Subgroups — C₃²×#5579 #13178956

Order 1728.

1648 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#946	C₂	1	2	yes	maximal, complemented
3	C₃²×#896	C₂	1	4	yes	maximal, complemented
4	C₃²×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
6	C₃²×C₄×D₁₂	C₂	1	2	yes	maximal
7	C₃²×#870	C₂	1	2	yes	maximal, complemented
8	C₃²×#869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#554	—	3	1	no	maximal
10	C₃×#5579	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
14	C₂×C₃²×C₄×D₃	C₂²	1	4	yes	—
15	C₂×C₃²×Dic₆	C₂²	1	2	yes	—
16	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄²	C₂²	1	1	yes	characteristic
19	C₃³×C₄²	C₂²	1	2	yes	—
20	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃²×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₃²×Dic₃⋊C₄	C₂²	1	4	yes	—
27	C₃²×C₄⋊Q₈	—	3	1	no	—
28	C₃²×#125	—	3	2	no	—
29	C₃²×C₂²⋊Q₈	—	3	2	no	—
30	C₃²×C₂²⋊Q₈	—	3	4	no	—
31	C₃²×C₄×Q₈	—	2	4	no	—
32	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic, complemented
33	C₃²×C₄×Q₈	C₂×C₃	1	4	yes	complemented
34	C₃²×C₄×D₄	—	3	2	no	—
35	C₃²×C₄×D₄	—	3	1	no	—
36	C₂×C₃²×C₄⋊C₄	—	3	2	no	—
37	C₃×#946	C₂×C₃	1	8	yes	complemented
38	C₃×#896	C₂×C₃	1	16	yes	complemented
39	C₃×D₃×C₄⋊C₄	C₂×C₃	1	8	yes	complemented
40	C₃×C₄×D₁₂	C₂×C₃	1	8	yes	—
41	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	—
42	C₃×#870	C₂×C₃	1	8	yes	complemented
43	C₃×#869	C₂×C₃	1	4	yes	complemented
44	C₂²×C₃²×D₃	C₂³	1	2	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
52	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
53	C₃²×D₁₂	Q₈	1	4	yes	complemented
54	C₃²×C₄×D₃	—	2	4	no	—
55	C₃²×C₄×D₃	—	4	4	no	—
56	C₃²×Dic₆	—	4	2	no	—
57	C₃×#554	—	3	4	no	—
58	#5579	C₃²	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	—	2	4	no	—
60	C₂×C₃²×Q₈	—	3	2	no	—
61	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
63	C₂×C₃²×D₄	—	3	1	no	—
64	C₂²×C₃²×C₄	—	3	2	no	—
65	C₂²×C₃²×C₄	—	3	4	no	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
67	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	16	yes	—
69	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	—
70	C₃²×C₄⋊C₄	—	2	4	no	—
71	C₃²×C₄⋊C₄	—	2	8	no	—
72	C₃²×C₄⋊C₄	—	3	4	no	—
73	C₃²×C₄⋊C₄	—	3	2	no	—
74	C₃²×C₄⋊C₄	—	3	1	no	—
75	C₃²×C₄⋊C₄	—	3	2	no	—
76	C₃²×C₄⋊C₄	—	3	4	no	—
77	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
79	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
81	C₃²×C₂²⋊C₄	—	3	2	no	—
82	C₃²×C₂²⋊C₄	—	3	4	no	—
83	C₃²×C₄²	—	2	8	no	—
84	C₃²×C₄²	—	2	4	no	—
85	C₃²×C₄²	C₂×D₃	1	2	yes	—
86	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
87	C₃²×C₄²	C₂²×C₃	1	4	yes	—
88	C₃²×C₄²	C₂²×C₃	1	8	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
91	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	16	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	16	yes	—
96	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
97	C₂×C₃²×D₃	—	2	2	no	—
98	C₂×C₃²×D₃	—	2	2	no	—
99	C₂×C₃²×D₃	C₂×Q₈	1	4	yes	—
100	C₃³×C₄	—	2	2	no	—
101	C₃³×C₄	—	2	1	no	—
102	C₃³×C₄	—	2	2	no	—
103	C₃³×C₄	C₂×Q₈	1	2	yes	—
104	C₃³×C₄	#41	1	2	yes	—
105	C₃²×Dic₃	—	2	2	no	—
106	C₃²×Dic₃	—	2	4	no	—
107	C₃×C₄⋊Q₈	—	3	4	no	—
108	C₃×#125	—	3	8	no	—
109	C₃×C₂²⋊Q₈	—	3	8	no	—
110	C₃×C₂²⋊Q₈	—	3	16	no	—
111	C₃×C₄×Q₈	—	2	4	no	—
112	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
113	C₃×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₃×C₄×D₄	—	3	8	no	—
115	C₃×C₄×D₄	—	3	4	no	—
116	C₂×C₃×C₄⋊C₄	—	3	8	no	—
117	#946	C₂×C₃²	1	2	yes	complemented
118	#896	C₂×C₃²	1	4	yes	complemented
119	D₃×C₄⋊C₄	C₂×C₃²	1	2	yes	complemented
120	C₄×D₁₂	C₂×C₃²	1	2	yes	—
121	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic
122	#870	C₂×C₃²	1	2	yes	complemented
123	#869	C₂×C₃²	1	1	yes	characteristic, complemented
124	C₂³×C₃²	—	3	2	no	—
125	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
126	C₃²×Q₈	—	2	16	no	—
127	C₃²×Q₈	—	2	2	no	—
128	C₃²×Q₈	—	2	8	no	—
129	C₃²×Q₈	—	12	2	no	—
130	C₃²×D₄	—	3	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	8	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	2	8	no	—
136	C₂×C₃²×C₄	—	3	2	no	—
137	C₂×C₃²×C₄	—	3	4	no	—
138	C₂×C₃²×C₄	—	6	4	no	—
139	C₂×C₃²×C₄	—	12	4	no	—
140	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
141	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
146	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
147	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
148	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
150	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
151	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
152	C₃×D₁₂	C₃×Q₈	1	16	yes	complemented
153	C₃×C₄×D₃	—	2	16	no	—
154	C₃×C₄×D₃	—	4	16	no	—
155	C₃×Dic₆	—	4	8	no	—
156	#554	—	3	1	no	Sylow
157	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₃³	C₂×#41	1	1	yes	characteristic
159	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
160	C₃²×D₃	—	2	4	no	—
161	C₂×C₃×Q₈	—	2	4	no	—
162	C₂×C₃×Q₈	—	3	8	no	—
163	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
164	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
165	C₂×C₃×D₄	—	3	4	no	—
166	C₂²×C₃×C₄	—	3	8	no	—
167	C₂²×C₃×C₄	—	3	16	no	—
168	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
170	C₂×C₄×D₃	C₂²×C₃²	1	4	yes	—
171	C₂×Dic₆	C₂²×C₃²	1	2	yes	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	8	no	—
174	C₃×C₄⋊C₄	—	3	16	no	—
175	C₃×C₄⋊C₄	—	3	16	no	—
176	C₃×C₄⋊C₄	—	3	8	no	—
177	C₃×C₄⋊C₄	—	3	4	no	—
178	C₃×C₄⋊C₄	—	3	8	no	—
179	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
180	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
181	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
183	C₃×C₂²⋊C₄	—	3	8	no	—
184	C₃×C₂²⋊C₄	—	3	16	no	—
185	C₃×C₄²	—	2	8	no	—
186	C₃×C₄²	—	2	4	no	—
187	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
188	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
189	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
190	C₃×C₄²	C₂²×C₃²	1	2	yes	—
191	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
192	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
193	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
194	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
195	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
196	Dic₃⋊C₄	C₂²×C₃²	1	4	yes	—
197	Dic₃⋊C₄	C₂²×C₃²	1	4	yes	—
198	C₂²×C₃²	—	2	4	no	—
199	C₂²×C₃²	—	3	4	no	—
200	C₂²×C₃²	—	6	2	no	—
201	C₂²×C₃²	—	6	2	no	—
202	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
203	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
204	C₂×C₃×D₃	—	2	8	no	—
205	C₂×C₃×D₃	—	2	8	no	—
206	C₂×C₃×D₃	C₂×C₃×Q₈	1	16	yes	—
207	C₃²×C₄	—	2	16	no	—
208	C₃²×C₄	—	2	2	no	—
209	C₃²×C₄	—	2	2	no	—
210	C₃²×C₄	—	2	1	no	—
211	C₃²×C₄	—	2	8	no	—
212	C₃²×C₄	—	2	8	no	—
213	C₃²×C₄	—	2	8	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	8	no	—
216	C₃²×C₄	—	4	8	no	—
217	C₃²×C₄	—	4	4	no	—
218	C₃²×C₄	—	6	2	no	—
219	C₃²×C₄	—	6	4	no	—
220	C₃²×C₄	#235	1	2	yes	—
221	C₃²×C₄	D₃×Q₈	1	2	yes	—
222	C₃²×C₄	C₂×C₃×Q₈	1	8	yes	—
223	C₃²×C₄	C₃×#41	1	8	yes	—
224	C₃×Dic₃	—	2	8	no	—
225	C₃×Dic₃	—	2	16	no	—
226	C₄⋊Q₈	—	3	1	no	—
227	#125	—	3	2	no	—
228	C₂²⋊Q₈	—	3	2	no	—
229	C₂²⋊Q₈	—	3	4	no	—
230	C₄×Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
231	C₄×D₄	—	3	2	no	—
232	C₄×D₄	—	3	1	no	—
233	C₂×C₄⋊C₄	—	3	2	no	—
234	C₃³	#554	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	3	8	no	—
236	C₂²×D₃	C₂³×C₃²	1	2	yes	—
237	C₃×Q₈	—	2	16	no	—
238	C₃×Q₈	—	2	8	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	12	8	no	—
241	C₃×D₄	—	3	16	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	3	8	no	—
248	C₂×C₃×C₄	—	3	16	no	—
249	C₂×C₃×C₄	—	6	16	no	—
250	C₂×C₃×C₄	—	12	16	no	—
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
256	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
257	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
258	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
261	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
262	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
263	D₁₂	C₃²×Q₈	1	4	yes	complemented
264	C₄×D₃	—	2	4	no	—
265	C₄×D₃	—	4	4	no	—
266	Dic₆	—	4	2	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	—	2	4	no	—
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	—	6	4	no	—
271	C₂×C₃²	C₂×#235	1	1	yes	characteristic
272	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
273	C₂×C₃²	#1009	1	1	yes	characteristic
274	C₂×C₃²	C₂²×C₃×Q₈	1	4	yes	—
275	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
276	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
277	C₃×D₃	—	2	16	no	—
278	C₂×Q₈	—	3	2	no	—
279	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
280	C₂×D₄	—	3	1	no	—
281	C₂²×C₄	—	3	2	no	—
282	C₂²×C₄	—	3	4	no	—
283	C₄⋊C₄	—	3	4	no	—
284	C₄⋊C₄	—	3	2	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	2	no	—
287	C₄⋊C₄	—	3	4	no	—
288	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
289	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
290	C₂²⋊C₄	—	3	2	no	—
291	C₂²⋊C₄	—	3	4	no	—
292	C₄²	C₂×C₃²×D₃	1	2	yes	—
293	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	3	16	no	—
296	C₂²×C₃	—	6	8	no	—
297	C₂²×C₃	—	6	8	no	—
298	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
299	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
300	C₂×D₃	—	2	2	no	—
301	C₂×D₃	—	2	2	no	—
302	C₂×D₃	C₂×C₃²×Q₈	1	4	yes	—
303	C₃×C₄	—	2	16	no	—
304	C₃×C₄	—	2	8	no	—
305	C₃×C₄	—	2	8	no	—
306	C₃×C₄	—	2	4	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	2	8	no	—
312	C₃×C₄	—	4	8	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	6	8	no	—
315	C₃×C₄	—	6	16	no	—
316	C₃×C₄	C₃×#235	1	8	yes	—
317	C₃×C₄	C₃×D₃×Q₈	1	8	yes	—
318	C₃×C₄	C₂×C₃²×Q₈	1	2	yes	—
319	C₃×C₄	C₃²×#41	1	2	yes	—
320	Dic₃	—	2	2	no	—
321	Dic₃	—	2	4	no	—
322	C₃²	—	2	4	no	—
323	C₃²	#5579	1	1	yes	characteristic, direct product factor
324	C₃²	C₃×#554	1	4	yes	complemented
325	C₂³	—	3	2	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	12	2	no	—
328	D₄	—	3	4	no	—
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	4	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	—	12	4	no	—
333	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
334	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
336	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
338	C₂×C₃	—	2	4	no	—
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	2	4	no	—
341	C₂×C₃	—	6	16	no	—
342	C₂×C₃	C₂×C₃×#235	1	4	yes	—
343	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
344	C₂×C₃	C₃×#1009	1	4	yes	—
345	C₂×C₃	C₂²×C₃²×Q₈	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
347	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
348	D₃	—	2	4	no	—
349	C₂²	—	3	4	no	—
350	C₂²	—	6	2	no	—
351	C₂²	—	6	2	no	—
352	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	6	2	no	—
357	C₄	—	6	4	no	—
358	C₄	C₃²×#235	1	2	yes	—
359	C₄	C₃²×D₃×Q₈	1	2	yes	—
360	C₃	—	2	4	no	—
361	C₃	C₃×#5579	1	4	yes	direct product factor
362	C₃	C₃²×#554	1	1	yes	characteristic, complemented
363	C₂	—	6	4	no	—
364	C₂	C₂×C₃²×#235	1	1	yes	characteristic
365	C₂	C₂×C₃²×D₃×Q₈	1	1	yes	characteristic
366	C₂	C₃²×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃²×D₁₂	C₂²
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
2. C₃²×#946	C₂	semidirect
3. C₃²×#896	C₂	semidirect
4. C₃²×D₃×C₄⋊C₄	C₂	semidirect
7. C₃²×#870	C₂	semidirect
8. C₃²×#869	C₂	semidirect
10. C₃×#5579	C₃	direct (N × H)
32. C₃²×C₄×Q₈	D₃	semidirect
33. C₃²×C₄×Q₈	C₂×C₃	semidirect
37. C₃×#946	C₂×C₃	semidirect
38. C₃×#896	C₂×C₃	semidirect
39. C₃×D₃×C₄⋊C₄	C₂×C₃	semidirect
42. C₃×#870	C₂×C₃	semidirect
43. C₃×#869	C₂×C₃	semidirect
53. C₃²×D₁₂	Q₈	semidirect
58. #5579	C₃²	direct (N × H)
112. C₃×C₄×Q₈	C₃×D₃	semidirect
113. C₃×C₄×Q₈	C₂×C₃²	semidirect
117. #946	C₂×C₃²	semidirect
118. #896	C₂×C₃²	semidirect
119. D₃×C₄⋊C₄	C₂×C₃²	semidirect
122. #870	C₂×C₃²	semidirect
123. #869	C₂×C₃²	semidirect
152. C₃×D₁₂	C₃×Q₈	semidirect
230. C₄×Q₈	C₃²×D₃	semidirect
234. C₃³	#554	semidirect
263. D₁₂	C₃²×Q₈	semidirect
323. C₃²	#5579	direct (N × H)
324. C₃²	C₃×#554	semidirect
361. C₃	C₃×#5579	direct (N × H)
362. C₃	C₃²×#554	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₄×Q₈	2
C₃²×#946	2
C₃²×#896	2
C₃²×D₃×C₄⋊C₄	2
C₃²×C₄×D₁₂	2
C₃²×#870	2
C₃²×#869	2
C₃²×#554	3
C₃×#5579	3

Subgroups — C32×#5579 #13178956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5579 #13178956