Subgroups — C₃×#19101 #10637708

Order 768.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1669	C₂	1	2	yes	maximal, complemented
5	C₃×#1667	C₂	1	2	yes	maximal, complemented
6	C₃×#1665	C₂	1	4	yes	maximal, complemented
7	C₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1540	C₂	1	2	yes	maximal, complemented
9	#19101	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×#135	—	2	1	no	—
11	C₂×C₃×#135	—	2	1	no	—
12	C₂³×C₃×C₈	—	2	1	no	—
13	C₃×#532	C₂²	1	2	yes	—
14	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
15	C₃×#495	—	2	1	no	—
16	C₃×#495	—	2	1	no	—
17	C₃×#494	C₂²	1	1	yes	characteristic, complemented
18	C₃×#493	C₂²	1	1	yes	characteristic, complemented
19	C₃×#492	C₂²	1	2	yes	complemented
20	C₃×#480	—	2	2	no	—
21	C₃×#474	C₂²	1	4	yes	—
22	C₃×#459	C₂²	1	4	yes	—
23	C₃×#447	—	2	2	no	—
24	C₃×C₄×D₈	—	2	4	no	—
25	C₃×C₈×D₄	—	2	1	no	—
26	C₃×C₈×D₄	—	2	1	no	—
27	C₃×C₈×D₄	C₂²	1	2	yes	—
28	C₃×C₈×D₄	C₂²	1	2	yes	—
29	C₃×#431	C₂²	1	2	yes	—
30	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊C₈	—	2	1	no	—
32	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
33	C₃×#335	C₂²	1	2	yes	complemented
34	C₃×#334	C₂²	1	2	yes	complemented
35	C₃×#332	C₂²	1	4	yes	complemented
36	C₃×#331	C₂²	1	4	yes	complemented
37	#3147	C₂×C₃	1	1	yes	characteristic, complemented
38	#3100	C₂×C₃	1	2	yes	complemented
39	C₂×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
40	#1669	C₂×C₃	1	2	yes	complemented
41	#1667	C₂×C₃	1	2	yes	complemented
42	#1665	C₂×C₃	1	4	yes	complemented
43	#1564	C₂×C₃	1	1	yes	characteristic, complemented
44	#1540	C₂×C₃	1	2	yes	complemented
45	C₂×C₃×#41	—	2	2	no	—
46	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
47	C₂³×C₃×C₄	—	2	1	no	—
48	C₃×#135	—	4	4	no	—
49	C₃×#135	—	4	4	no	—
50	C₂×C₃×Q₁₆	—	2	1	no	—
51	C₂×C₃×Q₁₆	—	2	1	no	—
52	C₂×C₃×SD₁₆	—	2	2	no	—
53	C₂×C₃×SD₁₆	—	2	2	no	—
54	C₂×C₃×D₈	—	2	4	no	—
55	C₂×C₃×D₈	—	2	1	no	—
56	C₂×C₃×D₈	—	2	1	no	—
57	C₂²×C₃×C₈	—	2	1	no	—
58	C₂²×C₃×C₈	—	2	2	no	—
59	C₂²×C₃×C₈	—	2	2	no	—
60	C₂²×C₃×C₈	—	4	4	no	—
61	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
63	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₃×#127	C₂³	1	2	yes	—
65	C₃×#124	—	2	2	no	—
66	C₃×#121	—	2	2	no	—
67	C₃×#121	—	2	2	no	—
68	C₃×C₄×D₄	—	2	1	no	—
69	C₃×C₄×D₄	—	2	2	no	—
70	C₃×C₄×D₄	—	2	1	no	—
71	C₃×C₄×D₄	—	2	2	no	—
72	C₃×C₄×D₄	D₄	1	2	yes	—
73	C₃×C₄×D₄	C₂³	1	2	yes	—
74	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
77	C₃×#107	—	2	4	no	—
78	C₃×C₄⋊C₈	—	2	1	no	—
79	C₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₃×C₄⋊C₈	C₂³	1	4	yes	—
81	C₃×#102	—	2	4	no	—
82	C₃×#102	—	2	4	no	—
83	C₃×C₂²⋊C₈	—	2	2	no	—
84	C₃×C₂²⋊C₈	—	2	2	no	—
85	C₃×C₂²⋊C₈	—	2	2	no	—
86	C₃×C₄×C₈	—	2	2	no	—
87	C₃×C₄×C₈	D₄	1	1	yes	characteristic
88	C₃×C₄×C₈	D₄	1	1	yes	characteristic
89	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
90	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
91	C₂×#135	—	2	1	no	—
92	C₂×#135	—	2	1	no	—
93	C₂³×C₈	—	2	1	no	—
94	#532	C₂²×C₃	1	2	yes	—
95	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
96	#495	—	2	1	no	—
97	#495	—	2	1	no	—
98	#494	C₂²×C₃	1	1	yes	characteristic, complemented
99	#493	C₂²×C₃	1	1	yes	characteristic, complemented
100	#492	C₂²×C₃	1	2	yes	complemented
101	#480	—	2	2	no	—
102	#474	C₂²×C₃	1	4	yes	—
103	#459	C₂²×C₃	1	4	yes	—
104	#447	—	2	2	no	—
105	C₄×D₈	—	2	4	no	—
106	C₈×D₄	—	2	1	no	—
107	C₈×D₄	—	2	1	no	—
108	C₈×D₄	C₂²×C₃	1	2	yes	—
109	C₈×D₄	C₂²×C₃	1	2	yes	—
110	#431	C₂²×C₃	1	2	yes	—
111	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	—	2	1	no	—
113	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
114	#335	C₂²×C₃	1	2	yes	complemented
115	#334	C₂²×C₃	1	2	yes	complemented
116	#332	C₂²×C₃	1	4	yes	complemented
117	#331	C₂²×C₃	1	4	yes	complemented
118	C₂⁴×C₃	—	2	1	no	—
119	C₃×#41	—	4	4	no	—
120	C₃×#41	—	4	4	no	—
121	C₂×C₃×Q₈	—	2	2	no	—
122	C₂×C₃×D₄	—	2	4	no	—
123	C₂×C₃×D₄	—	2	1	no	—
124	C₂×C₃×D₄	—	2	2	no	—
125	C₂×C₃×D₄	—	2	2	no	—
126	C₂×C₃×D₄	—	2	2	no	—
127	C₂×C₃×D₄	—	4	2	no	—
128	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	2	2	no	—
131	C₂²×C₃×C₄	—	2	2	no	—
132	C₂²×C₃×C₄	—	4	2	no	—
133	C₂²×C₃×C₄	—	4	2	no	—
134	C₂²×C₃×C₄	—	4	2	no	—
135	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	#41	1	1	yes	characteristic
138	C₃×Q₁₆	—	4	2	no	—
139	C₃×Q₁₆	—	4	2	no	—
140	C₃×SD₁₆	—	4	4	no	—
141	C₃×SD₁₆	—	4	4	no	—
142	C₃×D₈	—	4	2	no	—
143	C₃×D₈	—	4	8	no	—
144	C₃×D₈	—	4	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	4	no	—
147	C₂×C₃×C₈	—	2	2	no	—
148	C₂×C₃×C₈	—	4	2	no	—
149	C₂×C₃×C₈	—	4	4	no	—
150	C₂×C₃×C₈	—	4	4	no	—
151	C₂×C₃×C₈	D₈	1	4	yes	complemented
152	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	1	no	—
157	C₃×C₄⋊C₄	—	2	2	no	—
158	C₃×C₄⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₃×C₂²⋊C₄	—	2	2	no	—
161	C₃×C₂²⋊C₄	—	2	2	no	—
162	C₃×C₂²⋊C₄	—	4	2	no	—
163	C₃×C₂²⋊C₄	—	4	2	no	—
164	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
165	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
166	C₃×C₄²	#41	1	1	yes	characteristic
167	C₃×C₄²	C₂⁴	1	1	yes	characteristic
168	C₂×#41	—	2	2	no	—
169	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
170	C₂³×C₄	—	2	1	no	—
171	#135	—	4	4	no	—
172	#135	—	4	4	no	—
173	C₂×Q₁₆	—	2	1	no	—
174	C₂×Q₁₆	—	2	1	no	—
175	C₂×SD₁₆	—	2	2	no	—
176	C₂×SD₁₆	—	2	2	no	—
177	C₂×D₈	—	2	4	no	—
178	C₂×D₈	—	2	1	no	—
179	C₂×D₈	—	2	1	no	—
180	C₂²×C₈	—	2	1	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	—	2	2	no	—
183	C₂²×C₈	—	4	4	no	—
184	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
185	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
186	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
187	#127	C₂³×C₃	1	2	yes	—
188	#124	—	2	2	no	—
189	#121	—	2	2	no	—
190	#121	—	2	2	no	—
191	C₄×D₄	—	2	1	no	—
192	C₄×D₄	—	2	2	no	—
193	C₄×D₄	—	2	1	no	—
194	C₄×D₄	—	2	2	no	—
195	C₄×D₄	C₃×D₄	1	2	yes	—
196	C₄×D₄	C₂³×C₃	1	2	yes	—
197	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
200	#107	—	2	4	no	—
201	C₄⋊C₈	—	2	1	no	—
202	C₄⋊C₈	C₂³×C₃	1	2	yes	—
203	C₄⋊C₈	C₂³×C₃	1	4	yes	—
204	#102	—	2	4	no	—
205	#102	—	2	4	no	—
206	C₂²⋊C₈	—	2	2	no	—
207	C₂²⋊C₈	—	2	2	no	—
208	C₂²⋊C₈	—	2	2	no	—
209	C₄×C₈	—	2	2	no	—
210	C₄×C₈	C₃×D₄	1	1	yes	characteristic
211	C₄×C₈	C₃×D₄	1	1	yes	characteristic
212	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
214	C₂³×C₃	—	2	4	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	4	2	no	—
217	C₂³×C₃	—	4	2	no	—
218	C₂³×C₃	—	4	2	no	—
219	C₂³×C₃	#121	1	1	yes	characteristic
220	C₃×Q₈	—	4	2	no	—
221	C₃×Q₈	—	4	2	no	—
222	C₃×D₄	—	2	4	no	—
223	C₃×D₄	—	2	2	no	—
224	C₃×D₄	—	4	2	no	—
225	C₃×D₄	—	4	4	no	—
226	C₃×D₄	—	4	2	no	—
227	C₃×D₄	—	8	2	no	—
228	C₃×D₄	—	8	4	no	—
229	C₃×D₄	#135	1	4	yes	complemented
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	4	1	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	—	4	2	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	4	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	8	4	no	—
239	C₂×C₃×C₄	#121	1	1	yes	characteristic
240	C₂×C₃×C₄	#121	1	1	yes	characteristic
241	C₂×C₃×C₄	#121	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
243	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
244	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
247	C₃×C₈	—	2	1	no	—
248	C₃×C₈	—	2	1	no	—
249	C₃×C₈	—	4	2	no	—
250	C₃×C₈	—	4	4	no	—
251	C₃×C₈	C₂×D₈	1	2	yes	—
252	C₃×C₈	C₂×D₈	1	2	yes	—
253	C₂⁴	—	2	1	no	—
254	#41	—	4	4	no	—
255	#41	—	4	4	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂²×C₄	C₃×#41	1	1	yes	characteristic
273	Q₁₆	—	4	2	no	—
274	Q₁₆	—	4	2	no	—
275	SD₁₆	—	4	4	no	—
276	SD₁₆	—	4	4	no	—
277	D₈	—	4	2	no	—
278	D₈	—	4	8	no	—
279	D₈	—	4	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	—	4	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₃×D₈	1	4	yes	complemented
287	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
300	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
301	C₄²	C₃×#41	1	1	yes	characteristic
302	C₄²	C₂⁴×C₃	1	1	yes	characteristic
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	4	8	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	8	2	no	—
310	C₂²×C₃	—	8	2	no	—
311	C₂²×C₃	—	8	2	no	—
312	C₂²×C₃	#459	1	2	yes	—
313	C₂²×C₃	C₂×#121	1	1	yes	characteristic
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	8	2	no	—
319	C₃×C₄	#459	1	2	yes	—
320	C₃×C₄	C₂²×D₈	1	1	yes	characteristic
321	C₃×C₄	C₂×#135	1	2	yes	—
322	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₃×#121	1	1	yes	characteristic
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	2	no	—
336	D₄	—	8	2	no	—
337	D₄	—	8	4	no	—
338	D₄	C₃×#135	1	4	yes	complemented
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₃×#121	1	1	yes	characteristic
349	C₂×C₄	C₃×#121	1	1	yes	characteristic
350	C₂×C₄	C₃×#121	1	1	yes	characteristic
351	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
352	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
353	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	4	no	—
360	C₈	C₂×C₃×D₈	1	2	yes	—
361	C₈	C₂×C₃×D₈	1	2	yes	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	4	4	no	—
364	C₂×C₃	—	16	2	no	—
365	C₂×C₃	C₂×#459	1	1	yes	characteristic
366	C₂×C₃	#3050	1	1	yes	characteristic
367	C₂×C₃	#3067	1	1	yes	characteristic
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₃×#459	1	2	yes	—
378	C₂²	C₂×C₃×#121	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₃×#459	1	2	yes	—
385	C₄	C₂²×C₃×D₈	1	1	yes	characteristic
386	C₄	C₂×C₃×#135	1	2	yes	—
387	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₃	#19101	1	1	yes	characteristic, direct product factor, Sylow
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×C₃×#459	1	1	yes	characteristic
393	C₂	C₃×#3050	1	1	yes	characteristic
394	C₂	C₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃
socle	C₂²×C₃	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3147	C₂	semidirect
2. C₃×#3100	C₂	semidirect
3. C₂×C₃×C₈×D₄	C₂	semidirect
4. C₃×#1669	C₂	semidirect
5. C₃×#1667	C₂	semidirect
6. C₃×#1665	C₂	semidirect
7. C₃×#1564	C₂	semidirect
8. C₃×#1540	C₂	semidirect
9. #19101	C₃	direct (N × H)
17. C₃×#494	C₂²	semidirect
18. C₃×#493	C₂²	semidirect
19. C₃×#492	C₂²	semidirect
33. C₃×#335	C₂²	semidirect
34. C₃×#334	C₂²	semidirect
35. C₃×#332	C₂²	semidirect
36. C₃×#331	C₂²	semidirect
37. #3147	C₂×C₃	semidirect
38. #3100	C₂×C₃	semidirect
39. C₂×C₈×D₄	C₂×C₃	semidirect
40. #1669	C₂×C₃	semidirect
41. #1667	C₂×C₃	semidirect
42. #1665	C₂×C₃	semidirect
43. #1564	C₂×C₃	semidirect
44. #1540	C₂×C₃	semidirect
98. #494	C₂²×C₃	semidirect
99. #493	C₂²×C₃	semidirect
100. #492	C₂²×C₃	semidirect
114. #335	C₂²×C₃	semidirect
115. #334	C₂²×C₃	semidirect
116. #332	C₂²×C₃	semidirect
117. #331	C₂²×C₃	semidirect
151. C₂×C₃×C₈	D₈	semidirect
229. C₃×D₄	#135	semidirect
286. C₂×C₈	C₃×D₈	semidirect
338. D₄	C₃×#135	semidirect
388. C₃	#19101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3147	2
C₃×#3100	2
C₂×C₃×C₈×D₄	2
C₃×#1669	2
C₃×#1667	2
C₃×#1665	2
C₃×#1564	2
C₃×#1540	2
#19101	3

Subgroups — C3×#19101 #10637708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19101 #10637708