Subgroups — C₂×C₃×#5147 #11899543

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃	C₂×#213
commutator, cosocle	C₃×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₂²×C₃²×D₈	C₂
socle	C₂²×C₃²	C₂×D₈
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂×C₃×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×D₈	C₂	semidirect
2. C₂×C₃×#904	C₂	semidirect
3. C₂×C₃×#827	C₂	semidirect
4. C₃×#5147	C₂	direct (N × H)
5. C₂×C₃×#826	C₂	semidirect
6. C₂×C₃×#812	C₂	semidirect
8. C₂×#5147	C₃	direct (N × H)
14. C₂×C₃²×D₈	C₂²	semidirect
16. C₂×C₃×Dic₁₂	C₂²	semidirect
18. C₃×#904	C₂²	semidirect
19. C₂×C₃×D₂₄	C₂²	semidirect
21. C₃×#827	C₂²	semidirect
22. C₃×#826	C₂²	semidirect
23. C₃×#812	C₂²	semidirect
24. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
27. C₂²×C₃×D₈	D₃	semidirect
28. C₂²×C₃×D₈	C₂×C₃	semidirect
29. C₂×#904	C₂×C₃	semidirect
34. C₂×#827	C₂×C₃	semidirect
35. #5147	C₂×C₃	direct (N × H)
36. C₂×#826	C₂×C₃	semidirect
37. C₂×#812	C₂×C₃	semidirect
58. C₃×Dic₁₂	C₂³	semidirect
60. C₃×D₂₄	C₂³	semidirect
62. C₃×C₃⋊C₁₆	C₂³	semidirect
83. C₂×C₃×D₈	C₂×D₃	semidirect
85. C₂×C₃×D₈	C₂²×C₃	semidirect
89. C₂×Dic₁₂	C₂²×C₃	semidirect
91. #904	C₂²×C₃	semidirect
92. C₂×D₂₄	C₂²×C₃	semidirect
98. #827	C₂²×C₃	semidirect
99. #826	C₂²×C₃	semidirect
100. #812	C₂²×C₃	semidirect
101. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
125. C₂²×D₈	C₃×D₃	semidirect
187. Dic₁₂	C₂³×C₃	semidirect
189. D₂₄	C₂³×C₃	semidirect
192. C₃⋊C₁₆	C₂³×C₃	semidirect
215. C₂×D₈	C₂×C₃×D₃	semidirect
281. C₂×C₃²	#509	semidirect
342. C₃²	C₂×#509	semidirect
374. C₂×C₃	#5147	direct (N × H)
375. C₂×C₃	C₃×#509	semidirect
392. C₃	C₂×#5147	direct (N × H)
393. C₃	C₂×C₃×#509	semidirect
397. C₂	C₃×#5147	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×D₈	2
C₂×C₃×#904	2
C₂×C₃×#827	2
C₃×#5147	2
C₂×C₃×#826	2
C₂×C₃×#812	2
C₂×C₃×#509	3
C₂×#5147	3

Subgroups — C2×C3×#5147 #11899543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5147 #11899543