Subgroups — C₃×#78530 #11874471

Order 1152.

1383 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#908	C₂	1	4	yes	maximal, complemented
2	C₃×#5477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#874	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4712	C₂	1	4	yes	maximal, complemented
6	C₃×#4695	C₂	1	2	yes	maximal, complemented
7	C₃×#4693	C₂	1	2	yes	maximal, complemented
8	C₃×#3151	—	3	1	no	maximal
9	#78530	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	2	yes	—
11	C₂²×C₃×D₁₂	—	2	2	no	—
12	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
13	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₃×#930	—	2	2	no	—
16	C₃×#908	—	2	16	no	—
17	C₂×C₃×D₂₄	C₂²	1	8	yes	complemented
18	C₂×C₃×#204	C₂²	1	8	yes	complemented
19	C₃×#875	C₂²	1	2	yes	complemented
20	C₃×#874	—	2	2	no	—
21	C₃×#874	C₂²	1	2	yes	—
22	C₃×#874	C₂²	1	2	yes	—
23	C₃×#874	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×D₁₂	—	2	2	no	—
25	C₃×#869	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#97	C₂²	1	2	yes	complemented
27	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
28	C₂×C₃×AGL(1,ℤ/8)	—	3	4	no	—
29	C₃×#532	—	3	1	no	—
30	C₂×C₃×#127	—	3	1	no	—
31	C₂×#908	C₂×C₃	1	4	yes	complemented
32	#5477	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#874	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×#496	—	3	4	no	—
35	C₃×#493	—	3	2	no	—
36	C₃×#492	—	3	2	no	—
37	C₃×C₄×M₁₆	—	2	1	no	—
38	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
39	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
40	#4712	C₂×C₃	1	4	yes	complemented
41	#4695	C₂×C₃	1	2	yes	complemented
42	#4693	C₂×C₃	1	2	yes	complemented
43	C₂³×C₃×D₃	—	2	2	no	—
44	C₂²×C₃²×C₄	D₄	1	2	yes	—
45	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃×#67	—	2	2	no	—
47	C₃×#235	—	2	8	no	—
48	C₂×C₃×D₁₂	—	2	8	no	—
49	C₂×C₃×D₁₂	—	2	2	no	—
50	C₂×C₃×D₁₂	—	2	4	no	—
51	C₂×C₃×D₁₂	—	2	4	no	—
52	C₂×C₃×D₁₂	—	2	2	no	—
53	C₂×C₃×D₁₂	—	4	8	no	—
54	C₂×C₃×D₁₂	C₂³	1	4	yes	—
55	C₂×C₃×D₁₂	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₃	—	2	2	no	—
57	C₂×C₃×Dic₆	C₂³	1	2	yes	—
58	C₃²×M₁₆	D₄	1	8	yes	complemented
59	C₂×C₃²×C₈	C₂³	1	4	yes	—
60	C₃²×C₄²	D₄	1	2	yes	—
61	C₃²×C₄²	C₂³	1	1	yes	characteristic
62	C₃²×C₄²	C₂³	1	1	yes	characteristic
63	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₃×C₄⋊Dic₃	—	2	2	no	—
65	C₃×D₂₄	—	2	16	no	—
66	C₃×#204	—	2	16	no	—
67	#3151	—	3	1	no	Sylow
68	C₂×C₃×#41	—	3	2	no	—
69	C₂²×C₃×D₄	—	3	2	no	—
70	C₂²×C₃×D₄	—	6	2	no	—
71	C₂×#235	C₂²×C₃	1	2	yes	—
72	C₂²×D₁₂	—	2	2	no	—
73	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
74	C₃×AGL(1,ℤ/8)	—	6	16	no	—
75	C₂×C₃×SD₁₆	—	3	8	no	—
76	C₂×C₃×D₈	—	3	8	no	—
77	C₂×C₃×M₁₆	—	2	2	no	—
78	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
79	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
80	C₃×C₄⋊Q₈	—	3	1	no	—
81	C₃×#127	—	3	2	no	—
82	C₃×#127	—	3	2	no	—
83	C₃×#127	—	3	1	no	—
84	C₃×#127	—	6	2	no	—
85	C₃×#124	—	3	2	no	—
86	C₃×#121	—	6	2	no	—
87	C₃×C₄×D₄	—	6	2	no	—
88	C₂×C₃×C₄²	—	2	1	no	—
89	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
91	#930	—	2	2	no	—
92	#908	—	2	16	no	—
93	C₂×D₂₄	C₂²×C₃	1	8	yes	complemented
94	C₂×#204	C₂²×C₃	1	8	yes	complemented
95	#875	C₂²×C₃	1	2	yes	complemented
96	#874	—	2	2	no	—
97	#874	C₂²×C₃	1	2	yes	—
98	#874	C₂²×C₃	1	2	yes	—
99	#874	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₄×D₁₂	—	2	2	no	—
101	#869	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₃×#97	—	2	2	no	—
103	C₃×#97	C₂×D₃	1	2	yes	complemented
104	C₃×#97	C₂²×C₃	1	2	yes	complemented
105	C₃×C₄×C₈	—	2	2	no	—
106	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
107	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
108	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₃×D₃	—	2	4	no	—
110	C₂²×C₃×D₃	—	2	2	no	—
111	C₂²×C₃×D₃	—	4	8	no	—
112	C₂²×C₃×D₃	—	4	4	no	—
113	C₂×C₃²×C₄	—	2	4	no	—
114	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
115	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
117	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
118	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
119	C₃×#67	—	4	4	no	—
120	C₂×C₃×Dic₃	—	2	2	no	—
121	C₃×D₁₂	—	2	8	no	—
122	C₃×D₁₂	—	2	4	no	—
123	C₃×D₁₂	—	4	8	no	—
124	C₃×D₁₂	—	4	4	no	—
125	C₃×D₁₂	—	4	4	no	—
126	C₃×D₁₂	—	4	8	no	—
127	C₃×C₄×D₃	—	4	4	no	—
128	C₃×Dic₆	—	2	4	no	—
129	C₃²×C₈	C₂×D₄	1	8	yes	complemented
130	C₂×AGL(1,ℤ/8)	—	3	4	no	—
131	#532	—	3	1	no	—
132	C₂×#127	—	3	1	no	—
133	#496	—	3	4	no	—
134	#493	—	3	2	no	—
135	#492	—	3	2	no	—
136	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
137	C₂⁴×C₃	—	6	2	no	—
138	C₂³×D₃	—	2	2	no	—
139	C₃×#41	—	6	8	no	—
140	C₂×C₃×Q₈	—	3	2	no	—
141	C₂×C₃×D₄	—	3	2	no	—
142	C₂×C₃×D₄	—	3	4	no	—
143	C₂×C₃×D₄	—	6	2	no	—
144	C₂×C₃×D₄	—	6	8	no	—
145	C₂×C₃×D₄	—	6	2	no	—
146	C₂×C₃×D₄	—	6	4	no	—
147	C₂×C₃×D₄	—	6	4	no	—
148	C₂×C₃×D₄	—	6	2	no	—
149	C₂×C₃×D₄	—	12	8	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	6	2	no	—
153	C₂²×C₃×C₄	D₁₂	1	2	yes	—
154	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×#67	—	2	2	no	—
158	#235	—	2	8	no	—
159	C₂×D₁₂	—	2	8	no	—
160	C₂×D₁₂	—	2	2	no	—
161	C₂×D₁₂	—	2	2	no	—
162	C₂×D₁₂	—	2	4	no	—
163	C₂×D₁₂	—	2	4	no	—
164	C₂×D₁₂	—	4	8	no	—
165	C₂×D₁₂	C₂³×C₃	1	4	yes	—
166	C₂×D₁₂	C₂³×C₃	1	2	yes	—
167	C₂×C₄×D₃	—	2	2	no	—
168	C₂×Dic₆	C₂³×C₃	1	2	yes	—
169	C₃×SD₁₆	—	6	16	no	—
170	C₃×D₈	—	6	16	no	—
171	C₃×M₁₆	—	2	8	no	—
172	C₃×M₁₆	D₁₂	1	8	yes	complemented
173	C₃×M₁₆	C₃×D₄	1	8	yes	complemented
174	C₂×C₃×C₈	—	2	4	no	—
175	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
176	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
177	C₃×C₄⋊C₄	—	6	2	no	—
178	C₃×C₂²⋊C₄	—	6	4	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	—	2	1	no	—
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	D₁₂	1	2	yes	—
183	C₃×C₄²	C₃×D₄	1	2	yes	—
184	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
185	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
186	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
187	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
188	(C₂×D₃)⋊C₄	—	2	4	no	—
189	C₄⋊Dic₃	—	2	2	no	—
190	D₂₄	—	2	16	no	—
191	#204	—	2	16	no	—
192	C₂²×C₃²	—	2	2	no	—
193	C₂²×C₃²	#127	1	2	yes	—
194	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₃×D₃	—	4	2	no	—
196	C₂×C₃×D₃	—	4	4	no	—
197	C₂×C₃×D₃	—	4	8	no	—
198	C₂×C₃×D₃	—	4	4	no	—
199	C₂×C₃×D₃	—	8	8	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	#127	1	2	yes	—
202	C₃²×C₄	AGL(1,ℤ/8)	1	4	yes	complemented
203	C₃²×C₄	C₂²×D₄	1	2	yes	—
204	C₃×Dic₃	—	4	2	no	—
205	C₂×#41	—	3	2	no	—
206	C₂²×D₄	—	3	2	no	—
207	C₂²×D₄	—	6	2	no	—
208	AGL(1,ℤ/8)	—	6	16	no	—
209	C₂×SD₁₆	—	3	8	no	—
210	C₂×D₈	—	3	8	no	—
211	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
212	C₄⋊Q₈	—	3	1	no	—
213	#127	—	3	2	no	—
214	#127	—	3	2	no	—
215	#127	—	3	1	no	—
216	#127	—	6	2	no	—
217	#124	—	3	2	no	—
218	#121	—	6	2	no	—
219	C₄×D₄	—	6	2	no	—
220	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
221	#97	C₂×C₃×D₃	1	2	yes	complemented
222	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	—	6	2	no	—
225	C₂³×C₃	—	6	4	no	—
226	C₂³×C₃	—	12	8	no	—
227	C₂³×C₃	—	12	4	no	—
228	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
229	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂²×D₃	—	2	2	no	—
231	C₂²×D₃	—	2	4	no	—
232	C₂²×D₃	—	4	8	no	—
233	C₂²×D₃	—	4	4	no	—
234	C₃×Q₈	—	6	4	no	—
235	C₃×D₄	—	6	4	no	—
236	C₃×D₄	—	6	8	no	—
237	C₃×D₄	—	12	8	no	—
238	C₃×D₄	—	12	4	no	—
239	C₃×D₄	—	12	4	no	—
240	C₃×D₄	—	12	4	no	—
241	C₃×D₄	—	12	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	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	6	2	no	—
251	C₂×C₃×C₄	—	12	4	no	—
252	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
253	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
255	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
259	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
262	#67	—	4	4	no	—
263	C₂×Dic₃	—	2	2	no	—
264	D₁₂	—	2	8	no	—
265	D₁₂	—	2	4	no	—
266	D₁₂	—	4	8	no	—
267	D₁₂	—	4	4	no	—
268	D₁₂	—	4	4	no	—
269	D₁₂	—	4	8	no	—
270	C₄×D₃	—	4	4	no	—
271	Dic₆	—	2	4	no	—
272	C₃×C₈	—	2	8	no	—
273	C₃×C₈	C₂×D₁₂	1	8	yes	complemented
274	C₃×C₈	C₂×C₃×D₄	1	8	yes	complemented
275	C₂×C₃²	—	2	2	no	—
276	C₂×C₃²	C₂×#127	1	1	yes	characteristic
277	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	2	yes	—
278	C₃×D₃	—	8	2	no	—
279	C₃×D₃	—	8	4	no	—
280	C₂⁴	—	6	2	no	—
281	#41	—	6	8	no	—
282	C₂×Q₈	—	3	2	no	—
283	C₂×D₄	—	3	2	no	—
284	C₂×D₄	—	3	4	no	—
285	C₂×D₄	—	6	2	no	—
286	C₂×D₄	—	6	8	no	—
287	C₂×D₄	—	6	2	no	—
288	C₂×D₄	—	6	4	no	—
289	C₂×D₄	—	6	4	no	—
290	C₂×D₄	—	6	2	no	—
291	C₂×D₄	—	12	8	no	—
292	C₂²×C₄	—	6	2	no	—
293	C₂²×C₄	C₃×D₁₂	1	2	yes	—
294	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
295	SD₁₆	—	6	16	no	—
296	D₈	—	6	16	no	—
297	M₁₆	C₃×D₁₂	1	8	yes	complemented
298	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
299	C₄⋊C₄	—	6	2	no	—
300	C₂²⋊C₄	—	6	4	no	—
301	C₄²	C₃×D₁₂	1	2	yes	—
302	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	12	2	no	—
310	C₂²×C₃	—	12	4	no	—
311	C₂²×C₃	—	12	8	no	—
312	C₂²×C₃	—	12	4	no	—
313	C₂²×C₃	—	24	8	no	—
314	C₂²×C₃	#874	1	2	yes	—
315	C₂²×C₃	C₃×#127	1	2	yes	—
316	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
317	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
318	C₂×D₃	—	4	8	no	—
319	C₂×D₃	—	4	4	no	—
320	C₂×D₃	—	4	2	no	—
321	C₂×D₃	—	4	4	no	—
322	C₂×D₃	—	8	8	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	4	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	—	12	2	no	—
330	C₃×C₄	#874	1	2	yes	—
331	C₃×C₄	#908	1	4	yes	complemented
332	C₃×C₄	C₃×#127	1	2	yes	—
333	C₃×C₄	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
334	C₃×C₄	C₂²×D₁₂	1	2	yes	—
335	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
336	Dic₃	—	4	2	no	—
337	C₃²	#3151	1	1	yes	characteristic, complemented, Sylow
338	C₂³	—	6	2	no	—
339	C₂³	—	6	4	no	—
340	C₂³	—	12	8	no	—
341	C₂³	—	12	4	no	—
342	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
343	Q₈	—	6	4	no	—
344	D₄	—	6	4	no	—
345	D₄	—	6	8	no	—
346	D₄	—	12	8	no	—
347	D₄	—	12	4	no	—
348	D₄	—	12	8	no	—
349	D₄	—	12	4	no	—
350	D₄	—	12	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	6	2	no	—
353	C₂×C₄	—	12	4	no	—
354	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
355	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
356	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
357	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
359	C₈	C₂×C₃×D₁₂	1	8	yes	complemented
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	4	2	no	—
365	C₂×C₃	—	24	4	no	—
366	C₂×C₃	—	24	2	no	—
367	C₂×C₃	C₂×#874	1	1	yes	characteristic
368	C₂×C₃	C₂×#908	1	2	yes	—
369	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
370	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
371	D₃	—	8	4	no	—
372	D₃	—	8	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	12	8	no	—
375	C₂²	—	12	4	no	—
376	C₂²	—	12	2	no	—
377	C₂²	—	12	4	no	—
378	C₂²	—	24	8	no	—
379	C₂²	C₃×#874	1	2	yes	—
380	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	12	2	no	—
383	C₄	C₃×#874	1	2	yes	—
384	C₄	C₃×#908	1	4	yes	complemented
385	C₄	C₂²×C₃×D₁₂	1	2	yes	—
386	C₃	—	2	1	no	—
387	C₃	#78530	1	1	yes	characteristic, direct product factor
388	C₃	C₃×#3151	1	1	yes	characteristic, complemented
389	C₂	—	2	2	no	—
390	C₂	—	24	4	no	—
391	C₂	—	24	2	no	—
392	C₂	C₂×C₃×#874	1	1	yes	characteristic
393	C₂	C₂×C₃×#908	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×#3151
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#908	C₂	semidirect
2. C₃×#5477	C₂	semidirect
3. C₂×C₃×#874	C₂	semidirect
4. C₃²×C₄×M₁₆	C₂	semidirect
5. C₃×#4712	C₂	semidirect
6. C₃×#4695	C₂	semidirect
7. C₃×#4693	C₂	semidirect
9. #78530	C₃	direct (N × H)
17. C₂×C₃×D₂₄	C₂²	semidirect
18. C₂×C₃×#204	C₂²	semidirect
19. C₃×#875	C₂²	semidirect
23. C₃×#874	C₂²	semidirect
25. C₃×#869	C₂²	semidirect
26. C₃²×#97	C₂²	semidirect
27. C₃²×C₄×C₈	C₂²	semidirect
31. C₂×#908	C₂×C₃	semidirect
32. #5477	C₂×C₃	semidirect
33. C₂×#874	C₂×C₃	semidirect
38. C₃×C₄×M₁₆	D₃	semidirect
39. C₃×C₄×M₁₆	C₂×C₃	semidirect
40. #4712	C₂×C₃	semidirect
41. #4695	C₂×C₃	semidirect
42. #4693	C₂×C₃	semidirect
58. C₃²×M₁₆	D₄	semidirect
93. C₂×D₂₄	C₂²×C₃	semidirect
94. C₂×#204	C₂²×C₃	semidirect
95. #875	C₂²×C₃	semidirect
99. #874	C₂²×C₃	semidirect
101. #869	C₂²×C₃	semidirect
103. C₃×#97	C₂×D₃	semidirect
104. C₃×#97	C₂²×C₃	semidirect
106. C₃×C₄×C₈	C₂×D₃	semidirect
107. C₃×C₄×C₈	C₂²×C₃	semidirect
129. C₃²×C₈	C₂×D₄	semidirect
136. C₄×M₁₆	C₃×D₃	semidirect
172. C₃×M₁₆	D₁₂	semidirect
173. C₃×M₁₆	C₃×D₄	semidirect
202. C₃²×C₄	AGL(1,ℤ/8)	semidirect
221. #97	C₂×C₃×D₃	semidirect
222. C₄×C₈	C₂×C₃×D₃	semidirect
273. C₃×C₈	C₂×D₁₂	semidirect
274. C₃×C₈	C₂×C₃×D₄	semidirect
297. M₁₆	C₃×D₁₂	semidirect
331. C₃×C₄	#908	semidirect
333. C₃×C₄	C₃×AGL(1,ℤ/8)	semidirect
337. C₃²	#3151	semidirect
359. C₈	C₂×C₃×D₁₂	semidirect
384. C₄	C₃×#908	semidirect
387. C₃	#78530	direct (N × H)
388. C₃	C₃×#3151	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#908	2
C₃×#5477	2
C₂×C₃×#874	2
C₃²×C₄×M₁₆	2
C₃×#4712	2
C₃×#4695	2
C₃×#4693	2
C₃×#3151	3
#78530	3

Subgroups — C3×#78530 #11874471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78530 #11874471