Subgroups — C₃×#3012 #84876

Order 384.

764 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#452	C₂	1	2	yes	maximal, complemented
6	C₃×#450	C₂	1	2	yes	maximal, complemented
7	C₃×#449	C₂	1	2	yes	maximal, complemented
8	C₃×#447	C₂	1	2	yes	maximal, complemented
9	C₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	#3012	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×H(5,𝔽₂)	—	2	4	no	—
14	C₃×H(5,𝔽₂)	—	2	4	no	—
15	C₂×C₃×#41	—	2	1	no	—
16	C₂×C₃×#41	C₂²	1	2	yes	—
17	C₂×C₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×D₄	—	2	2	no	—
21	C₂²×C₃×D₄	—	2	1	no	—
22	C₂²×C₃×D₄	C₂²	1	2	yes	—
23	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
24	C₃×AGL(1,ℤ/8)	—	2	4	no	—
25	C₃×#135	—	2	4	no	—
26	C₂×C₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×SD₁₆	C₂²	1	2	yes	complemented
30	C₂×C₃×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×D₈	C₂²	1	2	yes	complemented
32	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₂²⋊Q₈	—	2	1	no	—
35	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₃×#121	—	2	1	no	—
37	C₃×#121	—	2	2	no	—
38	C₃×#121	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×#103	C₂²	1	2	yes	complemented
41	C₃×#102	C₂²	1	2	yes	complemented
42	C₃×#102	C₂²	1	2	yes	complemented
43	C₃×#102	C₂²	1	2	yes	complemented
44	C₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
45	C₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
46	C₂×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#135	C₂×C₃	1	1	yes	characteristic, complemented
49	#537	C₂×C₃	1	1	yes	characteristic, complemented
50	#452	C₂×C₃	1	2	yes	complemented
51	#450	C₂×C₃	1	2	yes	complemented
52	#449	C₂×C₃	1	2	yes	complemented
53	#447	C₂×C₃	1	2	yes	complemented
54	#417	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#102	C₂×C₃	1	1	yes	characteristic, complemented
56	#408	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂⁴×C₃	—	2	2	no	—
58	C₂⁴×C₃	—	2	1	no	—
59	C₃×#41	—	2	8	no	—
60	C₃×#41	—	2	4	no	—
61	C₃×#41	—	2	4	no	—
62	C₃×#41	—	2	2	no	—
63	C₃×#41	—	2	2	no	—
64	C₃×#41	—	2	2	no	—
65	C₃×#41	—	2	2	no	—
66	C₃×#41	—	2	2	no	—
67	C₃×#41	D₄	1	4	yes	complemented
68	C₂×C₃×Q₈	D₄	1	1	yes	characteristic
69	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×D₄	—	2	16	no	—
72	C₂×C₃×D₄	—	2	8	no	—
73	C₂×C₃×D₄	—	2	2	no	—
74	C₂×C₃×D₄	—	2	1	no	—
75	C₂×C₃×D₄	—	2	4	no	—
76	C₂×C₃×D₄	—	2	4	no	—
77	C₂×C₃×D₄	—	2	1	no	—
78	C₂×C₃×D₄	—	2	2	no	—
79	C₂×C₃×D₄	—	2	2	no	—
80	C₂×C₃×D₄	—	2	1	no	—
81	C₂×C₃×D₄	—	2	2	no	—
82	C₂×C₃×D₄	D₄	1	2	yes	—
83	C₂×C₃×D₄	D₄	1	1	yes	characteristic
84	C₂×C₃×D₄	D₄	1	4	yes	complemented
85	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₃×D₄	C₂³	1	2	yes	—
88	C₂²×C₃×C₄	—	2	2	no	—
89	C₂²×C₃×C₄	—	2	1	no	—
90	C₂²×C₃×C₄	—	2	1	no	—
91	C₂²×C₃×C₄	—	2	1	no	—
92	C₂²×C₃×C₄	C₂³	1	2	yes	—
93	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
94	C₃×Q₁₆	—	2	2	no	—
95	C₃×SD₁₆	—	2	2	no	—
96	C₃×SD₁₆	—	2	2	no	—
97	C₃×SD₁₆	—	2	4	no	—
98	C₃×D₈	—	2	2	no	—
99	C₃×D₈	—	2	4	no	—
100	C₃×M₁₆	—	2	2	no	—
101	C₂×C₃×C₈	—	2	2	no	—
102	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₈	C₂³	1	2	yes	—
105	C₃×C₄⋊C₄	—	2	1	no	—
106	C₃×C₄⋊C₄	—	2	2	no	—
107	C₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₃×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₂²⋊C₄	—	2	2	no	—
110	H(5,𝔽₂)	—	2	4	no	—
111	H(5,𝔽₂)	—	2	4	no	—
112	C₂×#41	—	2	1	no	—
113	C₂×#41	C₂²×C₃	1	2	yes	—
114	C₂×#41	C₂²×C₃	1	1	yes	characteristic
115	C₂×#41	C₂²×C₃	1	1	yes	characteristic
116	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂²×D₄	—	2	2	no	—
118	C₂²×D₄	—	2	1	no	—
119	C₂²×D₄	C₂²×C₃	1	2	yes	—
120	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
121	AGL(1,ℤ/8)	—	2	4	no	—
122	#135	—	2	4	no	—
123	C₂×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×SD₁₆	C₂²×C₃	1	2	yes	complemented
127	C₂×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₂×D₈	C₂²×C₃	1	2	yes	complemented
129	C₂×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂²⋊Q₈	—	2	1	no	—
132	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
133	#121	—	2	1	no	—
134	#121	—	2	2	no	—
135	#121	C₂²×C₃	1	2	yes	complemented
136	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
137	#103	C₂²×C₃	1	2	yes	complemented
138	#102	C₂²×C₃	1	2	yes	complemented
139	#102	C₂²×C₃	1	2	yes	complemented
140	#102	C₂²×C₃	1	2	yes	complemented
141	C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
142	C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
143	C₂³×C₃	—	2	8	no	—
144	C₂³×C₃	—	2	2	no	—
145	C₂³×C₃	—	2	1	no	—
146	C₂³×C₃	—	2	4	no	—
147	C₂³×C₃	—	2	1	no	—
148	C₂³×C₃	—	8	1	no	—
149	C₂³×C₃	—	8	1	no	—
150	C₂³×C₃	—	8	2	no	—
151	C₂³×C₃	—	8	2	no	—
152	C₂³×C₃	C₂×D₄	1	2	yes	—
153	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
154	C₃×Q₈	—	2	2	no	—
155	C₃×Q₈	—	2	1	no	—
156	C₃×Q₈	—	2	1	no	—
157	C₃×Q₈	—	2	1	no	—
158	C₃×Q₈	C₂×D₄	1	2	yes	—
159	C₃×D₄	—	2	8	no	—
160	C₃×D₄	—	2	8	no	—
161	C₃×D₄	—	2	4	no	—
162	C₃×D₄	—	2	4	no	—
163	C₃×D₄	—	2	2	no	—
164	C₃×D₄	—	2	4	no	—
165	C₃×D₄	—	2	2	no	—
166	C₃×D₄	—	2	1	no	—
167	C₃×D₄	—	2	1	no	—
168	C₃×D₄	—	2	1	no	—
169	C₃×D₄	—	4	2	no	—
170	C₃×D₄	—	8	2	no	—
171	C₃×D₄	C₂×D₄	1	2	yes	—
172	C₃×D₄	C₂×D₄	1	4	yes	—
173	C₂×C₃×C₄	—	2	8	no	—
174	C₂×C₃×C₄	—	2	1	no	—
175	C₂×C₃×C₄	—	2	4	no	—
176	C₂×C₃×C₄	—	2	2	no	—
177	C₂×C₃×C₄	—	2	2	no	—
178	C₂×C₃×C₄	—	2	2	no	—
179	C₂×C₃×C₄	—	2	1	no	—
180	C₂×C₃×C₄	—	4	2	no	—
181	C₂×C₃×C₄	—	8	1	no	—
182	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
183	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
184	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
185	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
186	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
187	C₃×C₈	—	2	1	no	—
188	C₃×C₈	—	2	1	no	—
189	C₃×C₈	—	2	2	no	—
190	C₂⁴	—	2	2	no	—
191	C₂⁴	—	2	1	no	—
192	#41	—	2	8	no	—
193	#41	—	2	4	no	—
194	#41	—	2	4	no	—
195	#41	—	2	2	no	—
196	#41	—	2	2	no	—
197	#41	—	2	2	no	—
198	#41	—	2	2	no	—
199	#41	—	2	2	no	—
200	#41	C₃×D₄	1	4	yes	complemented
201	C₂×Q₈	C₃×D₄	1	1	yes	characteristic
202	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
203	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
204	C₂×D₄	—	2	16	no	—
205	C₂×D₄	—	2	8	no	—
206	C₂×D₄	—	2	2	no	—
207	C₂×D₄	—	2	1	no	—
208	C₂×D₄	—	2	4	no	—
209	C₂×D₄	—	2	4	no	—
210	C₂×D₄	—	2	1	no	—
211	C₂×D₄	—	2	2	no	—
212	C₂×D₄	—	2	2	no	—
213	C₂×D₄	—	2	1	no	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	C₃×D₄	1	2	yes	—
216	C₂×D₄	C₃×D₄	1	1	yes	characteristic
217	C₂×D₄	C₃×D₄	1	4	yes	complemented
218	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
219	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
220	C₂×D₄	C₂³×C₃	1	2	yes	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	—	2	1	no	—
225	C₂²×C₄	C₂³×C₃	1	2	yes	—
226	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
227	Q₁₆	—	2	2	no	—
228	SD₁₆	—	2	2	no	—
229	SD₁₆	—	2	2	no	—
230	SD₁₆	—	2	4	no	—
231	D₈	—	2	2	no	—
232	D₈	—	2	4	no	—
233	M₁₆	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₈	C₂³×C₃	1	2	yes	—
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	C₂³×C₃	1	2	yes	—
241	C₂²⋊C₄	—	2	2	no	—
242	C₂²⋊C₄	—	2	2	no	—
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	—	2	1	no	—
245	C₂²×C₃	—	2	2	no	—
246	C₂²×C₃	—	2	4	no	—
247	C₂²×C₃	—	2	2	no	—
248	C₂²×C₃	—	2	2	no	—
249	C₂²×C₃	—	2	2	no	—
250	C₂²×C₃	—	4	2	no	—
251	C₂²×C₃	—	4	1	no	—
252	C₂²×C₃	—	4	2	no	—
253	C₂²×C₃	—	4	1	no	—
254	C₂²×C₃	—	4	1	no	—
255	C₂²×C₃	—	4	1	no	—
256	C₂²×C₃	—	4	1	no	—
257	C₂²×C₃	—	8	4	no	—
258	C₂²×C₃	—	8	8	no	—
259	C₂²×C₃	#120	1	2	yes	—
260	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₄	—	2	2	no	—
262	C₃×C₄	—	2	2	no	—
263	C₃×C₄	—	4	1	no	—
264	C₃×C₄	—	4	2	no	—
265	C₃×C₄	#120	1	2	yes	—
266	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
267	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
268	C₂³	—	2	8	no	—
269	C₂³	—	2	2	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	8	1	no	—
274	C₂³	—	8	1	no	—
275	C₂³	—	8	2	no	—
276	C₂³	—	8	2	no	—
277	C₂³	C₂×C₃×D₄	1	2	yes	—
278	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
279	Q₈	—	2	2	no	—
280	Q₈	—	2	1	no	—
281	Q₈	—	2	1	no	—
282	Q₈	—	2	1	no	—
283	Q₈	C₂×C₃×D₄	1	2	yes	—
284	D₄	—	2	8	no	—
285	D₄	—	2	8	no	—
286	D₄	—	2	4	no	—
287	D₄	—	2	4	no	—
288	D₄	—	2	2	no	—
289	D₄	—	2	4	no	—
290	D₄	—	2	2	no	—
291	D₄	—	2	1	no	—
292	D₄	—	2	1	no	—
293	D₄	—	2	1	no	—
294	D₄	—	4	2	no	—
295	D₄	—	8	2	no	—
296	D₄	C₂×C₃×D₄	1	2	yes	—
297	D₄	C₂×C₃×D₄	1	4	yes	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	8	1	no	—
307	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
308	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
310	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
311	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
312	C₈	—	2	1	no	—
313	C₈	—	2	1	no	—
314	C₈	—	2	2	no	—
315	C₂×C₃	—	2	2	no	—
316	C₂×C₃	—	4	2	no	—
317	C₂×C₃	—	4	4	no	—
318	C₂×C₃	—	4	2	no	—
319	C₂×C₃	—	8	1	no	—
320	C₂×C₃	C₂×#120	1	1	yes	characteristic
321	C₂×C₃	#576	1	1	yes	characteristic
322	C₂×C₃	#577	1	1	yes	characteristic
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	8	4	no	—
338	C₂²	—	8	8	no	—
339	C₂²	C₃×#120	1	2	yes	—
340	C₂²	C₂²×C₃×D₄	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	1	no	—
345	C₄	C₃×#120	1	2	yes	—
346	C₄	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₄	C₂²×C₃×D₄	1	1	yes	characteristic
348	C₃	#3012	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	2	2	no	—
350	C₂	—	4	2	no	—
351	C₂	—	4	4	no	—
352	C₂	—	4	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×C₃×#120	1	1	yes	characteristic
355	C₂	C₃×#576	1	1	yes	characteristic
356	C₂	C₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₃×#135	C₂	semidirect
4. C₃×#537	C₂	semidirect
5. C₃×#452	C₂	semidirect
6. C₃×#450	C₂	semidirect
7. C₃×#449	C₂	semidirect
8. C₃×#447	C₂	semidirect
9. C₃×#417	C₂	semidirect
10. C₂×C₃×#102	C₂	semidirect
11. C₃×#408	C₂	semidirect
12. #3012	C₃	direct (N × H)
19. C₂×C₃×#41	C₂²	semidirect
26. C₂×C₃×Q₁₆	C₂²	semidirect
27. C₂×C₃×SD₁₆	C₂²	semidirect
28. C₂×C₃×SD₁₆	C₂²	semidirect
29. C₂×C₃×SD₁₆	C₂²	semidirect
30. C₂×C₃×D₈	C₂²	semidirect
31. C₂×C₃×D₈	C₂²	semidirect
32. C₂×C₃×M₁₆	C₂²	semidirect
33. C₂²×C₃×C₈	C₂²	semidirect
35. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₂×C₃×C₄⋊C₄	C₂²	semidirect
40. C₃×#103	C₂²	semidirect
41. C₃×#102	C₂²	semidirect
42. C₃×#102	C₂²	semidirect
43. C₃×#102	C₂²	semidirect
44. C₃×C₂²⋊C₈	C₂²	semidirect
45. C₃×C₂²⋊C₈	C₂²	semidirect
46. C₂×H(5,𝔽₂)	C₂×C₃	semidirect
47. C₂×AGL(1,ℤ/8)	C₂×C₃	semidirect
48. C₂×#135	C₂×C₃	semidirect
49. #537	C₂×C₃	semidirect
50. #452	C₂×C₃	semidirect
51. #450	C₂×C₃	semidirect
52. #449	C₂×C₃	semidirect
53. #447	C₂×C₃	semidirect
54. #417	C₂×C₃	semidirect
55. C₂×#102	C₂×C₃	semidirect
56. #408	C₂×C₃	semidirect
67. C₃×#41	D₄	semidirect
84. C₂×C₃×D₄	D₄	semidirect
116. C₂×#41	C₂²×C₃	semidirect
123. C₂×Q₁₆	C₂²×C₃	semidirect
124. C₂×SD₁₆	C₂²×C₃	semidirect
125. C₂×SD₁₆	C₂²×C₃	semidirect
126. C₂×SD₁₆	C₂²×C₃	semidirect
127. C₂×D₈	C₂²×C₃	semidirect
128. C₂×D₈	C₂²×C₃	semidirect
129. C₂×M₁₆	C₂²×C₃	semidirect
130. C₂²×C₈	C₂²×C₃	semidirect
132. C₂²⋊Q₈	C₂²×C₃	semidirect
135. #121	C₂²×C₃	semidirect
136. C₂×C₄⋊C₄	C₂²×C₃	semidirect
137. #103	C₂²×C₃	semidirect
138. #102	C₂²×C₃	semidirect
139. #102	C₂²×C₃	semidirect
140. #102	C₂²×C₃	semidirect
141. C₂²⋊C₈	C₂²×C₃	semidirect
142. C₂²⋊C₈	C₂²×C₃	semidirect
200. #41	C₃×D₄	semidirect
217. C₂×D₄	C₃×D₄	semidirect
348. C₃	#3012	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×H(5,𝔽₂)	2
C₂×C₃×AGL(1,ℤ/8)	2
C₂×C₃×#135	2
C₃×#537	2
C₃×#452	2
C₃×#450	2
C₃×#449	2
C₃×#447	2
C₃×#417	2
C₂×C₃×#102	2
C₃×#408	2
#3012	3

Subgroups — C3×#3012 #84876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3012 #84876