Subgroups — C₃²×#5139 #13162575

Order 1728.

1196 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#825	C₂	1	4	yes	maximal, complemented
5	C₃²×#421	—	3	1	no	maximal
6	C₃×#5139	C₃	1	4	yes	maximal, direct product factor
7	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₃²×#67	—	2	1	no	—
9	C₃²×#235	—	2	1	no	—
10	C₃²×#235	—	2	1	no	—
11	C₃²×#235	C₄	1	2	yes	complemented
12	C₃²×#235	C₂²	1	2	yes	—
13	C₂×C₃²×D₁₂	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃²×C₄×D₃	—	2	1	no	—
15	C₂×C₃²×Dic₆	C₄	1	1	yes	characteristic, complemented
16	C₃³×M₁₆	—	2	1	no	—
17	C₃³×M₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃³×C₈	—	2	1	no	—
19	C₃²×#217	—	2	1	no	—
20	C₃²×C₄⋊Dic₃	—	2	1	no	—
21	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
22	C₂×C₃²×#41	—	3	1	no	—
23	C₂×C₃×#235	C₂×C₃	1	4	yes	—
24	C₂×C₃²×M₁₆	—	2	4	no	—
25	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃²×M₁₆	C₂×C₃	1	4	yes	complemented
27	C₃²×#117	—	3	1	no	—
28	C₃×#926	C₂×C₃	1	4	yes	complemented
29	C₃²×#104	—	3	4	no	—
30	C₃×#825	C₂×C₃	1	16	yes	complemented
31	C₂³×C₃³	D₄	1	1	yes	characteristic
32	C₂²×C₃²×D₃	—	2	1	no	—
33	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
36	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
38	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
39	C₃²×#67	—	2	2	no	—
40	C₃²×#67	—	2	2	no	—
41	C₂×C₃²×Dic₃	—	2	1	no	—
42	C₂×C₃²×Dic₃	—	2	2	no	—
43	C₃²×D₁₂	—	2	1	no	—
44	C₃²×D₁₂	C₂×C₄	1	2	yes	—
45	C₃²×C₄×D₃	—	2	2	no	—
46	C₃²×C₄×D₃	—	2	2	no	—
47	C₃²×Dic₆	—	2	1	no	—
48	C₃²×Dic₆	C₂×C₄	1	2	yes	—
49	C₃³×C₈	—	2	2	no	—
50	C₃×#421	—	3	4	no	—
51	#5139	C₃²	1	1	yes	characteristic, direct product factor
52	C₃²×#41	—	3	2	no	—
53	C₃²×#41	—	3	2	no	—
54	C₃²×#41	—	6	1	no	—
55	C₃²×#41	—	6	1	no	—
56	C₂×C₃²×Q₈	—	3	1	no	—
57	C₂×C₃²×D₄	—	3	1	no	—
58	C₂×C₃²×D₄	—	6	1	no	—
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	—	6	1	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
63	C₂×C₃×#67	—	2	4	no	—
64	C₃×#235	—	2	4	no	—
65	C₃×#235	—	2	4	no	—
66	C₃×#235	C₃×C₄	1	8	yes	complemented
67	C₃×#235	C₂²×C₃	1	8	yes	—
68	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	complemented
69	C₂×C₃×C₄×D₃	—	2	4	no	—
70	C₂×C₃×Dic₆	C₃×C₄	1	4	yes	complemented
71	C₃²×M₁₆	—	2	8	no	—
72	C₃²×M₁₆	—	2	8	no	—
73	C₃²×M₁₆	—	2	1	no	—
74	C₃²×M₁₆	—	2	4	no	—
75	C₃²×M₁₆	C₂×D₃	1	2	yes	complemented
76	C₃²×M₁₆	C₂²×C₃	1	8	yes	complemented
77	C₂×C₃²×C₈	—	2	8	no	—
78	C₂×C₃²×C₈	—	2	1	no	—
79	C₂×C₃²×C₈	—	2	4	no	—
80	C₃²×C₄⋊C₄	—	6	1	no	—
81	C₃²×C₂²⋊C₄	—	6	1	no	—
82	C₃²×C₄²	—	3	2	no	—
83	C₃×#217	—	2	4	no	—
84	C₃×C₄⋊Dic₃	—	2	4	no	—
85	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
86	C₂²×C₃³	—	4	1	no	—
87	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃²×D₃	—	2	2	no	—
91	C₂×C₃²×D₃	—	4	2	no	—
92	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
93	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
94	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
95	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
96	C₃²×Dic₃	—	2	2	no	—
97	C₃²×Dic₃	—	4	2	no	—
98	C₂×C₃×#41	—	3	4	no	—
99	C₂×#235	C₂×C₃²	1	1	yes	characteristic
100	C₂×C₃×M₁₆	—	2	4	no	—
101	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
102	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₃×#117	—	3	4	no	—
104	#926	C₂×C₃²	1	1	yes	characteristic, complemented
105	C₃×#104	—	3	16	no	—
106	#825	C₂×C₃²	1	4	yes	complemented
107	C₂³×C₃²	—	2	4	no	—
108	C₂³×C₃²	—	6	1	no	—
109	C₂³×C₃²	D₁₂	1	1	yes	characteristic
110	C₂³×C₃²	C₃×D₄	1	4	yes	—
111	C₂²×C₃×D₃	—	2	4	no	—
112	C₃²×Q₈	—	3	2	no	—
113	C₃²×Q₈	—	6	1	no	—
114	C₃²×D₄	—	3	2	no	—
115	C₃²×D₄	—	6	2	no	—
116	C₃²×D₄	—	6	2	no	—
117	C₃²×D₄	—	6	1	no	—
118	C₂×C₃²×C₄	—	2	4	no	—
119	C₂×C₃²×C₄	—	2	4	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	—	2	4	no	—
123	C₂×C₃²×C₄	—	2	4	no	—
124	C₂×C₃²×C₄	—	6	1	no	—
125	C₂×C₃²×C₄	—	6	2	no	—
126	C₂×C₃²×C₄	—	6	2	no	—
127	C₂×C₃²×C₄	—	6	2	no	—
128	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
131	C₂×C₃²×C₄	#67	1	1	yes	characteristic
132	C₂×C₃²×C₄	#67	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
134	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
135	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
136	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
137	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
140	C₃×#67	—	2	8	no	—
141	C₃×#67	—	2	8	no	—
142	C₂×C₃×Dic₃	—	2	4	no	—
143	C₂×C₃×Dic₃	—	2	8	no	—
144	C₃×D₁₂	—	2	4	no	—
145	C₃×D₁₂	C₂×C₃×C₄	1	8	yes	—
146	C₃×C₄×D₃	—	2	8	no	—
147	C₃×C₄×D₃	—	2	8	no	—
148	C₃×Dic₆	—	2	4	no	—
149	C₃×Dic₆	C₂×C₃×C₄	1	8	yes	—
150	C₃²×C₈	—	2	16	no	—
151	C₃²×C₈	—	2	2	no	—
152	C₃²×C₈	—	2	8	no	—
153	#421	—	3	1	no	Sylow
154	C₂×C₃³	—	2	1	no	—
155	C₂×C₃³	—	2	1	no	—
156	C₂×C₃³	—	2	1	no	—
157	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₃²×D₃	—	4	2	no	—
159	C₃×#41	—	3	8	no	—
160	C₃×#41	—	3	8	no	—
161	C₃×#41	—	6	4	no	—
162	C₃×#41	—	6	4	no	—
163	C₂×C₃×Q₈	—	3	4	no	—
164	C₂×C₃×D₄	—	3	4	no	—
165	C₂×C₃×D₄	—	6	4	no	—
166	C₂²×C₃×C₄	—	2	4	no	—
167	C₂²×C₃×C₄	—	6	4	no	—
168	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
169	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
170	C₂×#67	—	2	1	no	—
171	#235	—	2	1	no	—
172	#235	—	2	1	no	—
173	#235	C₃²×C₄	1	2	yes	complemented
174	#235	C₂²×C₃²	1	2	yes	—
175	C₂×D₁₂	C₃²×C₄	1	1	yes	characteristic, complemented
176	C₂×C₄×D₃	—	2	1	no	—
177	C₂×Dic₆	C₃²×C₄	1	1	yes	characteristic, complemented
178	C₃×M₁₆	—	2	8	no	—
179	C₃×M₁₆	—	2	4	no	—
180	C₃×M₁₆	—	2	1	no	—
181	C₃×M₁₆	—	2	8	no	—
182	C₃×M₁₆	C₂×C₃×D₃	1	8	yes	complemented
183	C₃×M₁₆	C₂²×C₃²	1	2	yes	complemented
184	C₂×C₃×C₈	—	2	8	no	—
185	C₂×C₃×C₈	—	2	4	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₃×C₄⋊C₄	—	6	4	no	—
188	C₃×C₂²⋊C₄	—	6	4	no	—
189	C₃×C₄²	—	3	8	no	—
190	#217	—	2	1	no	—
191	C₄⋊Dic₃	—	2	1	no	—
192	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
193	C₂²×C₃²	—	2	4	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	2	4	no	—
196	C₂²×C₃²	—	4	1	no	—
197	C₂²×C₃²	—	4	4	no	—
198	C₂²×C₃²	—	4	8	no	—
199	C₂²×C₃²	—	6	2	no	—
200	C₂²×C₃²	—	12	2	no	—
201	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
202	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
203	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
204	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
205	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
206	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
207	C₂×C₃×D₃	—	2	8	no	—
208	C₂×C₃×D₃	—	4	8	no	—
209	C₃²×C₄	—	2	4	no	—
210	C₃²×C₄	—	2	4	no	—
211	C₃²×C₄	—	2	4	no	—
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	—	6	2	no	—
214	C₃²×C₄	—	12	2	no	—
215	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
218	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
219	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
220	C₃²×C₄	C₂×#67	1	1	yes	characteristic
221	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
222	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
223	C₃×Dic₃	—	2	8	no	—
224	C₃×Dic₃	—	4	8	no	—
225	C₂×#41	—	3	1	no	—
226	C₂×M₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
227	#117	—	3	1	no	—
228	#104	—	3	4	no	—
229	C₃³	#421	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	6	4	no	—
232	C₂³×C₃	C₃×D₁₂	1	4	yes	—
233	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
234	C₂²×D₃	—	2	1	no	—
235	C₃×Q₈	—	3	8	no	—
236	C₃×Q₈	—	6	4	no	—
237	C₃×D₄	—	3	8	no	—
238	C₃×D₄	—	6	8	no	—
239	C₃×D₄	—	6	8	no	—
240	C₃×D₄	—	6	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	8	no	—
249	C₂×C₃×C₄	—	6	8	no	—
250	C₂×C₃×C₄	—	6	8	no	—
251	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
252	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
253	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
254	C₂×C₃×C₄	C₃×#67	1	4	yes	—
255	C₂×C₃×C₄	C₃×#67	1	4	yes	—
256	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
262	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
263	#67	—	2	2	no	—
264	#67	—	2	2	no	—
265	C₂×Dic₃	—	2	1	no	—
266	C₂×Dic₃	—	2	2	no	—
267	D₁₂	—	2	1	no	—
268	D₁₂	C₂×C₃²×C₄	1	2	yes	—
269	C₄×D₃	—	2	2	no	—
270	C₄×D₃	—	2	2	no	—
271	Dic₆	—	2	1	no	—
272	Dic₆	C₂×C₃²×C₄	1	2	yes	—
273	C₃×C₈	—	2	16	no	—
274	C₃×C₈	—	2	8	no	—
275	C₃×C₈	—	2	2	no	—
276	C₂×C₃²	—	2	8	no	—
277	C₂×C₃²	—	2	1	no	—
278	C₂×C₃²	—	2	1	no	—
279	C₂×C₃²	—	2	1	no	—
280	C₂×C₃²	—	2	4	no	—
281	C₂×C₃²	—	2	4	no	—
282	C₂×C₃²	—	2	4	no	—
283	C₂×C₃²	—	2	4	no	—
284	C₂×C₃²	—	4	4	no	—
285	C₂×C₃²	—	4	4	no	—
286	C₂×C₃²	—	12	2	no	—
287	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
288	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
289	C₃×D₃	—	4	8	no	—
290	#41	—	3	2	no	—
291	#41	—	3	2	no	—
292	#41	—	6	1	no	—
293	#41	—	6	1	no	—
294	C₂×Q₈	—	3	1	no	—
295	C₂×D₄	—	3	1	no	—
296	C₂×D₄	—	6	1	no	—
297	C₂²×C₄	—	6	1	no	—
298	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
299	M₁₆	—	2	1	no	—
300	M₁₆	C₂×C₃²×D₃	1	2	yes	complemented
301	C₂×C₈	—	2	1	no	—
302	C₄⋊C₄	—	6	1	no	—
303	C₂²⋊C₄	—	6	1	no	—
304	C₄²	—	3	2	no	—
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	4	4	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	8	no	—
311	C₂²×C₃	—	6	8	no	—
312	C₂²×C₃	—	12	8	no	—
313	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
314	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
315	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
318	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
319	C₂×D₃	—	2	2	no	—
320	C₂×D₃	—	4	2	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	6	8	no	—
326	C₃×C₄	—	12	8	no	—
327	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
328	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
329	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
330	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
331	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
332	C₃×C₄	C₂×C₃×#67	1	4	yes	—
333	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
334	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
335	Dic₃	—	2	2	no	—
336	Dic₃	—	4	2	no	—
337	C₃²	—	2	4	no	—
338	C₃²	#5139	1	1	yes	characteristic, direct product factor
339	C₃²	C₃×#421	1	4	yes	complemented
340	C₂³	—	6	1	no	—
341	C₂³	C₃²×D₁₂	1	1	yes	characteristic
342	Q₈	—	3	2	no	—
343	Q₈	—	6	1	no	—
344	D₄	—	3	2	no	—
345	D₄	—	6	2	no	—
346	D₄	—	6	2	no	—
347	D₄	—	6	1	no	—
348	C₂×C₄	—	6	1	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	6	2	no	—
352	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
353	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
354	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
355	C₂×C₄	C₃²×#67	1	1	yes	characteristic
356	C₂×C₄	C₃²×#67	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₂×C₃	—	2	8	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	4	no	—
365	C₂×C₃	—	2	4	no	—
366	C₂×C₃	—	2	4	no	—
367	C₂×C₃	—	4	4	no	—
368	C₂×C₃	—	4	4	no	—
369	C₂×C₃	—	12	8	no	—
370	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
371	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
372	D₃	—	4	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	6	2	no	—
375	C₂²	—	12	2	no	—
376	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
377	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₂²	C₂×C₃²×D₁₂	1	1	yes	characteristic
379	C₄	—	6	2	no	—
380	C₄	—	12	2	no	—
381	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
382	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
383	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
384	C₄	C₂×C₃²×#67	1	1	yes	characteristic
385	C₃	—	2	4	no	—
386	C₃	C₃×#5139	1	4	yes	direct product factor
387	C₃	C₃²×#421	1	1	yes	characteristic, complemented
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	12	2	no	—
392	C₂	C₂×C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	C₂×#67
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂×C₃³	C₂×C₂²⋊C₄
prime radical	C₂×C₃²×#235	C₂
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂×C₃²×M₁₆	D₃
hypocenter	C₃	C₃²×#421
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₃²×#926	C₂	semidirect
4. C₃²×#825	C₂	semidirect
6. C₃×#5139	C₃	direct (N × H)
11. C₃²×#235	C₄	semidirect
13. C₂×C₃²×D₁₂	C₄	semidirect
15. C₂×C₃²×Dic₆	C₄	semidirect
17. C₃³×M₁₆	C₂²	semidirect
21. C₃²×C₄×Dic₃	C₂²	semidirect
25. C₂×C₃²×M₁₆	D₃	semidirect
26. C₂×C₃²×M₁₆	C₂×C₃	semidirect
28. C₃×#926	C₂×C₃	semidirect
30. C₃×#825	C₂×C₃	semidirect
51. #5139	C₃²	direct (N × H)
66. C₃×#235	C₃×C₄	semidirect
68. C₂×C₃×D₁₂	C₃×C₄	semidirect
70. C₂×C₃×Dic₆	C₃×C₄	semidirect
75. C₃²×M₁₆	C₂×D₃	semidirect
76. C₃²×M₁₆	C₂²×C₃	semidirect
85. C₃×C₄×Dic₃	C₂²×C₃	semidirect
101. C₂×C₃×M₁₆	C₃×D₃	semidirect
102. C₂×C₃×M₁₆	C₂×C₃²	semidirect
104. #926	C₂×C₃²	semidirect
106. #825	C₂×C₃²	semidirect
173. #235	C₃²×C₄	semidirect
175. C₂×D₁₂	C₃²×C₄	semidirect
177. C₂×Dic₆	C₃²×C₄	semidirect
182. C₃×M₁₆	C₂×C₃×D₃	semidirect
183. C₃×M₁₆	C₂²×C₃²	semidirect
192. C₄×Dic₃	C₂²×C₃²	semidirect
226. C₂×M₁₆	C₃²×D₃	semidirect
229. C₃³	#421	semidirect
300. M₁₆	C₂×C₃²×D₃	semidirect
338. C₃²	#5139	direct (N × H)
339. C₃²	C₃×#421	semidirect
386. C₃	C₃×#5139	direct (N × H)
387. C₃	C₃²×#421	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#235	2
C₂×C₃³×M₁₆	2
C₃²×#926	2
C₃²×#825	2
C₃²×#421	3
C₃×#5139	3

Subgroups — C32×#5139 #13162575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5139 #13162575