₄⋊Dic₃	—	3	4	no	—
93	C₃×Dic₃⋊C₄	—	3	8	no	—
94	C₃×Dic₃⋊C₄	—	3	16	no	—
95	C₃×C₄×Dic₃	—	3	8	no	—
96	C₂²×C₃³	—	2	2	no	—
97	C₂²×C₃³	—	2	2	no	—
98	C₂²×C₃³	C₂×Q₈	1	4	yes	—
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₃³×C₄	—	2	2	no	—
101	C₃³×C₄	—	2	1	no	—
102	C₃³×C₄	C₂×Q₈	1	2	yes	—
103	C₃³×C₄	#41	1	2	yes	—
104	C₃×C₃⋊Dic₃	—	2	2	no	—
105	C₃×C₃⋊Dic₃	—	2	4	no	—
106	C₃×C₃⋊Dic₃	—	2	2	no	—
107	C₃×C₄⋊Q₈	—	9	1	no	—
108	C₃×#125	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	2	no	—
110	C₃×C₂²⋊Q₈	—	9	4	no	—
111	C₃×C₄×Q₈	—	9	1	no	—
112	C₃×C₄×D₄	—	2	4	no	—
113	C₃×C₄×D₄	—	9	2	no	—
114	C₃×C₄×D₄	C₃×D₃	1	4	yes	—
115	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	—	9	2	no	—
117	D₄×Dic₃	—	3	8	no	—
118	C₂×C₄⋊Dic₃	—	3	8	no	—
119	#924	—	3	8	no	—
120	#890	—	3	8	no	—
121	#878	—	3	16	no	—
122	#869	—	3	4	no	—
123	C₄×Dic₆	—	3	4	no	—
124	C₂³×C₃²	—	2	8	no	—
125	C₂³×C₃²	C₂²×D₃	1	8	yes	—
126	C₂³×C₃²	C₂³×C₃	1	2	yes	—
127	C₃²×D₄	—	2	16	no	—
128	C₃²×D₄	Dic₆	1	16	yes	complemented
129	C₃²×D₄	C₃×Q₈	1	4	yes	complemented
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	8	no	—
135	C₂×C₃²×C₄	—	2	16	no	—
136	C₂×C₃²×C₄	—	4	16	no	—
137	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
139	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
140	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
142	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
145	C₂×C₃⋊Dic₃	—	4	4	no	—
146	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
147	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
148	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
149	#634	—	2	2	no	—
150	#634	—	4	2	no	—
151	C₂×C₃×Dic₃	—	3	8	no	—
152	C₂×C₃×Dic₃	—	3	8	no	—
153	C₂×C₃×Dic₃	—	3	16	no	—
154	C₂×C₃×Dic₃	—	12	16	no	—
155	C₃×Dic₆	—	6	8	no	—
156	C₃×Dic₆	—	12	8	no	—
157	#554	—	9	1	no	Sylow
158	C₂×C₃³	—	2	4	no	—
159	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₃³	C₂×#41	1	1	yes	characteristic
161	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂×C₃×Q₈	—	9	1	no	—
163	C₂×C₃×Q₈	—	9	2	no	—
164	C₂×C₃×D₄	—	2	4	no	—
165	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
166	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	—	2	8	no	—
168	C₂²×C₃×C₄	—	9	4	no	—
169	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
170	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
171	C₂²×Dic₃	—	3	16	no	—
172	C₂×Dic₆	—	3	4	no	—
173	C₂×Dic₆	—	3	8	no	—
174	C₃×C₄⋊C₄	—	2	4	no	—
175	C₃×C₄⋊C₄	—	9	2	no	—
176	C₃×C₄⋊C₄	—	9	4	no	—
177	C₃×C₄⋊C₄	—	9	1	no	—
178	C₃×C₄⋊C₄	—	9	4	no	—
179	C₃×C₄⋊C₄	—	9	2	no	—
180	C₃×C₄⋊C₄	—	9	2	no	—
181	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
182	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	—	2	8	no	—
184	C₃×C₂²⋊C₄	—	9	4	no	—
185	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
186	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	—	9	2	no	—
189	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
190	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
191	#217	—	3	16	no	—
192	C₄⋊Dic₃	—	3	4	no	—
193	C₄⋊Dic₃	—	3	8	no	—
194	C₄⋊Dic₃	—	3	8	no	—
195	C₄⋊Dic₃	—	3	16	no	—
196	Dic₃⋊C₄	—	3	8	no	—
197	Dic₃⋊C₄	—	3	16	no	—
198	C₄×Dic₃	—	3	8	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	2	4	no	—
202	C₂²×C₃²	—	2	16	no	—
203	C₂²×C₃²	—	2	8	no	—
204	C₂²×C₃²	—	2	8	no	—
205	C₂²×C₃²	—	4	8	no	—
206	C₂²×C₃²	—	4	8	no	—
207	C₂²×C₃²	C₂×Dic₆	1	16	yes	—
208	C₂²×C₃²	C₂×C₃×Q₈	1	4	yes	—
209	C₂²×C₃²	C₂³×D₃	1	4	yes	—
210	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
211	C₃²×C₄	—	2	2	no	—
212	C₃²×C₄	—	2	1	no	—
213	C₃²×C₄	—	2	8	no	—
214	C₃²×C₄	—	2	8	no	—
215	C₃²×C₄	—	2	8	no	—
216	C₃²×C₄	—	2	4	no	—
217	C₃²×C₄	—	4	4	no	—
218	C₃²×C₄	—	4	8	no	—
219	C₃²×C₄	C₂×Dic₆	1	8	yes	—
220	C₃²×C₄	#237	1	8	yes	—
221	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
222	C₃²×C₄	C₃×#41	1	2	yes	—
223	C₃⋊Dic₃	—	2	2	no	—
224	C₃⋊Dic₃	—	2	4	no	—
225	C₃⋊Dic₃	—	2	2	no	—
226	C₃×Dic₃	—	6	8	no	—
227	C₃×Dic₃	—	6	16	no	—
228	C₃×Dic₃	—	6	8	no	—
229	C₄⋊Q₈	—	9	1	no	—
230	#125	—	9	2	no	—
231	C₂²⋊Q₈	—	9	2	no	—
232	C₂²⋊Q₈	—	9	4	no	—
233	C₄×Q₈	—	9	1	no	—
234	C₄×D₄	—	9	2	no	—
235	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	—	9	2	no	—
237	C₃³	#554	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	2	8	no	—
239	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
240	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
241	C₃×Q₈	—	18	2	no	—
242	C₃×Q₈	—	36	2	no	—
243	C₃×D₄	—	2	16	no	—
244	C₃×D₄	C₃×Dic₆	1	16	yes	complemented
245	C₃×D₄	#634	1	4	yes	complemented
246	C₂×C₃×C₄	—	2	16	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	8	no	—
252	C₂×C₃×C₄	—	4	16	no	—
253	C₂×C₃×C₄	—	9	2	no	—
254	C₂×C₃×C₄	—	9	2	no	—
255	C₂×C₃×C₄	—	9	4	no	—
256	C₂×C₃×C₄	—	36	4	no	—
257	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
258	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
261	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
265	C₂×Dic₃	—	3	8	no	—
266	C₂×Dic₃	—	3	8	no	—
267	C₂×Dic₃	—	3	16	no	—
268	C₂×Dic₃	—	12	16	no	—
269	Dic₆	—	6	8	no	—
270	Dic₆	—	12	8	no	—
271	C₂×C₃²	—	2	4	no	—
272	C₂×C₃²	—	2	4	no	—
273	C₂×C₃²	—	2	4	no	—
274	C₂×C₃²	—	2	4	no	—
275	C₂×C₃²	—	2	16	no	—
276	C₂×C₃²	—	4	16	no	—
277	C₂×C₃²	C₂²×Dic₆	1	4	yes	—
278	C₂×C₃²	C₂×#237	1	4	yes	—
279	C₂×C₃²	#1009	1	4	yes	—
280	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
281	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
282	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×Q₈	—	9	1	no	—
284	C₂×Q₈	—	9	2	no	—
285	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
286	C₂²×C₄	—	9	4	no	—
287	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
288	C₄⋊C₄	—	9	1	no	—
289	C₄⋊C₄	—	9	4	no	—
290	C₄⋊C₄	—	9	2	no	—
291	C₄⋊C₄	—	9	2	no	—
292	C₄⋊C₄	—	9	2	no	—
293	C₄⋊C₄	—	9	4	no	—
294	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
295	C₂²⋊C₄	—	9	4	no	—
296	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
297	C₄²	—	9	2	no	—
298	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
299	C₂²×C₃	—	2	8	no	—
300	C₂²×C₃	—	2	8	no	—
301	C₂²×C₃	—	2	2	no	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	4	no	—
304	C₂²×C₃	—	2	16	no	—
305	C₂²×C₃	—	4	8	no	—
306	C₂²×C₃	—	4	8	no	—
307	C₂²×C₃	C₂×C₃×Dic₆	1	16	yes	—
308	C₂²×C₃	C₂×#634	1	4	yes	—
309	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
310	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
311	C₃×C₄	—	2	8	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	8	no	—
316	C₃×C₄	—	2	8	no	—
317	C₃×C₄	—	4	8	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	—	18	2	no	—
320	C₃×C₄	—	18	2	no	—
321	C₃×C₄	—	18	4	no	—
322	C₃×C₄	C₂×C₃×Dic₆	1	8	yes	—
323	C₃×C₄	C₃×#237	1	8	yes	—
324	C₃×C₄	C₂×#634	1	2	yes	—
325	C₃×C₄	#3830	1	2	yes	—
326	Dic₃	—	6	8	no	—
327	Dic₃	—	6	16	no	—
328	Dic₃	—	6	8	no	—
329	C₃²	—	2	4	no	—
330	C₃²	#5543	1	4	yes	complemented
331	C₃²	C₃×#554	1	1	yes	characteristic, complemented
332	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
333	Q₈	—	18	2	no	—
334	Q₈	—	36	2	no	—
335	D₄	C₃×#634	1	4	yes	complemented
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	9	2	no	—
338	C₂×C₄	—	9	2	no	—
339	C₂×C₄	—	9	4	no	—
340	C₂×C₄	—	36	4	no	—
341	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
343	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
345	C₂×C₃	—	2	16	no	—
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	2	4	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	4	16	no	—
351	C₂×C₃	C₂²×C₃×Dic₆	1	4	yes	—
352	C₂×C₃	C₂×C₃×#237	1	4	yes	—
353	C₂×C₃	C₃×#1009	1	4	yes	—
354	C₂×C₃	C₂²×#634	1	1	yes	characteristic
355	C₂×C₃	C₂×#3830	1	1	yes	characteristic
356	C₂×C₃	#64366	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	C₂×C₃×#634	1	4	yes	—
360	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	1	no	—
363	C₄	—	18	2	no	—
364	C₄	—	18	2	no	—
365	C₄	—	18	4	no	—
366	C₄	C₂×C₃×#634	1	2	yes	—
367	C₄	C₃×#3830	1	2	yes	—
368	C₃	—	2	4	no	—
369	C₃	C₃×#5543	1	4	yes	complemented
370	C₃	#10596014	1	1	yes	characteristic, direct product factor
371	C₂	—	2	4	no	—
372	C₂	C₂²×C₃×#634	1	1	yes	characteristic
373	C₂	C₂×C₃×#3830	1	1	yes	characteristic
374	C₂	C₃×#64366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃³×D₄	C₂²
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#554
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
4. C₃×#64133	C₂	semidirect
5. C₃×#64099	C₂	semidirect
6. C₃×#64087	C₂	semidirect
7. C₃×#64078	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. #10596014	C₃	direct (N × H)
31. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
32. #64133	C₂×C₃	semidirect
33. #64099	C₂×C₃	semidirect
34. #64087	C₂×C₃	semidirect
35. #64078	C₂×C₃	semidirect
36. C₄×#634	C₂×C₃	semidirect
45. C₃³×D₄	Q₈	semidirect
128. C₃²×D₄	Dic₆	semidirect
129. C₃²×D₄	C₃×Q₈	semidirect
237. C₃³	#554	semidirect
244. C₃×D₄	C₃×Dic₆	semidirect
245. C₃×D₄	#634	semidirect
330. C₃²	#5543	semidirect
331. C₃²	C₃×#554	semidirect
335. D₄	C₃×#634	semidirect
369. C₃	C₃×#5543	semidirect
370. C₃	#10596014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×D₄	2
C₃×D₄×C₃⋊Dic₃	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₃×#64133	2
C₃×#64099	2
C₃×#64087	2
C₃×#64078	2
C₃×C₄×#634	2
#10596014	3
C₃×#5543	3

Subgroups — C3×#10596014 #13179296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596014 #13179296