Subgroups — C₃×#82031 #11899666

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5769	C₂	1	2	yes	maximal, complemented
2	C₃²×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5193	C₂	1	2	yes	maximal, complemented
4	C₃×#4919	C₂	1	2	yes	maximal, complemented
5	C₃×#4914	C₂	1	4	yes	maximal, complemented
6	C₃×D₃×D₁₆	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×D₄₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3415	—	3	1	no	maximal
10	#82031	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#1009	—	2	2	no	—
12	C₃²×#135	C₂²	1	2	yes	complemented
13	C₃×#949	—	2	2	no	—
14	C₃×#919	C₂²	1	4	yes	complemented
15	C₃×#914	—	2	4	no	—
16	C₃×D₃×D₈	C₂²	1	4	yes	complemented
17	C₂×C₃×D₂₄	C₂²	1	2	yes	complemented
18	C₃×#901	C₂²	1	1	yes	characteristic
19	C₃²×Q₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₃²×SD₃₂	C₂²	1	2	yes	complemented
21	C₃²×D₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×#828	C₂²	1	4	yes	complemented
24	C₃×#826	C₂²	1	4	yes	complemented
25	C₃×#812	C₂²	1	1	yes	characteristic, complemented
26	C₃×D₄₈	C₂²	1	2	yes	complemented
27	C₃×D₄₈	C₂²	1	2	yes	complemented
28	C₃×#798	C₂²	1	2	yes	complemented
29	C₃×D₃×C₁₆	C₂²	1	2	yes	complemented
30	C₃×#576	—	3	2	no	—
31	#5769	C₂×C₃	1	2	yes	complemented
32	C₃×#509	—	3	2	no	—
33	C₃×#509	—	3	4	no	—
34	C₃×#508	—	2	1	no	—
35	C₃×#508	—	3	2	no	—
36	C₃×#508	D₃	1	1	yes	characteristic, complemented
37	C₃×#508	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃×D₁₆	—	3	2	no	—
39	C₂×C₃×D₁₆	—	3	1	no	—
40	C₃×#504	—	3	1	no	—
41	#5193	C₂×C₃	1	2	yes	complemented
42	#4919	C₂×C₃	1	2	yes	complemented
43	#4914	C₂×C₃	1	4	yes	complemented
44	D₃×D₁₆	C₂×C₃	1	2	yes	complemented
45	C₂×D₄₈	C₂×C₃	1	1	yes	characteristic, complemented
46	#4901	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃²×#41	—	2	2	no	—
48	C₃×#239	—	2	4	no	—
49	C₃×D₃×D₄	—	2	4	no	—
50	C₃×D₃×D₄	—	4	4	no	—
51	C₃×#235	—	4	2	no	—
52	C₃×#235	D₄	1	1	yes	characteristic
53	C₂×C₃×D₁₂	—	2	2	no	—
54	C₂×C₃×D₁₂	—	4	2	no	—
55	C₃²×Q₁₆	C₂³	1	2	yes	—
56	C₃²×SD₁₆	—	2	2	no	—
57	C₃²×D₈	C₂³	1	2	yes	—
58	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
59	C₃×#215	—	2	4	no	—
60	C₃×#213	—	2	4	no	—
61	C₃×#208	D₄	1	1	yes	characteristic
62	C₃×D₂₄	—	2	2	no	—
63	C₃×D₂₄	C₂³	1	4	yes	—
64	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
65	C₃×D₃×C₈	C₂³	1	2	yes	—
66	C₃²×C₁₆	C₂³	1	1	yes	characteristic
67	C₃²×C₁₆	C₂³	1	1	yes	characteristic
68	C₃×C₃⋊C₁₆	C₂³	1	2	yes	—
69	#3415	—	3	1	no	Sylow
70	C₃×H(5,𝔽₂)	—	6	2	no	—
71	#1009	—	2	2	no	—
72	C₃×AGL(1,ℤ/8)	—	6	4	no	—
73	C₃×AGL(1,ℤ/8)	—	6	2	no	—
74	C₃×#135	—	2	2	no	—
75	C₃×#135	—	3	4	no	—
76	C₃×#135	C₂×D₃	1	2	yes	complemented
77	C₃×#135	C₂²×C₃	1	2	yes	complemented
78	C₂×C₃×D₈	—	3	4	no	—
79	C₂×C₃×D₈	—	3	2	no	—
80	C₃×#131	—	3	1	no	—
81	#949	—	2	2	no	—
82	#919	C₂²×C₃	1	4	yes	complemented
83	#914	—	2	4	no	—
84	D₃×D₈	C₂²×C₃	1	4	yes	complemented
85	C₂×D₂₄	C₂²×C₃	1	2	yes	complemented
86	#901	C₂²×C₃	1	1	yes	characteristic
87	C₃×Q₃₂	—	2	1	no	—
88	C₃×Q₃₂	C₂×D₃	1	1	yes	characteristic, complemented
89	C₃×Q₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₃×SD₃₂	—	2	2	no	—
91	C₃×SD₃₂	—	3	4	no	—
92	C₃×SD₃₂	C₂×D₃	1	2	yes	complemented
93	C₃×SD₃₂	C₂²×C₃	1	2	yes	complemented
94	C₃×D₁₆	—	2	1	no	—
95	C₃×D₁₆	—	3	4	no	—
96	C₃×D₁₆	—	3	2	no	—
97	C₃×D₁₆	—	3	2	no	—
98	C₃×D₁₆	C₂×D₃	1	1	yes	characteristic, complemented
99	C₃×D₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₃×M₃₂	—	3	1	no	—
101	C₃×M₃₂	—	3	2	no	—
102	C₂×C₃×C₁₆	—	2	1	no	—
103	C₂×C₃×C₁₆	—	3	2	no	—
104	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
106	#828	C₂²×C₃	1	4	yes	complemented
107	#826	C₂²×C₃	1	4	yes	complemented
108	#812	C₂²×C₃	1	1	yes	characteristic, complemented
109	D₄₈	C₂²×C₃	1	2	yes	complemented
110	D₄₈	C₂²×C₃	1	2	yes	complemented
111	#798	C₂²×C₃	1	2	yes	complemented
112	D₃×C₁₆	C₂²×C₃	1	2	yes	complemented
113	C₂²×C₃×D₃	—	4	2	no	—
114	C₂²×C₃×D₃	—	4	4	no	—
115	C₃²×Q₈	—	2	2	no	—
116	C₃²×D₄	—	2	2	no	—
117	C₃²×D₄	—	4	2	no	—
118	C₂×C₃²×C₄	—	4	2	no	—
119	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
120	C₃×#67	—	4	4	no	—
121	C₃×#67	D₈	1	2	yes	—
122	C₃×D₁₂	—	2	4	no	—
123	C₃×D₁₂	—	4	4	no	—
124	C₃×D₁₂	—	4	2	no	—
125	C₃×D₁₂	D₈	1	1	yes	characteristic
126	C₃×C₄×D₃	—	4	4	no	—
127	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
128	C₃×Dic₆	D₈	1	1	yes	characteristic
129	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
130	C₃²×C₈	C₂⁴	1	1	yes	characteristic
131	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
132	#576	—	3	2	no	—
133	#509	—	3	2	no	—
134	#509	—	3	4	no	—
135	#508	—	3	2	no	—
136	#508	C₃×D₃	1	1	yes	characteristic, complemented
137	C₂×D₁₆	—	3	2	no	—
138	C₂×D₁₆	—	3	1	no	—
139	#504	—	3	1	no	—
140	C₃×#41	—	2	2	no	—
141	C₃×#41	—	2	2	no	—
142	C₃×#41	—	3	1	no	—
143	C₃×#41	—	4	2	no	—
144	C₃×#41	—	6	4	no	—
145	C₃×#41	—	12	2	no	—
146	C₂×C₃×D₄	—	6	4	no	—
147	C₂×C₃×D₄	—	6	2	no	—
148	C₂×C₃×D₄	—	12	2	no	—
149	C₂×C₃×D₄	—	12	4	no	—
150	#239	—	2	4	no	—
151	D₃×D₄	—	2	4	no	—
152	D₃×D₄	—	4	4	no	—
153	#235	—	4	2	no	—
154	#235	C₃×D₄	1	1	yes	characteristic
155	C₂×D₁₂	—	2	2	no	—
156	C₂×D₁₂	—	4	2	no	—
157	C₃×Q₁₆	—	2	2	no	—
158	C₃×Q₁₆	C₂²×D₃	1	2	yes	—
159	C₃×Q₁₆	C₂³×C₃	1	2	yes	—
160	C₃×SD₁₆	—	2	2	no	—
161	C₃×SD₁₆	—	2	2	no	—
162	C₃×SD₁₆	—	4	2	no	—
163	C₃×SD₁₆	—	6	4	no	—
164	C₃×D₈	—	2	2	no	—
165	C₃×D₈	—	3	4	no	—
166	C₃×D₈	—	6	4	no	—
167	C₃×D₈	—	6	2	no	—
168	C₃×D₈	C₂²×D₃	1	2	yes	—
169	C₃×D₈	C₂³×C₃	1	2	yes	—
170	C₃×M₁₆	—	3	1	no	—
171	C₃×M₁₆	—	3	2	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	3	2	no	—
174	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
176	#215	—	2	4	no	—
177	#213	—	2	4	no	—
178	#208	C₃×D₄	1	1	yes	characteristic
179	D₂₄	—	2	2	no	—
180	D₂₄	C₂³×C₃	1	4	yes	—
181	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
182	D₃×C₈	C₂³×C₃	1	2	yes	—
183	C₃×C₁₆	—	2	1	no	—
184	C₃×C₁₆	—	2	1	no	—
185	C₃×C₁₆	—	3	2	no	—
186	C₃×C₁₆	C₂²×D₃	1	1	yes	characteristic
187	C₃×C₁₆	C₂²×D₃	1	1	yes	characteristic
188	C₃×C₁₆	C₂³×C₃	1	1	yes	characteristic
189	C₃×C₁₆	C₂³×C₃	1	1	yes	characteristic
190	C₃⋊C₁₆	C₂³×C₃	1	2	yes	—
191	C₂²×C₃²	—	4	2	no	—
192	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
193	C₂×C₃×D₃	—	4	4	no	—
194	C₂×C₃×D₃	—	16	4	no	—
195	C₂×C₃×D₃	—	16	2	no	—
196	C₂×C₃×D₃	C₂×D₈	1	2	yes	—
197	C₃²×C₄	—	4	2	no	—
198	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
199	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
200	C₃×Dic₃	C₂×D₈	1	2	yes	—
201	H(5,𝔽₂)	—	6	2	no	—
202	AGL(1,ℤ/8)	—	6	4	no	—
203	AGL(1,ℤ/8)	—	6	2	no	—
204	#135	—	3	4	no	—
205	#135	C₂×C₃×D₃	1	2	yes	complemented
206	C₂×D₈	—	3	4	no	—
207	C₂×D₈	—	3	2	no	—
208	#131	—	3	1	no	—
209	Q₃₂	C₂×C₃×D₃	1	1	yes	characteristic, complemented
210	SD₃₂	—	3	4	no	—
211	SD₃₂	C₂×C₃×D₃	1	2	yes	complemented
212	D₁₆	—	3	4	no	—
213	D₁₆	—	3	2	no	—
214	D₁₆	—	3	2	no	—
215	D₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
216	M₃₂	—	3	1	no	—
217	M₃₂	—	3	2	no	—
218	C₂×C₁₆	—	3	2	no	—
219	C₂×C₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
220	C₂³×C₃	—	12	4	no	—
221	C₂³×C₃	—	12	2	no	—
222	C₂²×D₃	—	4	2	no	—
223	C₂²×D₃	—	4	4	no	—
224	C₃×Q₈	—	2	2	no	—
225	C₃×Q₈	—	2	2	no	—
226	C₃×Q₈	—	3	1	no	—
227	C₃×Q₈	—	4	2	no	—
228	C₃×D₄	—	2	2	no	—
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	3	2	no	—
231	C₃×D₄	—	3	1	no	—
232	C₃×D₄	—	4	2	no	—
233	C₃×D₄	—	4	2	no	—
234	C₃×D₄	—	4	2	no	—
235	C₃×D₄	—	6	4	no	—
236	C₃×D₄	—	8	2	no	—
237	C₃×D₄	—	12	4	no	—
238	C₃×D₄	—	12	4	no	—
239	C₃×D₄	—	12	2	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	3	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	—	8	2	no	—
245	C₂×C₃×C₄	—	12	4	no	—
246	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
248	#67	—	4	4	no	—
249	#67	C₃×D₈	1	2	yes	—
250	D₁₂	—	2	4	no	—
251	D₁₂	—	4	4	no	—
252	D₁₂	—	4	2	no	—
253	D₁₂	C₃×D₈	1	1	yes	characteristic
254	C₄×D₃	—	4	4	no	—
255	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
256	Dic₆	C₃×D₈	1	1	yes	characteristic
257	C₃×C₈	—	2	1	no	—
258	C₃×C₈	—	2	1	no	—
259	C₃×C₈	—	3	2	no	—
260	C₃×C₈	D₃×D₄	1	1	yes	characteristic
261	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
262	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
263	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
264	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
265	C₂×C₃²	—	2	1	no	—
266	C₂×C₃²	—	8	2	no	—
267	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
268	C₃×D₃	—	2	2	no	—
269	C₃×D₃	—	8	4	no	—
270	#41	—	2	2	no	—
271	#41	—	3	1	no	—
272	#41	—	6	4	no	—
273	#41	—	12	2	no	—
274	C₂×D₄	—	6	4	no	—
275	C₂×D₄	—	6	2	no	—
276	C₂×D₄	—	12	2	no	—
277	C₂×D₄	—	12	4	no	—
278	Q₁₆	C₂²×C₃×D₃	1	2	yes	—
279	SD₁₆	—	2	2	no	—
280	SD₁₆	—	6	4	no	—
281	D₈	—	3	4	no	—
282	D₈	—	6	4	no	—
283	D₈	—	6	2	no	—
284	D₈	C₂²×C₃×D₃	1	2	yes	—
285	M₁₆	—	3	1	no	—
286	M₁₆	—	3	2	no	—
287	C₂×C₈	—	3	2	no	—
288	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₁₆	—	3	2	no	—
290	C₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
291	C₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	3	2	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	8	2	no	—
297	C₂²×C₃	—	12	4	no	—
298	C₂²×C₃	—	48	2	no	—
299	C₂²×C₃	—	48	4	no	—
300	C₂²×C₃	D₃×D₈	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
302	C₂×D₃	—	4	4	no	—
303	C₂×D₃	—	16	4	no	—
304	C₂×D₃	—	16	2	no	—
305	C₂×D₃	C₂×C₃×D₈	1	2	yes	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	3	2	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	8	2	no	—
312	C₃×C₄	D₃×D₈	1	1	yes	characteristic
313	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
314	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
315	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
316	Dic₃	C₂×C₃×D₈	1	2	yes	—
317	C₃²	#3415	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	12	4	no	—
319	C₂³	—	12	2	no	—
320	Q₈	—	2	2	no	—
321	Q₈	—	3	1	no	—
322	D₄	—	2	2	no	—
323	D₄	—	3	2	no	—
324	D₄	—	3	1	no	—
325	D₄	—	4	2	no	—
326	D₄	—	6	4	no	—
327	D₄	—	12	4	no	—
328	D₄	—	12	4	no	—
329	D₄	—	12	2	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	12	4	no	—
333	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
334	C₈	—	3	2	no	—
335	C₈	C₃×D₃×D₄	1	1	yes	characteristic
336	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	4	1	no	—
341	C₂×C₃	—	6	2	no	—
342	C₂×C₃	—	8	2	no	—
343	C₂×C₃	—	8	2	no	—
344	C₂×C₃	—	16	2	no	—
345	C₂×C₃	—	24	4	no	—
346	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
347	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
348	D₃	—	2	2	no	—
349	D₃	—	8	4	no	—
350	C₂²	—	3	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	12	4	no	—
353	C₂²	—	48	2	no	—
354	C₂²	—	48	4	no	—
355	C₂²	C₃×D₃×D₈	1	1	yes	characteristic
356	C₄	—	3	2	no	—
357	C₄	—	4	2	no	—
358	C₄	C₃×D₃×D₈	1	1	yes	characteristic
359	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
360	C₃	—	2	1	no	—
361	C₃	#82031	1	1	yes	characteristic, direct product factor
362	C₃	C₃×#3415	1	1	yes	characteristic, complemented
363	C₂	—	2	1	no	—
364	C₂	—	6	2	no	—
365	C₂	—	8	2	no	—
366	C₂	—	24	4	no	—
367	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₃²×#508	C₂
socle	C₂×C₃²	C₂²×D₈
hypercenter	C₃×#508	D₃
hypocenter	C₃	C₃×#3415
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#508

Complements

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

N	H ≅ G/N	type
1. C₃×#5769	C₂	semidirect
2. C₃²×#508	C₂	semidirect
3. C₃×#5193	C₂	semidirect
4. C₃×#4919	C₂	semidirect
5. C₃×#4914	C₂	semidirect
6. C₃×D₃×D₁₆	C₂	semidirect
7. C₂×C₃×D₄₈	C₂	semidirect
8. C₃×#4901	C₂	semidirect
10. #82031	C₃	direct (N × H)
12. C₃²×#135	C₂²	semidirect
14. C₃×#919	C₂²	semidirect
16. C₃×D₃×D₈	C₂²	semidirect
17. C₂×C₃×D₂₄	C₂²	semidirect
19. C₃²×Q₃₂	C₂²	semidirect
20. C₃²×SD₃₂	C₂²	semidirect
21. C₃²×D₁₆	C₂²	semidirect
22. C₂×C₃²×C₁₆	C₂²	semidirect
23. C₃×#828	C₂²	semidirect
24. C₃×#826	C₂²	semidirect
25. C₃×#812	C₂²	semidirect
26. C₃×D₄₈	C₂²	semidirect
27. C₃×D₄₈	C₂²	semidirect
28. C₃×#798	C₂²	semidirect
29. C₃×D₃×C₁₆	C₂²	semidirect
31. #5769	C₂×C₃	semidirect
36. C₃×#508	D₃	semidirect
37. C₃×#508	C₂×C₃	semidirect
41. #5193	C₂×C₃	semidirect
42. #4919	C₂×C₃	semidirect
43. #4914	C₂×C₃	semidirect
44. D₃×D₁₆	C₂×C₃	semidirect
45. C₂×D₄₈	C₂×C₃	semidirect
46. #4901	C₂×C₃	semidirect
76. C₃×#135	C₂×D₃	semidirect
77. C₃×#135	C₂²×C₃	semidirect
82. #919	C₂²×C₃	semidirect
84. D₃×D₈	C₂²×C₃	semidirect
85. C₂×D₂₄	C₂²×C₃	semidirect
88. C₃×Q₃₂	C₂×D₃	semidirect
89. C₃×Q₃₂	C₂²×C₃	semidirect
92. C₃×SD₃₂	C₂×D₃	semidirect
93. C₃×SD₃₂	C₂²×C₃	semidirect
98. C₃×D₁₆	C₂×D₃	semidirect
99. C₃×D₁₆	C₂²×C₃	semidirect
104. C₂×C₃×C₁₆	C₂×D₃	semidirect
105. C₂×C₃×C₁₆	C₂²×C₃	semidirect
106. #828	C₂²×C₃	semidirect
107. #826	C₂²×C₃	semidirect
108. #812	C₂²×C₃	semidirect
109. D₄₈	C₂²×C₃	semidirect
110. D₄₈	C₂²×C₃	semidirect
111. #798	C₂²×C₃	semidirect
112. D₃×C₁₆	C₂²×C₃	semidirect
136. #508	C₃×D₃	semidirect
205. #135	C₂×C₃×D₃	semidirect
209. Q₃₂	C₂×C₃×D₃	semidirect
211. SD₃₂	C₂×C₃×D₃	semidirect
215. D₁₆	C₂×C₃×D₃	semidirect
219. C₂×C₁₆	C₂×C₃×D₃	semidirect
317. C₃²	#3415	semidirect
361. C₃	#82031	direct (N × H)
362. C₃	C₃×#3415	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5769	2
C₃²×#508	2
C₃×#5193	2
C₃×#4919	2
C₃×#4914	2
C₃×D₃×D₁₆	2
C₂×C₃×D₄₈	2
C₃×#4901	2
C₃×#3415	3
#82031	3

Subgroups — C3×#82031 #11899666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#82031 #11899666