Subgroups — C₃²×#5114 #13162549

Order 1728.

1048 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#930	C₂	1	1	yes	maximal, characteristic
3	C₃²×#924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#204	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#821	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#465	—	3	1	no	maximal
9	C₃×#5114	C₃	1	4	yes	maximal, direct product factor
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃²×#67	—	2	1	no	—
12	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃³×C₈	—	2	2	no	—
15	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#217	—	2	1	no	—
18	C₃²×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₃²×Dic₃⋊C₄	—	2	1	no	—
22	C₃²×#204	—	2	2	no	—
23	C₂×C₃²×SD₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	2	4	no	—
25	C₂²×C₃²×C₈	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₃²×C₈	C₂×C₃	1	4	yes	complemented
27	C₃²×C₂²⋊Q₈	—	3	1	no	—
28	C₃²×#121	—	3	1	no	—
29	C₃×#930	C₂×C₃	1	4	yes	—
30	C₃×#924	C₂×C₃	1	4	yes	complemented
31	C₂×C₃×#204	C₂×C₃	1	4	yes	complemented
32	C₃²×#106	—	3	1	no	—
33	C₃²×#103	—	3	1	no	—
34	C₃²×#102	—	3	1	no	—
35	C₃×#821	C₂×C₃	1	4	yes	complemented
36	C₃×#817	C₂×C₃	1	4	yes	complemented
37	C₃×#816	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₂²×C₃²×D₃	—	2	1	no	—
40	C₂×C₃³×C₄	—	2	1	no	—
41	C₂×C₃³×C₄	—	2	1	no	—
42	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
44	C₃²×#67	—	4	2	no	—
45	C₂×C₃²×Dic₃	—	2	1	no	—
46	C₂×C₃²×Dic₃	—	2	1	no	—
47	C₂×C₃²×Dic₃	—	2	1	no	—
48	C₃²×D₁₂	—	2	1	no	—
49	C₃²×D₁₂	—	2	1	no	—
50	C₃²×Dic₆	—	2	1	no	—
51	C₃²×Dic₆	—	2	1	no	—
52	C₃³×C₈	—	2	1	no	—
53	C₃³×C₈	D₄	1	2	yes	complemented
54	C₃×#465	—	3	4	no	—
55	#5114	C₃²	1	1	yes	characteristic, direct product factor
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	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₃×#67	—	2	4	no	—
63	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
64	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
65	C₃²×SD₁₆	—	6	2	no	—
66	C₂×C₃²×C₈	—	2	16	no	—
67	C₂×C₃²×C₈	—	2	4	no	—
68	C₂×C₃²×C₈	—	2	4	no	—
69	C₂×C₃²×C₈	—	2	2	no	—
70	C₂×C₃²×C₈	—	2	8	no	—
71	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
74	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
75	C₃²×C₄⋊C₄	—	3	1	no	—
76	C₃²×C₄⋊C₄	—	3	1	no	—
77	C₃²×C₄⋊C₄	—	6	1	no	—
78	C₃²×C₂²⋊C₄	—	6	1	no	—
79	C₃²×C₂²⋊C₄	—	6	1	no	—
80	C₃×#217	—	2	4	no	—
81	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
82	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
83	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
84	C₃×Dic₃⋊C₄	—	2	4	no	—
85	C₃×#204	—	2	8	no	—
86	C₂²×C₃³	—	2	1	no	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	SD₁₆	1	2	yes	complemented
89	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃²×D₃	—	4	1	no	—
91	C₂×C₃²×D₃	—	4	1	no	—
92	C₂×C₃²×D₃	—	4	1	no	—
93	C₃³×C₄	—	2	1	no	—
94	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₃³×C₄	#41	1	1	yes	characteristic
96	C₃²×Dic₃	—	4	1	no	—
97	C₃²×Dic₃	—	4	1	no	—
98	C₃²×Dic₃	—	4	1	no	—
99	C₂×C₃×SD₁₆	—	3	4	no	—
100	C₂²×C₃×C₈	—	2	4	no	—
101	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
102	C₂²×C₃×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₃×C₂²⋊Q₈	—	3	4	no	—
104	C₃×#121	—	3	4	no	—
105	#930	C₂×C₃²	1	1	yes	characteristic
106	#924	C₂×C₃²	1	1	yes	characteristic, complemented
107	C₂×#204	C₂×C₃²	1	1	yes	characteristic, complemented
108	C₃×#106	—	3	4	no	—
109	C₃×#103	—	3	4	no	—
110	C₃×#102	—	3	4	no	—
111	#821	C₂×C₃²	1	1	yes	characteristic, complemented
112	#817	C₂×C₃²	1	1	yes	characteristic, complemented
113	#816	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₂³×C₃²	—	2	4	no	—
115	C₂³×C₃²	—	6	1	no	—
116	C₂³×C₃²	D₁₂	1	1	yes	characteristic
117	C₂³×C₃²	C₃×D₄	1	4	yes	—
118	C₂²×C₃×D₃	—	2	4	no	—
119	C₃²×Q₈	—	6	1	no	—
120	C₃²×Q₈	—	6	1	no	—
121	C₃²×D₄	—	6	1	no	—
122	C₃²×D₄	—	6	1	no	—
123	C₃²×D₄	—	12	2	no	—
124	C₂×C₃²×C₄	—	2	8	no	—
125	C₂×C₃²×C₄	—	2	8	no	—
126	C₂×C₃²×C₄	—	2	1	no	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	6	1	no	—
133	C₂×C₃²×C₄	—	6	1	no	—
134	C₂×C₃²×C₄	—	6	1	no	—
135	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
137	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
139	C₃×#67	—	4	8	no	—
140	C₂×C₃×Dic₃	—	2	4	no	—
141	C₂×C₃×Dic₃	—	2	4	no	—
142	C₂×C₃×Dic₃	—	2	4	no	—
143	C₃×D₁₂	—	2	4	no	—
144	C₃×D₁₂	—	2	4	no	—
145	C₃×Dic₆	—	2	4	no	—
146	C₃×Dic₆	—	2	4	no	—
147	C₃²×C₈	—	2	8	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃²×C₈	—	2	4	no	—
150	C₃²×C₈	—	2	8	no	—
151	C₃²×C₈	#67	1	2	yes	complemented
152	C₃²×C₈	C₃×D₄	1	8	yes	complemented
153	#465	—	3	1	no	Sylow
154	C₂×C₃³	—	2	2	no	—
155	C₂×C₃³	#121	1	1	yes	characteristic
156	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₃³	#135	1	1	yes	characteristic
158	C₃²×D₃	—	8	1	no	—
159	C₂×C₃×Q₈	—	3	4	no	—
160	C₂×C₃×D₄	—	3	4	no	—
161	C₂×C₃×D₄	—	6	4	no	—
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
164	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
165	C₂×#67	—	2	1	no	—
166	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
167	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
168	C₃×SD₁₆	—	6	8	no	—
169	C₂×C₃×C₈	—	2	16	no	—
170	C₂×C₃×C₈	—	2	8	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	2	4	no	—
173	C₂×C₃×C₈	—	2	4	no	—
174	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
175	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
176	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	3	4	no	—
179	C₃×C₄⋊C₄	—	3	4	no	—
180	C₃×C₄⋊C₄	—	6	4	no	—
181	C₃×C₂²⋊C₄	—	6	4	no	—
182	C₃×C₂²⋊C₄	—	6	4	no	—
183	#217	—	2	1	no	—
184	(C₂×D₃)⋊C₄	—	2	1	no	—
185	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
186	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
187	Dic₃⋊C₄	—	2	1	no	—
188	#204	—	2	2	no	—
189	C₂²×C₃²	—	2	8	no	—
190	C₂²×C₃²	—	2	8	no	—
191	C₂²×C₃²	—	2	1	no	—
192	C₂²×C₃²	—	2	1	no	—
193	C₂²×C₃²	—	2	4	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	2	8	no	—
196	C₂²×C₃²	—	2	4	no	—
197	C₂²×C₃²	—	12	1	no	—
198	C₂²×C₃²	—	12	1	no	—
199	C₂²×C₃²	—	12	1	no	—
200	C₂²×C₃²	#204	1	2	yes	complemented
201	C₂²×C₃²	C₃×SD₁₆	1	8	yes	complemented
202	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
203	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
204	C₂×C₃×D₃	—	4	4	no	—
205	C₂×C₃×D₃	—	4	4	no	—
206	C₂×C₃×D₃	—	4	4	no	—
207	C₃²×C₄	—	2	8	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃²×C₄	—	2	4	no	—
210	C₃²×C₄	—	2	4	no	—
211	C₃²×C₄	—	2	4	no	—
212	C₃²×C₄	—	12	1	no	—
213	C₃²×C₄	—	12	1	no	—
214	C₃²×C₄	—	12	1	no	—
215	C₃²×C₄	#235	1	1	yes	characteristic
216	C₃²×C₄	C₂×#67	1	1	yes	characteristic
217	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
218	C₃²×C₄	C₃×#41	1	4	yes	—
219	C₃×Dic₃	—	4	4	no	—
220	C₃×Dic₃	—	4	4	no	—
221	C₃×Dic₃	—	4	4	no	—
222	C₂×SD₁₆	—	3	1	no	—
223	C₂²×C₈	C₃²×D₃	1	1	yes	characteristic, complemented
224	C₂²⋊Q₈	—	3	1	no	—
225	#121	—	3	1	no	—
226	#106	—	3	1	no	—
227	#103	—	3	1	no	—
228	#102	—	3	1	no	—
229	C₃³	#465	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	—	6	4	no	—
236	C₃×Q₈	—	6	4	no	—
237	C₃×D₄	—	6	4	no	—
238	C₃×D₄	—	6	4	no	—
239	C₃×D₄	—	12	8	no	—
240	C₂×C₃×C₄	—	2	8	no	—
241	C₂×C₃×C₄	—	2	8	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	6	4	no	—
249	C₂×C₃×C₄	—	6	4	no	—
250	C₂×C₃×C₄	—	6	4	no	—
251	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
252	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
254	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
255	#67	—	4	2	no	—
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	—	2	1	no	—
259	D₁₂	—	2	1	no	—
260	D₁₂	—	2	1	no	—
261	Dic₆	—	2	1	no	—
262	Dic₆	—	2	1	no	—
263	C₃×C₈	—	2	8	no	—
264	C₃×C₈	—	2	4	no	—
265	C₃×C₈	—	2	1	no	—
266	C₃×C₈	—	2	8	no	—
267	C₃×C₈	C₃×#67	1	8	yes	complemented
268	C₃×C₈	C₃²×D₄	1	2	yes	complemented
269	C₂×C₃²	—	2	16	no	—
270	C₂×C₃²	—	2	8	no	—
271	C₂×C₃²	—	2	2	no	—
272	C₂×C₃²	—	2	4	no	—
273	C₂×C₃²	—	2	4	no	—
274	C₂×C₃²	—	2	4	no	—
275	C₂×C₃²	—	24	1	no	—
276	C₂×C₃²	C₂×#204	1	1	yes	characteristic
277	C₂×C₃²	#904	1	1	yes	characteristic
278	C₂×C₃²	#930	1	1	yes	characteristic
279	C₂×C₃²	C₃×#121	1	4	yes	—
280	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
281	C₂×C₃²	C₃×#135	1	4	yes	—
282	C₃×D₃	—	8	4	no	—
283	C₂×Q₈	—	3	1	no	—
284	C₂×D₄	—	3	1	no	—
285	C₂×D₄	—	6	1	no	—
286	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
287	SD₁₆	—	6	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
290	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
291	C₄⋊C₄	—	3	1	no	—
292	C₄⋊C₄	—	3	1	no	—
293	C₄⋊C₄	—	6	1	no	—
294	C₂²⋊C₄	—	6	1	no	—
295	C₂²⋊C₄	—	6	1	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	8	no	—
298	C₂²×C₃	—	2	4	no	—
299	C₂²×C₃	—	2	4	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	12	4	no	—
305	C₂²×C₃	—	12	4	no	—
306	C₂²×C₃	—	12	4	no	—
307	C₂²×C₃	C₃×#204	1	8	yes	complemented
308	C₂²×C₃	C₃²×SD₁₆	1	2	yes	complemented
309	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
310	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
311	C₂×D₃	—	4	1	no	—
312	C₂×D₃	—	4	1	no	—
313	C₂×D₃	—	4	1	no	—
314	C₃×C₄	—	2	8	no	—
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	2	4	no	—
319	C₃×C₄	—	12	4	no	—
320	C₃×C₄	—	12	4	no	—
321	C₃×C₄	—	12	4	no	—
322	C₃×C₄	C₃×#235	1	4	yes	—
323	C₃×C₄	C₂×C₃×#67	1	4	yes	—
324	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
325	C₃×C₄	C₃²×#41	1	1	yes	characteristic
326	Dic₃	—	4	1	no	—
327	Dic₃	—	4	1	no	—
328	Dic₃	—	4	1	no	—
329	C₃²	—	2	4	no	—
330	C₃²	#5114	1	1	yes	characteristic, direct product factor
331	C₃²	C₃×#465	1	4	yes	complemented
332	C₂³	—	6	1	no	—
333	C₂³	C₃²×D₁₂	1	1	yes	characteristic
334	Q₈	—	6	1	no	—
335	Q₈	—	6	1	no	—
336	D₄	—	6	1	no	—
337	D₄	—	6	1	no	—
338	D₄	—	12	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	—	6	1	no	—
343	C₂×C₄	—	6	1	no	—
344	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	C₃²×#67	1	2	yes	complemented
348	C₂×C₃	—	2	16	no	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	2	8	no	—
351	C₂×C₃	—	2	4	no	—
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	2	4	no	—
354	C₂×C₃	—	24	4	no	—
355	C₂×C₃	C₂×C₃×#204	1	4	yes	—
356	C₂×C₃	C₃×#904	1	4	yes	—
357	C₂×C₃	C₃×#930	1	4	yes	—
358	C₂×C₃	C₃²×#121	1	1	yes	characteristic
359	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
360	C₂×C₃	C₃²×#135	1	1	yes	characteristic
361	D₃	—	8	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	12	1	no	—
365	C₂²	—	12	1	no	—
366	C₂²	—	12	1	no	—
367	C₂²	C₃²×#204	1	2	yes	complemented
368	C₂²	C₂×C₃²×D₁₂	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	12	1	no	—
371	C₄	—	12	1	no	—
372	C₄	—	12	1	no	—
373	C₄	C₃²×#235	1	1	yes	characteristic
374	C₄	C₂×C₃²×#67	1	1	yes	characteristic
375	C₃	—	2	4	no	—
376	C₃	C₃×#5114	1	4	yes	direct product factor
377	C₃	C₃²×#465	1	1	yes	characteristic, complemented
378	C₂	—	2	2	no	—
379	C₂	—	24	1	no	—
380	C₂	C₂×C₃²×#204	1	1	yes	characteristic
381	C₂	C₃²×#904	1	1	yes	characteristic
382	C₂	C₃²×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³×C₃²
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₃²×#930	C₂
hypercenter	C₂²×C₃²×C₈	D₃
hypocenter	C₃	C₃²×#465
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₂²×C₃²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×C₈	C₂	semidirect
3. C₃²×#924	C₂	semidirect
4. C₂×C₃²×#204	C₂	semidirect
5. C₃²×#821	C₂	semidirect
6. C₃²×#817	C₂	semidirect
7. C₃²×#816	C₂	semidirect
9. C₃×#5114	C₃	direct (N × H)
25. C₂²×C₃²×C₈	D₃	semidirect
26. C₂²×C₃²×C₈	C₂×C₃	semidirect
30. C₃×#924	C₂×C₃	semidirect
31. C₂×C₃×#204	C₂×C₃	semidirect
35. C₃×#821	C₂×C₃	semidirect
36. C₃×#817	C₂×C₃	semidirect
37. C₃×#816	C₂×C₃	semidirect
53. C₃³×C₈	D₄	semidirect
55. #5114	C₃²	direct (N × H)
88. C₂²×C₃³	SD₁₆	semidirect
101. C₂²×C₃×C₈	C₃×D₃	semidirect
102. C₂²×C₃×C₈	C₂×C₃²	semidirect
106. #924	C₂×C₃²	semidirect
107. C₂×#204	C₂×C₃²	semidirect
111. #821	C₂×C₃²	semidirect
112. #817	C₂×C₃²	semidirect
113. #816	C₂×C₃²	semidirect
151. C₃²×C₈	#67	semidirect
152. C₃²×C₈	C₃×D₄	semidirect
200. C₂²×C₃²	#204	semidirect
201. C₂²×C₃²	C₃×SD₁₆	semidirect
223. C₂²×C₈	C₃²×D₃	semidirect
229. C₃³	#465	semidirect
267. C₃×C₈	C₃×#67	semidirect
268. C₃×C₈	C₃²×D₄	semidirect
307. C₂²×C₃	C₃×#204	semidirect
308. C₂²×C₃	C₃²×SD₁₆	semidirect
330. C₃²	#5114	direct (N × H)
331. C₃²	C₃×#465	semidirect
347. C₈	C₃²×#67	semidirect
367. C₂²	C₃²×#204	semidirect
376. C₃	C₃×#5114	direct (N × H)
377. C₃	C₃²×#465	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃³×C₈	2
C₃²×#930	2
C₃²×#924	2
C₂×C₃²×#204	2
C₃²×#821	2
C₃²×#817	2
C₃²×#816	2
C₃²×#465	3
C₃×#5114	3

Subgroups — C32×#5114 #13162549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5114 #13162549