Subgroups — C₃×#82019 #11899663

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5757	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5147	C₂	1	2	yes	maximal, complemented
4	C₃×#4912	C₂	1	2	yes	maximal, complemented
5	C₃×#4911	C₂	1	4	yes	maximal, complemented
6	C₃×D₃×D₁₆	C₂	1	2	yes	maximal, complemented
7	C₃×#4904	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	#82019	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#1004	—	2	2	no	—
12	C₂×C₃²×D₈	C₂²	1	2	yes	complemented
13	C₃×#932	—	2	2	no	—
14	C₃×#912	C₂²	1	4	yes	complemented
15	C₃×#911	—	2	4	no	—
16	C₃×D₃×D₈	C₂²	1	4	yes	complemented
17	C₃×#904	C₂²	1	2	yes	complemented
18	C₃×#901	C₂²	1	1	yes	characteristic
19	C₃²×D₁₆	C₂²	1	2	yes	complemented
20	C₃²×D₁₆	C₂²	1	2	yes	complemented
21	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₃×#827	C₂²	1	4	yes	complemented
23	C₃×#826	C₂²	1	4	yes	complemented
24	C₃×#812	C₂²	1	1	yes	characteristic, complemented
25	C₃×Dic₂₄	C₂²	1	1	yes	characteristic, complemented
26	C₃×#800	C₂²	1	2	yes	complemented
27	C₃×D₄₈	C₂²	1	1	yes	characteristic, 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	#5757	C₂×C₃	1	2	yes	complemented
32	C₃×#509	—	3	2	no	—
33	C₃×#509	—	3	4	no	—
34	C₃×#508	—	3	2	no	—
35	C₃×#508	—	3	1	no	—
36	C₂×C₃×D₁₆	—	2	1	no	—
37	C₂×C₃×D₁₆	—	3	2	no	—
38	C₂×C₃×D₁₆	D₃	1	1	yes	characteristic, complemented
39	C₂×C₃×D₁₆	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×#504	—	3	1	no	—
41	#5147	C₂×C₃	1	2	yes	complemented
42	#4912	C₂×C₃	1	2	yes	complemented
43	#4911	C₂×C₃	1	4	yes	complemented
44	D₃×D₁₆	C₂×C₃	1	2	yes	complemented
45	#4904	C₂×C₃	1	1	yes	characteristic, complemented
46	#4901	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₃²×D₄	—	2	2	no	—
48	C₂×C₃×#67	—	4	4	no	—
49	C₃×#237	—	2	4	no	—
50	C₃×#237	—	4	2	no	—
51	C₃×D₃×D₄	—	2	4	no	—
52	C₃×D₃×D₄	—	4	2	no	—
53	C₃×#235	—	2	2	no	—
54	C₃×#235	D₄	1	1	yes	characteristic
55	C₃²×D₈	—	2	2	no	—
56	C₃²×D₈	C₂³	1	4	yes	—
57	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
58	C₃×#214	—	2	4	no	—
59	C₃×#213	—	2	4	no	—
60	C₃×#208	D₄	1	1	yes	characteristic
61	C₃×Dic₁₂	C₂³	1	2	yes	—
62	C₃×D₂₄	C₂³	1	2	yes	—
63	C₃×#204	—	2	2	no	—
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	#1004	—	2	2	no	—
72	C₃×AGL(1,ℤ/8)	—	6	4	no	—
73	C₃×AGL(1,ℤ/8)	—	6	2	no	—
74	C₃×#135	—	3	4	no	—
75	C₃×#135	—	3	2	no	—
76	C₂×C₃×D₈	—	2	2	no	—
77	C₂×C₃×D₈	—	3	4	no	—
78	C₂×C₃×D₈	C₂×D₃	1	2	yes	complemented
79	C₂×C₃×D₈	C₂²×C₃	1	2	yes	complemented
80	C₃×#131	—	3	1	no	—
81	#932	—	2	2	no	—
82	#912	C₂²×C₃	1	4	yes	complemented
83	#911	—	2	4	no	—
84	D₃×D₈	C₂²×C₃	1	4	yes	complemented
85	#904	C₂²×C₃	1	2	yes	complemented
86	#901	C₂²×C₃	1	1	yes	characteristic
87	C₃×Q₃₂	—	3	1	no	—
88	C₃×SD₃₂	—	3	4	no	—
89	C₃×SD₃₂	—	3	2	no	—
90	C₃×D₁₆	—	2	2	no	—
91	C₃×D₁₆	—	2	2	no	—
92	C₃×D₁₆	—	3	4	no	—
93	C₃×D₁₆	—	3	1	no	—
94	C₃×D₁₆	C₂×D₃	1	2	yes	complemented
95	C₃×D₁₆	C₂×D₃	1	2	yes	complemented
96	C₃×D₁₆	C₂²×C₃	1	2	yes	complemented
97	C₃×D₁₆	C₂²×C₃	1	2	yes	complemented
98	C₃×M₃₂	—	3	1	no	—
99	C₃×M₃₂	—	3	2	no	—
100	C₂×C₃×C₁₆	—	2	1	no	—
101	C₂×C₃×C₁₆	—	3	2	no	—
102	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
104	#827	C₂²×C₃	1	4	yes	complemented
105	#826	C₂²×C₃	1	4	yes	complemented
106	#812	C₂²×C₃	1	1	yes	characteristic, complemented
107	Dic₂₄	C₂²×C₃	1	1	yes	characteristic, complemented
108	#800	C₂²×C₃	1	2	yes	complemented
109	D₄₈	C₂²×C₃	1	1	yes	characteristic, complemented
110	#798	C₂²×C₃	1	2	yes	complemented
111	D₃×C₁₆	C₂²×C₃	1	2	yes	complemented
112	C₂³×C₃²	—	4	2	no	—
113	C₂²×C₃×D₃	—	4	4	no	—
114	C₃²×D₄	—	2	4	no	—
115	C₃²×D₄	—	4	2	no	—
116	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
117	C₃×#67	—	4	2	no	—
118	C₃×#67	—	4	4	no	—
119	C₃×#67	—	4	4	no	—
120	C₃×#67	D₈	1	2	yes	—
121	C₂×C₃×Dic₃	—	4	4	no	—
122	C₃×D₁₂	—	2	2	no	—
123	C₃×D₁₂	D₈	1	1	yes	characteristic
124	C₃×C₄×D₃	—	4	2	no	—
125	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
126	C₃×Dic₆	—	2	2	no	—
127	C₃×Dic₆	D₈	1	1	yes	characteristic
128	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
129	C₃²×C₈	C₂⁴	1	1	yes	characteristic
130	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
131	#576	—	3	2	no	—
132	#509	—	3	2	no	—
133	#509	—	3	4	no	—
134	#508	—	3	2	no	—
135	#508	—	3	1	no	—
136	C₂×D₁₆	—	3	2	no	—
137	C₂×D₁₆	C₃×D₃	1	1	yes	characteristic, complemented
138	#504	—	3	1	no	—
139	C₃×#41	—	3	1	no	—
140	C₃×#41	—	6	4	no	—
141	C₃×#41	—	6	2	no	—
142	C₃×#41	—	12	2	no	—
143	C₂×C₃×D₄	—	2	2	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	4	2	no	—
146	C₂×C₃×D₄	—	6	4	no	—
147	C₂×C₃×D₄	—	12	2	no	—
148	C₂×C₃×D₄	—	12	4	no	—
149	C₂×#67	—	4	4	no	—
150	#237	—	2	4	no	—
151	#237	—	4	2	no	—
152	D₃×D₄	—	2	4	no	—
153	D₃×D₄	—	4	2	no	—
154	#235	—	2	2	no	—
155	#235	C₃×D₄	1	1	yes	characteristic
156	C₃×Q₁₆	—	3	2	no	—
157	C₃×SD₁₆	—	6	4	no	—
158	C₃×SD₁₆	—	6	2	no	—
159	C₃×D₈	—	2	2	no	—
160	C₃×D₈	—	2	2	no	—
161	C₃×D₈	—	2	4	no	—
162	C₃×D₈	—	3	2	no	—
163	C₃×D₈	—	4	2	no	—
164	C₃×D₈	—	6	4	no	—
165	C₃×D₈	C₂²×D₃	1	4	yes	—
166	C₃×D₈	C₂³×C₃	1	4	yes	—
167	C₃×M₁₆	—	3	1	no	—
168	C₃×M₁₆	—	3	2	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	3	2	no	—
171	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
173	#214	—	2	4	no	—
174	#213	—	2	4	no	—
175	#208	C₃×D₄	1	1	yes	characteristic
176	Dic₁₂	C₂³×C₃	1	2	yes	—
177	D₂₄	C₂³×C₃	1	2	yes	—
178	#204	—	2	2	no	—
179	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
180	D₃×C₈	C₂³×C₃	1	2	yes	—
181	C₃×C₁₆	—	2	1	no	—
182	C₃×C₁₆	—	2	1	no	—
183	C₃×C₁₆	—	3	2	no	—
184	C₃×C₁₆	C₂²×D₃	1	1	yes	characteristic
185	C₃×C₁₆	C₂²×D₃	1	1	yes	characteristic
186	C₃×C₁₆	C₂³×C₃	1	1	yes	characteristic
187	C₃×C₁₆	C₂³×C₃	1	1	yes	characteristic
188	C₃⋊C₁₆	C₂³×C₃	1	2	yes	—
189	C₂²×C₃²	—	4	4	no	—
190	C₂²×C₃²	—	16	2	no	—
191	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
192	C₂×C₃×D₃	—	4	2	no	—
193	C₂×C₃×D₃	—	16	4	no	—
194	C₂×C₃×D₃	C₂×D₈	1	2	yes	—
195	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
196	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
197	C₃×Dic₃	—	4	2	no	—
198	C₃×Dic₃	C₂×D₈	1	2	yes	—
199	H(5,𝔽₂)	—	6	2	no	—
200	AGL(1,ℤ/8)	—	6	4	no	—
201	AGL(1,ℤ/8)	—	6	2	no	—
202	#135	—	3	4	no	—
203	#135	—	3	2	no	—
204	C₂×D₈	—	3	4	no	—
205	C₂×D₈	C₂×C₃×D₃	1	2	yes	complemented
206	#131	—	3	1	no	—
207	Q₃₂	—	3	1	no	—
208	SD₃₂	—	3	4	no	—
209	SD₃₂	—	3	2	no	—
210	D₁₆	—	3	4	no	—
211	D₁₆	—	3	1	no	—
212	D₁₆	C₂×C₃×D₃	1	2	yes	complemented
213	D₁₆	C₂×C₃×D₃	1	2	yes	complemented
214	M₃₂	—	3	1	no	—
215	M₃₂	—	3	2	no	—
216	C₂×C₁₆	—	3	2	no	—
217	C₂×C₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
218	C₂³×C₃	—	4	2	no	—
219	C₂³×C₃	—	4	2	no	—
220	C₂³×C₃	—	8	2	no	—
221	C₂³×C₃	—	12	4	no	—
222	C₂²×D₃	—	4	4	no	—
223	C₃×Q₈	—	3	1	no	—
224	C₃×Q₈	—	6	2	no	—
225	C₃×D₄	—	2	4	no	—
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	3	2	no	—
228	C₃×D₄	—	3	1	no	—
229	C₃×D₄	—	4	4	no	—
230	C₃×D₄	—	4	2	no	—
231	C₃×D₄	—	4	2	no	—
232	C₃×D₄	—	6	2	no	—
233	C₃×D₄	—	8	2	no	—
234	C₃×D₄	—	12	4	no	—
235	C₃×D₄	—	12	4	no	—
236	C₃×D₄	—	12	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	3	2	no	—
239	C₂×C₃×C₄	—	12	4	no	—
240	C₂×C₃×C₄	—	12	2	no	—
241	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	#67	—	4	2	no	—
244	#67	—	4	4	no	—
245	#67	—	4	4	no	—
246	#67	C₃×D₈	1	2	yes	—
247	C₂×Dic₃	—	4	4	no	—
248	D₁₂	—	2	2	no	—
249	D₁₂	C₃×D₈	1	1	yes	characteristic
250	C₄×D₃	—	4	2	no	—
251	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
252	Dic₆	—	2	2	no	—
253	Dic₆	C₃×D₈	1	1	yes	characteristic
254	C₃×C₈	—	2	1	no	—
255	C₃×C₈	—	2	1	no	—
256	C₃×C₈	—	3	2	no	—
257	C₃×C₈	D₃×D₄	1	1	yes	characteristic
258	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
259	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
260	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
261	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
262	C₂×C₃²	—	2	1	no	—
263	C₂×C₃²	—	8	4	no	—
264	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
265	C₃×D₃	—	2	2	no	—
266	C₃×D₃	—	8	2	no	—
267	#41	—	3	1	no	—
268	#41	—	6	4	no	—
269	#41	—	6	2	no	—
270	#41	—	12	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	6	4	no	—
273	C₂×D₄	—	12	2	no	—
274	C₂×D₄	—	12	4	no	—
275	Q₁₆	—	3	2	no	—
276	SD₁₆	—	6	4	no	—
277	SD₁₆	—	6	2	no	—
278	D₈	—	2	2	no	—
279	D₈	—	3	2	no	—
280	D₈	—	6	4	no	—
281	D₈	C₂²×C₃×D₃	1	4	yes	—
282	M₁₆	—	3	1	no	—
283	M₁₆	—	3	2	no	—
284	C₂×C₈	—	3	2	no	—
285	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
286	C₁₆	—	3	2	no	—
287	C₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
288	C₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	3	2	no	—
291	C₂²×C₃	—	4	4	no	—
292	C₂²×C₃	—	4	4	no	—
293	C₂²×C₃	—	8	4	no	—
294	C₂²×C₃	—	12	2	no	—
295	C₂²×C₃	—	16	2	no	—
296	C₂²×C₃	—	16	2	no	—
297	C₂²×C₃	—	16	4	no	—
298	C₂²×C₃	—	48	4	no	—
299	C₂²×C₃	D₃×D₈	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
301	C₂×D₃	—	4	2	no	—
302	C₂×D₃	—	16	4	no	—
303	C₂×D₃	C₂×C₃×D₈	1	2	yes	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	3	2	no	—
307	C₃×C₄	—	12	2	no	—
308	C₃×C₄	D₃×D₈	1	1	yes	characteristic
309	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
310	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
311	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
312	Dic₃	—	4	2	no	—
313	Dic₃	C₂×C₃×D₈	1	2	yes	—
314	C₃²	#3415	1	1	yes	characteristic, complemented, Sylow
315	C₂³	—	4	2	no	—
316	C₂³	—	12	4	no	—
317	Q₈	—	3	1	no	—
318	Q₈	—	6	2	no	—
319	D₄	—	2	4	no	—
320	D₄	—	3	2	no	—
321	D₄	—	3	1	no	—
322	D₄	—	4	2	no	—
323	D₄	—	6	2	no	—
324	D₄	—	12	4	no	—
325	D₄	—	12	4	no	—
326	D₄	—	12	2	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	12	4	no	—
329	C₂×C₄	—	12	2	no	—
330	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
331	C₈	—	3	2	no	—
332	C₈	C₃×D₃×D₄	1	1	yes	characteristic
333	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
334	C₂×C₃	—	2	2	no	—
335	C₂×C₃	—	2	1	no	—
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	6	2	no	—
339	C₂×C₃	—	8	4	no	—
340	C₂×C₃	—	8	4	no	—
341	C₂×C₃	—	16	4	no	—
342	C₂×C₃	—	24	2	no	—
343	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
344	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
345	D₃	—	2	2	no	—
346	D₃	—	8	2	no	—
347	C₂²	—	3	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	12	2	no	—
350	C₂²	—	16	2	no	—
351	C₂²	—	48	4	no	—
352	C₂²	C₃×D₃×D₈	1	1	yes	characteristic
353	C₄	—	3	2	no	—
354	C₄	—	12	2	no	—
355	C₄	C₃×D₃×D₈	1	1	yes	characteristic
356	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
357	C₃	—	2	1	no	—
358	C₃	#82019	1	1	yes	characteristic, direct product factor
359	C₃	C₃×#3415	1	1	yes	characteristic, complemented
360	C₂	—	2	1	no	—
361	C₂	—	6	2	no	—
362	C₂	—	8	4	no	—
363	C₂	—	24	2	no	—
364	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	C₂×C₃²×D₁₆	C₂
socle	C₂×C₃²	C₂²×D₈
hypercenter	C₂×C₃×D₁₆	D₃
hypocenter	C₃	C₃×#3415
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#5757	C₂	semidirect
2. C₂×C₃²×D₁₆	C₂	semidirect
3. C₃×#5147	C₂	semidirect
4. C₃×#4912	C₂	semidirect
5. C₃×#4911	C₂	semidirect
6. C₃×D₃×D₁₆	C₂	semidirect
7. C₃×#4904	C₂	semidirect
8. C₃×#4901	C₂	semidirect
10. #82019	C₃	direct (N × H)
12. C₂×C₃²×D₈	C₂²	semidirect
14. C₃×#912	C₂²	semidirect
16. C₃×D₃×D₈	C₂²	semidirect
17. C₃×#904	C₂²	semidirect
19. C₃²×D₁₆	C₂²	semidirect
20. C₃²×D₁₆	C₂²	semidirect
21. C₂×C₃²×C₁₆	C₂²	semidirect
22. C₃×#827	C₂²	semidirect
23. C₃×#826	C₂²	semidirect
24. C₃×#812	C₂²	semidirect
25. C₃×Dic₂₄	C₂²	semidirect
26. C₃×#800	C₂²	semidirect
27. C₃×D₄₈	C₂²	semidirect
28. C₃×#798	C₂²	semidirect
29. C₃×D₃×C₁₆	C₂²	semidirect
31. #5757	C₂×C₃	semidirect
38. C₂×C₃×D₁₆	D₃	semidirect
39. C₂×C₃×D₁₆	C₂×C₃	semidirect
41. #5147	C₂×C₃	semidirect
42. #4912	C₂×C₃	semidirect
43. #4911	C₂×C₃	semidirect
44. D₃×D₁₆	C₂×C₃	semidirect
45. #4904	C₂×C₃	semidirect
46. #4901	C₂×C₃	semidirect
78. C₂×C₃×D₈	C₂×D₃	semidirect
79. C₂×C₃×D₈	C₂²×C₃	semidirect
82. #912	C₂²×C₃	semidirect
84. D₃×D₈	C₂²×C₃	semidirect
85. #904	C₂²×C₃	semidirect
94. C₃×D₁₆	C₂×D₃	semidirect
95. C₃×D₁₆	C₂×D₃	semidirect
96. C₃×D₁₆	C₂²×C₃	semidirect
97. C₃×D₁₆	C₂²×C₃	semidirect
102. C₂×C₃×C₁₆	C₂×D₃	semidirect
103. C₂×C₃×C₁₆	C₂²×C₃	semidirect
104. #827	C₂²×C₃	semidirect
105. #826	C₂²×C₃	semidirect
106. #812	C₂²×C₃	semidirect
107. Dic₂₄	C₂²×C₃	semidirect
108. #800	C₂²×C₃	semidirect
109. D₄₈	C₂²×C₃	semidirect
110. #798	C₂²×C₃	semidirect
111. D₃×C₁₆	C₂²×C₃	semidirect
137. C₂×D₁₆	C₃×D₃	semidirect
205. C₂×D₈	C₂×C₃×D₃	semidirect
212. D₁₆	C₂×C₃×D₃	semidirect
213. D₁₆	C₂×C₃×D₃	semidirect
217. C₂×C₁₆	C₂×C₃×D₃	semidirect
314. C₃²	#3415	semidirect
358. C₃	#82019	direct (N × H)
359. 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×#5757	2
C₂×C₃²×D₁₆	2
C₃×#5147	2
C₃×#4912	2
C₃×#4911	2
C₃×D₃×D₁₆	2
C₃×#4904	2
C₃×#4901	2
C₃×#3415	3
#82019	3

Subgroups — C3×#82019 #11899663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#82019 #11899663